reddit_organic_content.json

{
  "generated": "2026-01-06T05:03:15.412668",
  "total_posts": 202,
  "posts": [
    {
      "title": "Exploring Models of Visual Attention: From Saliency Maps to Biased Competition computationally",
      "body": "I recently dove into computational models of visual attention: from saliency maps to biased competition.\n\nThis report presents a computational investigation of visual attention mechanisms using models inspired by cognitive neuroscience research.  We implement the feature integration theory (FIT) framework to simulate visual search tasks, construct bottom-up saliency maps based on multi-feature integration, model the attentional spotlight using Gaussian spatial weighting functions, and analyze the attentional blink phenomenon in rapid serial visual presentation (RSVP) paradigms.\nThe key relationship is: S(x,y) = Σ(i=1 to N) wᵢ · Fᵢ(x,y)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cognitive-science/attention.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cognitive-science/attention.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cognitive-science/attention.tex",
      "source": "attention",
      "category": "cognitive-science"
    },
    {
      "title": "Visualizing Memory Models Curves and ACT-R with Python",
      "body": "I put together a simulation of memory models\\ curves and act-r.\n\nThis report presents computational models of human memory systems, including the Ebbinghaus forgetting curve, serial position effects, working memory capacity limits, and the ACT-R activation model.  We quantify retention decay, recall probability across list positions, Cowan's K capacity estimates, and base-level activation dynamics.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cognitive-science/memory_models.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cognitive-science/memory_models.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cognitive-science/memory_models.tex",
      "source": "memory_models",
      "category": "cognitive-science"
    },
    {
      "title": "Interactive Models of Human Decision Making: From Rational Choice to Bounded Rationality visualization",
      "body": "I put together a simulation of computational models of human decision making:\\\\\nfrom rational choice to bounded rationality.\n\nThis report presents a comprehensive computational analysis of human decision-making processes, spanning classical normative theories to modern descriptive models.  We examine expected utility theory as the rational benchmark, prospect theory's account of systematic deviations from rationality, drift-diffusion models for response time distributions, Bayesian frameworks for decision making under uncertainty, and reinforcement learning models of value-based choice.\nThe key relationship is: EU = Σ(i=1 to n) pᵢ · u(oᵢ)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cognitive-science/decision_making.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cognitive-science/decision_making.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cognitive-science/decision_making.tex",
      "source": "decision_making",
      "category": "cognitive-science"
    },
    {
      "title": "The math behind Market Economics: Supply, Demand, Elasticity, and Welfare Analysis - a simulation",
      "body": "I recently dove into market economics:\\\\\nsupply, demand, elasticity, and welfare analysis.\n\nThis report presents a computational analysis of market models.  We examine supply and demand curves, compute market equilibrium, analyze price elasticity, measure consumer and producer surplus, and evaluate the welfare effects of taxes and price controls.\nThe key relationship is: Q_d(P) = Qₛ(P)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/economics/market_model.tex\n\nWhat assumptions do you find most limiting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/economics/market_model.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/economics/market_model.tex",
      "source": "market_model",
      "category": "economics"
    },
    {
      "title": "The math behind Game Theory: Nash Equilibrium, Mixed Strategies, and Payoff Analysis - a simulation",
      "body": "I've been studying game theory:\\\\\nnash equilibrium, mixed strategies, and payoff analysis.\n\nThis report presents a computational analysis of game theory concepts.  We implement Nash equilibrium finding for 2-player games, analyze mixed strategies in zero-sum and non-zero-sum games, visualize payoff matrices, and explore classic games including Prisoner's Dilemma, Battle of the Sexes, and Matching Pennies.\nThe key relationship is: Payoffs:  (u₁(s₁ⁱ, s₂ʲ), u₂(s₁ⁱ, s₂ʲ))\n\nIt's fascinating to see the theory come alive in the simulation.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/economics/game_theory.tex\n\nHas anyone validated these models against real data?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/economics/game_theory.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/economics/game_theory.tex",
      "source": "game_theory",
      "category": "economics"
    },
    {
      "title": "Visualizing Signal Transduction Analysis Cascade Dynamics and Ultrasensitivity with Python",
      "body": "I've been studying signal transduction analysis\\ cascade dynamics and ultrasensitivity.\n\nSignal transduction pathways amplify and process extracellular signals through cascades of protein phosphorylation.  This report analyzes the MAPK (Mitogen-Activated Protein Kinase) cascade, demonstrating ultrasensitivity through the Goldbeter-Koshland function, Michaelis-Menten enzyme kinetics, dose-response behavior, and sensitivity to kinetic parameters.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/systems-biology/signal_transduction.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/systems-biology/signal_transduction.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/systems-biology/signal_transduction.tex",
      "source": "signal_transduction",
      "category": "systems-biology"
    },
    {
      "title": "Interactive Gene Regulatory Networks Models visualization",
      "body": "I've been fascinated by gene regulatory networks\\ models.\n\nGene regulatory networks (GRNs) control cellular behavior through complex interactions between genes, proteins, and regulatory elements.  This report implements multiple modeling frameworks for GRNs, including Boolean network models for discrete gene states, Hill function representations of cooperative binding, ordinary differential equation (ODE) models of gene expression dynamics, and bistable toggle switch systems.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/systems-biology/gene_regulatory.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/systems-biology/gene_regulatory.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/systems-biology/gene_regulatory.tex",
      "source": "gene_regulatory",
      "category": "systems-biology"
    },
    {
      "title": "Interactive Neutron Star Physics of State and Structure visualization",
      "body": "I've been exploring neutron star physics\\ of state and structure.\n\nAnalysis of neutron star structure including mass-radius relations, equation of state, and magnetic field properties..\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/neutron_stars.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astrophysics/neutron_stars.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/neutron_stars.tex",
      "source": "neutron_stars",
      "category": "astrophysics"
    },
    {
      "title": "Exploring Black Hole Physics Radius, Accretion, and Hawking Radiation computationally",
      "body": "I created a computational exploration of black hole physics\\ radius, accretion, and hawking radiation.\n\nComputational analysis of black hole physics including Schwarzschild geometry, accretion disk properties, and Hawking radiation calculations..\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/black_holes.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astrophysics/black_holes.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/black_holes.tex",
      "source": "black_holes",
      "category": "astrophysics"
    },
    {
      "title": "I built an interactive Gravitational Wave Physics, Detection, and Binary Systems simulation",
      "body": "I recently dove into gravitational wave physics\\, detection, and binary systems.\n\nAnalysis of gravitational wave generation, propagation, and detection including chirp mass calculations and LIGO sensitivity..\n\nIt's fascinating to see the theory come alive in the simulation.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/gravitational_waves.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astrophysics/gravitational_waves.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/gravitational_waves.tex",
      "source": "gravitational_waves",
      "category": "astrophysics"
    },
    {
      "title": "The math behind Galaxy Dynamics Curves and Dark Matter - a simulation",
      "body": "I wanted to visualize galaxy dynamics\\ curves and dark matter.\n\nAnalysis of galaxy dynamics including rotation curves, dark matter profiles, and scaling relations..\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/galaxy_dynamics.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astrophysics/galaxy_dynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astrophysics/galaxy_dynamics.tex",
      "source": "galaxy_dynamics",
      "category": "astrophysics"
    },
    {
      "title": "The math behind Gravitational Lensing: From Einstein Rings to Weak Lensing Surveys - a simulation",
      "body": "I wanted to visualize gravitational lensing: from einstein rings to weak lensing surveys.\n\nThis report presents a comprehensive computational analysis of gravitational lensing phenomena across multiple regimes.  We derive and analyze the deflection angle $ = 4GM/(c²b)$ for point mass lenses, compute Einstein ring radii for galaxy-scale strong lensing, simulate magnification maps for multiple image systems, and model microlensing light curves for exoplanet detection.\nThe key relationship is: α = 4GMc² b = 4GMc² 1b\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/relativity/gravitational_lensing.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/relativity/gravitational_lensing.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/relativity/gravitational_lensing.tex",
      "source": "gravitational_lensing",
      "category": "relativity"
    },
    {
      "title": "Exploring General Relativity: Computational Analysis of Curved Spacetime and Gravitatio... computationally",
      "body": "I wanted to visualize general relativity: computational analysis of curved spacetime and gravitational phenomena.\n\nThis report presents a comprehensive computational analysis of Einstein's general relativity, exploring the curvature of spacetime and its observational consequences.  We examine the Schwarzschild metric for spherically symmetric spacetimes, compute geodesic trajectories to analyze orbital precession (including Mercury's anomalous perihelion advance of 43 arcseconds per century), model gravitational wave signals from binary mergers, and investigate cosmological solutions via the Friedmann-Lema\\^.\nThe key relationship is: G_μν + Λ g_μν = 8π Gc⁴ T_μν\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/relativity/general_relativity.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/relativity/general_relativity.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/relativity/general_relativity.tex",
      "source": "general_relativity",
      "category": "relativity"
    },
    {
      "title": "Interactive Special Relativity: Lorentz Transformations and Relativistic Dynamics visualization",
      "body": "I've been exploring special relativity: lorentz transformations and relativistic dynamics.\n\nThis computational report presents a comprehensive analysis of special relativity through the Lorentz transformation framework.  We examine time dilation and length contraction effects across the full velocity range from non-relativistic to ultra-relativistic regimes, analyze the relativistic energy-momentum relation including rest mass energy and kinetic energy, construct spacetime diagrams showing worldlines and light cones, and verify theoretical predictions against experimental observations i.\nThe key relationship is: Δ t = γ Δ τ = Δ τ√1 - v²/c²\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/relativity/special_relativity.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/relativity/special_relativity.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/relativity/special_relativity.tex",
      "source": "special_relativity",
      "category": "relativity"
    },
    {
      "title": "Simulating Random Walks: From Discrete Paths to Brownian Motion - visualizing the math",
      "body": "I built an interactive model for random walks: from discrete paths to brownian motion.\n\nThis report presents a comprehensive analysis of random walks, examining the transition from discrete stochastic processes to continuous Brownian motion.  We investigate simple random walks in one, two, and three dimensions, establishing recurrence in dimensions $d 2$ and transience for $d 3$ through computational verification of P\\'olya's theorem.\nThe key relationship is: Sₙ = Σ(i=1 to n) Xᵢ\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/random_walks.tex\n\nHas anyone found good real-world applications to demonstrate?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/probability/random_walks.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/random_walks.tex",
      "source": "random_walks",
      "category": "probability"
    },
    {
      "title": "Exploring Markov Chains: Transition Matrices and Stationary Distributions computationally",
      "body": "I've been studying markov chains: transition matrices and stationary distributions.\n\nThis report presents a comprehensive computational analysis of discrete-time Markov chains, including the construction and analysis of transition matrices, computation of stationary distributions through eigenvalue decomposition and iterative methods, classification of states by recurrence and periodicity properties, and convergence to equilibrium under ergodic conditions.  We examine the Chapman-Kolmogorov equations governing multi-step transitions, demonstrate the fundamental theorem for irredu.\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/markov_chains.tex\n\nWhat numerical methods work best for you?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/probability/markov_chains.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/markov_chains.tex",
      "source": "markov_chains",
      "category": "probability"
    },
    {
      "title": "Visualizing Extreme Value Theory: Statistical Analysis of Rare Events with Python",
      "body": "I built an interactive model for extreme value theory: statistical analysis of rare events.\n\nThis report presents a comprehensive analysis of extreme value theory (EVT) and its applications to rare event prediction.  We examine the Fisher-Tippett-Gnedenko theorem, which establishes the generalized extreme value (GEV) distribution as the limiting distribution of block maxima, and the Peaks Over Threshold (POT) method using the generalized Pareto distribution (GPD).\nThe key relationship is: _n  ∞ P((X₁, , Xₙ) - bₙaₙ ≤ x) = G(x)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/extreme_value.tex\n\nWhat numerical methods work best for you?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/probability/extreme_value.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/extreme_value.tex",
      "source": "extreme_value",
      "category": "probability"
    },
    {
      "title": "The math behind Point Processes: Poisson and Hawkes Process Analysis - a simulation",
      "body": "I've been fascinated by point processes: poisson and hawkes process analysis.\n\nThis report presents a comprehensive computational analysis of temporal point processes, focusing on homogeneous and inhomogeneous Poisson processes and self-exciting Hawkes processes.  We implement simulation algorithms for each process type, analyze the statistical properties of inter-arrival times and counting processes, estimate intensity functions from observed data, and examine the clustering behavior characteristic of Hawkes processes.\nThe key relationship is: P(N(t) - N(s) = k) = Λ(s,t)ᵏk! e^-Λ(s,t)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/point_processes.tex\n\nHow do you approach teaching this topic?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/probability/point_processes.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/probability/point_processes.tex",
      "source": "point_processes",
      "category": "probability"
    },
    {
      "title": "The math behind Financial Time Series Analysis: ARIMA, GARCH, and Cointegration - a simulation",
      "body": "I created a computational exploration of financial time series analysis: arima, garch, and cointegration.\n\nThis report presents a comprehensive econometric analysis of financial time series using modern time series techniques.  We examine the stylized facts of asset returns including fat tails, volatility clustering, and leverage effects.\nThe key relationship is: φ(L)(1-L)ᵈ yₜ = θ(L)ₜ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/time_series_finance.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/financial-math/time_series_finance.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/time_series_finance.tex",
      "source": "time_series_finance",
      "category": "financial-math"
    },
    {
      "title": "Exploring Portfolio Optimization: Modern Portfolio Theory and Risk Management computationally",
      "body": "I've been exploring portfolio optimization: modern portfolio theory and risk management.\n\nThis report presents a comprehensive computational analysis of portfolio optimization using Modern Portfolio Theory (MPT).  We examine the mean-variance framework introduced by Markowitz, construct efficient frontiers for multi-asset portfolios, derive optimal portfolio weights under various constraints, and analyze risk-adjusted performance using the Sharpe ratio.\nThe key relationship is: μₚ = wᵀ μ\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/portfolio_optimization.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/financial-math/portfolio_optimization.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/portfolio_optimization.tex",
      "source": "portfolio_optimization",
      "category": "financial-math"
    },
    {
      "title": "Exploring Quantitative Risk Management: at Risk and Coherent Risk Measures computationally",
      "body": "I recently dove into quantitative risk management:\\ at risk and coherent risk measures.\n\nThis report presents a comprehensive analysis of modern risk measurement techniques for financial portfolios.  We implement three approaches to Value at Risk (VaR) calculation—historical simulation, variance-covariance (parametric), and Monte Carlo methods—and examine the coherent risk measure Expected Shortfall (CVaR).\nThe key relationship is: VaR_α = -∈f\\x ∈ R : F(x) > α\\ = -F⁻¹(α)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/risk_management.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/financial-math/risk_management.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/risk_management.tex",
      "source": "risk_management",
      "category": "financial-math"
    },
    {
      "title": "I built an interactive Option Pricing: Black-Scholes Model and Greeks Analysis simulation",
      "body": "I recently dove into option pricing: black-scholes model and greeks analysis.\n\nThis report presents a comprehensive computational analysis of option pricing using the Black-Scholes framework.  We derive and implement the closed-form solutions for European call and put options, compute the sensitivity measures known as Greeks (delta, gamma, theta, vega, rho), and compare analytical methods with numerical approaches including binomial tree models and Monte Carlo simulation.\nThe key relationship is: C(S,t) = S N(d₁) - K e^-r(T-t) N(d₂)\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/option_pricing.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/financial-math/option_pricing.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/financial-math/option_pricing.tex",
      "source": "option_pricing",
      "category": "financial-math"
    },
    {
      "title": "Simulating Magnetic Resonance Imaging: Signal Formation, Contrast Mechanisms, and K-Space - visualizing the math",
      "body": "I recently dove into magnetic resonance imaging:\\\\\nsignal formation, contrast mechanisms, and k-space.\n\nThis report presents a comprehensive analysis of MRI signal formation and image reconstruction.  We implement the Bloch equations, analyze T1 and T2 contrast mechanisms, demonstrate k-space encoding, compare pulse sequences, and evaluate image artifacts.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/medical-physics/mri_signal.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/medical-physics/mri_signal.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/medical-physics/mri_signal.tex",
      "source": "mri_signal",
      "category": "medical-physics"
    },
    {
      "title": "Simulating Computed Tomography: Image Reconstruction and Artifact Analysis - visualizing the math",
      "body": "I've been fascinated by computed tomography:\\\\\nimage reconstruction and artifact analysis.\n\nThis report presents a comprehensive analysis of CT image reconstruction algorithms.  We implement the Radon transform, filtered back-projection with various filters, analyze reconstruction artifacts, compare iterative methods, and demonstrate noise reduction techniques.\nThe key relationship is: P(ω, θ) = F(ωθ, ωθ)\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/medical-physics/ct_reconstruction.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/medical-physics/ct_reconstruction.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/medical-physics/ct_reconstruction.tex",
      "source": "ct_reconstruction",
      "category": "medical-physics"
    },
    {
      "title": "Exploring Radiation Dosimetry: Depth-Dose Distributions and Treatment Planning computationally",
      "body": "I built an interactive model for radiation dosimetry:\\\\\ndepth-dose distributions and treatment planning.\n\nThis report presents a comprehensive analysis of radiation dosimetry for external beam radiotherapy.  We compute depth-dose distributions for photon, electron, and proton beams, analyze tissue inhomogeneity corrections, evaluate dose-volume histograms, and compare treatment planning techniques.\nThe key relationship is: D = ddm\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/medical-physics/radiation_dosimetry.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/medical-physics/radiation_dosimetry.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/medical-physics/radiation_dosimetry.tex",
      "source": "radiation_dosimetry",
      "category": "medical-physics"
    },
    {
      "title": "The math behind Qubit Operations and Quantum Gates: Pauli Gates, Superposition, Entanglement,... - a simulation",
      "body": "I built an interactive model for qubit operations and quantum gates:\\\\\npauli gates, superposition, entanglement, and bell states.\n\nThis report explores fundamental qubit operations and quantum gates.  We implement Pauli gates (X, Y, Z), demonstrate superposition using Hadamard gates, create entangled Bell states, and visualize quantum states on the Bloch sphere.\nThe key relationship is: ψ = α0 + β1,  |α|² + |β|² = 1\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-computing/qubit_operations.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-computing/qubit_operations.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-computing/qubit_operations.tex",
      "source": "qubit_operations",
      "category": "quantum-computing"
    },
    {
      "title": "Interactive Quantum Gate Operations and Qubit Visualization Bloch Sphere Dynamics and Gat... visualization",
      "body": "I've been exploring quantum gate operations and qubit visualization\\\\\n bloch sphere dynamics and gate sequences.\n\nThis document explores single-qubit quantum gates and their geometric representation on the Bloch sphere.  We implement matrix representations of common gates (Pauli, Hadamard, phase gates), visualize state evolution, and analyze gate sequences for quantum algorithms.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-computing/quantum_gates.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-computing/quantum_gates.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-computing/quantum_gates.tex",
      "source": "quantum_gates",
      "category": "quantum-computing"
    },
    {
      "title": "Simulating Grover's Quantum Search Algorithm: Oracle, Diffusion, and Amplitude Amplifica... - visualizing the math",
      "body": "I wanted to visualize grover's quantum search algorithm:\\\\\noracle, diffusion, and amplitude amplification.\n\nThis report presents a comprehensive analysis of Grover's quantum search algorithm.  We implement the oracle and diffusion operators, demonstrate amplitude amplification, analyze the quadratic speedup over classical search, and explore the algorithm's complexity.\nThe key relationship is: ψ = Σ(x=0)^N-1 αₓ x\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-computing/grover_search.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-computing/grover_search.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-computing/grover_search.tex",
      "source": "grover_search",
      "category": "quantum-computing"
    },
    {
      "title": "The math behind Metapopulation Dynamics: Patch Occupancy Models and Spatial Population Persis... - a simulation",
      "body": "I've been studying metapopulation dynamics: patch occupancy models and spatial population persistence.\n\nMetapopulation theory provides a framework for understanding how spatial population structure influences persistence in fragmented landscapes.  We analyze the classical Levins model of patch occupancy dynamics, where local populations experience colonization and extinction at the patch level.\nThe key relationship is: dpdt = cp(1-p) - ep\n\nIt's fascinating to see the theory come alive in the simulation.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/metapopulation.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/ecology/metapopulation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/metapopulation.tex",
      "source": "metapopulation",
      "category": "ecology"
    },
    {
      "title": "Interactive Food Web Dynamics: Trophic Structure, Stability, and Network Properties visualization",
      "body": "I built an interactive model for food web dynamics: trophic structure, stability, and network properties.\n\nThis computational ecology report examines food web dynamics through the lens of network theory and population dynamics.  We analyze trophic structure using the cascade model, investigate predator-prey oscillations via Lotka-Volterra equations, and assess community stability through eigenvalue analysis of Jacobian matrices.\nThe key relationship is: C = LS²\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/food_webs.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/ecology/food_webs.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/food_webs.tex",
      "source": "food_webs",
      "category": "ecology"
    },
    {
      "title": "Interactive Species Distribution Modeling Entropy and Niche Theory visualization",
      "body": "I've been studying species distribution modeling\\ entropy and niche theory.\n\nSpecies distribution models (SDMs) predict species occurrence across geographic space based on environmental correlates and presence records.  We implement maximum entropy modeling following the MaxEnt framework to estimate habitat suitability for a hypothetical montane species.\nThe key relationship is: P^*(x) = _P H(P) = -∫ P(x)  P(x) \\, dx\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/species_distribution.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/ecology/species_distribution.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/species_distribution.tex",
      "source": "species_distribution",
      "category": "ecology"
    },
    {
      "title": "The math behind Island Biogeography: Equilibrium Theory and Species-Area Relationships - a simulation",
      "body": "I put together a simulation of island biogeography: equilibrium theory and species-area relationships.\n\nThis report presents a comprehensive computational analysis of the MacArthur-Wilson Theory of Island Biogeography, examining the dynamic equilibrium between immigration and extinction rates as determinants of island species richness.  We model immigration as a function of island isolation, extinction as a function of island area, and derive equilibrium species number $S^*$ for islands varying in size and distance from mainland source pools.\nThe key relationship is: I(S^*) = E(S^*)\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/island_biogeography.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/ecology/island_biogeography.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/ecology/island_biogeography.tex",
      "source": "island_biogeography",
      "category": "ecology"
    },
    {
      "title": "I built an interactive Elliptic Curve Cryptography: From Mathematical Foundations to Digital Signatures simulation",
      "body": "I created a computational exploration of elliptic curve cryptography: from mathematical foundations to digital signatures.\n\nThis report presents a comprehensive analysis of elliptic curve cryptography (ECC), exploring the mathematical foundations of elliptic curves over finite fields and their application to public-key cryptography.  We implement point addition and scalar multiplication algorithms, demonstrate the Elliptic Curve Digital Signature Algorithm (ECDSA), and analyze the computational hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP) that underpins ECC security.\nThe key relationship is: y² ≡ x³ + ax + b ±odp\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cryptography/elliptic_curves.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cryptography/elliptic_curves.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cryptography/elliptic_curves.tex",
      "source": "elliptic_curves",
      "category": "cryptography"
    },
    {
      "title": "I built an interactive RSA Encryption: Implementation and Security Analysis simulation",
      "body": "I've been fascinated by rsa encryption: implementation and security analysis.\n\nThis report presents a comprehensive computational analysis of the RSA (Rivest-Shamir-Adleman) public-key cryptosystem, examining the mathematical foundations of modular exponentiation, key generation procedures, encryption and decryption operations, and security considerations.  We implement RSA encryption with various key sizes (512-bit to 2048-bit), analyze the computational complexity of modular exponentiation algorithms, demonstrate the relationship between prime factorization difficulty and.\nThe key relationship is: φ(pq) = (p-1)(q-1)\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cryptography/rsa_encryption.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cryptography/rsa_encryption.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cryptography/rsa_encryption.tex",
      "source": "rsa_encryption",
      "category": "cryptography"
    },
    {
      "title": "I built an interactive Cryptographic Hash Functions: SHA-256 Analysis and Security Properties simulation",
      "body": "I created a computational exploration of cryptographic hash functions: sha-256 analysis and security properties.\n\nThis report presents a comprehensive computational analysis of cryptographic hash functions, with focus on the SHA-256 algorithm and its security properties.  We examine the three fundamental requirements of cryptographic hash functions: preimage resistance, second preimage resistance, and collision resistance.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cryptography/hash_functions.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cryptography/hash_functions.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cryptography/hash_functions.tex",
      "source": "hash_functions",
      "category": "cryptography"
    },
    {
      "title": "Interactive Population Dynamics: Predator-Prey Models and Stability Analysis visualization",
      "body": "I built an interactive model for population dynamics: predator-prey models and stability analysis.\n\nThis tutorial presents a comprehensive analysis of predator-prey population dynamics using the Lotka-Volterra equations and their extensions.  We examine the classical model, perform stability analysis of equilibrium points, and explore modifications including carrying capacity and functional responses.\nThe key relationship is: J = pmatrix\n0 & -β x^* \\\\\nδ y^* & 0\npmatrix\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/population_dynamics.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biology/population_dynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/population_dynamics.tex",
      "source": "population_dynamics",
      "category": "biology"
    },
    {
      "title": "Interactive Epidemiological Modeling: SIR Dynamics Parameter Sensitivity, Interventions, ... visualization",
      "body": "I recently dove into epidemiological modeling: sir dynamics\\\\\n parameter sensitivity, interventions, and real-world context.\n\nThis report presents a comprehensive analysis of the SIR (Susceptible-Infected-Recovered) compartmental model for infectious disease dynamics.  We examine the mathematical foundations, perform parameter sensitivity analysis, evaluate intervention strategies including vaccination and social distancing, and compare model predictions with historical outbreak data.\nThe key relationship is: R₀ = βγ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/epidemiology_sir.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biology/epidemiology_sir.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/epidemiology_sir.tex",
      "source": "epidemiology_sir",
      "category": "biology"
    },
    {
      "title": "I built an interactive Evolutionary Dynamics: Selection, Drift, and Fitness Landscapes simulation",
      "body": "I recently dove into evolutionary dynamics: selection, drift, and fitness landscapes.\n\nThis chapter explores the fundamental forces driving evolutionary change in populations.  We analyze natural selection under various fitness schemes, examine the stochastic effects of genetic drift in finite populations, and investigate the interplay between mutation and selection.\nThe key relationship is: Δ p = p q [p(w_AA - w_Aa) + q(w_Aa - w_aa)]w\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/evolutionary_dynamics.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biology/evolutionary_dynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/evolutionary_dynamics.tex",
      "source": "evolutionary_dynamics",
      "category": "biology"
    },
    {
      "title": "Interactive Enzyme Kinetics: Michaelis-Menten Analysis and Inhibition Studies visualization",
      "body": "I wanted to visualize enzyme kinetics: michaelis-menten analysis and inhibition studies.\n\nThis laboratory report presents a comprehensive analysis of enzyme kinetics using the Michaelis-Menten framework and its linearizations.  We examine the kinetic parameters $Kₘ$ and $V_max$ for a model enzyme system, analyze three types of reversible inhibition (competitive, uncompetitive, and mixed), and compare parameter estimation methods including Lineweaver-Burk, Eadie-Hofstee, and Hanes-Woolf plots.\nThe key relationship is: v₀ = V_max[S]Kₘ + [S]\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/enzyme_kinetics.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biology/enzyme_kinetics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/enzyme_kinetics.tex",
      "source": "enzyme_kinetics",
      "category": "biology"
    },
    {
      "title": "Interactive Logistic Growth Models: Density Dependence and Population Regulation visualization",
      "body": "I created a computational exploration of logistic growth models: density dependence and population regulation.\n\nThis study presents a comprehensive analysis of logistic population growth models and their extensions.  We examine the classic logistic equation, the Allee effect (positive density dependence at low populations), interspecific competition, and sustainable harvesting strategies.\nThe key relationship is: dNdt = rN(1 - NK)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/logistic_growth.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biology/logistic_growth.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biology/logistic_growth.tex",
      "source": "logistic_growth",
      "category": "biology"
    },
    {
      "title": "Exploring Seismic Wave Propagation: Earth Structure and Travel Time Analysis computationally",
      "body": "I've been studying seismic wave propagation: earth structure and travel time analysis.\n\nThis technical report presents a comprehensive analysis of seismic wave propagation through Earth's interior.  We examine P-wave and S-wave velocities in different Earth layers, compute travel times using ray theory, and analyze seismograms to determine Earth structure.\nThe key relationship is: ν = V_P² - 2V_S²2(V_P² - V_S²)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/seismic_waves.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geophysics/seismic_waves.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/seismic_waves.tex",
      "source": "seismic_waves",
      "category": "geophysics"
    },
    {
      "title": "I built an interactive Gravity Anomaly Analysis: Forward Modeling and Inversion of Subsurface Densit... simulation",
      "body": "I built an interactive model for gravity anomaly analysis: forward modeling and inversion of subsurface density structures.\n\nThis technical report presents comprehensive computational analysis of gravity anomalies arising from subsurface density variations.  We implement forward modeling for multiple geometric bodies including spheres, cylinders, and rectangular prisms, along with Bouguer and terrain corrections.\nThe key relationship is: U(r) = G ∫_V ρ(r')|r - r'| dV'\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/gravity_anomaly.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geophysics/gravity_anomaly.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/gravity_anomaly.tex",
      "source": "gravity_anomaly",
      "category": "geophysics"
    },
    {
      "title": "The math behind Plate Tectonics: Thermal Evolution, Plate Motion, and Mantle Convection - a simulation",
      "body": "I wanted to visualize plate tectonics: thermal evolution, plate motion, and mantle convection.\n\nThis technical report presents comprehensive computational analysis of plate tectonic processes including lithospheric cooling, seafloor subsidence, heat flow evolution, and plate kinematics.  We implement the half-space and plate cooling models, analyze Euler pole rotation kinematics, and model mantle convection using Rayleigh-Benard theory.\nThe key relationship is: ∂ T∂ t = κ ∇² T\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/plate_tectonics.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geophysics/plate_tectonics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/plate_tectonics.tex",
      "source": "plate_tectonics",
      "category": "geophysics"
    },
    {
      "title": "Visualizing Earth's Magnetic Field: Dipole Model, Secular Variation, and IGRF Analysis with Python",
      "body": "I put together a simulation of earth's magnetic field: dipole model, secular variation, and igrf analysis.\n\nThis technical report presents comprehensive computational analysis of Earth's main magnetic field using the geocentric axial dipole model and spherical harmonic representations.  We implement field component calculations (radial, meridional, total intensity, inclination, declination), model the International Geomagnetic Reference Field (IGRF), and analyze secular variation.\nThe key relationship is: B = -∇ V\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/magnetic_field.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geophysics/magnetic_field.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geophysics/magnetic_field.tex",
      "source": "magnetic_field",
      "category": "geophysics"
    },
    {
      "title": "Visualizing Quantum Scattering Theory: Cross Sections and Partial Wave Analysis with Python",
      "body": "I've been fascinated by quantum scattering theory: cross sections and partial wave analysis.\n\nThis report presents a comprehensive computational analysis of quantum scattering theory, examining differential and total cross sections, partial wave decomposition, and the Born approximation.  We analyze Rutherford scattering from Coulomb potentials, extract phase shifts from numerical solutions of the radial Schrödinger equation, verify the optical theorem, and investigate resonance phenomena through the Breit-Wigner formula.\nThe key relationship is: dσdΩ = |f(θ, φ)|²\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/scattering.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-mechanics/scattering.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/scattering.tex",
      "source": "scattering",
      "category": "quantum-mechanics"
    },
    {
      "title": "Exploring Quantum Harmonic Oscillator: Quantization and Wavefunctions computationally",
      "body": "I put together a simulation of quantum harmonic oscillator:\\ quantization and wavefunctions.\n\nThis report presents a comprehensive computational analysis of the quantum harmonic oscillator, one of the most fundamental exactly-solvable systems in quantum mechanics.  We derive the energy eigenvalues $Eₙ = (n + 1/2)$ and construct wavefunctions using Hermite polynomials.\nThe key relationship is: H = p²2m + 12mω²x²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/harmonic_oscillator.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-mechanics/harmonic_oscillator.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/harmonic_oscillator.tex",
      "source": "harmonic_oscillator",
      "category": "quantum-mechanics"
    },
    {
      "title": "Interactive Time-Independent Perturbation Theory: and Zeeman Effects in Hydrogen visualization",
      "body": "I recently dove into time-independent perturbation theory:\\ and zeeman effects in hydrogen.\n\nThis report presents a comprehensive analysis of time-independent perturbation theory applied to hydrogen atom energy levels.  We examine non-degenerate and degenerate perturbation theory, computing first and second-order energy corrections for the quantum harmonic oscillator.\nThe key relationship is: Eₙ^(1) = ψₙ^(0) | V | ψₙ^(0)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/perturbation_theory.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-mechanics/perturbation_theory.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/perturbation_theory.tex",
      "source": "perturbation_theory",
      "category": "quantum-mechanics"
    },
    {
      "title": "I built an interactive The Hydrogen Atom: Exact Solution of the Schrödinger Equation simulation",
      "body": "I created a computational exploration of the hydrogen atom: exact solution of the schrödinger equation.\n\nThe hydrogen atom represents the only exactly solvable atomic system in quantum mechanics, providing fundamental insights into atomic structure and spectroscopy.  This computational analysis solves the time-independent Schrödinger equation in spherical coordinates, yielding the complete set of wavefunctions $_nlm(r,,)$ characterized by quantum numbers $n$ (principal), $l$ (orbital angular momentum), and $m$ (magnetic).\nThe key relationship is: Eₙ = -mₑ e⁴2(4πε₀)²²1n² = -13.6 eVn²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/hydrogen_atom.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/quantum-mechanics/hydrogen_atom.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/quantum-mechanics/hydrogen_atom.tex",
      "source": "hydrogen_atom",
      "category": "quantum-mechanics"
    },
    {
      "title": "Interactive Numerical Integration Methods: Quadrature Algorithms and Error Analysis visualization",
      "body": "I wanted to visualize numerical integration methods:\\\\\nquadrature algorithms and error analysis.\n\nThis report presents a comprehensive analysis of numerical integration (quadrature) methods.  We implement and compare the trapezoidal rule, Simpson's rule, Romberg integration, and Gaussian quadrature.\nThe key relationship is: I = ∫ₐᵇ f(x) \\, dx\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/integration.tex\n\nHas anyone found good real-world applications to demonstrate?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/numerical-methods/integration.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/integration.tex",
      "source": "integration",
      "category": "numerical-methods"
    },
    {
      "title": "Interactive Partial Differential Equations: Finite Difference Methods and Stability Analysis visualization",
      "body": "I've been fascinated by partial differential equations:\\\\\nfinite difference methods and stability analysis.\n\nThis report presents finite difference methods for solving partial differential equations (PDEs).  We implement explicit and implicit schemes for the heat equation and wave equation, analyze stability using von Neumann analysis, and demonstrate the CFL condition.\nThe key relationship is: G = 1 - 4r²(kΔ x2)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/pde_solver.tex\n\nHow do you approach teaching this topic?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/numerical-methods/pde_solver.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/pde_solver.tex",
      "source": "pde_solver",
      "category": "numerical-methods"
    },
    {
      "title": "Simulating Root Finding Algorithms: Convergence Analysis and Comparison - visualizing the math",
      "body": "I've been fascinated by root finding algorithms:\\\\\nconvergence analysis and comparison.\n\nThis report presents a comprehensive analysis of root-finding algorithms for nonlinear equations.  We implement and compare bisection, Newton-Raphson, secant, and Brent's methods.\nThe key relationship is: x_n+1 = xₙ - f(xₙ)f'(xₙ)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/root_finding.tex\n\nWhat's your favorite way to illustrate this concept?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/numerical-methods/root_finding.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/root_finding.tex",
      "source": "root_finding",
      "category": "numerical-methods"
    },
    {
      "title": "The math behind Numerical Methods for Ordinary Differential Equations: A Comparative Analysis... - a simulation",
      "body": "I've been studying numerical methods for ordinary differential equations:\\\\\na comparative analysis of integration schemes.\n\nThis technical report presents a comprehensive comparison of numerical methods for solving ordinary differential equations.  We implement and analyze Forward Euler, fourth-order Runge-Kutta (RK4), and adaptive Runge-Kutta-Fehlberg (RKF45) methods.\nThe key relationship is: dydt = f(t, y),  y(t₀) = y₀\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/ode_solver.tex\n\nWhat's your favorite way to illustrate this concept?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/numerical-methods/ode_solver.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/numerical-methods/ode_solver.tex",
      "source": "ode_solver",
      "category": "numerical-methods"
    },
    {
      "title": "I built an interactive Radiometric Dating: Isotope Geochronology and Age Determination simulation",
      "body": "I've been fascinated by radiometric dating:\\\\\nisotope geochronology and age determination.\n\nThis report presents a comprehensive analysis of radiometric dating methods.  We examine radioactive decay kinetics, implement isochron dating for Rb-Sr and U-Pb systems, analyze concordia-discordia relationships, calculate closure temperatures, and demonstrate carbon-14 dating for recent samples.\nThe key relationship is: N(t) = N₀ e^-λ t\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/earth-science/radiometric_dating.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/earth-science/radiometric_dating.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/earth-science/radiometric_dating.tex",
      "source": "radiometric_dating",
      "category": "earth-science"
    },
    {
      "title": "The math behind Microwave Engineering Analysis-Parameters, Transmission Lines, and Impedance ... - a simulation",
      "body": "I created a computational exploration of microwave engineering analysis\\-parameters, transmission lines, and impedance matching.\n\nThis computational study presents comprehensive analysis of microwave network parameters, including S-parameter characterization of two-port networks, transmission line impedance transformations, Smith chart impedance matching techniques, and microstrip transmission line design.  We analyze VSWR (Voltage Standing Wave Ratio), return loss, insertion loss, and reflection coefficients for practical microwave circuits operating at frequencies from 1 GHz to 10 GHz.\nThe key relationship is: Z₀ = √LC,  β = ω√LC = 2π fvₚ\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/microwave.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/electromagnetics/microwave.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/microwave.tex",
      "source": "microwave",
      "category": "electromagnetics"
    },
    {
      "title": "Exploring Antenna Design and Analysis: Radiation Patterns and Array Synthesis computationally",
      "body": "I put together a simulation of antenna design and analysis: radiation patterns and array synthesis.\n\nThis engineering report presents a comprehensive computational analysis of antenna design principles, including radiation pattern characterization, dipole antenna theory, linear array synthesis, aperture antenna analysis, and impedance matching techniques.  We examine the fundamental parameters of antenna performance including gain, directivity, beamwidth, and radiation efficiency.\nThe key relationship is: Fₙ(θ, φ) = |E(θ, φ)||E|_max\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/antenna_design.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/electromagnetics/antenna_design.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/antenna_design.tex",
      "source": "antenna_design",
      "category": "electromagnetics"
    },
    {
      "title": "Simulating Electromagnetic Wave Propagation: From Maxwell's Equations to Waveguides - visualizing the math",
      "body": "I built an interactive model for electromagnetic wave propagation: from maxwell's equations to waveguides.\n\nThis technical report presents a comprehensive computational analysis of electromagnetic wave propagation phenomena derived from Maxwell's equations.  We examine plane wave solutions in free space and lossy media, analyze reflection and transmission at dielectric interfaces using Fresnel coefficients, investigate rectangular waveguide modes with cutoff frequencies and dispersion relations, and characterize skin depth and attenuation in conductors.\nThe key relationship is: ∇² E = μ  ∂² E∂ t²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/wave_propagation.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/electromagnetics/wave_propagation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/wave_propagation.tex",
      "source": "wave_propagation",
      "category": "electromagnetics"
    },
    {
      "title": "The math behind Electromagnetic Compatibility Engineering, Filtering, and Compliance Analysis - a simulation",
      "body": "I put together a simulation of electromagnetic compatibility engineering\\, filtering, and compliance analysis.\n\nElectromagnetic compatibility (EMC) ensures that electronic systems operate without causing or suffering from electromagnetic interference (EMI).  This report presents comprehensive computational analysis of EMC engineering principles including shielding effectiveness, filter design, grounding strategies, and regulatory compliance.\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/emc.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/electromagnetics/emc.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electromagnetics/emc.tex",
      "source": "emc",
      "category": "electromagnetics"
    },
    {
      "title": "Simulating Atmospheric Dynamics Wind and Thermal Balance - visualizing the math",
      "body": "I've been exploring atmospheric dynamics\\ wind and thermal balance.\n\nAnalysis of atmospheric dynamics including geostrophic balance, thermal wind, and jet stream formation..\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/atmospheric-science/atmospheric_dynamics.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/atmospheric-science/atmospheric_dynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/atmospheric-science/atmospheric_dynamics.tex",
      "source": "atmospheric_dynamics",
      "category": "atmospheric-science"
    },
    {
      "title": "The math behind Radiative Transfer-Lambert Law and Greenhouse Effect - a simulation",
      "body": "I've been exploring radiative transfer\\-lambert law and greenhouse effect.\n\nAnalysis of radiative transfer in the atmosphere including absorption, scattering, and the greenhouse effect..\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/atmospheric-science/radiative_transfer.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/atmospheric-science/radiative_transfer.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/atmospheric-science/radiative_transfer.tex",
      "source": "radiative_transfer",
      "category": "atmospheric-science"
    },
    {
      "title": "Simulating Air Pollution Dispersion Plume Modeling - visualizing the math",
      "body": "I put together a simulation of air pollution dispersion\\ plume modeling.\n\nComputational analysis of air pollution dispersion using Gaussian plume models and deposition calculations..\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/atmospheric-science/air_pollution.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/atmospheric-science/air_pollution.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/atmospheric-science/air_pollution.tex",
      "source": "air_pollution",
      "category": "atmospheric-science"
    },
    {
      "title": "Visualizing Ocean Currents: Geostrophic Flow and Wind-Driven Circulation with Python",
      "body": "I've been fascinated by ocean currents: geostrophic flow and wind-driven circulation and wanted to share what I learned.\nThe key relationship is: f k × u_g = -1ρ₀ ∇ p\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/oceanography/ocean_currents.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/oceanography/ocean_currents.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/oceanography/ocean_currents.tex",
      "source": "ocean_currents",
      "category": "oceanography"
    },
    {
      "title": "I built an interactive Ocean Wave Dynamics: Dispersion, Spectra, and Coastal Processes simulation",
      "body": "I created a computational exploration of ocean wave dynamics: dispersion, spectra, and coastal processes and wanted to share what I learned.\nThe key relationship is: η(x, t) = a (kx - ω t)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/oceanography/wave_dynamics.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/oceanography/wave_dynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/oceanography/wave_dynamics.tex",
      "source": "wave_dynamics",
      "category": "oceanography"
    },
    {
      "title": "Interactive Optimal Control Theory: From LQR to Model Predictive Control visualization",
      "body": "I put together a simulation of optimal control theory: from lqr to model predictive control.\n\nThis technical report presents a comprehensive treatment of optimal control theory, covering both classical and modern methodologies.  We examine the Linear Quadratic Regulator (LQR) framework and its solution via the Riccati equation, derive necessary conditions for optimality using Pontryagin's Maximum Principle, explore dynamic programming and the Hamilton-Jacobi-Bellman equation, analyze time-optimal bang-bang control, and demonstrate model predictive control for constrained systems.\nThe key relationship is: x(t) = f(x(t), u(t), t)\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/control-theory/optimal_control.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/control-theory/optimal_control.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/control-theory/optimal_control.tex",
      "source": "optimal_control",
      "category": "control-theory"
    },
    {
      "title": "Exploring Nonlinear Control Systems: Stability Analysis and Advanced Control Design computationally",
      "body": "I built an interactive model for nonlinear control systems: stability analysis and advanced control design.\n\nThis report presents a comprehensive analysis of nonlinear control systems using Lyapunov stability theory, phase plane methods, and advanced nonlinear control design techniques.  We examine the stability of equilibrium points for representative nonlinear systems, demonstrate feedback linearization for affine nonlinear systems, design sliding mode controllers with chattering reduction, and apply backstepping to cascade systems.\nThe key relationship is: x = f(x, u, t)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/control-theory/nonlinear_control.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/control-theory/nonlinear_control.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/control-theory/nonlinear_control.tex",
      "source": "nonlinear_control",
      "category": "control-theory"
    },
    {
      "title": "Simulating Adaptive Control Systems: Model Reference and Self-Tuning Approaches - visualizing the math",
      "body": "I put together a simulation of adaptive control systems: model reference and self-tuning approaches.\n\nThis report presents a comprehensive analysis of adaptive control systems with emphasis on Model Reference Adaptive Control (MRAC) and Self-Tuning Regulators (STR).  We examine the stability guarantees provided by Lyapunov-based adaptation laws, analyze the role of persistent excitation in parameter convergence, and compare direct versus indirect adaptive approaches.\nThe key relationship is: _t  ∞ [y(t) - yₘ(t)] = 0\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/control-theory/adaptive_control.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/control-theory/adaptive_control.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/control-theory/adaptive_control.tex",
      "source": "adaptive_control",
      "category": "control-theory"
    },
    {
      "title": "Simulating Stress Analysis: Mohr's Circle and Failure Theories - visualizing the math",
      "body": "I've been studying stress analysis: mohr's circle and failure theories.\n\nThis report presents computational analysis of stress states in solid mechanics.  We examine stress transformation using Mohr's circle, principal stresses, von Mises equivalent stress, and common failure theories.\nThe key relationship is: σ = pmatrix σₓ & τ_xy \\\\ τ_xy & σ_y pmatrix\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/stress_analysis.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mechanical-engineering/stress_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/stress_analysis.tex",
      "source": "stress_analysis",
      "category": "mechanical-engineering"
    },
    {
      "title": "The math behind Heat Transfer Analysis: Conduction, Convection, and Fins - a simulation",
      "body": "I built an interactive model for heat transfer analysis: conduction, convection, and fins.\n\nThis report presents computational analysis of heat transfer mechanisms including conduction through composite walls, convection correlations, fin analysis, and heat exchanger design.  Python-based computations provide quantitative analysis with dynamic visualization of temperature distributions and heat flux.\nThe key relationship is: q = -k dTdx\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/heat_transfer.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mechanical-engineering/heat_transfer.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/heat_transfer.tex",
      "source": "heat_transfer",
      "category": "mechanical-engineering"
    },
    {
      "title": "Simulating Vibration Analysis: SDOF Systems and Modal Analysis - visualizing the math",
      "body": "I wanted to visualize vibration analysis: sdof systems and modal analysis.\n\nThis report presents computational analysis of mechanical vibrations including free and forced response of single degree of freedom (SDOF) systems, damping effects, frequency response, and modal analysis.  Python-based computations provide quantitative analysis with dynamic visualization.\nThe key relationship is: mx + cx + kx = F(t)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/vibration_analysis.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mechanical-engineering/vibration_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/vibration_analysis.tex",
      "source": "vibration_analysis",
      "category": "mechanical-engineering"
    },
    {
      "title": "Exploring Thermodynamic Cycles: Efficiency Analysis computationally",
      "body": "I've been exploring thermodynamic cycles: efficiency analysis.\n\nThis report presents computational analysis of thermodynamic power cycles including Carnot, Otto, Diesel, and Rankine cycles.  We examine ideal and actual cycle efficiencies, P-v and T-s diagrams, and parametric studies.\nThe key relationship is: η_Carnot = 1 - T_LT_H\n\nThe visualization really helped me understand the underlying dynamics.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/thermodynamics_cycle.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mechanical-engineering/thermodynamics_cycle.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/thermodynamics_cycle.tex",
      "source": "thermodynamics_cycle",
      "category": "mechanical-engineering"
    },
    {
      "title": "Visualizing Pipe Flow Analysis: Darcy-Weisbach and Friction Factors with Python",
      "body": "I've been studying pipe flow analysis: darcy-weisbach and friction factors.\n\nThis report presents computational analysis of pipe flow using the Darcy-Weisbach equation.  We examine Reynolds number regimes, friction factor correlations including the Colebrook-White equation, the Moody diagram, minor losses, and pipe network analysis.\nThe key relationship is: Re = ρ V Dμ = V Dν\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/fluid_flow.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mechanical-engineering/fluid_flow.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mechanical-engineering/fluid_flow.tex",
      "source": "fluid_flow",
      "category": "mechanical-engineering"
    },
    {
      "title": "Simulating Radioactive Decay Chains: Bateman Equations and Activity Calculations - visualizing the math",
      "body": "I created a computational exploration of radioactive decay chains: bateman equations and activity calculations.\n\nThis technical report presents comprehensive computational analysis of radioactive decay chains using the Bateman equations.  We implement solutions for sequential decay series, compute activities as functions of time, and analyze equilibrium conditions including secular and transient equilibrium.\nThe key relationship is: dNdt = -λ N\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nuclear-physics/radioactive_decay.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/nuclear-physics/radioactive_decay.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nuclear-physics/radioactive_decay.tex",
      "source": "radioactive_decay",
      "category": "nuclear-physics"
    },
    {
      "title": "Simulating Nuclear Binding Energy: Semi-Empirical Mass Formula and Nuclear Stability - visualizing the math",
      "body": "I've been studying nuclear binding energy: semi-empirical mass formula and nuclear stability.\n\nThis technical report presents comprehensive computational analysis of nuclear binding energies using the semi-empirical mass formula (SEMF).  We implement the Bethe-Weizs\\\"acker model with volume, surface, Coulomb, asymmetry, and pairing terms to predict nuclear masses and stability.\nThe key relationship is: B(A,Z) = [Zmₚ + Nmₙ - M(A,Z)]c²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nuclear-physics/binding_energy.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/nuclear-physics/binding_energy.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nuclear-physics/binding_energy.tex",
      "source": "binding_energy",
      "category": "nuclear-physics"
    },
    {
      "title": "The math behind Nuclear Reactor Kinetics: Point Kinetics Model and Delayed Neutron Analysis - a simulation",
      "body": "I built an interactive model for nuclear reactor kinetics: point kinetics model and delayed neutron analysis.\n\nThis technical report presents comprehensive computational analysis of nuclear reactor kinetics using the point kinetics equations with delayed neutrons.  We implement solutions for reactivity transients, analyze the role of delayed neutron precursors in reactor control, and compute reactor periods for various reactivity insertions.\nThe key relationship is: ρ = k_eff - 1k_eff\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nuclear-physics/reactor_kinetics.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/nuclear-physics/reactor_kinetics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nuclear-physics/reactor_kinetics.tex",
      "source": "reactor_kinetics",
      "category": "nuclear-physics"
    },
    {
      "title": "The math behind Automated Signal Analysis Report - a simulation",
      "body": "I put together a simulation of automated signal analysis report and wanted to share what I learned.\nThe key relationship is: H(s) = ωₙ²s² + 2ζωₙ s + ωₙ²\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/pythontex/engineering_report.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/pythontex/engineering_report.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/pythontex/engineering_report.tex",
      "source": "engineering_report",
      "category": "pythontex"
    },
    {
      "title": "Visualizing Genetic Algorithms: Evolutionary Optimization and Function Approximation with Python",
      "body": "I put together a simulation of genetic algorithms: evolutionary optimization and function approximation.\n\nThis report presents a comprehensive analysis of genetic algorithms (GAs) as bio-inspired optimization methods.  We explore chromosome representations (binary, real-valued, permutation encodings), selection mechanisms (tournament, roulette wheel, rank-based), genetic operators (single-point, two-point, uniform crossover; bit-flip, Gaussian, and swap mutation), and fitness landscape theory including the schema theorem and building block hypothesis.\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/genetic_algorithms.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/computational-biology/genetic_algorithms.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/genetic_algorithms.tex",
      "source": "genetic_algorithms",
      "category": "computational-biology"
    },
    {
      "title": "Exploring Cellular Automata: From Elementary Rules to Biological Systems computationally",
      "body": "I've been studying cellular automata: from elementary rules to biological systems.\n\nThis report presents a comprehensive computational analysis of cellular automata (CA) as models for biological systems.  We examine elementary one-dimensional CA including Wolfram's Rule 30 (chaotic), Rule 110 (class IV complexity), and Rule 184 (traffic flow), followed by two-dimensional systems including Conway's Game of Life and its pattern classification.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/cellular_automata.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/computational-biology/cellular_automata.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/cellular_automata.tex",
      "source": "cellular_automata",
      "category": "computational-biology"
    },
    {
      "title": "Interactive Metabolic Network Modeling: Flux Balance Analysis and Constraint-Based Optimi... visualization",
      "body": "I wanted to visualize metabolic network modeling: flux balance analysis and constraint-based optimization.\n\nThis report presents a comprehensive computational analysis of metabolic networks using constraint-based modeling approaches.  We construct stoichiometric matrices for a simplified central carbon metabolism network, perform Flux Balance Analysis (FBA) to predict optimal growth rates under nutrient limitations, analyze elementary flux modes to identify minimal functional pathways, and apply Metabolic Control Analysis (MCA) to quantify pathway regulation.\nThe key relationship is: S v = 0\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/metabolic_networks.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/computational-biology/metabolic_networks.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/metabolic_networks.tex",
      "source": "metabolic_networks",
      "category": "computational-biology"
    },
    {
      "title": "Visualizing Protein Folding Simulation: Energy Landscapes and Folding Kinetics with Python",
      "body": "I've been fascinated by protein folding simulation: energy landscapes and folding kinetics.\n\nThis computational study investigates protein folding through simplified lattice models and energy landscape analysis.  We implement the hydrophobic-polar (HP) model to simulate folding on a 2D square lattice, employ Monte Carlo methods to explore conformational space, and analyze folding thermodynamics and kinetics.\nThe key relationship is: Δ G_fold = Δ H_fold - TΔ S_fold\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/protein_folding.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/computational-biology/protein_folding.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computational-biology/protein_folding.tex",
      "source": "protein_folding",
      "category": "computational-biology"
    },
    {
      "title": "Interactive Data Science: Comprehensive Statistical Analysis visualization",
      "body": "I wanted to visualize data science: comprehensive statistical analysis.\n\nThis document presents a comprehensive statistical analysis workflow including descriptive statistics, hypothesis testing, confidence intervals, ANOVA, correlation analysis, and regression diagnostics.  We demonstrate parametric and non-parametric tests, effect size calculations, and multiple testing corrections using Python's scipy and statsmodels libraries.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/data-science/statistical_analysis.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/data-science/statistical_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/data-science/statistical_analysis.tex",
      "source": "statistical_analysis",
      "category": "data-science"
    },
    {
      "title": "Visualizing Time Series Analysis and Forecasting with Python",
      "body": "I've been exploring time series analysis and forecasting.\n\nThis document presents a comprehensive analysis of time series data, including decomposition into trend, seasonality, and residual components, autocorrelation analysis, ARIMA modeling, and forecasting with prediction intervals.  The analysis demonstrates statistical tests for stationarity and model selection criteria.\nThe key relationship is: yₜ = Tₜ + Sₜ + Rₜ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/data-science/time_series.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/data-science/time_series.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/data-science/time_series.tex",
      "source": "time_series",
      "category": "data-science"
    },
    {
      "title": "Exploring Data Visualization: Principles and Practice computationally",
      "body": "I've been studying data visualization: principles and practice.\n\nThis document explores comprehensive data visualization techniques, including various plot types for different data characteristics, color palette design with accessibility considerations, perceptual principles, and dashboard composition.  We demonstrate best practices for effective visual communication of quantitative information.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/data-science/visualization.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/data-science/visualization.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/data-science/visualization.tex",
      "source": "visualization",
      "category": "data-science"
    },
    {
      "title": "Exploring Pulsar Timing: From Spin-down to Gravitational Wave Detection A Comprehensive... computationally",
      "body": "I wanted to visualize pulsar timing: from spin-down to gravitational wave detection\\\\\n a comprehensive analysis of pulsar astrophysics.\n\nThis comprehensive analysis explores pulsar timing theory and applications, from basic spin-down physics to gravitational wave detection via pulsar timing arrays.  We derive the fundamental pulsar equations including period derivatives, characteristic ages, and magnetic field strengths.\nThe key relationship is: τ_c = P(n-1)P = P2P\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/pulsar_timing.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astronomy/pulsar_timing.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/pulsar_timing.tex",
      "source": "pulsar_timing",
      "category": "astronomy"
    },
    {
      "title": "Simulating Exoplanet Transit Photometry: Light Curves and Planetary Parameters A Compreh... - visualizing the math",
      "body": "I wanted to visualize exoplanet transit photometry: light curves and planetary parameters\\\\\n a comprehensive analysis of transit detection methods.\n\nThis comprehensive analysis presents the theory and practice of exoplanet detection via transit photometry.  We develop analytic models for transit light curves including the effects of limb darkening, derive expressions for transit depth, duration, and impact parameter, and demonstrate parameter extraction from simulated observations.\nThe key relationship is: p_transit = R_ + Rₚa ≈ R_a\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/exoplanet_transit.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astronomy/exoplanet_transit.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/exoplanet_transit.tex",
      "source": "exoplanet_transit",
      "category": "astronomy"
    },
    {
      "title": "I built an interactive Cosmological Expansion: From Hubble's Law to Dark Energy A Comprehensive Anal... simulation",
      "body": "I've been exploring cosmological expansion: from hubble's law to dark energy\\\\\n a comprehensive analysis of the $λ$cdm model.\n\nThis comprehensive analysis explores the expansion history of the universe from observational foundations to theoretical frameworks.  We examine Hubble's law and its modern calibrations, derive the Friedmann equations governing cosmic evolution, and analyze different cosmological models including matter-dominated, radiation-dominated, and dark energy-dominated universes.\nThe key relationship is: v = H₀ d\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/cosmological_expansion.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astronomy/cosmological_expansion.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/cosmological_expansion.tex",
      "source": "cosmological_expansion",
      "category": "astronomy"
    },
    {
      "title": "Simulating Stellar Evolution: From Main Sequence to Stellar Remnants A Comprehensive Ana... - visualizing the math",
      "body": "I've been studying stellar evolution: from main sequence to stellar remnants\\\\\n a comprehensive analysis of the hr diagram and nuclear burning stages.\n\nThis comprehensive analysis explores stellar structure and evolution through the Hertzsprung-Russell diagram.  We derive the fundamental stellar relations including the mass-luminosity relation, main sequence lifetime, and Stefan-Boltzmann law.\nThe key relationship is: L = 4π R² σ T_eff⁴\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/stellar_evolution.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/astronomy/stellar_evolution.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/astronomy/stellar_evolution.tex",
      "source": "stellar_evolution",
      "category": "astronomy"
    },
    {
      "title": "Exploring Spiking Neural Networks: Population Dynamics and Synchronization computationally",
      "body": "I've been fascinated by spiking neural networks:\\\\\npopulation dynamics and synchronization.\n\nThis report presents a comprehensive analysis of spiking neural network dynamics.  We implement leaky integrate-and-fire neurons, analyze population synchronization, compute spike train statistics, examine balanced excitation-inhibition, and investigate network oscillations.\nThe key relationship is: τₘ dVdt = -(V - V_rest) + Rₘ I_syn\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/neuroscience/neural_network.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/neuroscience/neural_network.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/neuroscience/neural_network.tex",
      "source": "neural_network",
      "category": "neuroscience"
    },
    {
      "title": "The math behind EEG Signal Analysis: Spectral Decomposition and Brain State Classification - a simulation",
      "body": "I built an interactive model for eeg signal analysis:\\\\\nspectral decomposition and brain state classification.\n\nThis report presents a comprehensive analysis of electroencephalography (EEG) signal processing.  We implement spectral analysis methods, extract frequency band power, compute event-related potentials, analyze connectivity measures, and classify brain states.\nThe key relationship is: S_xx(f) = _T∞1T|∫₀ᵀ x(t)e^-i2π ftdt|²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/neuroscience/eeg_analysis.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/neuroscience/eeg_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/neuroscience/eeg_analysis.tex",
      "source": "eeg_analysis",
      "category": "neuroscience"
    },
    {
      "title": "I built an interactive Hodgkin-Huxley Model: Action Potential Generation and Ion Channel Dynamics simulation",
      "body": "I've been studying hodgkin-huxley model:\\\\\naction potential generation and ion channel dynamics.\n\nThis report presents a comprehensive analysis of the Hodgkin-Huxley model for action potential generation.  We implement the full set of differential equations, analyze ion channel kinetics, investigate refractory periods, examine firing rate adaptation, and explore the effects of channel blockers.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/neuroscience/action_potential.tex\n\nWhat biological systems have you modeled?",
      "image_url": null,
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/neuroscience/action_potential.tex",
      "source": "action_potential",
      "category": "neuroscience"
    },
    {
      "title": "I built an interactive Multiple Regression Analysis: Model Building and Diagnostics simulation",
      "body": "I put together a simulation of multiple regression analysis: model building and diagnostics and wanted to share what I learned.\nThe key relationship is: Y = β₀ + β₁ X₁ + β₂ X₂ + ·s + βₚ Xₚ + ε\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/statistics/regression_analysis.tex\n\nHas anyone found good real-world applications to demonstrate?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/statistics/regression_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/statistics/regression_analysis.tex",
      "source": "regression_analysis",
      "category": "statistics"
    },
    {
      "title": "Visualizing Statistical Hypothesis Testing: Theory and Applications with Python",
      "body": "I recently dove into statistical hypothesis testing: theory and applications and wanted to share what I learned.\nThe key relationship is: p = P(T ≥ t_obs | H₀)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/statistics/hypothesis_testing.tex\n\nHow do you approach teaching this topic?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/statistics/hypothesis_testing.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/statistics/hypothesis_testing.tex",
      "source": "hypothesis_testing",
      "category": "statistics"
    },
    {
      "title": "Visualizing Bayesian Inference: From Prior to Posterior Parameter Estimation with Markov ... with Python",
      "body": "I've been studying bayesian inference: from prior to posterior\\\\\n parameter estimation with markov chain monte carlo.\n\nThis tutorial provides a comprehensive introduction to Bayesian inference for parameter estimation.  We implement conjugate prior analysis for binomial data and develop a Metropolis-Hastings MCMC sampler for Bayesian linear regression.\nThe key relationship is: p(θ|k, n) = Beta(α + k, β + n - k)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/statistics/bayesian.tex\n\nHow do you approach teaching this topic?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/statistics/bayesian.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/statistics/bayesian.tex",
      "source": "bayesian",
      "category": "statistics"
    },
    {
      "title": "Interactive Sound Propagation Analysis Equations and Transmission Loss visualization",
      "body": "I built an interactive model for sound propagation analysis\\ equations and transmission loss.\n\nAnalysis of sound wave propagation through various media, including acoustic impedance, transmission coefficients, and transmission loss calculations..\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/acoustics/sound_propagation.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/acoustics/sound_propagation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/acoustics/sound_propagation.tex",
      "source": "sound_propagation",
      "category": "acoustics"
    },
    {
      "title": "The math behind Musical Acoustics Analysis and Instrument Modeling - a simulation",
      "body": "I put together a simulation of musical acoustics\\ analysis and instrument modeling.\n\nComputational analysis of musical acoustics including harmonic series, string vibrations, wind instrument resonances, and psychoacoustic phenomena..\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/acoustics/musical_acoustics.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/acoustics/musical_acoustics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/acoustics/musical_acoustics.tex",
      "source": "musical_acoustics",
      "category": "acoustics"
    },
    {
      "title": "The math behind Room Acoustics Analysis and Sound Field Modeling - a simulation",
      "body": "I've been exploring room acoustics analysis\\ and sound field modeling.\n\nThis technical report presents computational analysis of room acoustics including reverberation time calculations using Sabine and Eyring equations, sound absorption modeling, and acoustic parameter optimization..\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/acoustics/room_acoustics.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/acoustics/room_acoustics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/acoustics/room_acoustics.tex",
      "source": "room_acoustics",
      "category": "acoustics"
    },
    {
      "title": "I built an interactive Molecular Dynamics Simulation: Lennard-Jones Potentials to Thermodynamic Prop... simulation",
      "body": "I recently dove into molecular dynamics simulation:\\ lennard-jones potentials to thermodynamic properties.\n\nMolecular dynamics (MD) simulations provide atomistic insight into the behavior of matter by solving Newton's equations of motion for systems of interacting particles.  This document develops a complete MD simulation framework, starting from the Lennard-Jones potential for pairwise interactions, implementing the velocity Verlet integration algorithm, and extracting thermodynamic properties including temperature, pressure, and radial distribution functions.\nThe key relationship is: F_ij = F_LJ(r_ij) r_ijr_ij\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemistry/molecular_dynamics.tex\n\nHas anyone implemented similar kinetics models?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/chemistry/molecular_dynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemistry/molecular_dynamics.tex",
      "source": "molecular_dynamics",
      "category": "chemistry"
    },
    {
      "title": "Interactive Chemical Reaction Kinetics: Rate Laws, Mechanisms, and Catalysis visualization",
      "body": "I created a computational exploration of chemical reaction kinetics: rate laws, mechanisms, and catalysis.\n\nThis study presents a comprehensive analysis of chemical reaction kinetics, examining rate laws for reactions of different orders, temperature dependence through the Arrhenius equation, and the effects of catalysis on reaction rates.  We analyze experimental concentration-time data to determine rate constants, activation energies, and pre-exponential factors.\nThe key relationship is: Rate = -1ad[A]dt = k[A]ᵐ[B]ⁿ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemistry/reaction_kinetics.tex\n\nWhat reaction systems have you found most illustrative?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/chemistry/reaction_kinetics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemistry/reaction_kinetics.tex",
      "source": "reaction_kinetics",
      "category": "chemistry"
    },
    {
      "title": "Exploring Cosmic Inflation: Slow-Roll Dynamics and Primordial Perturbations computationally",
      "body": "I built an interactive model for cosmic inflation: slow-roll dynamics and primordial perturbations.\n\nThis report presents a comprehensive computational analysis of inflationary cosmology within the slow-roll approximation.  We examine the dynamics of a scalar field (the inflaton) driving exponential expansion in the early universe, calculate slow-roll parameters ($$, $$) that govern the duration and ending of inflation, and compute the primordial power spectra for scalar and tensor perturbations.\nThe key relationship is: φ + 3Hφ + V'(φ) = 0\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cosmology/inflation.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cosmology/inflation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cosmology/inflation.tex",
      "source": "inflation",
      "category": "cosmology"
    },
    {
      "title": "Visualizing Big Bang Cosmology: Friedmann Dynamics and Primordial Nucleosynthesis with Python",
      "body": "I've been exploring big bang cosmology: friedmann dynamics and primordial nucleosynthesis.\n\nThis computational analysis examines the thermal and dynamical history of the early universe within the framework of the standard $$CDM cosmological model.  We numerically solve the Friedmann equations to determine scale factor evolution through the radiation-dominated, matter-dominated, and dark-energy-dominated epochs.\nThe key relationship is: T(z) = T₀(1+z)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cosmology/big_bang.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cosmology/big_bang.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cosmology/big_bang.tex",
      "source": "big_bang",
      "category": "cosmology"
    },
    {
      "title": "Exploring Cosmic Structure Formation: Linear Growth and Nonlinear Collapse computationally",
      "body": "I wanted to visualize cosmic structure formation: linear growth and nonlinear collapse.\n\nThis report presents a comprehensive computational analysis of cosmic structure formation from linear perturbations in the early universe to nonlinear halo collapse.  We solve the linear growth equation to compute the growth factor $D(z)$ and growth rate $f(z)$, calculate the matter power spectrum $P(k)$ using the BBKS transfer function, apply the Press-Schechter formalism to predict halo mass functions, and examine the two-point correlation function including baryon acoustic oscillation (BAO) fe.\nThe key relationship is: δ(x, t) = ρ(x, t) - ρ(t)ρ(t)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cosmology/structure_formation.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/cosmology/structure_formation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/cosmology/structure_formation.tex",
      "source": "structure_formation",
      "category": "cosmology"
    },
    {
      "title": "I built an interactive Biomechanics Mechanics and Viscoelasticity simulation",
      "body": "I recently dove into biomechanics\\ mechanics and viscoelasticity.\n\nAnalysis of biological tissue mechanics including stress-strain relationships, viscoelasticity, and bone mechanics..\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/biomechanics.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biomedical/biomechanics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/biomechanics.tex",
      "source": "biomechanics",
      "category": "biomedical"
    },
    {
      "title": "The math behind Medical Imaging Reconstruction and Segmentation - a simulation",
      "body": "I've been studying medical imaging\\ reconstruction and segmentation.\n\nThis report presents comprehensive medical image processing techniques including CT reconstruction via filtered backprojection, image enhancement through CLAHE and histogram equalization, segmentation algorithms (thresholding, watershed), noise reduction filters (Gaussian, median, bilateral), and quantitative quality assessment using PSNR, SSIM, and CNR metrics.  The analysis demonstrates practical implementations of core medical imaging algorithms with computed quality metrics.\n\nThe visualization really helped me understand the underlying dynamics.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/medical_imaging.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biomedical/medical_imaging.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/medical_imaging.tex",
      "source": "medical_imaging",
      "category": "biomedical"
    },
    {
      "title": "Simulating Biosignal Processing and EEG Analysis - visualizing the math",
      "body": "I've been studying biosignal processing\\ and eeg analysis.\n\nThis document presents advanced biosignal processing techniques for electrocardiogram (ECG), electroencephalogram (EEG), and electromyogram (EMG) signals.  We implement R-peak detection for heart rate analysis, frequency band decomposition for brain activity monitoring, and envelope detection for muscle activation patterns.\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/biosignal_processing.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biomedical/biosignal_processing.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/biosignal_processing.tex",
      "source": "biosignal_processing",
      "category": "biomedical"
    },
    {
      "title": "I built an interactive Pharmacokinetics Models and Drug Concentration simulation",
      "body": "I've been exploring pharmacokinetics\\ models and drug concentration.\n\nComputational modeling of drug absorption, distribution, metabolism, and elimination using compartment models..\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/pharmacokinetics.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/biomedical/pharmacokinetics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/biomedical/pharmacokinetics.tex",
      "source": "pharmacokinetics",
      "category": "biomedical"
    },
    {
      "title": "Interactive Network Epidemiology: Epidemic Dynamics on Complex Contact Networks visualization",
      "body": "I recently dove into network epidemiology: epidemic dynamics on complex contact networks.\n\nThis computational report investigates epidemic dynamics on complex contact networks, extending traditional compartmental models to structured populations.  We analyze SIR and SIS dynamics on Erdős-Rényi random networks, scale-free Barabási-Albert networks, and Watts-Strogatz small-world networks.\nThe key relationship is: τ_c =  k  k²  -  k\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/epidemiology/network_epidemics.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/epidemiology/network_epidemics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/epidemiology/network_epidemics.tex",
      "source": "network_epidemics",
      "category": "epidemiology"
    },
    {
      "title": "Simulating Spatial Epidemiology: Reaction-Diffusion Models and Traveling Wave Solutions - visualizing the math",
      "body": "I put together a simulation of spatial epidemiology: reaction-diffusion models and traveling wave solutions.\n\nThis report presents a comprehensive computational analysis of spatial epidemic dynamics using reaction-diffusion partial differential equations.  We examine the Fisher-KPP equation and spatial SIR models, analyzing traveling wave solutions, minimum wave speeds, and spatial clustering patterns.\nThe key relationship is: ∂ u∂ t = D∂² u∂ x² + f(u)\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/epidemiology/spatial_epidemiology.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/epidemiology/spatial_epidemiology.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/epidemiology/spatial_epidemiology.tex",
      "source": "spatial_epidemiology",
      "category": "epidemiology"
    },
    {
      "title": "Interactive SEIR Epidemic Model: Basic Reproduction Number and Intervention Strategies visualization",
      "body": "I created a computational exploration of seir epidemic model: basic reproduction number and intervention strategies.\n\nThis report presents a comprehensive analysis of the SEIR (Susceptible-Exposed-Infected-Recovered) compartmental model for infectious disease dynamics.  We derive the basic reproduction number $R₀$ from first principles, analyze disease-free and endemic equilibria, compute vaccination thresholds for herd immunity, and fit the model to synthetic outbreak data.\nThe key relationship is: R₀ = βγ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/epidemiology/seir_model.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/epidemiology/seir_model.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/epidemiology/seir_model.tex",
      "source": "seir_model",
      "category": "epidemiology"
    },
    {
      "title": "Exploring Phase III Clinical Trial Analysis computationally",
      "body": "I've been studying phase iii clinical trial analysis and wanted to share what I learned.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/knitr/clinical_report.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/knitr/clinical_report.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/knitr/clinical_report.tex",
      "source": "clinical_report",
      "category": "knitr"
    },
    {
      "title": "I built an interactive Inventory Management: Economic Order Quantity and Stochastic Models simulation",
      "body": "I built an interactive model for inventory management: economic order quantity and stochastic models.\n\nThis report presents a comprehensive computational analysis of inventory management models under both deterministic and stochastic demand.  We derive and analyze the Economic Order Quantity (EOQ) model, examine continuous review $(s,Q)$ and periodic review $(s,S)$ policies, solve the newsvendor problem under various demand distributions, and compute optimal safety stock levels for specified service targets.\nThe key relationship is: TC(Q) = KDQ + hQ2\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/inventory_models.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/operations-research/inventory_models.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/inventory_models.tex",
      "source": "inventory_models",
      "category": "operations-research"
    },
    {
      "title": "I built an interactive Production Scheduling: Algorithms and Optimization Strategies simulation",
      "body": "I put together a simulation of production scheduling: algorithms and optimization strategies.\n\nThis report presents a comprehensive analysis of deterministic scheduling problems across multiple machine configurations.  We examine single-machine scheduling with SPT (Shortest Processing Time) and EDD (Earliest Due Date) rules, parallel machine scheduling using LPT (Longest Processing Time) heuristics, two-machine flow shop scheduling via Johnson's algorithm, and job shop scheduling complexity.\nThe key relationship is: C_max^LPTC_max^OPT ≤ 43 - 13m\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/scheduling.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/operations-research/scheduling.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/scheduling.tex",
      "source": "scheduling",
      "category": "operations-research"
    },
    {
      "title": "Simulating Linear Programming: Simplex Method, Duality, and Sensitivity Analysis - visualizing the math",
      "body": "I built an interactive model for linear programming: simplex method, duality, and sensitivity analysis.\n\nThis technical report presents a comprehensive analysis of linear programming (LP) techniques, including graphical solutions for two-variable problems, the simplex algorithm for higher-dimensional optimization, duality theory, and sensitivity analysis.  We examine a production planning problem, demonstrate the simplex tableau method, derive the dual problem, and analyze shadow prices and reduced costs.\nThe key relationship is: yᵢ^* (bᵢ - Σ(j=1 to n) a_ijxⱼ^* ) = 0\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/linear_programming.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/operations-research/linear_programming.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/linear_programming.tex",
      "source": "linear_programming",
      "category": "operations-research"
    },
    {
      "title": "The math behind Queueing Theory: Performance Analysis of Service Systems - a simulation",
      "body": "I built an interactive model for queueing theory: performance analysis of service systems.\n\nThis report presents a comprehensive analysis of queueing systems using analytical and computational methods.  We examine M/M/1, M/M/c, and M/G/1 queue models, deriving performance metrics including expected queue length, waiting time, and system utilization.\nThe key relationship is: Pₙ = (1 - ρ)ρⁿ,  n = 0, 1, 2,\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/queueing_theory.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/operations-research/queueing_theory.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/operations-research/queueing_theory.tex",
      "source": "queueing_theory",
      "category": "operations-research"
    },
    {
      "title": "Exploring Process Control and Cascade Systems computationally",
      "body": "I recently dove into process control\\ and cascade systems.\n\nThis report presents computational analysis of feedback control systems in chemical process engineering.  We examine first-order and second-order system dynamics, PID controller design, closed-loop performance, and Ziegler-Nichols tuning methods.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/process_control.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/chemical-engineering/process_control.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/process_control.tex",
      "source": "process_control",
      "category": "chemical-engineering"
    },
    {
      "title": "Interactive Separation Processes and Absorption visualization",
      "body": "I created a computational exploration of separation processes\\ and absorption.\n\nDesign of separation operations including McCabe-Thiele distillation analysis, minimum reflux ratio calculations, flash distillation, and membrane separation.  Computational methods determine theoretical stages, operating lines, and separation efficiency for binary distillation columns and membrane systems.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/separation_processes.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/chemical-engineering/separation_processes.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/separation_processes.tex",
      "source": "separation_processes",
      "category": "chemical-engineering"
    },
    {
      "title": "Interactive Reaction Engineering and PFR Design visualization",
      "body": "I created a computational exploration of reaction engineering\\ and pfr design.\n\nThis report presents comprehensive computational analysis of chemical reactor design and kinetics, focusing on batch reactors, continuous stirred tank reactors (CSTRs), and plug flow reactors (PFRs).  We investigate first-order and second-order reaction kinetics, residence time distributions, temperature effects via Arrhenius behavior, and reactor performance comparisons using Levenspiel plots.\nThe key relationship is: dC_Adt = -r_A\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/reaction_engineering.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/chemical-engineering/reaction_engineering.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/reaction_engineering.tex",
      "source": "reaction_engineering",
      "category": "chemical-engineering"
    },
    {
      "title": "Simulating Mass Transfer and Convective Transport - visualizing the math",
      "body": "I wanted to visualize mass transfer\\ and convective transport.\n\nMass transfer describes the movement of chemical species due to concentration gradients (diffusion) and bulk fluid motion (convection).  This computational analysis examines Fick's laws of diffusion, film theory mass transfer coefficients, and packed column design for gas-liquid absorption.\nThe key relationship is: J_A = -D_AB dC_Adx\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/mass_transfer.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/chemical-engineering/mass_transfer.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/chemical-engineering/mass_transfer.tex",
      "source": "mass_transfer",
      "category": "chemical-engineering"
    },
    {
      "title": "Simulating Crystal Structure Analysis: Unit Cells, Miller Indices, X-Ray Diffraction Pat... - visualizing the math",
      "body": "I created a computational exploration of crystal structure analysis: unit cells, miller indices,\\ x-ray diffraction patterns.\n\nThis technical report presents a comprehensive analysis of crystal structures in materials science.  We examine unit cell geometry, Miller index notation, interplanar spacing calculations, and X-ray diffraction pattern simulation.\nThe key relationship is: d_hkl = a√h² + k² + l²\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/materials-science/crystal_structure.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/materials-science/crystal_structure.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/materials-science/crystal_structure.tex",
      "source": "crystal_structure",
      "category": "materials-science"
    },
    {
      "title": "Simulating Binary Phase Diagrams: Computational Analysis - visualizing the math",
      "body": "I created a computational exploration of binary phase diagrams: computational analysis.\n\nThis report presents computational analysis of binary phase diagrams in materials science.  We examine isomorphous and eutectic systems, the lever rule for phase fraction calculations, cooling curve analysis, and Gibbs phase rule applications.\nThe key relationship is: F = C - P + 2\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/materials-science/phase_diagram.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/materials-science/phase_diagram.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/materials-science/phase_diagram.tex",
      "source": "phase_diagram",
      "category": "materials-science"
    },
    {
      "title": "Visualizing Diffusion in Materials Science: Computational Analysis with Python",
      "body": "I've been studying diffusion in materials science: computational analysis.\n\nThis report presents computational analysis of diffusion phenomena in materials science.  We examine Fick's first and second laws, analytical solutions including error function profiles, numerical simulation of concentration evolution, and the Kirkendall effect in binary diffusion couples.\nThe key relationship is: J = -D ∂ C∂ x\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/materials-science/diffusion.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/materials-science/diffusion.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/materials-science/diffusion.tex",
      "source": "diffusion",
      "category": "materials-science"
    },
    {
      "title": "The math behind Fundamental Plasma Parameters: Debye Shielding to Wave Propagation - a simulation",
      "body": "I put together a simulation of fundamental plasma parameters:\\ debye shielding to wave propagation.\n\nWe present a comprehensive computational analysis of fundamental plasma parameters spanning laboratory, space, and fusion plasmas.  Starting from the Debye length and plasma frequency, we derive characteristic length and time scales that govern collective behavior.\nThe key relationship is: ν_ei = nₑ e⁴ Λ12π^3/2 ε₀² mₑ^1/2 (k_B Tₑ)^3/2\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/plasma-physics/plasma_parameters.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/plasma-physics/plasma_parameters.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/plasma-physics/plasma_parameters.tex",
      "source": "plasma_parameters",
      "category": "plasma-physics"
    },
    {
      "title": "Exploring Magnetohydrodynamics: Plasma Confinement and Stability computationally",
      "body": "I've been exploring magnetohydrodynamics: plasma confinement and stability.\n\nMagnetohydrodynamics (MHD) describes the macroscopic behavior of electrically conducting fluids, treating plasma as a single conducting fluid coupled to electromagnetic fields.  This report presents computational analysis of fundamental MHD wave modes, stability boundaries, and magnetic reconnection dynamics.\nThe key relationship is: ω⁴ - k²(ω²)(v_A² + cₛ²) + k⁴ v_A² cₛ² ²θ = 0\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/plasma-physics/mhd.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/plasma-physics/mhd.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/plasma-physics/mhd.tex",
      "source": "mhd",
      "category": "plasma-physics"
    },
    {
      "title": "Simulating Plasma Wave Dispersion and Kinetic Theory Analysis of Electrostatic and Elect... - visualizing the math",
      "body": "I've been studying plasma wave dispersion and kinetic theory\\ analysis of electrostatic and electromagnetic modes.\n\nThis computational study examines wave propagation in magnetized plasmas using kinetic theory.  We derive and numerically solve dispersion relations for electrostatic waves (Langmuir and ion acoustic modes) and electromagnetic waves (ordinary and extraordinary modes).\nThe key relationship is: ω² ≈ ω_pe² (1 + 3k² λ_De²)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/plasma-physics/plasma_waves.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/plasma-physics/plasma_waves.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/plasma-physics/plasma_waves.tex",
      "source": "plasma_waves",
      "category": "plasma-physics"
    },
    {
      "title": "Simulating Grid Integration of Variable Renewable Energy: Solar PV and Wind Power Analys... - visualizing the math",
      "body": "I've been exploring grid integration of variable renewable energy:\\\\\nsolar pv and wind power analysis with energy storage.\n\nThis report presents a comprehensive computational analysis of renewable energy integration challenges in modern electric grids.  We examine the variability characteristics of solar photovoltaic (PV) and wind power generation, analyze the duck curve phenomenon resulting from high solar penetration, calculate energy storage requirements for grid balancing, and assess grid stability metrics under various renewable penetration scenarios.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/power-systems/renewable_integration.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/power-systems/renewable_integration.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/power-systems/renewable_integration.tex",
      "source": "renewable_integration",
      "category": "power-systems"
    },
    {
      "title": "Simulating Transient Stability Analysis Equation and Equal Area Criterion - visualizing the math",
      "body": "I've been fascinated by transient stability analysis\\ equation and equal area criterion.\n\nThis report presents a comprehensive computational analysis of power system transient stability using the swing equation framework.  We examine rotor angle dynamics under large disturbances such as three-phase faults, apply the equal area criterion to assess stability margins, and determine critical clearing times for single-machine infinite-bus (SMIB) systems.\nThe key relationship is: M d²δdt² + D dδdt = Pₘ - Pₑ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/power-systems/transient_stability.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/power-systems/transient_stability.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/power-systems/transient_stability.tex",
      "source": "transient_stability",
      "category": "power-systems"
    },
    {
      "title": "Visualizing Load Flow Analysis Using Newton-Raphson Method 5-Bus Test System with Python",
      "body": "I've been studying load flow analysis using newton-raphson method\\ 5-bus test system.\n\nThis report presents a comprehensive load flow analysis of the IEEE 5-bus test system using the Newton-Raphson method.  We implement the full power flow solution algorithm, construct the Jacobian matrix, and analyze voltage profiles, real and reactive power flows, and system losses.\nThe key relationship is: Pᵢ = Σ(k=1 to n) |Vᵢ||Vₖ||Y_ik|(θ_ik - δᵢ + δₖ)\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/power-systems/load_flow.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/power-systems/load_flow.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/power-systems/load_flow.tex",
      "source": "load_flow",
      "category": "power-systems"
    },
    {
      "title": "Simulating Particle Scattering Cross Sections: Rutherford, Mott, and Form Factor Analysis - visualizing the math",
      "body": "I put together a simulation of particle scattering cross sections: rutherford, mott, and form factor analysis.\n\nThis technical report presents comprehensive computational analysis of particle scattering cross sections.  We implement the Rutherford formula for classical Coulomb scattering, Mott cross section with relativistic and spin corrections, and nuclear form factors for extended charge distributions.\nThe key relationship is: dNdt = I₀ n dσdΩ dΩ\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/particle-physics/cross_section.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/particle-physics/cross_section.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/particle-physics/cross_section.tex",
      "source": "cross_section",
      "category": "particle-physics"
    },
    {
      "title": "Simulating Standard Model Physics: Coupling Evolution and Grand Unification - visualizing the math",
      "body": "I've been studying standard model physics: coupling evolution and grand unification.\n\nThis technical report presents comprehensive computational analysis of the Standard Model gauge couplings and their renormalization group evolution.  We implement one-loop and two-loop running of the electromagnetic, weak, and strong coupling constants, analyze gauge unification scenarios in the MSSM, and compute threshold corrections.\nThe key relationship is: dαᵢ⁻¹dμ = -bᵢ2π\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/particle-physics/standard_model.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/particle-physics/standard_model.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/particle-physics/standard_model.tex",
      "source": "standard_model",
      "category": "particle-physics"
    },
    {
      "title": "Exploring Particle Decay Kinematics: Two-Body and Three-Body Phase Space Analysis computationally",
      "body": "I built an interactive model for particle decay kinematics: two-body and three-body phase space analysis.\n\nThis technical report presents comprehensive computational analysis of relativistic decay kinematics for unstable particles.  We implement energy-momentum conservation for two-body and three-body decays, compute Lorentz transformations between rest and laboratory frames, analyze Dalitz plots for three-body phase space, and calculate decay widths from matrix elements.\nThe key relationship is: m_12² = (p₁ + p₂)²,  m_23² = (p₂ + p₃)²\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/particle-physics/decay_kinematics.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/particle-physics/decay_kinematics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/particle-physics/decay_kinematics.tex",
      "source": "decay_kinematics",
      "category": "particle-physics"
    },
    {
      "title": "Interactive Gene Expression Analysis: From RNA-Seq to Pathway Enrichment A Comprehensive ... visualization",
      "body": "I recently dove into gene expression analysis: from rna-seq to pathway enrichment\\\\\n a comprehensive guide to differential expression analysis.\n\nThis comprehensive analysis presents methods for analyzing gene expression data from RNA-sequencing experiments.  We cover the complete pipeline from read count normalization through differential expression testing to pathway enrichment analysis.\nThe key relationship is: TPMᵢ = cᵢ/lᵢΣ(j) cⱼ/lⱼ × 10⁶\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/gene_expression.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/bioinformatics/gene_expression.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/gene_expression.tex",
      "source": "gene_expression",
      "category": "bioinformatics"
    },
    {
      "title": "Interactive Phylogenetic Analysis: Tree Reconstruction and Evolutionary Inference Distanc... visualization",
      "body": "I built an interactive model for phylogenetic analysis: tree reconstruction and evolutionary inference\\\\\n distance methods, maximum likelihood, and bootstrap support.\n\nThis comprehensive analysis presents methods for reconstructing phylogenetic trees from molecular sequence data.  We cover distance-based methods (UPGMA, Neighbor-Joining), character-based approaches, and statistical support via bootstrapping.\nThe key relationship is: d = -34(1 - 4p3)\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/phylogenetics.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/bioinformatics/phylogenetics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/phylogenetics.tex",
      "source": "phylogenetics",
      "category": "bioinformatics"
    },
    {
      "title": "I built an interactive Sequence Alignment: Dynamic Programming and Scoring Matrices Global and Local... simulation",
      "body": "I put together a simulation of sequence alignment: dynamic programming and scoring matrices\\\\\n global and local alignment with statistical significance.\n\nThis comprehensive analysis presents algorithms for pairwise sequence alignment.  We implement the Needleman-Wunsch algorithm for global alignment and Smith-Waterman for local alignment using dynamic programming.\nThe key relationship is: γ(g) = d + (g-1) · e\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/sequence_alignment.tex\n\nHas anyone else explored computational approaches here?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/bioinformatics/sequence_alignment.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/sequence_alignment.tex",
      "source": "sequence_alignment",
      "category": "bioinformatics"
    },
    {
      "title": "Simulating Protein Structure Analysis: From Backbone Geometry to Fold Recognition Ramach... - visualizing the math",
      "body": "I recently dove into protein structure analysis: from backbone geometry to fold recognition\\\\\n ramachandran analysis, secondary structure, and structural comparison.\n\nThis comprehensive analysis presents methods for analyzing protein three-dimensional structure.  We cover backbone dihedral angle analysis through Ramachandran plots, secondary structure prediction using propensity scales, structural comparison using RMSD and TM-score, and contact map analysis for fold topology.\nThe key relationship is: RMSD = √1NΣ(i=1 to N)|rᵢ^A - rᵢ^B|²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/protein_structure.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/bioinformatics/protein_structure.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/bioinformatics/protein_structure.tex",
      "source": "protein_structure",
      "category": "bioinformatics"
    },
    {
      "title": "Interactive Procedural Generation Functions and Algorithmic Content Creation visualization",
      "body": "I built an interactive model for procedural generation\\ functions and algorithmic content creation.\n\nProcedural content generation uses algorithmic techniques to create game environments, terrains, vegetation, and structures.  This report implements five fundamental algorithms: Perlin noise for natural-looking terrain, the diamond-square algorithm for heightmap generation, L-systems for botanical structures, cellular automata for cave systems, and Poisson disk sampling for spatially distributed object placement.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/game-development/procedural_generation.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/game-development/procedural_generation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/game-development/procedural_generation.tex",
      "source": "procedural_generation",
      "category": "game-development"
    },
    {
      "title": "Simulating Physics Simulation Body Dynamics - visualizing the math",
      "body": "I put together a simulation of physics simulation\\ body dynamics.\n\nReal-time physics simulation is fundamental to game development, enabling realistic object motion, collision responses, and environmental interactions.  This report implements core game physics algorithms including Verlet integration for stable particle dynamics, impulse-based collision resolution, spring-damper systems, and projectile motion with aerodynamic drag.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/game-development/physics_simulation.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/game-development/physics_simulation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/game-development/physics_simulation.tex",
      "source": "physics_simulation",
      "category": "game-development"
    },
    {
      "title": "Simulating Pathfinding Algorithms* and Dijkstra Comparison for Game AI - visualizing the math",
      "body": "I've been studying pathfinding algorithms\\* and dijkstra comparison for game ai.\n\nThis report implements and compares optimal pathfinding algorithms for game AI navigation.  We present comprehensive implementations of A* and Dijkstra's algorithm on grid-based environments, comparing Manhattan, Euclidean, and diagonal distance heuristics.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/game-development/pathfinding.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/game-development/pathfinding.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/game-development/pathfinding.tex",
      "source": "pathfinding",
      "category": "game-development"
    },
    {
      "title": "I built an interactive Photonic Crystals: Band Structure and Optical Properties simulation",
      "body": "I built an interactive model for photonic crystals: band structure and optical properties.\n\nPhotonic crystals are periodic dielectric structures that exhibit photonic band gaps—frequency ranges in which electromagnetic wave propagation is forbidden.  This report presents computational analysis of one-dimensional (1D) Bragg stacks using transfer matrix methods, examining band structure formation, reflectance spectra, defect mode engineering, and slow light phenomena.\nThe key relationship is: R = |M_21M_11|²\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/photonics/photonic_crystals.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/photonics/photonic_crystals.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/photonics/photonic_crystals.tex",
      "source": "photonic_crystals",
      "category": "photonics"
    },
    {
      "title": "The math behind Laser Physics: Rate Equations, Threshold Analysis, and Gaussian Beam Propagation - a simulation",
      "body": "I recently dove into laser physics: rate equations, threshold analysis, and gaussian beam propagation.\n\nThis report presents a comprehensive computational analysis of laser physics fundamentals, including Einstein A and B coefficients, population inversion dynamics, threshold conditions for laser oscillation, cavity mode structures, and Gaussian beam propagation.  We derive the rate equations from first principles, analyze the threshold pump power for a four-level laser system (Nd:YAG-like), simulate relaxation oscillations and Q-switching dynamics, and characterize Gaussian beam propagation includ.\nThe key relationship is: g₂g₁ B_12 = B_21,  A_21 = 8π hν³c³ B_21\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/photonics/laser_physics.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/photonics/laser_physics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/photonics/laser_physics.tex",
      "source": "laser_physics",
      "category": "photonics"
    },
    {
      "title": "I built an interactive Nonlinear Optics: Second Harmonic Generation, Kerr Effect, and Optical Solitons simulation",
      "body": "I put together a simulation of nonlinear optics: second harmonic generation, kerr effect, and optical solitons.\n\nThis report presents a comprehensive computational analysis of nonlinear optical phenomena in χ⁽²⁾ and χ⁽³⁾ media.  We examine second harmonic generation (SHG) with phase matching considerations, the optical Kerr effect and self-phase modulation, four-wave mixing processes, and optical soliton propagation governed by the nonlinear Schrödinger equation.\nThe key relationship is: n_ω(θ) = n_2ω(θ)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/photonics/nonlinear_optics.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/photonics/nonlinear_optics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/photonics/nonlinear_optics.tex",
      "source": "nonlinear_optics",
      "category": "photonics"
    },
    {
      "title": "Simulating Soil Mechanics Analysis Stress, Bearing Capacity, and Consolidation - visualizing the math",
      "body": "I recently dove into soil mechanics analysis\\ stress, bearing capacity, and consolidation.\n\nThis report presents comprehensive geotechnical analysis including effective stress calculations, Mohr-Coulomb failure criteria, bearing capacity design using Terzaghi's theory, one-dimensional consolidation settlement, and slope stability assessment.  Computational methods are applied to practical foundation design scenarios with parametric studies examining the influence of soil properties on engineering behavior.\nThe key relationship is: σ' = σ - u\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/civil-engineering/soil_mechanics.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/civil-engineering/soil_mechanics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/civil-engineering/soil_mechanics.tex",
      "source": "soil_mechanics",
      "category": "civil-engineering"
    },
    {
      "title": "Interactive Structural Analysis Deflection and Moment Distribution visualization",
      "body": "I've been studying structural analysis\\ deflection and moment distribution.\n\nThis report presents comprehensive computational analysis of fundamental structural elements including simply supported beams, statically determinate trusses, and influence lines for moving loads.  Classical beam theory is applied to determine bending moments, shear forces, and elastic deflections under uniformly distributed loading.\nThe key relationship is: EI d⁴ wdx⁴ = q(x)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/civil-engineering/structural_analysis.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/civil-engineering/structural_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/civil-engineering/structural_analysis.tex",
      "source": "structural_analysis",
      "category": "civil-engineering"
    },
    {
      "title": "Exploring Traffic Flow Model and Congestion computationally",
      "body": "I created a computational exploration of traffic flow\\ model and congestion.\n\nThis report presents a comprehensive computational analysis of traffic flow theory, implementing the Lighthill-Whitham-Richards (LWR) continuum model, Greenshields' fundamental diagram, and queuing analysis at signalized intersections.  We derive traffic wave propagation characteristics, compute capacity using fundamental relationships, analyze Webster's delay formula for signal timing optimization, and demonstrate shock wave formation during congestion onset.\nThe key relationship is: v(k) = v_f (1 - kkⱼ)\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/civil-engineering/traffic_flow.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/civil-engineering/traffic_flow.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/civil-engineering/traffic_flow.tex",
      "source": "traffic_flow",
      "category": "civil-engineering"
    },
    {
      "title": "Exploring Optics: Optical Fiber Mode Analysis computationally",
      "body": "I recently dove into optics: optical fiber mode analysis and wanted to share what I learned.\nThe key relationship is: V = 2π aλ√n₁² - n₂² = 2π aλ · NA\n\nIt's fascinating to see the theory come alive in the simulation.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/fiber_modes.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/optics/fiber_modes.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/fiber_modes.tex",
      "source": "fiber_modes",
      "category": "optics"
    },
    {
      "title": "Visualizing Optics: Gaussian Beam Propagation with Python",
      "body": "I put together a simulation of optics: gaussian beam propagation and wanted to share what I learned.\nThe key relationship is: I(r, z) = I₀ (w₀w(z))² (-2r²w(z)²)\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/gaussian_beam.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/optics/gaussian_beam.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/gaussian_beam.tex",
      "source": "gaussian_beam",
      "category": "optics"
    },
    {
      "title": "The math behind Optics: Thin Film Interference and Coatings - a simulation",
      "body": "I put together a simulation of optics: thin film interference and coatings and wanted to share what I learned.\nThe key relationship is: r_ij = nᵢ - nⱼnᵢ + nⱼ\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/thin_film.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/optics/thin_film.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/thin_film.tex",
      "source": "thin_film",
      "category": "optics"
    },
    {
      "title": "Interactive Diffraction Grating Spectroscopy: Principles and Applications visualization",
      "body": "I recently dove into diffraction grating spectroscopy: principles and applications and wanted to share what I learned.\nThe key relationship is: d(θᵢ + θₘ) = mλ\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/diffraction_grating.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/optics/diffraction_grating.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/diffraction_grating.tex",
      "source": "diffraction_grating",
      "category": "optics"
    },
    {
      "title": "Interactive Optics: Polarization States and Jones Calculus visualization",
      "body": "I wanted to visualize optics: polarization states and jones calculus and wanted to share what I learned.\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/polarization.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/optics/polarization.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/polarization.tex",
      "source": "polarization",
      "category": "optics"
    },
    {
      "title": "Simulating Optics: Interference Patterns and Analysis - visualizing the math",
      "body": "I put together a simulation of optics: interference patterns and analysis and wanted to share what I learned.\nThe key relationship is: I = I₁ + I₂ + 2√I₁ I₂δ\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/interference_patterns.tex\n\nHas anyone else explored similar simulations?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/optics/interference_patterns.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/optics/interference_patterns.tex",
      "source": "interference_patterns",
      "category": "optics"
    },
    {
      "title": "Interactive Global Carbon Cycle Modeling: Reservoirs, Fluxes, and Anthropogenic Perturbation visualization",
      "body": "I created a computational exploration of global carbon cycle modeling: reservoirs, fluxes, and anthropogenic perturbation.\n\nThis technical report presents a comprehensive analysis of the global carbon cycle using box models to represent carbon exchange between atmosphere, ocean, and terrestrial biosphere.  We examine natural carbon fluxes, anthropogenic emissions, and the resulting changes in atmospheric CO$₂$ concentration.\nThe key relationship is: C_A  (PgC) = CO₂  (ppm)2.13\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/climate-science/carbon_cycle.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/climate-science/carbon_cycle.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/climate-science/carbon_cycle.tex",
      "source": "carbon_cycle",
      "category": "climate-science"
    },
    {
      "title": "Visualizing Global Temperature Modeling: Energy Balance and Climate Sensitivity with Python",
      "body": "I've been exploring global temperature modeling: energy balance and climate sensitivity.\n\nThis study presents energy balance models for global mean surface temperature, examining radiative forcing from greenhouse gases and the response of the climate system.  We analyze zero-dimensional and one-dimensional models, calculate climate sensitivity from different feedback mechanisms, and compare model projections with observations.\nThe key relationship is: F = 5.35 (CC₀)  W/m²\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/climate-science/temperature_model.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/climate-science/temperature_model.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/climate-science/temperature_model.tex",
      "source": "temperature_model",
      "category": "climate-science"
    },
    {
      "title": "Visualizing Earth's Energy Balance Model: Sensitivity and Radiative Forcing with Python",
      "body": "I've been exploring earth's energy balance model:\\ sensitivity and radiative forcing.\n\nThis document develops the fundamental physics of Earth's energy balance, from the Stefan-Boltzmann law governing planetary radiation to the greenhouse effect and climate sensitivity.  We derive the zero-dimensional energy balance model, calculate equilibrium temperatures with and without an atmosphere, and explore how changes in radiative forcing translate to temperature changes.\nThe key relationship is: F = σ T⁴\neq:stefan-boltzmann\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/climate-science/energy_balance.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/climate-science/energy_balance.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/climate-science/energy_balance.tex",
      "source": "energy_balance",
      "category": "climate-science"
    },
    {
      "title": "The math behind Chaos Theory and Nonlinear Dynamics: Analysis of Deterministic Chaos in Dynam... - a simulation",
      "body": "I built an interactive model for chaos theory and nonlinear dynamics:\\\\\nanalysis of deterministic chaos in dynamical systems.\n\nThis technical report presents a comprehensive computational analysis of chaotic dynamical systems.  We examine the logistic map, compute bifurcation diagrams showing the route to chaos through period-doubling, calculate Lyapunov exponents as quantitative measures of chaos, and simulate the Lorenz attractor demonstrating strange attractor dynamics.\nThe key relationship is: |δ x(t)| ≈ e^λ t |δ x(0)|\n\nThe visualization really helped me understand the underlying dynamics.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mathematics/chaos.tex\n\nWhat numerical methods work best for you?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mathematics/chaos.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mathematics/chaos.tex",
      "source": "chaos",
      "category": "mathematics"
    },
    {
      "title": "I built an interactive Ordinary Differential Equations: Phase Portraits, Stability Analysis, and Lim... simulation",
      "body": "I created a computational exploration of ordinary differential equations:\\\\\nphase portraits, stability analysis, and limit cycles.\n\nThis report provides a comprehensive computational analysis of ordinary differential equations (ODEs).  We examine first and second-order ODEs, construct phase portraits for autonomous systems, perform stability analysis of equilibrium points, and investigate limit cycles in nonlinear oscillators.\nThe key relationship is: dydt + p(t)y = q(t)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mathematics/differential_eq.tex\n\nHow do you approach teaching this topic?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mathematics/differential_eq.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mathematics/differential_eq.tex",
      "source": "differential_eq",
      "category": "mathematics"
    },
    {
      "title": "Simulating Fractal Geometry and Self-Similarity: Computational Analysis of Fractal Struc... - visualizing the math",
      "body": "I wanted to visualize fractal geometry and self-similarity:\\\\\ncomputational analysis of fractal structures.\n\nThis report presents a computational exploration of fractal geometry, examining the Mandelbrot set, Julia sets, Sierpinski triangle, and Koch snowflake.  We compute fractal dimensions using box-counting methods, analyze escape-time algorithms, and investigate the self-similar structures that characterize these mathematical objects.\nThe key relationship is: D = _ε  0  N(ε)(1/ε)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mathematics/fractals.tex\n\nWhat's your favorite way to illustrate this concept?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/mathematics/fractals.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/mathematics/fractals.tex",
      "source": "fractals",
      "category": "mathematics"
    },
    {
      "title": "Simulating Digital Filter Design: FIR and IIR Filters - visualizing the math",
      "body": "I've been studying digital filter design: fir and iir filters and wanted to share what I learned.\nThe key relationship is: H(z) = Σ(k=0 to N) bₖ z^-k\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/signal-processing/digital_filter.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/signal-processing/digital_filter.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/signal-processing/digital_filter.tex",
      "source": "digital_filter",
      "category": "signal-processing"
    },
    {
      "title": "Visualizing FFT Spectral Analysis: Audio Signal Processing From Time Domain to Frequency ... with Python",
      "body": "I recently dove into fft spectral analysis: audio signal processing\\\\\n from time domain to frequency domain and back.\n\nThis lab report demonstrates the application of the Fast Fourier Transform (FFT) for spectral analysis of audio signals.  We synthesize a complex waveform containing multiple harmonic components, analyze its frequency content, design and apply digital filters, and investigate windowing effects on spectral leakage.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/signal-processing/fft_analysis.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/signal-processing/fft_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/signal-processing/fft_analysis.tex",
      "source": "fft_analysis",
      "category": "signal-processing"
    },
    {
      "title": "Exploring Convolution and Linear Time-Invariant Systems computationally",
      "body": "I built an interactive model for convolution and linear time-invariant systems and wanted to share what I learned.\nThe key relationship is: (f * g)(t) = ∫_-∞→∞ f(τ) g(t - τ) \\, dτ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/signal-processing/convolution.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/signal-processing/convolution.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/signal-processing/convolution.tex",
      "source": "convolution",
      "category": "signal-processing"
    },
    {
      "title": "I built an interactive Flood Frequency Analysis: Statistical Methods for Design Flow Estimation simulation",
      "body": "I put together a simulation of flood frequency analysis: statistical methods for design flow estimation.\n\nThis report presents a comprehensive flood frequency analysis using annual maximum flow data to estimate design floods for hydraulic structures.  We apply three probability distributions (Gumbel extreme value, Log-Pearson Type III, and generalized extreme value) fitted using L-moments and maximum likelihood estimation.\nThe key relationship is: T = 1P\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/hydrology/flood_frequency.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/hydrology/flood_frequency.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/hydrology/flood_frequency.tex",
      "source": "flood_frequency",
      "category": "hydrology"
    },
    {
      "title": "Simulating Rainfall-Runoff Modeling: Unit Hydrograph Theory and SCS Curve Number Method - visualizing the math",
      "body": "I wanted to visualize rainfall-runoff modeling: unit hydrograph theory and scs curve number method.\n\nThis engineering report presents a comprehensive analysis of rainfall-runoff transformation using the unit hydrograph approach and the Soil Conservation Service (SCS) Curve Number method.  We develop synthetic unit hydrographs using the Nash cascade model, compute excess rainfall from design storms using the SCS-CN method, and apply discrete convolution to generate direct runoff hydrographs.\nThe key relationship is: Q(t) = ∫₀ᵗ iₑ(τ) · u(t - τ) \\, dτ\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/hydrology/rainfall_runoff.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/hydrology/rainfall_runoff.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/hydrology/rainfall_runoff.tex",
      "source": "rainfall_runoff",
      "category": "hydrology"
    },
    {
      "title": "Visualizing Groundwater Flow Analysis: Darcy's Law and Well Hydraulics with Python",
      "body": "I created a computational exploration of groundwater flow analysis: darcy's law and well hydraulics.\n\nThis technical report presents comprehensive computational analysis of groundwater flow in porous media, focusing on aquifer hydraulics and well dynamics.  We examine the fundamental principles of Darcy's law, develop analytical solutions for radial flow to wells using the Theis equation and Cooper-Jacob approximation, and implement numerical finite difference methods for solving the 2D groundwater flow equation.\nThe key relationship is: q = -K dhdx\n\nThe visualization really helped me understand the underlying dynamics.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/hydrology/groundwater_flow.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/hydrology/groundwater_flow.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/hydrology/groundwater_flow.tex",
      "source": "groundwater_flow",
      "category": "hydrology"
    },
    {
      "title": "Interactive Neural Network Training: A Complete Pipeline From Architecture Design to Perf... visualization",
      "body": "I've been studying neural network training: a complete pipeline\\\\\n from architecture design to performance analysis.\n\nThis tutorial provides a comprehensive walkthrough of training a neural network for function approximation.  We implement a multi-layer perceptron from scratch using NumPy, demonstrating forward propagation, backpropagation, and gradient descent optimization.\nThe key relationship is: ∂ L∂ W^(l) = δ^(l) (a^(l-1))ᵀ\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/neural_network.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/machine-learning/neural_network.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/neural_network.tex",
      "source": "neural_network",
      "category": "machine-learning"
    },
    {
      "title": "Exploring Linear Regression: OLS, Gradient Descent, and Regularization computationally",
      "body": "I built an interactive model for linear regression: ols, gradient descent, and regularization.\n\nThis document presents a comprehensive analysis of linear regression methods including ordinary least squares (OLS), gradient descent optimization, and regularization techniques (Ridge and Lasso).  We examine model diagnostics, multicollinearity detection, and cross-validation for hyperparameter tuning.\nThe key relationship is: y = Xβ + ε,  ε ∼ N(0, σ² I)\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/linear_regression.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/machine-learning/linear_regression.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/linear_regression.tex",
      "source": "linear_regression",
      "category": "machine-learning"
    },
    {
      "title": "I built an interactive Decision Trees: Theory and Implementation simulation",
      "body": "I built an interactive model for decision trees: theory and implementation.\n\nThis document presents a comprehensive analysis of decision tree algorithms for classification and regression.  We explore information gain, Gini impurity, and variance reduction as splitting criteria, implement tree construction from scratch, examine pruning techniques, and analyze feature importance measures.\nThe key relationship is: H(S) = -∑_c=1^C p_c ₂ p_c\n\nThe visualization really helped me understand the underlying dynamics.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/decision_tree.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/machine-learning/decision_tree.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/decision_tree.tex",
      "source": "decision_tree",
      "category": "machine-learning"
    },
    {
      "title": "Interactive Support Vector Machines: Kernels and Classification visualization",
      "body": "I created a computational exploration of support vector machines: kernels and classification.\n\nThis document presents a comprehensive analysis of Support Vector Machines (SVM) including hard and soft margin classification, the kernel trick for nonlinear decision boundaries, hyperparameter tuning (C and gamma), and multi-class strategies.  We visualize decision boundaries, support vectors, and margin regions.\nThe key relationship is: _w,b 12\\|w\\|²  subject to  yᵢ(w · xᵢ + b) ≥ 1\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/svm.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/machine-learning/svm.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/svm.tex",
      "source": "svm",
      "category": "machine-learning"
    },
    {
      "title": "Visualizing K-Means Clustering: Algorithm and Analysis with Python",
      "body": "I built an interactive model for k-means clustering: algorithm and analysis.\n\nThis document presents a comprehensive study of K-means clustering, including algorithm implementation, convergence analysis, cluster quality metrics (silhouette score, inertia), the elbow method for optimal K selection, and comparison with other clustering approaches.  We demonstrate practical considerations for initialization and scaling.\nThe key relationship is: J = Σ(k=1)^K ∑_i ∈ Cₖ \\|xᵢ - μₖ\\|²\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/kmeans.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/machine-learning/kmeans.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/machine-learning/kmeans.tex",
      "source": "kmeans",
      "category": "machine-learning"
    },
    {
      "title": "I built an interactive Computer Science: Graph Algorithms and Network Analysis simulation",
      "body": "I've been studying computer science: graph algorithms and network analysis.\n\nThis document presents a comprehensive analysis of fundamental graph algorithms including shortest path algorithms (Dijkstra, Bellman-Ford, Floyd-Warshall), minimum spanning trees (Prim, Kruskal), graph traversal (BFS, DFS), and network flow algorithms.  We implement these algorithms in Python and analyze their time complexity, correctness, and practical applications in network routing, social network analysis, and optimization problems.\nThe key relationship is: d[v] = _u ∈ adj(v) \\d[u] + w(u, v)\\\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computer-science/graph_algorithms.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/computer-science/graph_algorithms.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computer-science/graph_algorithms.tex",
      "source": "graph_algorithms",
      "category": "computer-science"
    },
    {
      "title": "I built an interactive Computer Science: Sorting Algorithm Analysis and Comparison simulation",
      "body": "I built an interactive model for computer science: sorting algorithm analysis and comparison.\n\nThis document presents a comprehensive analysis of sorting algorithms including comparison-based sorts (QuickSort, MergeSort, HeapSort, InsertionSort, BubbleSort) and non-comparison sorts (CountingSort, RadixSort).  We implement each algorithm in Python, measure their empirical performance across different input sizes and distributions, analyze time and space complexity, and compare their stability and practical applicability.\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computer-science/sorting_algorithms.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/computer-science/sorting_algorithms.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/computer-science/sorting_algorithms.tex",
      "source": "sorting_algorithms",
      "category": "computer-science"
    },
    {
      "title": "I built an interactive Navier-Stokes Equations: Viscous Flow Analysis Boundary Layer Theory simulation",
      "body": "I put together a simulation of navier-stokes equations: viscous flow analysis\\ boundary layer theory.\n\nThis technical report presents analytical and computational solutions to the Navier-Stokes equations for canonical viscous flow problems.  We analyze Couette flow, Poiseuille flow, and boundary layer development using Python-based numerical methods.\nThe key relationship is: Re = ρ U Lμ = U Lν\n\nThe visualization really helped me understand the underlying dynamics.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/fluid-dynamics/navier_stokes.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/fluid-dynamics/navier_stokes.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/fluid-dynamics/navier_stokes.tex",
      "source": "navier_stokes",
      "category": "fluid-dynamics"
    },
    {
      "title": "Simulating Network Science: Graph Metrics and Community Detection - visualizing the math",
      "body": "I recently dove into network science: graph metrics and community detection.\n\nNetwork science provides tools for analyzing complex systems through graph theory.  This document demonstrates computational methods for calculating centrality measures, detecting community structure, analyzing random graph models, and characterizing small-world and scale-free properties.\nThe key relationship is: C_D(v) = (v)n-1\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/other/network_analysis.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/other/network_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/other/network_analysis.tex",
      "source": "network_analysis",
      "category": "other"
    },
    {
      "title": "The math behind Information Theory: Entropy, Coding, and Channel Capacity - a simulation",
      "body": "I created a computational exploration of information theory: entropy, coding, and channel capacity and wanted to share what I learned.\nThe key relationship is: H(X) = -∑_x ∈ X p(x) ₂ p(x)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/other/information_theory.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/other/information_theory.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/other/information_theory.tex",
      "source": "information_theory",
      "category": "other"
    },
    {
      "title": "The math behind Optimization: Gradient Descent Methods and Convergence Analysis - a simulation",
      "body": "I built an interactive model for optimization: gradient descent methods and convergence analysis.\n\nOptimization algorithms find minima of objective functions and are fundamental to machine learning, scientific computing, and engineering design.  This document demonstrates gradient descent variants (vanilla, momentum, RMSprop, Adam), Newton's method, quasi-Newton methods (BFGS), and constrained optimization.\nThe key relationship is: x_k+1 = xₖ - α ∇ f(xₖ)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/other/optimization.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/other/optimization.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/other/optimization.tex",
      "source": "optimization",
      "category": "other"
    },
    {
      "title": "I built an interactive Color Perception Chromaticity simulation",
      "body": "I recently dove into color perception\\ chromaticity.\n\nThis report presents a comprehensive computational analysis of human color perception, including trichromatic cone fundamentals, CIE chromaticity systems, opponent color channels, and color vision deficiencies.  We model the spectral sensitivities of L, M, and S cones, compute chromaticity coordinates in CIE 1931 color space, analyze color discrimination thresholds via MacAdam ellipses, and simulate protanopic, deuteranopic, and tritanopic color blindness.\nThe key relationship is: Sᵢ(λ) = [-(λ - λ_peak,i)²2σᵢ²]\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/psychophysics/color_perception.tex\n\nWhat parameters do you find most interesting to vary?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/psychophysics/color_perception.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/psychophysics/color_perception.tex",
      "source": "color_perception",
      "category": "psychophysics"
    },
    {
      "title": "Simulating Signal Detection-prime and ROC - visualizing the math",
      "body": "I built an interactive model for signal detection\\-prime and roc.\n\nSignal Detection Theory (SDT) provides a mathematical framework for quantifying perceptual sensitivity and decision criteria in psychophysical tasks.  This report implements computational methods to calculate detectability ($d'$), response bias ($$ and $c$), and receiver operating characteristic (ROC) curves.\nThe key relationship is: d' = μₛ - μₙσ = μₛσ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/psychophysics/signal_detection.tex\n\nHow do you typically visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/psychophysics/signal_detection.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/psychophysics/signal_detection.tex",
      "source": "signal_detection",
      "category": "psychophysics"
    },
    {
      "title": "Exploring Weber-Fechner Law computationally",
      "body": "I've been studying weber-fechner law\\.\n\nThis document presents a comprehensive computational analysis of classical psychophysical laws governing the relationship between physical stimulus intensity and perceived sensation magnitude.  We implement Weber's Law for just noticeable differences, Fechner's logarithmic law, Stevens' power law, psychometric functions, and the method of constant stimuli.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/psychophysics/weber_fechner.tex\n\nWhat approaches have you found useful for teaching this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/psychophysics/weber_fechner.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/psychophysics/weber_fechner.tex",
      "source": "weber_fechner",
      "category": "psychophysics"
    },
    {
      "title": "The math behind Image Filtering and Denoising: Comparative Analysis of Spatial and Frequency ... - a simulation",
      "body": "I recently dove into image filtering and denoising: comparative analysis of spatial and frequency domain methods.\n\nThis report presents a comprehensive analysis of image filtering techniques for noise reduction and enhancement.  We examine linear filters (Gaussian, box, Laplacian), frequency domain methods (Fourier-based filtering), and non-linear approaches (median, bilateral, non-local means).\nThe key relationship is: g(x,y) = F\\f(x,y)\\\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/image_filtering.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/image-processing/image_filtering.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/image_filtering.tex",
      "source": "image_filtering",
      "category": "image-processing"
    },
    {
      "title": "Visualizing Image Segmentation: Thresholding, Clustering, and Graph-Based Methods with Python",
      "body": "I've been exploring image segmentation: thresholding, clustering, and graph-based methods.\n\nThis report presents a comprehensive analysis of image segmentation techniques including thresholding methods (Otsu's method, adaptive thresholding), region-based approaches (region growing, split-and-merge), clustering algorithms (K-means, mean-shift, SLIC superpixels), and graph-based methods (graph cuts, normalized cuts, watershed transform).  We evaluate segmentation quality using Intersection over Union (IoU), Dice coefficient, and boundary F-score metrics.\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/segmentation.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/image-processing/segmentation.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/segmentation.tex",
      "source": "segmentation",
      "category": "image-processing"
    },
    {
      "title": "Interactive Mathematical Morphology: Fundamental Operations and Applications visualization",
      "body": "I wanted to visualize mathematical morphology: fundamental operations and applications.\n\nThis report presents a comprehensive analysis of mathematical morphology, focusing on fundamental operations (erosion, dilation, opening, closing) and their applications in binary and grayscale image processing.  We examine the algebraic properties of morphological operators, demonstrate their use in noise removal, edge detection, and feature extraction, and analyze the effects of structuring element shape and size on operation outcomes.\nThe key relationship is: A  B = \\z  B_z ⊂eq A\\\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/morphological.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/image-processing/morphological.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/morphological.tex",
      "source": "morphological",
      "category": "image-processing"
    },
    {
      "title": "Simulating Edge Detection: From Gradient Operators to Multi-Scale Analysis - visualizing the math",
      "body": "I've been exploring edge detection: from gradient operators to multi-scale analysis.\n\nThis report presents a comprehensive analysis of edge detection algorithms in digital image processing.  We examine gradient-based methods (Sobel, Prewitt, Roberts), the Canny edge detector with its multi-stage pipeline, and Laplacian-based approaches including zero-crossing detection.\nThe key relationship is: ∇ I = [∂ I∂ x, ∂ I∂ y]ᵀ\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/edge_detection.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/image-processing/edge_detection.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/image-processing/edge_detection.tex",
      "source": "edge_detection",
      "category": "image-processing"
    },
    {
      "title": "Exploring Marine Population Genetics: Drift, Gene Flow, and F-Statistics computationally",
      "body": "I recently dove into marine population genetics: drift, gene flow, and f-statistics.\n\nThis report presents a comprehensive computational analysis of marine population genetics, examining fundamental evolutionary forces that shape genetic diversity in marine organisms.  We simulate Hardy-Weinberg equilibrium conditions, quantify genetic drift using Wright-Fisher models, estimate effective population size (Ne) from temporal allele frequency changes, model gene flow under island and stepping-stone migration patterns, and calculate F-statistics (FST, FIS, FIT) to assess population str.\nThe key relationship is: p' ∼ Binomial(2N, p) / (2N)\n\nThe visualization really helped me understand the underlying dynamics.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/marine-biology/population_genetics.tex\n\nWhat parameters are most sensitive in your experience?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/marine-biology/population_genetics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/marine-biology/population_genetics.tex",
      "source": "population_genetics",
      "category": "marine-biology"
    },
    {
      "title": "Interactive Ocean Productivity: Photosynthesis-Irradiance Relationships and Nutrient-Limi... visualization",
      "body": "I created a computational exploration of ocean productivity: photosynthesis-irradiance relationships and nutrient-limited primary production.\n\nThis report presents a comprehensive computational analysis of ocean primary productivity, focusing on photosynthesis-irradiance (P-I) relationships, nutrient limitation dynamics, and seasonal phytoplankton bloom patterns.  We examine the classic P-I curve parameterization (Jassby \\& Platt 1976), Michaelis-Menten nutrient uptake kinetics, depth-integrated net primary production (NPP), and the interplay between mixed layer dynamics and euphotic zone structure.\nThe key relationship is: V([N]) = V_max[N]Kₛ + [N]\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/marine-biology/ocean_productivity.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/marine-biology/ocean_productivity.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/marine-biology/ocean_productivity.tex",
      "source": "ocean_productivity",
      "category": "marine-biology"
    },
    {
      "title": "The math behind Fisheries Population Models:-Recruitment Dynamics and Sustainable Harvesting - a simulation",
      "body": "I recently dove into fisheries population models:\\-recruitment dynamics and sustainable harvesting.\n\nThis report presents a comprehensive computational analysis of fisheries population models used in sustainable fisheries management.  We examine surplus production models including the Schaefer and Fox formulations, calculate maximum sustainable yield (MSY) and optimal fishing effort, analyze stock-recruitment relationships through Beverton-Holt and Ricker models, and investigate age-structured population dynamics.\nThe key relationship is: dBdt = rB(1 - BK) - qEB\n\nThe visualization really helped me understand the underlying dynamics.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/marine-biology/fisheries_models.tex\n\nWhat biological systems have you modeled?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/marine-biology/fisheries_models.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/marine-biology/fisheries_models.tex",
      "source": "fisheries_models",
      "category": "marine-biology"
    },
    {
      "title": "The math behind Isotope Geochemistry and Radiogenic Dating - a simulation",
      "body": "I created a computational exploration of isotope geochemistry\\ and radiogenic dating.\n\nThis document presents computational methods for isotope geochemistry, including delta notation calculations, Rayleigh fractionation modeling, two-component mixing, and radiogenic dating via isochron analysis.  We demonstrate temperature-dependent oxygen isotope fractionation, carbon isotope systematics in closed systems, and Rb-Sr geochronology applied to crustal rocks.\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geochemistry/isotope_geochemistry.tex\n\nWhat visualization approaches work well for this?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geochemistry/isotope_geochemistry.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geochemistry/isotope_geochemistry.tex",
      "source": "isotope_geochemistry",
      "category": "geochemistry"
    },
    {
      "title": "The math behind Aqueous Geochemistry - a simulation",
      "body": "I created a computational exploration of aqueous geochemistry\\.\n\nThis template provides a comprehensive computational framework for aqueous geochemistry, covering chemical equilibria, speciation diagrams, activity corrections, and mineral saturation.  We implement the Henderson-Hasselbalch equation for acid-base systems, Debye-H\\\"uckel activity coefficients for ionic solutions, carbonate speciation across pH gradients, and saturation indices for mineral dissolution.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geochemistry/aqueous_geochemistry.tex\n\nHas anyone implemented similar kinetics models?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geochemistry/aqueous_geochemistry.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geochemistry/aqueous_geochemistry.tex",
      "source": "aqueous_geochemistry",
      "category": "geochemistry"
    },
    {
      "title": "Visualizing Mineral Thermodynamics Equilibria with Python",
      "body": "I created a computational exploration of mineral thermodynamics\\ equilibria.\n\nThis document presents computational thermodynamic analysis of mineral phase equilibria, including Gibbs free energy calculations for metamorphic reactions, construction of pressure-temperature phase diagrams using the Clapeyron equation, temperature-dependent equilibrium constants via the van't Hoff equation, and solid solution thermodynamics for Fe-Mg olivine.  Applications include predicting mineral stability fields in crustal and mantle conditions, calculating reaction boundaries for index mi.\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geochemistry/mineral_thermodynamics.tex\n\nHas anyone implemented similar kinetics models?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/geochemistry/mineral_thermodynamics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/geochemistry/mineral_thermodynamics.tex",
      "source": "mineral_thermodynamics",
      "category": "geochemistry"
    },
    {
      "title": "Interactive Explorations in Partition Theory and Topology visualization",
      "body": "I put together a simulation of explorations in partition theory and topology and wanted to share what I learned.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/sagetex/math_thesis.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/sagetex/math_thesis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/sagetex/math_thesis.tex",
      "source": "math_thesis",
      "category": "sagetex"
    },
    {
      "title": "Visualizing Agent-Based Modeling: Emergent Behavior from Simple Rules with Python",
      "body": "I built an interactive model for agent-based modeling: emergent behavior from simple rules and wanted to share what I learned.\nThe key relationship is: D = 12 Σ(i=1 to N) | aᵢA - bᵢB |\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/simulations/agent_based.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/simulations/agent_based.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/simulations/agent_based.tex",
      "source": "agent_based",
      "category": "simulations"
    },
    {
      "title": "I built an interactive Monte Carlo Methods: Sampling, Integration, and MCMC simulation",
      "body": "I built an interactive model for monte carlo methods: sampling, integration, and mcmc and wanted to share what I learned.\nThe key relationship is: I = ∫ₐᵇ f(x) \\, dx ≈ b-aN Σ(i=1 to N) f(xᵢ)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nFeel free to fork this for your own projects. The code is well-commented for learning.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/simulations/monte_carlo.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/simulations/monte_carlo.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/simulations/monte_carlo.tex",
      "source": "monte_carlo",
      "category": "simulations"
    },
    {
      "title": "Visualizing Stochastic Differential Equations: Modeling Random Processes with Python",
      "body": "I've been exploring stochastic differential equations: modeling random processes and wanted to share what I learned.\nThe key relationship is: dXₜ = μ(Xₜ, t)\\,dt + σ(Xₜ, t)\\,dWₜ\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/simulations/stochastic.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/simulations/stochastic.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/simulations/stochastic.tex",
      "source": "stochastic",
      "category": "simulations"
    },
    {
      "title": "I built an interactive PN Junction Physics: Electrostatic Analysis and Current-Voltage Characteristics simulation",
      "body": "I recently dove into pn junction physics: electrostatic analysis and current-voltage characteristics.\n\nThis report presents a comprehensive computational analysis of PN junction physics, covering the formation of the depletion region, built-in potential, electrostatic field profiles, current-voltage characteristics governed by the Shockley diode equation, junction capacitance (both depletion and diffusion), and breakdown mechanisms.  We analyze silicon PN junctions with varying doping concentrations, compute key parameters including built-in voltage ($V_bi = 0.\nThe key relationship is: V_bi = kTq (N_A N_Dnᵢ²)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/semiconductor/pn_junctions.tex\n\nWhat parameters do you find most interesting?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/semiconductor/pn_junctions.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/semiconductor/pn_junctions.tex",
      "source": "pn_junctions",
      "category": "semiconductor"
    },
    {
      "title": "The math behind MOSFET Device Physics: Threshold Voltage Modeling and I-V Characterization - a simulation",
      "body": "I've been exploring mosfet device physics: threshold voltage modeling and i-v characterization.\n\nThis technical report presents a comprehensive analysis of Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) device physics, including threshold voltage derivation, current-voltage characteristics, and short-channel effects.  We examine the threshold voltage equation $V_th = V_FB + 2_F + Q_dep/C_ox$, analyze transfer and output characteristics across multiple bias conditions, and investigate drain-induced barrier lowering (DIBL), velocity saturation, and subthreshold swing degrad.\nThe key relationship is: V_th = V_FB + 2φ_F + Q_depC_ox\n\nIt's fascinating to see the theory come alive in the simulation.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/semiconductor/mosfet.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/semiconductor/mosfet.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/semiconductor/mosfet.tex",
      "source": "mosfet",
      "category": "semiconductor"
    },
    {
      "title": "I built an interactive Semiconductor Band Theory: From Bloch's Theorem to Effective Mass simulation",
      "body": "I've been studying semiconductor band theory: from bloch's theorem to effective mass.\n\nThis comprehensive analysis of semiconductor band theory provides computational insights into the electronic structure of crystalline solids.  We derive band structures using the Kronig-Penney model for one-dimensional periodic potentials, compute effective masses from parabolic band approximations, and calculate density of states for various dimensionalities.\nThe key relationship is: ψ_k(r) = e^ik · r u_k(r)\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/semiconductor/band_theory.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/semiconductor/band_theory.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/semiconductor/band_theory.tex",
      "source": "band_theory",
      "category": "semiconductor"
    },
    {
      "title": "The math behind Sentiment Analysis: Lexicon-Based and Machine Learning Approaches - a simulation",
      "body": "I've been fascinated by sentiment analysis: lexicon-based and machine learning approaches and wanted to share what I learned.\nThe key relationship is: S_compound = Σ(i=1 to n) vᵢ√(Σ(i=1 to n) vᵢ)² + α\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nlp/sentiment.tex\n\nWhat approaches have you found useful?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/nlp/sentiment.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nlp/sentiment.tex",
      "source": "sentiment",
      "category": "nlp"
    },
    {
      "title": "Visualizing Word Embeddings: Skip-gram Model and Vector Semantics with Python",
      "body": "I created a computational exploration of word embeddings: skip-gram model and vector semantics and wanted to share what I learned.\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nlp/word_embeddings.tex\n\nHow do you visualize these concepts?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/nlp/word_embeddings.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nlp/word_embeddings.tex",
      "source": "word_embeddings",
      "category": "nlp"
    },
    {
      "title": "Exploring Text Analysis: TF-IDF Vectorization and Document Similarity computationally",
      "body": "I've been fascinated by text analysis: tf-idf vectorization and document similarity and wanted to share what I learned.\nThe key relationship is: TF(t, d) = f_t,d∑_t' ∈ d f_t',d\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nlp/text_analysis.tex\n\nHas anyone else explored this topic computationally?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/nlp/text_analysis.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/nlp/text_analysis.tex",
      "source": "text_analysis",
      "category": "nlp"
    },
    {
      "title": "Visualizing Robotics: A* and RRT Path Planning Algorithms with Python",
      "body": "I've been exploring robotics: a* and rrt path planning algorithms.\n\nThis document presents a comprehensive analysis of path planning algorithms for mobile robots and manipulators.  We implement and compare A* search for grid-based planning, Rapidly-exploring Random Trees (RRT) for sampling-based planning, and potential field methods for reactive navigation.\nThe key relationship is: f(n) = g(n) + h(n)\n\nIt's fascinating to see the theory come alive in the simulation.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/robotics/path_planning.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/robotics/path_planning.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/robotics/path_planning.tex",
      "source": "path_planning",
      "category": "robotics"
    },
    {
      "title": "The math behind Robotics: PID Motor Control and Tuning - a simulation",
      "body": "I recently dove into robotics: pid motor control and tuning.\n\nThis document presents a comprehensive analysis of Proportional-Integral-Derivative (PID) control for robotic motor systems.  We implement continuous and discrete PID controllers, analyze the effects of each gain component on system response, explore automatic tuning methods including Ziegler-Nichols and Cohen-Coon, and demonstrate applications to DC motor position and velocity control.\nThe key relationship is: u(t) = Kₚ e(t) + Kᵢ ∫₀ᵗ e(τ) dτ + K_d de(t)dt\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/robotics/pid_control.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/robotics/pid_control.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/robotics/pid_control.tex",
      "source": "pid_control",
      "category": "robotics"
    },
    {
      "title": "Exploring Robot Kinematics: Forward and Inverse Analysis computationally",
      "body": "I recently dove into robot kinematics: forward and inverse analysis.\n\nThis document presents a comprehensive analysis of robot kinematics using the Denavit-Hartenberg (DH) convention.  We explore forward kinematics for a 3-DOF planar manipulator and 6-DOF articulated arm, implement inverse kinematics solutions using both geometric and numerical methods, compute the Jacobian matrix for velocity analysis, and visualize the robot workspace.\nThe key relationship is: ⁰Tₙ = ⁰T₁ · ¹T₂ ·  · ^n-1Tₙ = Π(ᵢ₌₁ⁿ) ^i-1Tᵢ\n\nThe visualization really helped me understand the underlying dynamics.\n\nAll the math is typeset in LaTeX with embedded Python/Sage code - a great learning resource.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/robotics/kinematics.tex\n\nWhat design parameters do you find most critical?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/robotics/kinematics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/robotics/kinematics.tex",
      "source": "kinematics",
      "category": "robotics"
    },
    {
      "title": "The math behind Rocket Propulsion Analysis: Thrust Curves, Specific Impulse, and Staging Opti... - a simulation",
      "body": "I've been exploring rocket propulsion analysis: thrust curves, specific impulse, and staging optimization\\\\\n a comprehensive study of chemical rocket performance.\n\nThis laboratory report presents a comprehensive analysis of rocket propulsion systems.  We examine thrust curves for different propellant combinations, compare specific impulse values, and optimize multi-stage rocket configurations using the Tsiolkovsky equation.\nThe key relationship is: I_sp = Fm g₀ = vₑg₀\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/rocket_propulsion.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/aerospace/rocket_propulsion.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/rocket_propulsion.tex",
      "source": "rocket_propulsion",
      "category": "aerospace"
    },
    {
      "title": "I built an interactive Atmospheric Reentry Analysis: Heat Flux, Trajectory, and Ablation Modeling A ... simulation",
      "body": "I created a computational exploration of atmospheric reentry analysis: heat flux, trajectory, and ablation modeling\\\\\n a comprehensive study of ballistic and lifting reentry profiles.\n\nThis research paper presents a comprehensive analysis of atmospheric reentry dynamics for spacecraft vehicles.  We develop and compare ballistic and lifting reentry trajectories, computing time histories of altitude, velocity, deceleration, and stagnation-point heat flux.\nThe key relationship is: β = mC_D A\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/atmospheric_reentry.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/aerospace/atmospheric_reentry.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/atmospheric_reentry.tex",
      "source": "atmospheric_reentry",
      "category": "aerospace"
    },
    {
      "title": "Exploring Aerodynamic Lift Analysis: From Thin Airfoil Theory to Computational Modeling... computationally",
      "body": "I built an interactive model for aerodynamic lift analysis: from thin airfoil theory to computational modeling\\\\\n multi-airfoil comparison with reynolds number effects.\n\nThis technical report presents a comprehensive analysis of aerodynamic lift characteristics for various airfoil configurations.  We examine lift coefficient behavior as a function of angle of attack across multiple NACA airfoil series, investigate Reynolds number effects on boundary layer transition, and compute optimal flight conditions for maximum aerodynamic efficiency.\nThe key relationship is: C_L = L12ρ V² S\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nDownload the .tex file to run locally, or use CoCalc's free tier to experiment in the browser.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/aerodynamic_lift.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/aerospace/aerodynamic_lift.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/aerodynamic_lift.tex",
      "source": "aerodynamic_lift",
      "category": "aerospace"
    },
    {
      "title": "Visualizing Orbital Mechanics: Hohmann Transfers, Orbital Elements, and Ground Tracks A C... with Python",
      "body": "I've been fascinated by orbital mechanics: hohmann transfers, orbital elements, and ground tracks\\\\\n a comprehensive analysis of spacecraft trajectory design.\n\nThis textbook-style analysis presents the fundamentals of orbital mechanics for spacecraft mission design.  We examine Hohmann transfer orbits between circular orbits, compute orbital elements from state vectors, and generate ground tracks for various orbit types.\nThe key relationship is: v = √μ (2r - 1a)\n\nThe visualization really helped me understand the underlying dynamics.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/orbital_mechanics.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/aerospace/orbital_mechanics.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/orbital_mechanics.tex",
      "source": "orbital_mechanics",
      "category": "aerospace"
    },
    {
      "title": "The math behind Satellite Coverage Analysis: Ground Coverage, Revisit Times, and Constellatio... - a simulation",
      "body": "I wanted to visualize satellite coverage analysis: ground coverage, revisit times, and constellation design\\\\\n a comprehensive study of earth observation and communication systems.\n\nThis technical report presents a comprehensive analysis of satellite ground coverage for Earth observation and communication missions.  We compute instantaneous coverage footprints, revisit times for single satellites and constellations, and analyze Walker constellation parameters for global coverage.\nThe key relationship is: ρ = (R_ER_E + h_min) - _min\n\nIt's fascinating to see the theory come alive in the simulation.\n\nThe template is fully editable - plug in your own parameters and see how the results change.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/satellite_coverage.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/aerospace/satellite_coverage.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/aerospace/satellite_coverage.tex",
      "source": "satellite_coverage",
      "category": "aerospace"
    },
    {
      "title": "Simulating Control Systems Analysis: A Comprehensive Tutorial on Feedback Control Design - visualizing the math",
      "body": "I put together a simulation of control systems analysis: a comprehensive tutorial on\\ feedback control design.\n\nThis tutorial provides a comprehensive analysis of classical control system design techniques.  We examine transfer function modeling, frequency response analysis through Bode and Nyquist plots, root locus methods for stability analysis, and PID controller tuning strategies.\nThe key relationship is: T(s) = C(s)G(s)1 + C(s)G(s) = L(s)1 + L(s)\n\nWhat surprised me was how sensitive the results are to initial conditions.\n\nGreat for homework, teaching demos, or exploring the topic on your own.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electrical-engineering/control_systems.tex\n\nWhat simulation tools do you typically use?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/electrical-engineering/control_systems.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electrical-engineering/control_systems.tex",
      "source": "control_systems",
      "category": "electrical-engineering"
    },
    {
      "title": "Interactive RC Circuit Analysis: Transient Response, Frequency Domain, Filter Design Labo... visualization",
      "body": "I've been fascinated by rc circuit analysis: transient response, frequency domain,\\ filter design laboratory report.\n\nThis laboratory report presents a comprehensive analysis of RC circuits, covering transient response characteristics, Laplace transform methods, frequency domain analysis, and filter design applications.  Through computational analysis with Python, we demonstrate charging and discharging dynamics, time constant determination, Bode plot interpretation, and the design of low-pass, high-pass, and band-pass filter configurations.\nThe key relationship is: τ = RC\n\nPlaying with the parameters reveals some counterintuitive behavior.\n\nThe LaTeX source includes all the computational code - modify it to explore different scenarios.\n\nHere's the interactive simulation I put together: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electrical-engineering/rc_circuit.tex\n\nHas anyone applied this to real-world problems?",
      "image_url": "https://raw.githubusercontent.com/Ok-landscape/computational-pipeline/main/latex-templates/images/electrical-engineering/rc_circuit.png",
      "cocalc_url": "https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/latex-templates/templates/electrical-engineering/rc_circuit.tex",
      "source": "rc_circuit",
      "category": "electrical-engineering"
    }
  ]
}