compare_small_inertia_theories.ipynb

Kernel: Python 3 (ipykernel)

from Dabade16 import deltaC_dabade16, calculate_eccentricity
from Einarsson15 import deltaC_einarsson15, load_betas, Einarsson_interface, fit_C
import numpy as np
import matplotlib.pyplot as plt

Parameters

#aspect ratio
r=0.56
#Reynolds number
Rep=0.1
#Initial condition
IC = np.array([0.0,0.9,0.1])
IC = IC / np.linalg.norm(IC)
#time-line
time = np.linspace(0,500.0,500000)
#shear-rate
gammadot=3.1

Theory of Dabade et al., 2016

###calculate the theory of dabade
dabade16 = deltaC_dabade16(r=r)
e0 = calculate_eccentricity(r)
###scaling factor for the oblate ellipsoid
ftr = e0**2

# Theory of Einarsson et al., 2015

einarsson15 = deltaC_einarsson15(r=r,Rep=Rep,dir='',IC=IC,time=time,gammadot=gammadot)

/Users/davide/Downloads/Joint_paper_figures/jupyter_notebook_submission/figure_5/Einarsson15.py:89: RuntimeWarning: invalid value encountered in arccos
  theta = np.arccos(n3[orbit_inds])

plt.figure(figsize=(7,4))
###plot the theory of Einarsson
C = einarsson15[0,1:-1]
dC = einarsson15[0,2:] - einarsson15[0,:-2]
plt.plot(C/(C+1),dC/(C**2+1)/Rep*ftr,label=r'$Einarsson \ et \ al.,\ 2015$',c='red',ls='--')
###plot the theory of Dabade
C = dabade16[:,0]
dC = dabade16[:,1]+dabade16[:,2]
plt.plot(C/(C+1),dC/(C**2+1)*ftr,label=r'$Dabade \ et \ al.,\ 2016$',c='k',ls=':')
plt.legend();
plt.xlim(0,1);
plt.axhline(0.0,c='grey',alpha=0.3);
plt.ylabel(r'$\Delta C/(C^2+1)\times Re_p^{-1} \times {\xi_0}^2$',fontsize=15);
plt.xlabel(r'$C/(C+1)$',fontsize=15,labelpad=0.5);
plt.savefig('ELL06_compare_einarsson_dabade_theories.png',format='png',dpi=300, bbox_inches='tight');