Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download
601 views
unlisted
ubuntu2404
�

�6i�4��
�dZddlZddlZejd��Zejdd���Zejdd���Zejd��Z	d	�Z
d
ed
zzdedzzz
d
zedze
e��ze
e��zez
zdezddedzzz
dzzzZed
ze
e��eee
e��zdz
zzzdezddedzzz
dzzzZedzedze
e��ze
e��zez
zdezddedzzz
dzzzZ
e
Ze
dzZeZd
ed
zzdedzzz
dzedzdze
e��zez
zdezddedzzz
dzzzZeed
zezed
zdz
e
e��zzzdddedzzz
dzzzZeedzzZeedzzZedzdedzzdedzzzdedzzz
dedzzzded
zzz
dedzzzdzzdedzzdedzzdedzzz
ded
zzz
d edzzzd
z
zedzze
e��d
zzz
d!ezd"edzzd#edzzz
d$edzzz
d%edzzzd&ed
zzz
d'edzzzd(z
zed
zze
e��d
zzzed)edzzd*edzzz
d+edzzzd,edzzz
d-edzzzd.ed
zzz
d/edzzz
d0zze
e��zzd
d1ed zzd2edzzz
d3edzzzd4edzzz
d5edzzz
d6edzzzd7ed
zzz
d8edzzzd9z
ze
e��dzzz
d:edzzd;dedzzzd
zzd<edzzd
edzzeze
e��zzdzzd<ed
zzdezzd
ed
zze
e��zzzd
edzzdz
e
e��zd
ezz
zd;zzZedzd=ed!zzd>edzzzd?edzzz
d@ed
zzzdezz
d!edzzedzdzzedzze
e��d
zzzd
ed
zzd!edzzded
zzz
dAedzzz
dzzeze
e��dzzz
dedzzdBedzzz
dCedzzzdDed
zzz
dEedzzz
dze
e��zzzdeded
zzz
dzzd<edzzd
edzzeze
e��zzdzzd<ed
zzdezzd
ed
zze
e��zzzd;zzZedzdFedzzdGedzzzdHedzzz
dIed
zzzdJedzzz
dKzzdedzzdedzzed
zzd
edzzz
dzzedzze
e��d
zzz
d!ezdedzzdLedzzzdMedzzz
dNed
zzzdOedzzz
dzzed
zze
e��d
zzzdPedQzzdRedSzzz
dTed!zzzdUedzzz
dVedzzzdWed
zzz
dXezze
e��zzd
dYedzzdFedzzz
dZedzzzd[edzzz
d\edzzzd]ed
zzz
d^edzzzd_z
ze
e��dzzzd:edzzd;dedzzzd
zzd<edzzd
edzzeze
e��zzdzzd<ed
zzdezzd
ed
zze
e��zzzd
edzzdz
e
e��zd
ezz
zd;zzZeZed`zZed`zZedzdaedzzdbedzzz
dcedzzzdded
zzz
deedzzzdfz
zd!edzzd!edzzdedzzz
dzzedzze
e��d
zzzd
ezdgedzzdhedzzz
diedzzzdjed
zzzdkedzzz
dlzzed
zze
e��d
zzz
dmedQzzdnedSzzzdoed!zzz
dpedzzzdqedzzz
dred
zzz
dsezze
e��zzdtedzzduedzzz
dvedzzzdwedzzz
dxedzzz
dyed
zzzdzedzzz
d{ze
e��dzzzdeded
zzz
dzzd<edzzd
edzzeze
e��zzdzzd<ed
zzdezzd
ed
zze
e��zzzd
edzzdz
e
e��zd
ezz
zd;zzZedzdedzzd|edzzz
d}edzzzd~ed
zzzdCedzzz
d{zzd!ed
zzd
ed
zzdedzzzdz
zedzze
e��d
zzz
d
ezdsedzzdedzzz
d�edzzzdied
zzz
d�edzzzdz
zed
zze
e��d
zzzedgedzzd�edzzz
d�edzzzd�edzzz
d?ed
zzzd(edzzz
dzze
e��zzd�edzzd�edzzzd�edzzz
d�edzzzd�edzzz
d�ed
zzzd�edzzz
dze
e��dzzzdeded
zzz
dzzd<edzzd
edzzeze
e��zzdzzd<ed
zzdezzd
ed
zze
e��zzzd
edzzdz
e
e��zd
ezz
zd;zzZedzdFedzzdGedzzzdHedzzz
dIed
zzzdJedzzz
dKzzdedzzdedzzed
zzd
edzzz
dzzedzze
e��d
zzz
d!ezdedzzdLedzzzdMedzzz
dNed
zzzdOedzzz
dzzed
zze
e��d
zzzdPedQzzdRedSzzz
dTed!zzzdUedzzz
dVedzzzdWed
zzz
dXezze
e��zzd
dYedzzdFedzzz
dZedzzzd[edzzz
d\edzzzd]ed
zzz
d^edzzzd_z
ze
e��dzzzd�edzzdedzzdz
d
zzd<edzzd
edzzeze
e��zzdzzd<ed
zzdezzd
ed
zze
e��zzzd
edzzdz
e
e��zd
ezz
zd;zzZeZdejzZ dejzedz
zedzd;zzZ!dejzde	dzdze	dzedzzdzzd�zzdz
zZ"dejzedz
dzzedzd�zzZ#d
ejzdedzzd
ej$e	dzdze	dzedzzdzz��zde	dzzz
dz
zd
ezej$e	dzdze	dzedzzdzz��zzej$e	dzdze	dzedzzdzz��zd
d
e	dzzdzzed
zzej$e	dzdze	dzedzzdzz��zzed
zej$e	dzdze	dzedzzdzz��d e	d
ze	dzzzz
dz
zzdz
zedzdz
dzej$e	dzdze	dzedzzdzz��zd;zzZ%ejedzdz
zedzd�zzZ&ejd�e	dzdze	dzedzzdzzd�zze	dzedzdzzzd
zze	d�zzedzdz
d;zzZ'ejedz
dzzedzd�zzZ(ejedzdz
zde	d
zzed
zze	dzedzd
zdedzzej$e	dzdze	dzedzzdzz��zz
zzd
edzdzzej$e	dzdze	dzedzzdzz��dz
zz
ze	d�zzedzdz
d<zzZ)d��Z*d��Z+d��Z,d�d��Z-dS)�z�
Created on Fri Nov  7 18:39:55 2025

@author: davide
Methods that calculates the orbit variation delta_C for an oblate particle given its aspect ratio
�Nz\kappa�xiT)�positivez
\overline{xi}�Cc�B�dtj|dz|dz
z��zS)N��?�)�sym�log)�vals �O/Users/ziqiwang/PD/MP_PD/2025-JFM/Jupyter_notebook_figures/figure_4/Dabade16.py�invcothr
s#���#�'�3�q�5�3�q�5�/�*�*�*�*������r�(�ix����iF�
i��iA.�i5$i�������	i i4�ii�i�i 
ilil6i�Ri�7iAi�
i�ii�i�i�i�i�i�
iQ�:i�����������i������s�Z��W��!�4izi!i{i�iA	iV���i�i4����
iD�i�i�(iiO�,���mi�i�ii7�g@�Qi�i2i�i��6�l���E���i����ii�i=i��O�$i�i�i�i
��iic�����D�N�I�#iviiii^���i*ii@ii��a�xg�����������rc��%�|dk�r�t�ttdzdz
dzt|i�����}t
�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}	t�ttdzdz
dzt|i�����}
t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}t�ttdzdz
dzt|i�����}
t �ttdzdz
dzt|i�����}t"�ttdzdz
dzt|i�����}t$�ttdzdz
dzt|i�����}t&�ttdzdz
dzt|i�����}t(�ttdzdz
dzt|i�����}t*�ttdzdz
dzt|i�����}t,�ttdzdz
dzt|i�����}t.�ttdzdz
dzt|i�����}�
n ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}t
tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}	ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}
ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}t1j|�t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz} t1j| �t|i�������}ttdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}!t1j|!�t|i�������}
t tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}"t1j|"�t|i�������}t"tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}#t1j|#�t|i�������}t$tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}$t1j|$�t|i�������}t&tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}%t1j|%�t|i�������}t(tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}&t1j|&�t|i�������}t*tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}'t1j|'�t|i�������}t,tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz}(t1j|(�t|i�������}t.tdzz�ttdzdz
dztt0jtdzdz
dzzi��tdzz})t1j|)�t|i�������}||||||||	|
|||
||||||||fS)z(returns the shape-dependent coefficients��?rrr)�F1p_def�subs�xibr�evalf�F2p_def�F3p_def�F4p_def�F5p_def�F6p_def�G1p_def�G2p_def�G3p_def�G4p_def�F1f_def�F2f_def�F3f_def�F4f_def�F5f_def�F6f_def�G1f_def�G2f_def�G3f_def�G4f_defr	�I�re)*�r�e0�F1p_eff�F2p_eff�F3p_eff�F4p_eff�F5p_eff�F6p_eff�G1p_eff�G2p_eff�G3p_eff�G4p_eff�F1f_eff�F2f_eff�F3f_eff�F4f_eff�F5f_eff�F6f_eff�G1f_eff�G2f_eff�G3f_eff�G4f_eff�F1p_tmp�F2p_tmp�F3p_tmp�F4p_tmp�F5p_tmp�F6p_tmp�G1p_tmp�G2p_tmp�G3p_tmp�G4p_tmp�F1f_tmp�F2f_tmp�F3f_tmp�F4f_tmp�F5f_tmp�F6f_tmp�G1f_tmp�G2f_tmp�G3f_tmp�G4f_tmps*                                          r�shape_coeffsr�rs����u�u��,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B���,�,��R��U�1�W�s�N�2�b�9�:�:�@�@�B�B����B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���B��E�M�'�'��b�!�e�A�g��^�B�s�u�b�!�e�A�g�PS�^�?S�(T�U�U�XZ�\]�X]�^���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���b�!�e�O�)�)�3��A��a��#�~�b����A��a��RU�~�AU�*V�W�W�Z\�^_�Z_�`���6�'�,�,��2�w�/�/�5�5�7�7�8�8�8���G�G�G�G�G�G�G�G�T[��7�7�7�7�7�7�7�7�SZ�\�\rc� �t||��\}}}}}}}}	}
}}}
}}}}}}}}tdtdzzdz
zttzzt|zt
|zzt|zzt|zzt|zzt|zt|	zzt|
zzt|zzzz�
ttdzdz
dzt|t|i�����}tdtdzzdz
zttzzt|zt
|
zzt|zzt|zzt|zzt|zt|zzt|zzt|zzzz�
ttdzdz
dzt|t|i�����}tdtdzzdz
zttzzt|zt
|zzt|zzt|zzt|zzt|zt|	zzt|
zzt|zzzz�
ttdzdz
dzt|t|i�����}tdtdzzdz
zttzzt|zt
|
zzt|zzt|zzt|zzt|zt|zzt|zzt|zzzz�
ttdzdz
dzt|t|i�����}|dkr||fS|dkr
|dkr||fSdSdS)NrrrrM�)r�rrrP�I1�I2�I3�I4�I5I6�J1�J2�J3�J4rO�krQ)rg�ee�F1p�F2p�F3p�F4p�F5p�F6p�G1p�G2p�G3p�G4p�F1f�F2f�F3f�F4f�F5f�F6f�G1f�G2f�G3f�G4f�particle_inertia_prolate�fluid_inertia_prolate�particle_inertia_oblate�fluid_inertia_oblates                          r�inertial_contributionsr��s,��Vb�cd�eg�Vh�Vh�S�C��C��C��C��C��C��C��C��C��C�PS�!"�A�b�!�e�G�A�I���3��!7�"�S�&��C��-��3��:N�r�RU�v�:U�W[�]`�V`�:`��S�&��C��-��3��&�r�#�v�-�:/�"0�15��s�B��E�!�G�c�>�"�R�PQ�RS�6T�1U�1U�V[�V[�V]�V]����"�a�%���	�]�B�s�F�3�b��f�R��V�m�B�s�F�6J�2�c�6�6Q�SW�Y\�R\�6\��S�&��C��-��3��&�r�#�v�-�6/�0�15��s�B��E�!�G�c�>�"�R�PQ�RS�6T�1U�1U�V[�V[�V]�V]�� �!�B��E�'�!�)�}�b��f�5��3��r�#�v�
�b��f�8L�R�PS�V�8S�UY�[^�T^�8^��S�&��C��-��3��&�r�#�v�-�8/� 0�15��s�B��E�!�G�c�>�"�R�PQ�RS�6T�1U�1U�V[�V[�V]�V]���q��Q��w�q�y�M�2�c�6�2�R��V�B�s�F�]�2�c�6�5I�"�S�&�5P�RV�X[�Q[�5[��S�&��C��-��3��&�r�#�v�-�5/�0�15��s�B��E�!�G�c�>�"�R�PQ�RS�6T�1U�1U�V[�V[�V]�V]����u�u�'�(=�=�=�	
�3���1�S�5�5�&�';�;�;�
��5�5rc�|�|dkr||dzdz
dzzS|dkr|dkrdd|dzz
dzzStd���)z1calculate particle eccentricity from aspect ratiorMrrrr�z1Please pass a valid aspect ratio > 0.0 and != 1.0)�
ValueError)rgs r�calculate_eccentricityr��sW���3�w�w��!�Q�$�q�&�3����	
�S���Q��W�W��!�A�q�D�&�3�����L�M�M�Mr��Q����?c��t|��}t||��\}}|�htjtjddd��tjddd��f��}tj|tjddd��f��}g}g}tt
|����D]n}||}|�t|i��}	|�	||	g��|�t|i��}	|�	|	���otj
|��}tj
|��}tj||f��S)zjreturns particle and fluid inertia orbit variations for the given aspect ratio and range of orbit costantsNg�h㈵��>g�������?�drr)r�r��np�concatenate�linspace�range�lenrOr�append�array�column_stack)
rg�Cranger��PINE�FINE�CDC_pine�CDC_fine�j�CVAL�datas
          r�deltaC_dabade16r��s3��
 ��	"�	"�B�&�q��,�,�I�D��
�~�����W�S��!=�!=�b�k�!�A�c�>R�>R� S�T�T�������A�c�#�(>�(>� ?�@�@���H��H�
�3�v�;�;�
�
�����a�y���y�y�!�D��"�"������d��$�$�$��y�y�!�D��"�"�����������x��!�!�H��x��!�!�H�
�?�H�X�.�/�/�/r)r�N).�__doc__�sympyr	�numpyr��symbolsr�rrPrr
rNrRrSrTrUrVrWrXrYrZr[r\r]r^r_r`rarbrcrd�pir�r�r�r��sqrtr�r�r�r�r�r�r�r�r��rr�<module>r�s��������������C�K������S�[���%�%�%���S�[��4�0�0�0���C�K�����+�+�+�
�R��U�7�1�R��U�7�?�1��r�1�u�W�W�R�[�[�0������<�R�?�
@�#�b�&�!�A�b�RS�e�G�)�VW��BW�
X��

�q�&�'�'�"�+�+�b�"�W�W�R�[�[�.��"2�3�3�
4�b��e�Q�q��Q��w�Y��N�6J�
K����F�(�B��E�'�'�"�+�+�%�g�g�b�k�k�1�"�4�
5�s�2�v�q��2�q�5��y�1�n�7L�
M��
���(�Q�,��
��
�b�!�e�G�A�b�!�e�G�O�A��
��Q��q��'�'�"�+�+� 5�b� 8�
9�R��U�A�a��A��g�I�PQ�>�=Q�
R��
��A��v�b�y�"�a�%��'�7�7�2�;�;�.�.�/�B��!�B��E�'�	�A�~�4E�
F��
�B��E�/���)�b�!�e�
��
��7�D��b��M�$�r�B�x�-�/��R�!�W��<�U�2��7�]�J�4�PR�UV�PW�<�W�X\�]_�bc�]d�Xd�d�ef�f�g�	�B��G��R��Q��Z��2��7�
�*�2�b�1�g�:�5�b��a��j�@��B�	C�C�!�H�	L�W�W�UW�[�[�[\�M]�	]�^�^_�`b�^b��r�B�x�<��B��H��$�R��Q��Z�/��B��G��;�C��Q��K�G��B�QR�G��S�TV�V�_X�X[�^_�X`�_a��7�2�;�;���_����R�"�X�
�d�2��8�m� ;�E�"�r�(�N� J�5�QS�VW�QX�=� X�Y^�_a�de�_f�Yf� f�	�R�!�W��!��"�q�'�\�!"�"%�!&�'�'.�w�r�{�{�3�3�45�d�2��8�m�D��b��M�6Q�RV�WY�\^�W_�R_�6_�	
�b�2�h��7��B��G�|�7$�$(��a��L�71�15�b�1�g��7>�>A�"�q�'�k�7J�JL�7M�4N�NU�g�VX�k�k�\]�N^�4_�	_��r�A�w�;��1�R�!�W�9���*�*�B�r�A�w�J�q��q��z�"�}�W�W�R�[�[�7P�,P�QR�,R�S�
�R�!�W�*�Q�r�T�/�!�C�!�H�*�W�W�R�[�[�0�
0�2�45�b�1�g�I�a�K������3L�Q�r�T�3Q�S�VX�Z�
Z��
�!�H�b��a��j��B��G��+�C��Q��K�7��2��7�
�B�2�b�5�H�	
�3��8��R�!�W�Q�Y�	��Q��	'������a�(8�	8�9�9:�3��8��Q�r�A�w�Y�r�RT�WX�RY�z�EY�Z\�]_�bc�]d�Zd�Ed�eg�Eg�9h�ik�9k�ls�ls�tv�lw�lw�z{�l|�9|�}�
�R�"�X�+�b��a��j�
 ��R�!�W��
,�R��Q��Z�
7��2��7�
�
B�2�
E�w�w�r�{�{�	R�S�
T�U�
�b��2��7��l�a�
 �
 �"�R�!�W�*�Q�s�Q�x�Z��]�7�7�2�;�;�-F�"F�q�"H�
I�
�R�!�W�*�Q�r�T�/�!�C�!�H�*�W�W�R�[�[�0�
0�2�57�
9�9��

��G�S��b��\�#�b�1�g�+�-�d�2��7�l�:�4��Q��<�G��R�RS�W��T�UX�X�Y�	�B��G��Q�r�A�w�Y�r�A�w�&�q��a��y�0��2�	3�C�!�H�	<�W�W�R�[�[�1�=M�	M�
N�NO�PR�d�TV�WY�\^�W_�T_�`b�ce�hi�cj�`j�Tj�kn�oq�tu�ov�kv�Tv�	�R�!�W��U���a��[�U!�!#�U$�O%�%(�1�X�O.�.5�g�b�k�k�A�.>�O?�
?�@D�R�"�X�
�c�RT�WY�RZ�l�@Z�[_�`b�ef�`g�[g�@g�	�r�A�w��A��B��G�|�A$�$'��Q��K�A0�02�2��A6�7>�w�r�{�{�@C�
C�DE�c�"�r�(�l�SV�WY�\^�W_�S_�F_�	�R�"�X��G��"�q�'�k�G"�"&�r�A�w�,�G/�/3�B��G�|�G<�<?��Q��K�GH�HJ�GK�DL�LS�G�TV�K�K�Z[�L\�D]�
]�^�
�b�1�g�+�r�!�B��G�)�|�q�)�
)�2�b�1�g�:�a��a��j��m�G�G�B�K�K�6O�+O�PQ�+Q�
R�TV�WY�\]�W^�T^�_`�ac�_c�Tc�	
�3��8��G�G�B�K�K�	�U �!�#$�R�!�W�9�Q�;������";�A�b�D�"@�B�EG�
I�I�����)�c�/���)�c�/��
��7�B�r�B�x�K��B��G��+�D��a��L�8��b�1�g��E�c�"�q�'�k�Q�RT�T�U�	
�2��7��A�b�1�g�I�a��Q��i�'��)�	*�3��8�	3�G�G�B�K�K�!�4D�	D�E�EF�r�T�3�r�TV�x�<�X[�\^�ab�\c�Xc�Kc�df�gi�lm�gn�dn�Kn�	�R�!�W��L���a��[�L!�!#�L$�F%�%(�1�X�F.�.5�g�b�k�k�A�.>�F?�?�@D�R�"�X�
�d�SU�XZ�S[�m�@[�\`�ac�fg�ah�\h�@h�	
�b�1�g��A��2��7�l�A#�#%�b�1�g�:�A.�.0��e�A4�5<�W�R�[�[�@A�A��b�2�h�,�t�B��H�}�
$�T�"�r�(�]�
2�4��Q��<�
?��B��G��
K�D�QS�VW�QX�L�
X�Y\�]_�bc�]d�Yd�
d�eg�
g�	�����q�	�
�	�
��1�R�!�W�9���2�2�B�r�A�w�J�q��q��z�"�}�W�W�UW�[�[�?X�4X�YZ�4Z�[�
�R�!�W�*�Q�r�T�/�!�C�!�H�*�W�W�R�[�[�0�
0�2�45�b�1�g�I�a�K������3L�Q�r�T�3Q�S�VX�Z�Z��
��G�8�R��R��[��R�!�W��,�S��a��[�8��B��G��C�C��Q��K�O�PR�R�S�	
�2��7��A�b�1�g�I�a��Q��i�'��)�	*�3��8�	3�G�G�B�K�K�!�4D�	D�E�EF�r�T�
�b�2�h�;�r�"�q�'�z�!�"�R�!�W�*�,�R��Q��Z�7��2��7�
�B�1�D�FF�FI�A�h�FO�OV�w�WY�{�{�]^�O_�F`�`�
�S��b��\�#�b�2�h�,�
&�t�B��G�|�
3�C��Q��K�
?��B��G��
K�B�r�TU�w�J�
V�WY�
Y�	Z�
�'�"�+�+�
���B��H�}�S��b��\�1�$�r�B�x�-�?��R�!�W��L�	
�b�1�g����"�q�'�k�"�"$�R�!�W�*�-�-.�/�07�����a�0@�A�	A��r�!�B��G�)�|�q�!�!�2�b�1�g�:�a��a��j��m�G�G�B�K�K�.G�#G��#I�J�
�R�!�W�*�Q�r�T�/�!�C�!�H�*�W�W�R�[�[�0�
0�2�45�b�1�g�I�a�K������3L�Q�r�T�3Q�S�VX�Z�
Z����7�C��R��L��R�!�W��,�T�"�q�'�\�9�$�r�A�w�,�F�t�B�QR�G�|�S�TW�W�X�	�B��G��Q�r�A�w�Y�r�A�w�&�q��a��y�0��2�	3�C�!�H�	<�W�W�R�[�[�1�=M�	M�N�	
�2��r�"�r�(�{�2�b�1�g�:�%�c�"�q�'�k�1�#�b�1�g�+�=�c�"�q�'�k�I�"�L�	M�c�TU�h�	V�W^�W^�_a�Wb�Wb�ef�Wg�	g�h��r�B�x�-��B��H��
$�T�"�q�'�\�
1�%��Q��-�
?��R�!�W��
L�S�QS�VW�QX�[�
X�Y[�\^�Y^�
^�	�����
����B��H��S��b��\�1�#�b�2�h�,�>�s�2��7�{�J�4�PR�UV�PW�<�W�X\�]_�bc�]d�Xd�d�	�R�!�W������ �����q�)�*�	*�
-0��Q��K��2��7��1���8J�,J�B�r�TU�w�J�WX�Y\�_`�Ya�Wa�bd�Wd�el�el�mo�ep�ep�Wp�Lp�qr�Lr�,s�
�R�!�W�*�Q�r�T�/�!�C�!�H�*�W�W�R�[�[�0�
0�-2�45�b�1�g�I�a�K������3L�Q�r�T�3Q�-S�VX�,Z�Z��
�)���S�V�8���S�V�8�Q�q�S�>�1�Q�3�"�+����S�V�8�Q��Q����A��F�1�q�6�M�!�O�,��5�
5�a�
7�8���S�V�8�Q�q�S�A�J���!��r�{�"��	
�3�6��1�Q��V�8�Q�x�s�x��Q����A��F�1�q�6�M�!�O�(D�E�E�E�a��A��h�N�q�P�Q��q�S����1�q�6�!�8�a�!�f�Q��V�m�A�o�.�	/�	/�/�0�
�S�X�q�1�v�a�x�!�a�&��Q��-��/�*�+�+�,�,-�q��Q��x��z�N�1�q�6�,A�(�#�(�A�PQ�F�ST�H�WX�[\�W]�^_�bc�^d�Wd�ef�Wf�Kg�Bh�Bh�,h�i���V�X�S�X�q�1�v�a�x�!�a�&��Q��-��/�2�
3�
3�B��A��q�1�v�
�4F�
F�q�
H�I�J�KL�L�
M�N�	�1�v�a�x�1�o�h�c�h��A��q��1�q�6�!�a�&�=��?�;�<�<�<��C�	D���6�1�q�6�!�8��a��c�R�[� ��	�f�W�b�1�a�4��6�A�q�D��A��I�a�K�(�3�.�.�q�!�t�Q�q�S�1�H�}�<�Q�>�?��B��G��A��a��SU��V���6�1�Q�3�!�*��a��c�R�[� ��	�f�W�a�!�f�Q�h���1�q�6��!�a�&���Q��!�A�#���A�a�!�f�H�X�S�X�q�ST�v�VW�x�Z[�^_�Z`�ab�ef�ag�Zg�hi�Zi�Nj�Ek�Ek�<k�1k�)l�l���A��q��\�8�3�8�Q��V�A�X��A��q�1�v�
�a��8�9�9�!�;�<�=�>�>?�"�g�F�GH�1�v�a�x�SU�FV�W��E\�E\�E\�P
<�
<�
<�N�N�N�0�0�0�0�0�0r