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Commit d0adf500 by Jigyasa Watwani
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rewritten with only stress and density, substituted velocity in terms of stress

parent 588ce712
Inline Side-by-side
Showing with 96 additions and 152 deletions
basic_model_only_density/tissue_maxwell.py
import numpy as np zimport numpy as np
import dolfin as df import dolfin as df
import progressbar import progressbar
import os import os
...@@ -25,114 +25,69 @@ class Tissue(object): ...@@ -25,114 +25,69 @@ class Tissue(object):
scalar_element = df.FiniteElement('P', self.mesh.ufl_cell(), 1) scalar_element = df.FiniteElement('P', self.mesh.ufl_cell(), 1)
# v, rho, stress # stress, rho
mixed_element = df.MixedElement([scalar_element, mixed_element = df.MixedElement([scalar_element, scalar_element])
scalar_element,
scalar_element])
# define function space with this mixed element # define function space with this mixed element
self.function_space = df.FunctionSpace(self.mesh, mixed_element)
if self.zero_rho_boundary: self.function_space = df.FunctionSpace(self.mesh, mixed_element)
self.rho_boundary = 0.0
else:
self.rho_boundary = self.average_rho
self.bc = df.DirichletBC(self.function_space.sub(1), bc1 = df.DirichletBC(self.function_space.sub(0), df.Constant(0.0), 'on_boundary')
df.Constant(self.rho_boundary), bc2 = df.DirichletBC(self.function_space.sub(1), df.Constant(0.0), 'on_boundary')
'on_boundary') self.bc = ([bc1, bc2])
self.function0 = df.Function(self.function_space) self.function0 = df.Function(self.function_space)
self.function = df.Function(self.function_space) self.function = df.Function(self.function_space)
def active_stress(self, rho):
if self.active_death:
return (-self.lamda * rho * (rho - self.active_stress_setpoint)/(rho + self.saturation_rho)
)
else:
return (-self.lamda * rho /(rho + self.saturation_rho)
)
def fluid_stress(self, v):
return self.viscosity * v.dx(0)
def diffusion_reaction_rho(self, rho, trho):
return (self.diffusion_rho * df.inner(rho.dx(0), trho.dx(0))
- self.turnover_rho * df.inner(rho * (1 - rho/self.average_rho),
trho)
)
def setup_initial_conditions(self): def setup_initial_conditions(self):
# ic for rho # ic for stress
if self.zero_rho_boundary: stress0 = df.interpolate(df.Expression(
base_rho = 0.0 'cos(PI*x[0]/L)*cos(PI*x[0]/L)',
else: L=self.system_size,
base_rho = self.average_rho PI=np.pi, degree=1),
self.function_space.sub(0).collapse())
rho0 = df.interpolate(df.Expression( rho0 = df.interpolate(df.Expression(
'base_rho + cos(PI*x[0]/L)*cos(PI*x[0]/L)', 'cos(PI*x[0]/L)*cos(PI*x[0]/L)',
L=self.system_size, L=self.system_size,
base_rho=base_rho, PI=np.pi, degree=1),
degree=1, PI=np.pi), self.function_space.sub(1).collapse()
self.function_space.sub(1).collapse()) )
df.assign(self.function0, [stress0, rho0])
# ic for stress
stress0 = df.Constant(0.0)
stress0 = df.interpolate(stress0, self.function_space.sub(2).collapse())
# add noise
noise_rho = (self.noise_level
* (2 * np.random.random(rho0.vector().size()) - 1))
noise_stress = (self.noise_level
* (2 * np.random.random(stress0.vector().size()) - 1))
rho0.vector()[:] = rho0.vector()[:] + noise_rho
stress0.vector()[:] = stress0.vector()[:] + noise_stress
# find velocity
VFS = self.function_space.sub(0).collapse()
v0 = df.Function(VFS)
tv0 = df.TestFunction(VFS)
v0form = (self.friction * df.inner(v0, tv0)
+ df.inner(stress0, tv0.dx(0))
) * df.dx
df.solve(v0form == 0, v0) def active_stress(self, rho):
df.assign(self.function0, [v0, rho0, stress0]) return -self.lamda * rho/(rho + self.saturation_rho)
def setup_weak_forms(self): def setup_weak_forms(self):
v0, rho0, stress0 = df.split(self.function0) stress0, rho0 = df.split(self.function0)
v, rho, stress = df.split(self.function) stress, rho = df.split(self.function)
tv, trho, tstress = df.TestFunctions(self.function_space)
tstress, trho = df.TestFunctions(self.function_space)
vform = (self.friction * df.inner(v, tv)
+ df.inner(stress, tv.dx(0)) stressform = ( df.inner(stress - self.active_stress(rho), tstress)
+ (self.viscosity/self.elasticity) *
df.inner((1/self.timestep) * (stress - stress0 - self.active_stress(rho) + self.active_stress(rho0)), tstress)
+ (self.viscosity/(self.elasticity*self.friction)) *
df.inner(stress0.dx(0) * (stress0.dx(0) - self.active_stress(rho0).dx(0)), tstress)
+ (self.viscosity/self.friction) *
df.inner(stress.dx(0), tstress.dx(0))
) )
rhoform = (df.inner((rho - rho0)/self.timestep, trho) rhoform = (df.inner((rho - rho0)/self.timestep, trho)
+ df.inner((v0 * rho0).dx(0), trho) + (1/self.friction) * df.inner((rho0 * stress0.dx(0)).dx(0), trho)
+ self.diffusion_reaction_rho(rho, trho) + self.diffusion_rho * df.inner(rho.dx(0), trho.dx(0))
) - self.turnover_rho * df.inner(rho * (1 - rho/self.average_rho), trho)
stressform = ( (self.viscosity/self.elasticity) *
( df.inner((stress - self.active_stress(rho)- stress0 + self.active_stress(rho0))/self.timestep, tstress)
+ df.inner(v0 * (stress0 - self.active_stress(rho0)).dx(0), tstress)
)
+ df.inner(stress - self.active_stress(rho), tstress)
- df.inner(self.fluid_stress(v), tstress)
) )
self.form = (vform + rhoform + stressform) * df.dx self.form = (stressform + rhoform)*df.dx
def solve(self, DIR=''): def solve(self, DIR=''):
self.vFile = df.XDMFFile(os.path.join(DIR,
'%s_velocity.xdmf' % self.timestamp))
self.rhoFile = df.XDMFFile(os.path.join(DIR,
'%s_density.xdmf' % self.timestamp))
self.stressFile = df.XDMFFile(os.path.join(DIR, self.stressFile = df.XDMFFile(os.path.join(DIR,
'%s_stress.xdmf' % self.timestamp)) '%s_stress.xdmf' % self.timestamp))
self.rhoFile = df.XDMFFile(os.path.join(DIR,
'%s_density.xdmf' % self.timestamp))
self.setup_initial_conditions() self.setup_initial_conditions()
...@@ -142,31 +97,26 @@ class Tissue(object): ...@@ -142,31 +97,26 @@ class Tissue(object):
self.time = 0.0 self.time = 0.0
savesteps = int(self.savetime/self.timestep) savesteps = int(self.savetime/self.timestep)
maxsteps = int(self.maxtime/self.timestep) maxsteps = int(self.maxtime/self.timestep)
v, rho, stress = self.function0.split(deepcopy=True) stress, rho = self.function0.split(deepcopy=True)
self.vFile.write_checkpoint(v, 'velocity', self.time)
self.rhoFile.write_checkpoint(rho, 'density', self.time)
self.stressFile.write_checkpoint(stress, 'stress', self.time) self.stressFile.write_checkpoint(stress, 'stress', self.time)
self.rhoFile.write_checkpoint(rho, 'density', self.time)
for steps in progressbar.progressbar(range(1, maxsteps + 1)): for steps in progressbar.progressbar(range(1, maxsteps + 1)):
df.solve(self.form == 0, self.function, self.bc) df.solve(self.form == 0, self.function, self.bc)
self.function0.assign(self.function) self.function0.assign(self.function)
self.time += self.timestep self.time += self.timestep
v, rho, stress = self.function0.split(deepcopy=True) stress, rho = self.function0.split(deepcopy=True)
if steps % savesteps == 0: if steps % savesteps == 0:
self.vFile.write_checkpoint(v, 'velocity', self.stressFile.write_checkpoint(stress, 'stress',
self.time, append=True) self.time, append=True)
self.rhoFile.write_checkpoint(rho, 'density', self.rhoFile.write_checkpoint(rho, 'density',
self.time, append=True) self.time, append=True)
self.stressFile.write_checkpoint(stress, 'stress',
self.time, append=True)
# move mesh # move mesh
dr = df.project(v * self.timestep, self.function_space.sub(0).collapse()) dr = df.project((1/self.friction)*(stress.dx(0)) * self.timestep, self.function_space.sub(0).collapse())
df.ALE.move(self.mesh, dr) df.ALE.move(self.mesh, dr)
self.vFile.close()
self.rhoFile.close()
self.stressFile.close() self.stressFile.close()
self.rhoFile.close()
if __name__ == '__main__': if __name__ == '__main__':
import json, datetime import json, datetime
......
basic_model_only_density/viz_tissue_maxwell.py
...@@ -30,12 +30,9 @@ def visualize(params, DIR=''): ...@@ -30,12 +30,9 @@ def visualize(params, DIR=''):
params['system_size']/2) params['system_size']/2)
# Read data # Read data
v = np.zeros((len(times), mesh.num_vertices()))
rho = np.zeros((len(times), mesh.num_vertices())) rho = np.zeros((len(times), mesh.num_vertices()))
stress = np.zeros_like(v) stress = np.zeros_like(rho)
vFile = df.XDMFFile(os.path.join(DIR,
'%s_velocity.xdmf' % params['timestamp']))
rhoFile = df.XDMFFile(os.path.join(DIR, rhoFile = df.XDMFFile(os.path.join(DIR,
'%s_density.xdmf' % params['timestamp'])) '%s_density.xdmf' % params['timestamp']))
stressFile = df.XDMFFile(os.path.join(DIR, stressFile = df.XDMFFile(os.path.join(DIR,
...@@ -47,17 +44,14 @@ def visualize(params, DIR=''): ...@@ -47,17 +44,14 @@ def visualize(params, DIR=''):
for steps in progressbar.progressbar(range(savesteps+1)): for steps in progressbar.progressbar(range(savesteps+1)):
mesh.coordinates()[:] = geometry[steps] mesh.coordinates()[:] = geometry[steps]
SFS = df.FunctionSpace(mesh, 'P', 1) SFS = df.FunctionSpace(mesh, 'P', 1)
vi, rhoi, stressi = df.Function(SFS), df.Function(SFS), df.Function(SFS) rhoi, stressi = df.Function(SFS), df.Function(SFS)
vFile.read_checkpoint(vi, 'velocity', steps)
rhoFile.read_checkpoint(rhoi, 'density', steps) rhoFile.read_checkpoint(rhoi, 'density', steps)
stressFile.read_checkpoint(stressi, 'stress', steps) stressFile.read_checkpoint(stressi, 'stress', steps)
v[steps] = vi.compute_vertex_values(mesh)
rho[steps] = rhoi.compute_vertex_values(mesh) rho[steps] = rhoi.compute_vertex_values(mesh)
stress[steps] = stressi.compute_vertex_values(mesh) stress[steps] = stressi.compute_vertex_values(mesh)
vFile.close()
rhoFile.close() rhoFile.close()
stressFile.close() stressFile.close()
...@@ -68,19 +62,19 @@ def visualize(params, DIR=''): ...@@ -68,19 +62,19 @@ def visualize(params, DIR=''):
fig, axes = plt.subplots(2, 1, sharex=True, figsize=(8,8)) fig, axes = plt.subplots(2, 1, sharex=True, figsize=(8,8))
axes[-1].set_xlabel(r'$x$') axes[-1].set_xlabel(r'$x$')
axes[0].set_ylabel(r'$\rho/\rho_0$') axes[0].set_ylabel(r'$\rho/\rho_0$')
axes[1].set_ylabel(r'$v/v_0$') axes[1].set_ylabel('stress')
axes[0].set_xlim(np.min(geometry), np.max(geometry)) axes[0].set_xlim(np.min(geometry), np.max(geometry))
axes[0].set_ylim(0, np.max(rho)+0.05) axes[0].set_ylim(0, np.max(rho)+0.05)
axes[1].set_ylim(np.min(v)-0.05, np.max(v)+0.05) axes[1].set_ylim(np.min(stress)-0.05, np.max(stress)+0.05)
rhoplot, = axes[0].plot(geometry[0], rho[0], 'g-', ms=3) rhoplot, = axes[0].plot(geometry[0], rho[0], 'g-', ms=3)
velplot, = axes[1].plot(geometry[0], v[0], 'r-', ms=3) velplot, = axes[1].plot(geometry[0], stress[0], 'r-', ms=3)
def update(value): def update(value):
ti = np.abs(times - value).argmin() ti = np.abs(times - value).argmin()
rhoplot.set_ydata(rho[ti]) rhoplot.set_ydata(rho[ti])
rhoplot.set_xdata(geometry[ti]) rhoplot.set_xdata(geometry[ti])
velplot.set_ydata(v[ti]) velplot.set_ydata(stress[ti])
velplot.set_xdata(geometry[ti]) velplot.set_xdata(geometry[ti])
plt.draw() plt.draw()
...@@ -91,23 +85,23 @@ def visualize(params, DIR=''): ...@@ -91,23 +85,23 @@ def visualize(params, DIR=''):
slider.drawon = False slider.drawon = False
slider.on_changed(update) slider.on_changed(update)
# plt.show() plt.show()
print('Saving movie-...') # print('Saving movie-...')
FPS = 100 # FPS = 100
movFile = os.path.join(DIR, '%s_fields.mov' % params['timestamp']) # movFile = os.path.join(DIR, '%s_fields.mov' % params['timestamp'])
fps = float(FPS) # fps = float(FPS)
command = "ffmpeg -y -r" # command = "ffmpeg -y -r"
options = "-b:v 3600k -qscale:v 4 -vcodec mpeg4" # options = "-b:v 3600k -qscale:v 4 -vcodec mpeg4"
tmp_dir = TemporaryDirectory() # tmp_dir = TemporaryDirectory()
get_filename = lambda x: os.path.join(tmp_dir.name, x) # get_filename = lambda x: os.path.join(tmp_dir.name, x)
for tt in progressbar.progressbar(range(len(times))): # for tt in progressbar.progressbar(range(len(times))):
slider.set_val(times[tt]) # slider.set_val(times[tt])
fr = get_filename("%03d.png" % tt) # fr = get_filename("%03d.png" % tt)
fig.savefig(fr, facecolor=fig.get_facecolor(), dpi=100) # fig.savefig(fr, facecolor=fig.get_facecolor(), dpi=100)
os.system(command + " " + str(fps) # os.system(command + " " + str(fps)
+ " -i " + tmp_dir.name + os.sep # + " -i " + tmp_dir.name + os.sep
+ "%03d.png " + options + " " + movFile) # + "%03d.png " + options + " " + movFile)
tmp_dir.cleanup() # tmp_dir.cleanup()
# plotting the stresses # plotting the stresses
active_stress = -params['lamda'] * rho/(rho + params['saturation_rho']) active_stress = -params['lamda'] * rho/(rho + params['saturation_rho'])
...@@ -139,39 +133,39 @@ def visualize(params, DIR=''): ...@@ -139,39 +133,39 @@ def visualize(params, DIR=''):
fc='#999999') fc='#999999')
slider.drawon = False slider.drawon = False
slider.on_changed(update_2) slider.on_changed(update_2)
# plt.show() plt.show()
# make movie # make movie
print('Saving movie-...') # print('Saving movie-...')
FPS = 50 # FPS = 50
movFile = os.path.join(DIR, '%s_stresses.mov' % params['timestamp']) # movFile = os.path.join(DIR, '%s_stresses.mov' % params['timestamp'])
fps = float(FPS) # fps = float(FPS)
command = "ffmpeg -y -r" # command = "ffmpeg -y -r"
options = "-b:v 3600k -qscale:v 4 -vcodec mpeg4" # options = "-b:v 3600k -qscale:v 4 -vcodec mpeg4"
tmp_dir = TemporaryDirectory() # tmp_dir = TemporaryDirectory()
get_filename = lambda x: os.path.join(tmp_dir.name, x) # get_filename = lambda x: os.path.join(tmp_dir.name, x)
for tt in progressbar.progressbar(range(len(times))): # for tt in progressbar.progressbar(range(len(times))):
slider.set_val(times[tt]) # slider.set_val(times[tt])
fr = get_filename("%03d.png" % tt) # fr = get_filename("%03d.png" % tt)
fig1.savefig(fr, facecolor=fig1.get_facecolor(), dpi=100) # fig1.savefig(fr, facecolor=fig1.get_facecolor(), dpi=100)
os.system(command + " " + str(fps) # os.system(command + " " + str(fps)
+ " -i " + tmp_dir.name + os.sep # + " -i " + tmp_dir.name + os.sep
+ "%03d.png " + options + " " + movFile) # + "%03d.png " + options + " " + movFile)
tmp_dir.cleanup() # tmp_dir.cleanup()
# L(t) vs t # L(t) vs t
length = geometry[:,-1,0]-geometry[:,0,0] # length = geometry[:,-1,0]-geometry[:,0,0]
fig2, ax2 = plt.subplots(1, 1, figsize=(8, 8)) # fig2, ax2 = plt.subplots(1, 1, figsize=(8, 8))
ax2.set_xlabel('$t$') # ax2.set_xlabel('$t$')
ax2.set_ylabel('$L(t)$') # ax2.set_ylabel('$L(t)$')
ax2.set_xlim(np.min(times), np.max(times)) # ax2.set_xlim(np.min(times), np.max(times))
ax2.set_ylim(np.min(length)-0.05, np.max(length)+0.05) # ax2.set_ylim(np.min(length)-0.05, np.max(length)+0.05)
ax2.plot(times, length) # ax2.plot(times, length)
plt.savefig("%s.png" %params['timestamp']) # plt.savefig("%s.png" %params['timestamp'])
# plt.show() # # plt.show()
np.save('%s_length.npy' %params['timestamp'], length) # np.save('%s_length.npy' %params['timestamp'], length)
print(length[-1]) # print(length[-1])
print(length[-1]-length[-3]) # print(length[-1]-length[-3])
# fig3, ax3 = plt.subplots(1, 1, figsize=(8, 8)) # fig3, ax3 = plt.subplots(1, 1, figsize=(8, 8))
# ax3.set_xlabel('$\log t$') # ax3.set_xlabel('$\log t$')
......
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