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Commit 2982497b by Jigyasa Watwani
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added boundary condition and more active stress flags

parent e152c6f8
Inline Side-by-side
Showing with 71 additions and 33 deletions
growing_domain/full_model/growing_domain.py
......@@ -47,7 +47,12 @@ class Growing_Domain(object):
self.function_space = df.FunctionSpace(self.mesh, mixed_element)
# dirichlet boundaries for rho
if self.dirichlet_boundary_rho:
if self.zero_rho_boundary:
self.bc = df.DirichletBC(self.function_space.sub(2), df.Constant(0.0), 'on_boundary')
elif self.rho0_boundary:
self.bc = df.DirichletBC(self.function_space.sub(2), df.Constant(self.average_rho), 'on_boundary')
# define the reqd functions on this function space
self.f = df.Function(self.function_space) # f at current time
......@@ -57,22 +62,21 @@ class Growing_Domain(object):
return df.inner(df.div(vel * conc), tconc)
def active_stress(self, rho, c, v):
if self.morphogen_mediated_active_stress:
return self.lamda * rho/(rho + self.saturation_rho) * (c-self.average_c) * df.Identity(self.dimension)
if self.rho_t_dependent_active_stress:
if self.density_dependent_turnover_rho:
rho_t_dependence = (self.diffusion_rho*df.div(df.nabla_grad(rho))
- self.turnover_rho * rho * (rho - self.average_rho)
- df.div(rho * v))
else:
rho_t_dependence = (self.diffusion_rho*df.div(df.nabla_grad(rho))
- self.turnover_rho * (rho - self.average_rho)
- df.div(rho * v))
return self.lamda * rho_t_dependence/(rho + self.saturation_rho) * df.Identity(self.dimension)
else:
if self.saturating_density_active_stress:
return self.lamda * rho/(rho + self.saturation_rho)* df.Identity(self.dimension)
elif self.difference_in_morphogen_active_stress:
return self.lamda * (c-self.average_c) * df.Identity(self.dimension)
elif self.difference_in_density_active_stress:
return self.lamda * (c-self.average_rho) * df.Identity(self.dimension)
elif self.saturating_density_and_difference_in_density_active_stress:
return self.lamda * (rho*(rho-self.average_rho))/(rho + self.saturation_rho) * df.Identity(self.dimension)
elif self.saturating_density_and_difference_in_morphogen_active_stress:
return self.lamda * (rho*(c-self.average_c))/(rho + self.saturation_rho) * df.Identity(self.dimension)
def epsilon(self, v):
return df.sym(df.nabla_grad(v))
......@@ -92,22 +96,29 @@ class Growing_Domain(object):
def stress(self, u, v, rho, c):
return (self.passive_stress(u, v) + self.active_stress(rho, c, v))
def reaction_rho(self, rho, trho):
def reaction_rho(self, rho, trho, c):
if self.morphogen_mediated_turnover_rho:
return self.average_c * df.inner(rho - self.average_rho, trho)
return self.turnover_rho * df.inner((c - self.average_c/2)*(rho - self.average_rho), trho)
elif self.morphogen_mediated_average_rho:
return self.turnover_rho * df.inner(rho - self.average_c, trho)
elif self.density_dependent_turnover_rho: # to model that cells are born or die only where the density is non-zero
return self.turnover_rho * df.inner(rho * (rho - self.average_rho), trho)
elif self.density_dependent_turnover_rho:
# to model that cells are born or die only where the density is non-zero
# tanh approximation: Theta = 1+ tanh = 1 + rho - rho^3/3! + . . .
return self.turnover_rho * df.inner((1 + rho) * (rho - self.average_rho), trho)
else:
return self.turnover_rho * df.inner(rho - self.average_rho, trho)
def reaction_c(self, c, tc):
return self.turnover_c * df.inner(c - self.average_c, tc)
def diffusion_reaction_rho(self, rho, trho):
def diffusion_reaction_rho(self, rho, trho, c):
return (self.diffusion_rho * df.inner(df.nabla_grad(rho), df.nabla_grad(trho))
+ self.reaction_rho(rho, trho))
+ self.reaction_rho(rho, trho, c))
def diffusion_reaction_c(self, c, tc):
return (self.diffusion_c * df.inner(df.nabla_grad(c), df.nabla_grad(tc))
......@@ -125,14 +136,23 @@ class Growing_Domain(object):
u0.vector()[:] = u0.vector()[:] + noise_u
# ic for rho
r2 = "+".join(['x['+str(i)+']*x['+str(i)+']' for i in range(self.dimension)])
if self.dimension==1:
rho0='1-cos(2*pi*x[0]/R)'
else:
# for rho=rho_0 boundary condition
# rho0 = "%s" % str(self.average_rho)
# rho0 = '(a/2)*(1 + tanh((sqrt(%s) - r0)/w))' %r2
# grad rho=0 boundary condition
rho0 = '1 + 0.1 * a * cos(2.0*pi*%s/R)' %r2
# rho = 0 boundary condition
# circular domain --> circular domain
rho0 = '(a/2)*(1-tanh((sqrt(%s) - r0)/w))' %r2
# rho0 = '(a/2)*(1 - tanh((sqrt(%s) - r0)/w))' %r2
# rho0 = 'a*(1-tanh((sqrt(%s) - r0)/w))' %r2 # grows to a different size
# circular domain --> elliptical domain (w=0.19, lambda = -10, k=1)
......@@ -144,13 +164,14 @@ class Growing_Domain(object):
# circular --> kidney (w=0.8, r0=0.5, k=0.1, lambda=-30)
# rho0 = 'x[0]*(1-tanh((sqrt(%s) - r0)/w))' %r2
rho0 = df.interpolate(df.Expression(rho0, pi=np.pi, R=self.system_size, a=self.average_rho, r0=0.5, w=0.3, degree=1), self.function_space.sub(2).collapse())
rho0 = df.interpolate(df.Expression(rho0, pi=np.pi, R=self.system_size, a=self.average_rho, r0=0.5, w=0.19, degree=1), self.function_space.sub(2).collapse())
# add noise
noise_rho = self.noise_level * (2 * np.random.random(rho0.vector().size()) - 1)
rho0.vector()[:] = rho0.vector()[:] + noise_rho
# ic for c
if self.morphogen:
# c0 = "%s" % str(5.0)
# c0 = '1 + 0.1*a*cos(2.0*pi*sqrt(%s)/R)' %r2 # shrinks and stops
c0 = '1 + 0.1*a*cos(2.0*pi*%s/R)' %r2 # grows and stops
# c0 = '1 + 0.1*a*cos(2.0*pi*x[0]/R)' # grows very slightly, shrinks even more slightly, changes shape
......@@ -195,7 +216,7 @@ class Growing_Domain(object):
rhoform = (df.inner((rho - rho0)/self.timestep, trho)
+ self.advection(rho0, v0, trho)
+ self.diffusion_reaction_rho(rho, trho)
+ self.diffusion_reaction_rho(rho, trho, c)
)
if self.morphogen:
......@@ -236,7 +257,12 @@ class Growing_Domain(object):
for steps in progressbar.progressbar(range(1, maxsteps + 1)):
# solve
if self.dirichlet_boundary_rho:
df.solve(self.form == 0, self.f, self.bc)
elif self.neumann_boundary_rho:
if self.zero_grad_rho_boundary:
df.solve(self.form==0, self.f)
# update
self.f0.assign(self.f)
if self.morphogen:
......@@ -257,6 +283,7 @@ class Growing_Domain(object):
df.ALE.move(self.mesh, dr)
# update time
self.time += self.timestep
self.uFile.close()
self.vFile.close()
self.rhoFile.close() # def save_data_uvrho(self):
......
growing_domain/full_model/parameters.json
......@@ -5,32 +5,42 @@
"resolution" : 100,
"system_size" : 1,
"meshfile" : "disk.xml.gz",
"morphogen_mediated_active_stress": false,
"rho_t_dependent_active_stress" : true,
"dirichlet_boundary_rho": false,
"zero_rho_boundary":false,
"rho0_boundary": false,
"neumann_boundary_rho": true,
"zero_grad_rho_boundary": true,
"difference_in_density_active_stress": false,
"difference_in_morphogen_active_stress": false,
"saturating_density_active_stress": true,
"saturating_density_and_difference_in_morphogen_active_stress": false,
"saturating_density_and_difference_in_density_active_stress":false,
"morphogen_mediated_turnover_rho": false,
"density_dependent_turnover_rho": true,
"morphogen_mediated_average_rho": false,
"bulk_elasticity" : 1.0,
"shear_elasticity": 1.0,
"shear_viscosity" : 1.0,
"bulk_viscosity" : 1.0,
"friction" : 1.0,
"lamda": -0.1,
"lamda": -1.0,
"diffusion_rho" : 1.0,
"morphogen_mediated_turnover_rho": false,
"density_dependent_turnover_rho": false,
"morphogen_mediated_average_rho": false,
"turnover_rho" : 1.0,
"average_rho" : 1.0,
"saturation_rho" : 1.0,
"diffusion_c" : 1.0,
"turnover_c" : 1.0,
"average_c" : 1.0,
"noise_level": 0.0,
"timestep" : 0.1,
"savetime": 0.2,
"maxtime" : 40
"maxtime" : 100.0
}
\ No newline at end of file
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