psi_, mu_, nu_, nuhat_ = df.split(u_)
psi_1, mu_1, nu_1, nuhat_1 = df.split(u_1)
# Create intial conditions
if parameters["restart_folder"] is None:
u_init = CircularStripedIC(u_, degree=1)
# u_init = RandomIC(u_, degree=1)
# u_init = AroundStripedIC(u_, degree=1)
# u_init = AlongStripedIC(u_, degree=1)
# u_init = MMSIC(u_, geo_map, degree=1)
u_1.interpolate(u_init)
u_.assign(u_1)
else:
load_checkpoint(parameters["restart_folder"], u_, u_1)
w = QuarticPotential()
# Define the functional form of the reduced temperature (if
# non-uniforum temperature desired)
tau_h = 3 # High temperature (parameter)
rh = 4*R/5 # Radius where temperature shifts
k = 1/100 # Temperature shift rate
taufunction = df.Expression(
'tau + (tauh-tau)/(1 + exp(-k*(x[0]*x[0]+x[1]*x[1]-rh*rh ) ) )',
k=k, tau=tau, tauh=tau_h, rh=rh, degree=2)
# Choose between uniform (tau) or non-uniform (taufunction) reduced
# temperature:
dw_lin = w.derivative_linearized(psi, psi_1, taufunction)
# dw_lin = w.derivative_linearized(psi, psi_1, tau)
# Create intial conditions
if parameters["restart_folder"] is None:
init_mode = parameters["init_mode"]
if init_mode == "random":
u_init = RandomIC(u_, amplitude=1e-1, degree=1)
elif init_mode == "striped":
u_init = StripedIC(u_, alpha=parameters["alpha"]*np.pi/180.0, degree=1)
else:
exit("No init_mode set.")
u_1.interpolate(u_init)
u_.assign(u_1)
else:
load_checkpoint(parameters["restart_folder"], u_, u_1)
w = QuarticPotential()
#dw_lin = w.derivative_linearized(psi, psi_1, tau)
dw_stab = w.derivative_stab(psi_, psi_1, tau)
# Define some UFL indices:
i, j, k, l = ufl.Index(), ufl.Index(), ufl.Index(), ufl.Index()
# Brazovskii-Swift (conserved PFC with dc/dt = grad^2 delta F/delta c)
m_NL = F_psi_NL = (1 + geo_map.K * h**2/12) * dw_stab * xi
m_0 = (4 * nu_ * xi
- 4 * geo_map.gab[i, j]*nu_.dx(i)*xi.dx(j))
m_2 = (2 * (geo_map.H * nuhat_ - geo_map.K*nu_)*xi
- 4 * geo_map.Kab[i, j]*nuhat_.dx(i)*xi.dx(j)
+ 5 * geo_map.K * geo_map.gab[i, j]*nu_.dx(i)*xi.dx(j)
- 2 * geo_map.H * (geo_map.gab[i, j]*nuhat_.dx(i)*xi.dx(j)
if parameters["restart_folder"] is None:
init_mode = parameters["init_mode"]
if init_mode == "random":
u_init = RandomIC(u_, amplitude=1e-1, degree=1)
elif init_mode == "striped":
u_init = StripedIC(u_,
alpha=parameters["alpha"] * np.pi / 180.0,
degree=1)
else:
exit("No init_mode set.")
u_1.interpolate(u_init)
u_.assign(u_1)
else:
load_checkpoint(parameters["restart_folder"], u_, u_1)
w = QuarticPotential()
# Define the functional form of the reduced temperature (if non-uniforum temperature desired)
tau_h = 3 # High temperature (parameter)
rh = 4 * R / 5 # Radius where temperature shifts
k = 1 / 100 # Temperature shift rate
#taufunction = df.Expression('tau + (tauh-tau)/(1 + exp(-k*(x[0]*x[0]+x[1]*x[1]-rh*rh ) ) )', k=k, tau=tau, tauh=tau_h, rh=rh, degree=2)
taufunction = tau
# Choose between uniform (tau) or non-uniform (taufunction) reduced temperature:
dw_lin = w.derivative_linearized(psi, psi_1, taufunction)
#dw_lin = w.derivative_linearized(psi, psi_1, tau)
#dw_lin = w.derivative_linearized(psi, psi_1, tau)
dw_stab = w.derivative_stab(psi_, psi_1, taufunction)