def diffusivity_tensor(setup):
v0 = .001
geo, phys = setup.geo, setup.phys
r = setup.geop.rMolecule
dim = setup.phys.dim
cyl = setup.phys.cyl
if geo.mesh.num_cells() < setup.solverp.Nmax:
pugh.prerefine(setup, True)
iterative = False
if dim == 3 and geo.mesh.num_cells() > 2e5:
#pnps.SimpleStokesProblem.method["lusolver"] = "superlu"
pnps.SimpleStokesProblem.method["kparams"]["maximum_iterations"] = 5000
iterative = True #False
else:
iterative = False
U0 = dolfin.Constant(tuple(0. for i in range(dim)))
W = pnps.SimpleStokesProblem.space(geo.mesh)
bcs = [
geo.BC(W.sub(0), U0, "dnab"),
geo.BC(W.sub(0), U0, "memb"),
geo.BC(W.sub(0), U0, "sideb"),
geo.BC(W.sub(1), dolfin.Constant(0.0), "upperb")
]
if setup.physp.bulkbc:
bcs.append(geo.BC(W.sub(0), U0, "bulk"))
gamma = np.zeros((dim, dim))
for i0 in range(dim):
U1 = dolfin.Constant(tuple(
(v0 if i == i0 else 0.) for i in range(dim)))
bcmol = [geo.BC(W.sub(0), U1, "moleculeb")]
stokes = nano.solve_pde(pnps.SimpleStokesProblem,
geo=geo,
cyl=cyl,
phys=phys,
iterative=iterative,
bcs=bcs + bcmol)
F = stokes.evaluate(phys.Fdrag)["Fdrag"]
gamma[:, i0] = abs(np.array(F) / v0)
#dolfin.plot(stokes.solutions()[0])
#dolfin.plot(stokes.solutions()[1])
pi = phys.pi
eta = phys.eta
kT = phys.kT
gamma0 = 6. * pi * eta * r * 1e-9
print "gamma (simulation):\n", gamma
print "gamma (stokes law):", gamma0
print
D = kT * np.linalg.inv(gamma)
D0 = kT / gamma0
print "D (simulation):\n", D
print "D (stokes law):", D0
print "Reducing factor due to confinement:\n", D / D0
return D / D0
def diffusivity(setup):
v0 = .001
geo, phys = setup.geo, setup.phys
r = setup.geop.rMolecule
dim = setup.phys.dim
cyl = setup.phys.cyl
if geo.mesh.num_cells() < setup.solverp.Nmax:
pugh.prerefine(setup, True)
if dim == 3:
pnps.SimpleStokesProblem.method["kparams"]["maximum_iterations"] = 5000
iterative = True
else:
iterative = False
U0 = dolfin.Constant(tuple(0. for i in range(dim)))
U1 = dolfin.Constant(
tuple((v0 if i == dim - 1 else 0.) for i in range(dim)))
W = pnps.SimpleStokesProblem.space(geo.mesh)
bcs = [
geo.BC(W.sub(0), U0, "dnab"),
geo.BC(W.sub(0), U0, "memb"),
geo.BC(W.sub(0), U0, "sideb"),
geo.BC(W.sub(0), U1, "moleculeb"),
geo.BC(W.sub(1), dolfin.Constant(0.0), "upperb")
]
if setup.physp.bulkbc:
bcs.append(geo.BC(W.sub(0), U0, "bulk"))
stokes = nano.solve_pde(pnps.SimpleStokesProblem,
geo=geo,
cyl=cyl,
phys=phys,
iterative=iterative,
bcs=bcs)
F = stokes.evaluate(phys.Fdrag)["Fdrag"]
print F
pi = phys.pi
eta = phys.eta
kT = phys.kT
gamma = abs(F[dim - 1] / v0)
gamma0 = 6. * pi * eta * r * 1e-9
print "gamma (simulation):", gamma
print "gamma (stokes law):", gamma0
print
D = kT / gamma
D0 = kT / gamma0
print "D (simulation):", D
print "D (stokes law):", D0
print "Reducing factor due to confinement:", D / D0
return D / D0
VVV = dolfin.TensorFunctionSpace(meshp, "CG", 1, shape=(dim, dim))
D = dolfin.Function(VVV)
v2d = dolfin.vertex_to_dof_map(VVV)
Dv = D.vector()
for k, (i, j) in enumerate(product(i3, i3)):
Dv[np.ascontiguousarray(v2d[k::dim**2])] = np.ascontiguousarray(Da[:,
i,
j])
setup.phys.update(Dp=D, Dm=D)
#embed()
return D
# set up domain with protein
ddata = dict(name="Dpugh", r=0.11, dim=2)
setup = pugh.Setup(x0=[0., 0., 10.],
dim=2,
h=1.,
Nmax=1e5,
diamPore=6. * np.sqrt(np.pi) / 2.,
cheapest=True,
diffusivity_data=ddata)
plotter = pugh.Plotter(setup)
pugh.prerefine(setup, True)
print "getting D"
D = set_D_with_protein(setup)
print "plotting"
plotter.plot(D[0, 0], title="Dxx")
dolfin.interactive()
def prerefine(self, visualize=False):
return prerefine(self, visualize=visualize)
fz = interp1d(z, Dz)
fn = interp1d(x, Dn)
ft = interp1d(x, Dt)
import matplotlib.pyplot as plt
plt.plot(z, fz(z), "s-")
plt.figure()
plt.plot(x, fn(x), "s-")
plt.plot(x, ft(x), "s-")
# get geometry, prerefine mesh, compute distance function
setup = pugh.Setup(dim=params.dim,
x0=None,
h=params.h,
Nmax=params.Nmax,
cheapest=True)
pugh.prerefine(setup, visualize=True)
dist = distance_boundary_from_geo(setup.geo)
VV = dolfin.VectorFunctionSpace(setup.geo.mesh, "CG", 1)
normal = dolfin.project(dolfin.grad(dist), VV)
plotter = pugh.Plotter(setup)
plotter.plot_vector(normal, "normal")
#functions, mesh = f.get_functions("pugh_distance", h=h)
#dist = functions["y"]
def transformation(n, Dn, Dt):
D = np.diag([Dn, Dt, Dt]) if len(n) == 3 else np.diag([Dn, Dt])
U, S, V = np.linalg.svd(np.matrix(n))
# U, S = 1., |n|
# V = orthogonal coordinate basis with n/|n| as first vector