def diffusivity_field_simple(setup, r, ddata_bulk, boundary="poresolidb"):
"interpolates diffusivity field defined on the geometry given by setup"
# build 1D interpolations from data
fn, ft = preprocess_Dr(ddata_bulk, r)
setup.prerefine(visualize=True)
dist = distance_boundary_from_geo(setup.geo, boundary)
VV = dolfin.VectorFunctionSpace(setup.geo.mesh, "CG", 1)
normal = dolfin.project(dolfin.grad(dist), VV)
phys = setup.phys
D0 = phys.kT / (6. * np.pi * phys.eta * r * 1e-9)
def DBulk(x, i):
r = dist(x)
n = normal(x)
Dn = D0 * float(fn(r))
Dt = D0 * float(ft(r))
D = transformation(n, Dn, Dt)
return D[i][i]
D = lambda i: dict(fluid=lambda x: DBulk(x, i), )
dim = setup.geop.dim
DD = [harmonic_interpolation(setup, subdomains=D(i)) for i in range(dim)]
D = dolfin.Function(VV)
dolfin.assign(D, DD)
return dict(dist=dist, D=D)
def diffusivity_field(setup,
r,
ddata_r=None,
ddata_z=None,
boundary="dnab",
poreregion="poreregion"):
"interpolates diffusivity field defined on the geometry given by setup"
"needs: molecule radius r, radial and vertical D profiles ddata_r, ddata_z"
"the geometry needs to have subdomains poreregion and bulkfluid"
if ddata_r is None:
ddata_r = diff_profile_plane(r)
if ddata_z is None:
return diffusivity_field_simple(setup, r, ddata_r, boundary=boundary)
# build 1D interpolations from data
data = ddata_z
z = [x[2] for x in data["x"]]
data, z = fields._sorted(data, z)
Dz = data["D"]
fz = interp1d(z, Dz)
fn, ft = preprocess_Dr(ddata_r, r)
setup.prerefine(visualize=True)
dist = distance_boundary_from_geo(setup.geo, boundary)
VV = dolfin.VectorFunctionSpace(setup.geo.mesh, "CG", 1)
normal = dolfin.project(dolfin.grad(dist), VV)
phys = setup.phys
D0 = phys.kT / (6. * np.pi * phys.eta * r * 1e-9)
def DPore(x, i):
r = dist(x)
z = x[-1]
Dz = float(fz(z))
n = normal(x)
Dn = D0 * float(fn(r))
Dt = D0 * float(ft(r))
D = transformation(n, Dz * Dn, Dz * Dt)
return D[i][i]
def DBulk(x, i):
r = dist(x)
n = normal(x)
Dn = D0 * float(fn(r))
Dt = D0 * float(ft(r))
D = transformation(n, Dn, Dt)
return D[i][i]
D = lambda i: {
"bulkfluid": lambda x: DBulk(x, i),
poreregion: lambda x: DPore(x, i)
}
dim = setup.geop.dim
DD = [harmonic_interpolation(setup, subdomains=D(i)) for i in range(dim)]
D = dolfin.Function(VV)
dolfin.assign(D, DD)
return dict(dist=dist, D=D)
# create random points
N = user_params(N=1000).N
R, H = domain.params["R"], domain.params["H"]
px = 2*R*np.random.random(N) - R
py = 2*R*np.random.random(N) - R
pz = H*np.random.random(N) - H/2.
points = zip(px, py, pz)
# prepare mesh containing points
domain.write_gmsh_code(h)
domain.insert_points(points, h, forbidden=["dna", "membrane"])
geo = domain.code_to_mesh()
mesh = geo.mesh
with Log("harmonic interpolation..."):
# interpolate function from point values
values = np.sin(np.array(points)[:,2]/5.)
f = lambda x: np.sin(x[2]/5.)
fexp = dolfin.Expression("sin(x[2]/5.)", domain=mesh, degree=1)
u = harmonic_interpolation(geo, points, values,
dict(pore=f),
dict(upperb=fexp, lowerb=fexp))
with Log("plotting..."):
dolfin.plot(mesh)
dolfin.plot(u)
Plotter().plot(u)
dolfin.interactive()
def DBulk(x, i):
r = dist(x)
n = normal(x)
Dn = D0 * float(fn(r))
Dt = D0 * float(ft(r))
D = transformation(n, Dn, Dt)
return D[i][i]
D = lambda i: dict(
bulkfluid=lambda x: DBulk(x, i),
poreregion=lambda x: DPore(x, i),
)
# TODO: save geo along with functions
DD = [
harmonic_interpolation(setup, subdomains=D(i))
for i in range(params.dim)
]
D = dolfin.Function(VV)
dolfin.assign(D, DD)
f.save_functions("Dpugh", params, dist=dist, D=D)
f.update()
plt.show()
def get_D(params):
functions, mesh = f.get_functions("Dpugh", **params)
D = functions["D"]
D = dolfin.as_matrix(np.diag([D[i] for i in range(params.dim)]))
return D