def preprocess_Dr(data, r, normalize=True):
x = data["x"] #[xx[0] for xx in data["x"]]
data, x = fields._sorted(data, x)
Dt = [d[2][2] for d in data["D"]]
Dn = [d[0][0] for d in data["D"]]
eps = 1e-2
x = [-1., -eps, r] + x + [1000.]
if normalize:
Dn = [d / Dn[-1] for d in Dn]
Dt = [d / Dt[-1] for d in Dt]
Dn = [0., 0., eps] + Dn + [1.]
Dt = [0., 0., eps] + Dt + [1.]
fn = interp1d(x, Dn)
ft = interp1d(x, Dt)
return fn, ft
return list(B)
def smootha(l):
A = np.array(l)
B = A[:]
ker = np.array([10., 12., 15., 12., 10.])
ker = ker / np.sum(ker)
n = int(ker.shape[0] / 2.)
for i in range(n, A.shape[0] - n):
B[i] = np.inner(A[i - n:i + n + 1], ker)
return list(B)
x = [z[0] for z in data["x"]]
data, x = fields._sorted(data, x)
eps = 5e-3
x_ = x[:]
#x_.extend([1.,1.+eps,1.+2*eps,1.+3*eps])
x.extend([(x[-1] + 1.) / 2., 1., 1. + eps, 1. + 2 * eps, 1. + 3 * eps,
1. + 4 * eps, 1. + 5 * eps])
dstr = ["x", "y", "z"]
Dxx = [D[0][0] for D in data["D"]]
Dyy = [D[1][1] for D in data["D"]]
Dzz = [D[2][2] for D in data["D"]]
Dxx_ = [D[0][0] for D in data["D"]]
Dyy_ = [D[1][1] for D in data["D"]]
Dzz_ = [D[2][2] for D in data["D"]]
Dxx.extend([0., 0., 0., 0., 0., 0., 0.])
Dyy.extend([Dyy[-1] / 2., 0., 0., 0., 0., 0., 0.])
Dzz.extend([Dzz[-1] / 2., 0., 0., 0., 0., 0., 0.])
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)
import numpy as np
import nanopores.tools.fields as fields
import os
import nanopores
DATADIR = os.path.join(nanopores.HOME, "Dropbox", "nanopores", "fields")
FIGDIR = os.path.join(nanopores.HOME, "Dropbox", "nanopores", "figures")
FIGDIR = os.path.join(nanopores.HOME, "papers", "pnps-numerics", "figures")
fields.set_dir(DATADIR)
fields.update()
#data = fields.get_fields("howorka_velo1", Nmax=1e4)
data = fields.get_fields("howorka_velo3D_2")
#z = [x[2] for x in data["x"]]
z = [x[0] for x in data["x"]]
data, z = fields._sorted(data, z)
## modify
i = 0
rad = lambda x: sum(t**2 for t in x)
#rad = lambda x: x[2]
#v0 = [rad(x) for x in data["v0"]]
#v1 = [rad(x) for x in data["v1"]]
z.pop(-1)
data["v0"].pop(-1)
data["v1"].pop(-1)
plt.plot(z, [x[0] for x in data["v0"]],
"o-",
color="#000099",
label=r"$v_r$ (exact)")