From 4665e64ecee55f9aece17ae6f283990f0029d993 Mon Sep 17 00:00:00 2001
From: Lars Hubatsch <hubatsch@pks.mpg.de>
Date: Thu, 17 Sep 2020 09:17:23 +0200
Subject: [PATCH] Radial Droplet FRAP qualitatively works.
But only up to a factor between different partitionings/diffusion coefficients outside.
Problem: Maybe need different concentration scaling for radial problem?
---
FloryHugg_DiffUnbleached.ipynb | 57 ++++++++++++++++------------------
1 file changed, 27 insertions(+), 30 deletions(-)
diff --git a/FloryHugg_DiffUnbleached.ipynb b/FloryHugg_DiffUnbleached.ipynb
index 87c67f8..74ecc4b 100644
--- a/FloryHugg_DiffUnbleached.ipynb
+++ b/FloryHugg_DiffUnbleached.ipynb
@@ -15,7 +15,7 @@
"\n",
"# domain = ms.Sphere(df.Point(0, 0, 0), 1.0)\n",
"# mesh = ms.generate_mesh(domain, 50)\n",
- "mesh = df.UnitIntervalMesh(100000)\n",
+ "mesh = df.UnitIntervalMesh(10000)\n",
"dt = 0.000001\n",
"\n",
"F = df.FunctionSpace(mesh, 'CG', 1)"
@@ -30,17 +30,28 @@
"def calc_sim(c0, c_tot, Ga0):\n",
" tc = df.TestFunction(F)\n",
" c = df.Function(F)\n",
- " # Weak form\n",
- " form = ((df.inner((c-c0)/dt, tc) +\n",
- " df.inner(df.grad(c), df.grad((1-c_tot)/Ga0*tc))) -\n",
- " df.inner(df.grad(c_tot), df.grad((1-c_tot)/Ga0/c_tot*c*tc))-\n",
- " tc*df.inner(df.grad(c), df.grad((1-c_tot)/Ga0))+\n",
- " tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c/Ga0))) * df.dx\n",
+ " X = df.SpatialCoordinate(mesh)\n",
+ "# X.interpolate(df.Expression('x[0]', degree=1))\n",
+ " # Weak form 1D:\n",
+ "# form = ((df.inner((c-c0)/dt, tc) +\n",
+ "# df.inner(df.grad(c), df.grad((1-c_tot)/Ga0*tc))) -\n",
+ "# df.inner(df.grad(c_tot), df.grad((1-c_tot)/Ga0/c_tot*c*tc))-\n",
+ "# tc*df.inner(df.grad(c), df.grad((1-c_tot)/Ga0))+\n",
+ "# tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c/Ga0))) * df.dx\n",
+ " \n",
+ " # Weak form radial symmetry:\n",
+ " form = ((df.inner((c-c0)/dt, tc*X[0]*X[0]) +\n",
+ " df.inner(df.grad(c), df.grad((1-c_tot)/Ga0*tc*X[0]*X[0]))) -\n",
+ " df.inner(df.grad(c_tot), df.grad((1-c_tot)/Ga0/c_tot*c*tc*X[0]*X[0]))-\n",
+ " tc*df.inner(df.grad(c), df.grad((1-c_tot)/Ga0*X[0]*X[0]))+\n",
+ " tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c/Ga0*X[0]*X[0]))-\n",
+ " (1-c_tot)/Ga0*2*X[0]*c.dx(0)*tc+\n",
+ " (1-c_tot)/Ga0/c_tot*c*2*X[0]*c_tot.dx(0)*tc) * df.dx\n",
" t = 0\n",
" # Solve in time\n",
" ti = time.time()\n",
- " for i in range(6):\n",
- " print(time.time() - ti)\n",
+ " for i in range(60):\n",
+ "# print(time.time() - ti)\n",
" df.solve(form == 0, c)\n",
" df.assign(c0, c)\n",
" t += dt\n",
@@ -66,21 +77,21 @@
"c0_1 = df.Function(F)\n",
"c_tot_1 = df.Function(F)\n",
"Ga0_1 = df.Function(F)\n",
- "c_tot_1.interpolate(df.Expression('0*tanh(35000*(x[0]-0.01))+0.9', degree=1))\n",
+ "c_tot_1.interpolate(df.Expression('0*tanh(350000*(x[0]-0.01))+0.9', degree=1))\n",
"c0_1.interpolate(df.Expression(('x[0]<0.01 ? 0 :'\n",
- " '0*tanh(35000*(x[0]-0.01))+0.9'),\n",
+ " '0*tanh(350000*(x[0]-0.01))+0.9'),\n",
" degree=1))\n",
- "Ga0_1.interpolate(df.Expression('4.*(tanh(35000*(x[0]-0.01))+1)+1', degree=1))\n",
+ "Ga0_1.interpolate(df.Expression('4.*(tanh(350000*(x[0]-0.01))+1)+1', degree=1))\n",
"\n",
"# 1D, high partitioning\n",
"c0_9 = df.Function(F)\n",
"c_tot_9 = df.Function(F)\n",
"Ga0_9 = df.Function(F)\n",
- "c_tot_9.interpolate(df.Expression('0.4*tanh(-35000*(x[0]-0.01))+0.5', degree=1))\n",
+ "c_tot_9.interpolate(df.Expression('0.4*tanh(-350000*(x[0]-0.01))+0.5', degree=1))\n",
"c0_9.interpolate(df.Expression(('x[0]<0.01 ? 0 :'\n",
- " '0.4*tanh(-35000*(x[0]-0.01))+0.5'),\n",
+ " '0.4*tanh(-350000*(x[0]-0.01))+0.5'),\n",
" degree=1))\n",
- "Ga0_9.interpolate(df.Expression('0*(tanh(-35000*(x[0]-0.01))+1)+1', degree=1))\n",
+ "Ga0_9.interpolate(df.Expression('0*(tanh(-350000*(x[0]-0.01))+1)+1', degree=1))\n",
"\n",
"\n",
"c0_1 = calc_sim(c0_1, c_tot_1, Ga0_1)\n",
@@ -94,7 +105,7 @@
"outputs": [],
"source": [
"# 1D:\n",
- "plt.plot(np.linspace(0, 1, 10000), [c0_1([x]) for x in np.linspace(0, 1, 10000)])\n",
+ "plt.plot(np.linspace(0, 1, 10000), [1.5*c0_1([x]) for x in np.linspace(0, 1, 10000)])\n",
"plt.plot(np.linspace(0, 1, 10000), [c0_9([x]) for x in np.linspace(0, 1, 10000)])\n",
"plt.xlim(0, 0.1)\n",
"# plt.ylim(0, 0.3)\n",
@@ -102,18 +113,6 @@
"# plt.plot(np.linspace(0, 0.5, 1000), [c0([x, 0, 0]) for x in np.linspace(0, 0.5, 1000)])"
]
},
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# 1D:\n",
- "plt.plot(np.linspace(0, 1, 10000), [c0([x]) for x in np.linspace(0, 1, 10000)])\n",
- "# plt.xlim(0, 0.1)\n",
- "# plt.ylim(0., 0.3)"
- ]
- },
{
"cell_type": "code",
"execution_count": null,
@@ -146,8 +145,6 @@
"metadata": {},
"outputs": [],
"source": [
- "import dolfin as df\n",
- "\n",
"mesh = df.UnitIntervalMesh(1000)\n",
"dt = 0.001\n",
"F = df.FunctionSpace(mesh, 'CG', 1)\n",
--
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