Examples_different_geometries.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples visualizing different geometries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import infinite_conformal as infinite_conformal\n",
    "import infinite_fourier as infinite_fourier\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic example of potential with simple geometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6549234995791352e-11 F/m\n"
     ]
    }
   ],
   "source": [
    "# declare geometry\n",
    "epss=[1,5,2] # dielectric constant of layer 1, 2 and 3\n",
    "t=[0.2] #thickness of layer 2\n",
    "etas=[0.3,0] # cover fraction of electrodes, between layer 1 and 2 and between layer 2 and 3\n",
    "# declare model parameters\n",
    "LAcomp=2 # number of linear algebra componens\n",
    "max_n=180 # number of fourier components\n",
    "# make case\n",
    "simple_geometry_case = infinite_fourier.multiple_recursive_images(etas,t,epss,epss,LAcomp,max_n,accuracy_limit=10**-15,hybrid=True)\n",
    "print(simple_geometry_case.get_C(), 'F/m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 42%|████▏     | 42/101 [00:00<00:00, 416.22it/s]/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:140: RuntimeWarning: invalid value encountered in multiply\n",
      "  np.poly1d.__init__(self, poly.coeffs * float(kn))\n",
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:1977: RuntimeWarning: overflow encountered in double_scalars\n",
      "  kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n\n",
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:1977: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n\n",
      "100%|██████████| 101/101 [00:00<00:00, 153.43it/s]\n"
     ]
    }
   ],
   "source": [
    "y=np.arange(-0.5,0.5001,0.01)\n",
    "x=np.arange(-0.5,0.5001,0.01)\n",
    "V_simple_geometry_case=np.zeros((len(y),len(x)))\n",
    "for j in tqdm.tqdm(range(len(y))):\n",
    "    v = simple_geometry_case.get_V(x,y[j])\n",
    "    V_simple_geometry_case[j,:] += v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(x, y)\n",
    "fig, ax = plt.subplots(1,1)\n",
    "# plot potential\n",
    "levels=np.arange(-0.5,0.51,0.05)\n",
    "CS=ax.contourf(xx,yy, V_simple_geometry_case,levels,cmap='RdBu',alpha=0.7)\n",
    "cbar=fig.colorbar(CS, ax=ax)\n",
    "ax.set_aspect('equal', 'box')\n",
    "# set_labels \n",
    "ax.set_xlabel(r\"$x'$ [-]\")\n",
    "ax.set_ylabel(r\"$y'$ [-]\")\n",
    "cbar.set_label(r'Potential [V]')\n",
    "# draw electrodes \n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[0,0],[0,0]],'k',solid_capstyle='butt')\n",
    "# shade the film \n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,0),   # (x,y)\n",
    "            1,          # width\n",
    "            t[0],          # height\n",
    "            facecolor=[0,0,0,0.1]))\n",
    "# add dielectric constant\n",
    "ax.text(0,-0.3,r'$\\varepsilon$ = '+str(epss[0]), ha='center',va='center')\n",
    "ax.text(0,t[0]/2,r'$\\varepsilon$ = '+str(epss[1]), ha='center',va='center')\n",
    "ax.text(0,0.4,r'$\\varepsilon$ = '+str(epss[2]), ha='center',va='center')\n",
    "# flip y axis\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Anisotropic film"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.319288371528966e-11 F/m\n"
     ]
    }
   ],
   "source": [
    "# declare geometry\n",
    "eps_x=[1,20,2] # in-plane dielectric constant of layer 1, 2 and 3\n",
    "eps_y=[1,5,2] # out-of-plane dielectric constant of layer 1, 2 and 3\n",
    "t=[0.2] #thickness of layer 2\n",
    "etas=[0.3,0] # cover fraction of electrodes, between layer 1 and 2 and between layer 2 and 3\n",
    "# declare model parameters\n",
    "LAcomp=2 # number of linear algebra componens\n",
    "max_n=180 # number of fourier components\n",
    "# make case\n",
    "anisotropy_case = infinite_fourier.multiple_recursive_images(etas,t,eps_x,eps_y,LAcomp,max_n,accuracy_limit=10**-15,hybrid=True)\n",
    "print(anisotropy_case.get_C(), 'F/m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:00<00:00, 728.85it/s]\n"
     ]
    }
   ],
   "source": [
    "y=np.arange(-0.5,0.5001,0.01)\n",
    "x=np.arange(-0.5,0.5001,0.01)\n",
    "V_anisotropy_case=np.zeros((len(y),len(x)))\n",
    "for j in tqdm.tqdm(range(len(y))):\n",
    "    v = anisotropy_case.get_V(x,y[j])\n",
    "    V_anisotropy_case[j,:] += v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(x, y)\n",
    "fig, ax = plt.subplots(1,1)\n",
    "# plot potential\n",
    "levels=np.arange(-0.5,0.51,0.05)\n",
    "CS=ax.contourf(xx,yy, V_anisotropy_case,levels,cmap='RdBu',alpha=0.7)\n",
    "cbar=fig.colorbar(CS, ax=ax)\n",
    "ax.set_aspect('equal', 'box')\n",
    "# set_labels \n",
    "ax.set_xlabel(r\"$x'$ [-]\")\n",
    "ax.set_ylabel(r\"$y'$ [-]\")\n",
    "cbar.set_label(r'Potential [V]')\n",
    "# draw electrodes \n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[0,0],[0,0]],'k',solid_capstyle='butt')\n",
    "# shade the film \n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,0),   # (x,y)\n",
    "            1,          # width\n",
    "            t[0],          # height\n",
    "            facecolor=[0,0,0,0.1]))\n",
    "# add dielectric constant\n",
    "ax.text(0,-0.3,r'$\\varepsilon$ = '+str(eps_x[0]), ha='center',va='center')\n",
    "ax.text(0,t[0]/2,r'$\\varepsilon_x,\\varepsilon_y$ = '+str(eps_x[1])+', '+str(eps_y[1]), ha='center',va='center')\n",
    "ax.text(0,0.4,r'$\\varepsilon$ = '+str(eps_x[2]), ha='center',va='center')\n",
    "# flip y axis\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple layers, bottom electrode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.206625930901074e-12 F/m\n"
     ]
    }
   ],
   "source": [
    "# declare geometry\n",
    "epss=[1,5,2,1] # dielectric constant of layer 1, 2, 3 and 4 (below the continious electrode)\n",
    "t=[0.1,0.2] #thickness of layer 2 and 3\n",
    "etas=[0.3,0,1] # cover fraction of electrodes, between layer 1 and 2, between layer 2 and 3 and between layer 3 and 4\n",
    "    # by setting the cover fractio to 1, the potential at the associated electrodes is automatically set to 0\n",
    "# declare model parameters\n",
    "LAcomp=[2,0,4] # number of linear algebra componens for the different interfaces\n",
    "max_n=180 # number of fourier components\n",
    "# make case\n",
    "mlbe_case = infinite_fourier.multiple_recursive_images(etas,t,epss,epss,LAcomp,max_n,accuracy_limit=10**-15,hybrid=True)\n",
    "print(mlbe_case.get_C(), 'F/m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 68%|██████▊   | 69/101 [00:00<00:00, 275.58it/s]/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:140: RuntimeWarning: invalid value encountered in multiply\n",
      "  np.poly1d.__init__(self, poly.coeffs * float(kn))\n",
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:1977: RuntimeWarning: overflow encountered in double_scalars\n",
      "  kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n\n",
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:1977: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n\n",
      "100%|██████████| 101/101 [00:01<00:00, 94.18it/s]\n"
     ]
    }
   ],
   "source": [
    "y=np.arange(-0.5,0.5001,0.01)\n",
    "x=np.arange(-0.5,0.5001,0.01)\n",
    "V_mlbe_case=np.zeros((len(y),len(x)))\n",
    "for j in tqdm.tqdm(range(len(y))):\n",
    "    v = mlbe_case.get_V(x,y[j])\n",
    "    V_mlbe_case[j,:] += v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(x, y)\n",
    "fig, ax = plt.subplots(1,1)\n",
    "# plot potential\n",
    "levels=np.arange(-0.5,0.51,0.05)\n",
    "CS=ax.contourf(xx,yy, V_mlbe_case,levels,cmap='RdBu',alpha=0.7)\n",
    "cbar=fig.colorbar(CS, ax=ax)\n",
    "ax.set_aspect('equal', 'box')\n",
    "# set_labels \n",
    "ax.set_xlabel(r\"$x'$ [-]\")\n",
    "ax.set_ylabel(r\"$y'$ [-]\")\n",
    "cbar.set_label(r'Potential [V]')\n",
    "# draw electrodes \n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[0,0],[0,0]],'k',solid_capstyle='butt')\n",
    "ax.plot([-0.5,0.5],[t[1]+t[0],t[1]+t[0]],'k',solid_capstyle='butt')\n",
    "# shade the films\n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,0),   # (x,y)\n",
    "            1,          # width\n",
    "            t[0],          # height\n",
    "            facecolor=[0,0,0,0.2]))\n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,t[0]),   # (x,y)\n",
    "            1,          # width\n",
    "            t[1],          # height\n",
    "            facecolor=[0,0,0,0.1]))\n",
    "# add dielectric constant\n",
    "ax.text(0,-0.3,r'$\\varepsilon$ = '+str(epss[0]), ha='center',va='center')\n",
    "ax.text(0,t[0]/2,r'$\\varepsilon$ = '+str(epss[1]), ha='center',va='center')\n",
    "ax.text(0,t[1]/2+t[0],r'$\\varepsilon$ = '+str(epss[2]), ha='center',va='center')\n",
    "# flip y axis\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Electrodes both sides of film, symmetrical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7973539448429468e-11 F/m\n"
     ]
    }
   ],
   "source": [
    "# declare geometry\n",
    "epss=[1,5,1] # dielectric constant of layer 1, 2, 3 and 4 (below the continious electrode)\n",
    "t=[0.2] #thickness of layer 2 and 3\n",
    "etas=[0.3,0.3] # cover fraction of electrodes, between layer 1 and 2, between layer 2 and 3 and between layer 3 and 4\n",
    "# declare model parameters\n",
    "LAcomp=[2,2] # number of linear algebra componens for the different interfaces\n",
    "max_n=180 # number of fourier components\n",
    "# make case\n",
    "both_sides_case = infinite_fourier.multiple_recursive_images(etas,t,epss,epss,LAcomp,max_n,accuracy_limit=10**-15,hybrid=True)\n",
    "print(both_sides_case.get_C(), 'F/m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:00<00:00, 423.96it/s]\n"
     ]
    }
   ],
   "source": [
    "y=np.arange(-0.4,0.6001,0.01)\n",
    "x=np.arange(-0.5,0.5001,0.01)\n",
    "V_both_sides_case=np.zeros((len(y),len(x)))\n",
    "for j in tqdm.tqdm(range(len(y))):\n",
    "    v = both_sides_case.get_V(x,y[j])\n",
    "    V_both_sides_case[j,:] += v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(x, y)\n",
    "fig, ax = plt.subplots(1,1)\n",
    "# plot potential\n",
    "levels=np.arange(-0.5,0.51,0.05)\n",
    "CS=ax.contourf(xx,yy, V_both_sides_case,levels,cmap='RdBu',alpha=0.7)\n",
    "cbar=fig.colorbar(CS, ax=ax)\n",
    "ax.set_aspect('equal', 'box')\n",
    "# set_labels \n",
    "ax.set_xlabel(r\"$x'$ [-]\")\n",
    "ax.set_ylabel(r\"$y'$ [-]\")\n",
    "cbar.set_label(r'Potential [V]')\n",
    "# draw electrodes \n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[0,0],[0,0]],'k',solid_capstyle='butt')\n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[t[0],t[0]],[t[0],t[0]]],'k',solid_capstyle='butt')\n",
    "# shade the film \n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,0),   # (x,y)\n",
    "            1,          # width\n",
    "            t[0],          # height\n",
    "            facecolor=[0,0,0,0.1]))\n",
    "# add dielectric constant\n",
    "ax.text(0,-0.3,r'$\\varepsilon$ = '+str(epss[0]), ha='center',va='center')\n",
    "ax.text(0,t[0]/2,r'$\\varepsilon$ = '+str(epss[1]), ha='center',va='center')\n",
    "ax.text(0,0.4,r'$\\varepsilon$ = '+str(epss[2]), ha='center',va='center')\n",
    "# flip y axis\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Thick electrodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7998856789565858e-11 F/m\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:140: RuntimeWarning: invalid value encountered in multiply\n",
      "  np.poly1d.__init__(self, poly.coeffs * float(kn))\n"
     ]
    }
   ],
   "source": [
    "# declare geometry\n",
    "epss=[1,1,1,5,2] # dielectric constant of layer 1, 2, 3 and 4 (below the continious electrode)\n",
    "t=[0.05,0.05,0.2] # multiple layers\n",
    "etas=[0.3,0.3,0.3,0] # cover fraction of electrodes between layers\n",
    "# declare model parameters\n",
    "LAcomp=4 # number of linear algebra componens for the different interfaces\n",
    "max_n=180 # number of fourier components\n",
    "# make case\n",
    "thicke_electrodes_case = infinite_fourier.multiple_recursive_images(etas,t,epss,epss,LAcomp,max_n,accuracy_limit=10**-15,hybrid=True)\n",
    "print(thicke_electrodes_case.get_C(), 'F/m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 29%|██▊       | 29/101 [00:00<00:00, 280.34it/s]/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:140: RuntimeWarning: invalid value encountered in multiply\n",
      "  np.poly1d.__init__(self, poly.coeffs * float(kn))\n",
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:1977: RuntimeWarning: overflow encountered in double_scalars\n",
      "  kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n\n",
      "/usr/local/lib/python3.6/site-packages/scipy/special/orthogonal.py:1977: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  kn = _gam(2 * n + 1) / _gam(n + 1)**2 / 2.0**n\n",
      "100%|██████████| 101/101 [00:01<00:00, 91.11it/s]\n"
     ]
    }
   ],
   "source": [
    "y=np.arange(-0.4,0.6001,0.01)\n",
    "x=np.arange(-0.5,0.5001,0.01)\n",
    "V_thicke_electrodes_case=np.zeros((len(y),len(x)))\n",
    "for j in tqdm.tqdm(range(len(y))):\n",
    "    v = thicke_electrodes_case.get_V(x,y[j])\n",
    "    V_thicke_electrodes_case[j,:] += v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(x, y)\n",
    "fig, ax = plt.subplots(1,1)\n",
    "# plot potential\n",
    "levels=np.arange(-0.5,0.51,0.05)\n",
    "CS=ax.contourf(xx,yy, V_thicke_electrodes_case,levels,cmap='RdBu',alpha=0.7)\n",
    "cbar=fig.colorbar(CS, ax=ax)\n",
    "ax.set_aspect('equal', 'box')\n",
    "# set_labels \n",
    "ax.set_xlabel(r\"$x'$ [-]\")\n",
    "ax.set_ylabel(r\"$y'$ [-]\")\n",
    "cbar.set_label(r'Potential [V]')\n",
    "# draw electrodes \n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[0]*2]*2,'k',solid_capstyle='butt')\n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[1]/2]],[[t[0]]*2]*2,'k',solid_capstyle='butt')\n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[2]/2]],[[t[0]+t[1]]*2]*2,'k',solid_capstyle='butt')\n",
    "# shade the film \n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,0),   # (x,y)\n",
    "            1,          # width\n",
    "            t[0],          # height\n",
    "            facecolor=[0,0,0,0.05]))\n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,t[0]),   # (x,y)\n",
    "            1,          # width\n",
    "            t[1],          # height\n",
    "            facecolor=[0,0,0,0.03]))\n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,t[0]+t[1]),   # (x,y)\n",
    "            1,          # width\n",
    "            t[2],          # height\n",
    "            facecolor=[0,0,0,0.1]))\n",
    "# add dielectric constant\n",
    "ax.text(0,-0.2,r'$\\varepsilon$ = '+str(epss[0]), ha='center',va='center')\n",
    "ax.text(0,t[0]/2,r'$\\varepsilon$ = '+str(epss[1]), ha='center',va='center')\n",
    "ax.text(0,t[0]+t[1]/2,r'$\\varepsilon$ = '+str(epss[2]), ha='center',va='center')\n",
    "ax.text(0,t[0]+t[1]+t[2]/2,r'$\\varepsilon$ = '+str(epss[3]), ha='center',va='center')\n",
    "ax.text(0,0.4,r'$\\varepsilon$ = '+str(epss[4]), ha='center',va='center')\n",
    "# flip y axis\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Electrodes both sides of film, asymmetrical = Quadrupole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Capacitance between all left vs all right electrodes\n",
      "-6.462348535570529e-27 = ~0 F/m\n",
      "The capacitance of the quadrupole may be calculated by integrating the electric field\n"
     ]
    }
   ],
   "source": [
    "# declare geometry\n",
    "epss=[1,5,1] # dielectric constant of layer 1, 2, 3 and 4 (below the continious electrode)\n",
    "t=[0.2] #thickness of layer 2 and 3\n",
    "etas=[0.3,0.3] # cover fraction of electrodes, between layer 1 and 2, between layer 2 and 3 and between layer 3 and 4\n",
    "# declare model parameters\n",
    "LAcomp=[2,2] # number of linear algebra componens for the different interfaces\n",
    "max_n=180 # number of fourier components\n",
    "# make case\n",
    "both_sides_case_asym = infinite_fourier.multiple_recursive_images(etas,t,epss,epss,LAcomp,max_n,accuracy_limit=10**-15,voltages=[0.5,-0.5],hybrid=True)\n",
    "print('Capacitance between all left vs all right electrodes')\n",
    "print(both_sides_case_asym.get_C(), '= ~0 F/m')\n",
    "print('The capacitance of the quadrupole may be calculated by integrating the electric field')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:00<00:00, 395.42it/s]\n"
     ]
    }
   ],
   "source": [
    "y=np.arange(-0.4,0.6001,0.01)\n",
    "x=np.arange(-0.5,0.5001,0.01)\n",
    "V_both_sides_case_asym=np.zeros((len(y),len(x)))\n",
    "for j in tqdm.tqdm(range(len(y))):\n",
    "    v = both_sides_case_asym.get_V(x,y[j])\n",
    "    V_both_sides_case_asym[j,:] += v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(x, y)\n",
    "fig, ax = plt.subplots(1,1)\n",
    "# plot potential\n",
    "levels=np.arange(-0.5,0.51,0.05)\n",
    "CS=ax.contourf(xx,yy, V_both_sides_case_asym,levels,cmap='RdBu',alpha=0.7)\n",
    "cbar=fig.colorbar(CS, ax=ax)\n",
    "ax.set_aspect('equal', 'box')\n",
    "# set_labels \n",
    "ax.set_xlabel(r\"$x'$ [-]\")\n",
    "ax.set_ylabel(r\"$y'$ [-]\")\n",
    "cbar.set_label(r'Potential [V]')\n",
    "# draw electrodes \n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[0,0],[0,0]],'k',solid_capstyle='butt')\n",
    "ax.plot([[-0.5,0.5],[-0.5+etas[0]/2,0.5-etas[0]/2]],[[t[0],t[0]],[t[0],t[0]]],'k',solid_capstyle='butt')\n",
    "# shade the film \n",
    "ax.add_patch(matplotlib.patches.Rectangle(\n",
    "            (-0.5,0),   # (x,y)\n",
    "            1,          # width\n",
    "            t[0],          # height\n",
    "            facecolor=[0,0,0,0.1]))\n",
    "# add dielectric constant\n",
    "ax.text(0,-0.3,r'$\\varepsilon$ = '+str(epss[0]), ha='center',va='center')\n",
    "ax.text(0,t[0]/2,r'$\\varepsilon$ = '+str(epss[1]), ha='center',va='center')\n",
    "ax.text(0,0.4,r'$\\varepsilon$ = '+str(epss[2]), ha='center',va='center')\n",
    "# flip y axis\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}