From d01108862ebe57a9529070ad719c84437530ce8b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?R=C3=A9mi=20Delaporte-Mathurin?=
 <40028739+RemDelaporteMathurin@users.noreply.github.com>
Date: Thu, 29 Jun 2023 22:21:59 +0000
Subject: [PATCH 1/2] modified task 3, now a permeation barrier model

---
 tasks/task3.ipynb | 501 +++++++++++++++++++++++++++++-----------------
 1 file changed, 322 insertions(+), 179 deletions(-)

diff --git a/tasks/task3.ipynb b/tasks/task3.ipynb
index 9e8e6c5..885a4f6 100644
--- a/tasks/task3.ipynb
+++ b/tasks/task3.ipynb
@@ -5,53 +5,11 @@
          "cell_type": "markdown",
          "metadata": {},
          "source": [
-            "# Multi-materials simulation\n",
-            "\n",
-            "In this demo, we will perform a multi-materials simulation. This will be our problem case.\n",
-            "The following FESTIM features will be used:\n",
-            "- Multi-materials\n",
-            "- Meshing:\n",
-            "    - mesh from vertices\n",
-            "- Boundary conditions:\n",
-            "    - Recombination flux\n",
-            "- Exports:\n",
-            "    - txt exports\n",
-            "    - Flux computations\n",
-            "    - Integrations over volumes for inventories calculation\n",
-            "- Plotting with matplotlib\n",
-            "\n",
-            "## 1. Problem definition\n",
-            "The domain is a composite slab comprised of 3 subdomains of W/Cu/W as described below:\n",
-            " <p align=\"center\">\n",
-            "  <img src=\"https://user-images.githubusercontent.com/40028739/104934903-e10d7500-59aa-11eb-9296-17de99140701.jpg\" width=\"40%\">\n",
-            "</p>\n",
-            "\n",
-            "- $\\Omega = [0;1.5\\times10^{-7}]$\n",
-            "- $\\Omega_1 = [0;5\\times10^{-8}]$ (W left)\n",
-            "- $\\Omega_2 = [5\\times10^{-8};1\\times10^{-7}] $ (Cu)\n",
-            "- $\\Omega_3 = [1\\times10^{-7};1.5\\times10^{-7}]$ (W right)\n",
-            "\n",
-            "The diffusion coefficient is defined as:\n",
-            "- $D(T) = \\begin{cases}\n",
-            "    4.1\\times 10^{-7} \\exp{(-0.39/k_B T)}, & \\text{on } \\Omega_1 \\text{ and } \\Omega_3\\\\\n",
-            "    1.5\\times 10^{-7} \\exp{(-0.15/k_B T)}, & \\text{on } \\Omega_2\n",
-            "    \\end{cases}$\n",
-            "\n",
-            "A trap is defined per material and are defined as:\n",
-            "- Trap 1 in $\\Omega_2$ and $\\Omega_3$:\n",
-            "    - Density: $n_1 = 1.3\\times 10^{-3} \\text{ at.fr.}$\n",
-            "    - Trapping rate: $k(T) = 3.8 \\times 10^{-17} \\exp{(-0.39/k_B T)} \\text{ s}^{-1}$\n",
-            "    - Detrapping rate: $p(T) = 8.4\\times 10^{12} \\exp{(-1.2/k_B T)} \\text{ s}^{-1}$\n",
-            "- Trap 2 in $\\Omega_2$:\n",
-            "    - Density: $n_2 = 5\\times10^{-5} \\text{ at.fr.}$\n",
-            "    - Trapping rate: $k(T) = 6 \\times 10^{-17} \\exp{(-0.39/k_B T)} \\text{ s}^{-1}$\n",
-            "    - Detrapping rate: $p(T) = 8\\times10^{13} \\exp{(-1.0/k_B T)} \\text{ s}^{-1}$\n",
-            "\n",
-            "\n",
-            "A Dirichlet boundary conditions will be imposed on $\\Gamma_\\mathrm{left}$ and a recombination flux is imposed on $\\Gamma_\\mathrm{right}$.\n",
-            "- $c_\\mathrm{m} = 10^{20} \\; \\mathrm{m}^{-3} \\quad \\text{on } \\Gamma_\\mathrm{left}$\n",
-            "- $-D \\nabla c_\\mathrm{m} \\cdot n = -K c_\\mathrm{m}^2 \\quad \\text{on }\\Gamma_\\mathrm{right}$\n",
-            "with $K = 2.9\\times 10^{-14} \\exp{(-1.92/k_B T)} \\; \\mathrm{m}^4 \\mathrm{s}^{-1}$"
+            "# Permeation barrier modelling\n",
+            "\n",
+            "In this task, we will model permeation barriers on tungsten and compute the associated Permeation Reduction Factor (PRF).\n",
+            "\n",
+            "The PRF is the ratio of the steady state permeation flux without barriers by that of the case with barriers."
          ]
       },
       {
@@ -59,260 +17,445 @@
          "cell_type": "markdown",
          "metadata": {},
          "source": [
-            "## 2. Implementation\n",
-            "The first step is to create a FESTIM Simulation object"
+            "## 1) Model with barrier\n",
+            "\n",
+            "Let's first create a model where tungsten is coated with 1 micron of barrier material on both sides."
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 1,
          "metadata": {},
          "outputs": [],
          "source": [
             "import festim as F\n",
             "\n",
-            "my_model = F.Simulation()"
+            "model_barrier = F.Simulation()"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "Let's create three `Material` instances for the three subdomains and assign it to `model_barrier.materials`.\n",
+            "\n",
+            "> Note:\n",
+            ">\n",
+            "> By default, the solubility law of the materials is `\"sievert\"`.\n",
+            ">\n",
+            "> However, it can be changed by overriding the `solubility_law` argument to `\"henry\"`"
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 2,
          "metadata": {},
          "outputs": [],
          "source": [
-            "tungsten_left = F.Material(\n",
+            "barrier_thick = 1e-6\n",
+            "substrate_thick = 3e-3\n",
+            "\n",
+            "barrier_left = F.Material(\n",
             "    id=1,\n",
-            "    D_0=4.1e-7,\n",
+            "    D_0=1e-8,\n",
             "    E_D=0.39,\n",
-            "    S_0=1.87e24,\n",
+            "    S_0=1e22,\n",
             "    E_S=1.04,\n",
-            "    borders=[0, 0.5e-7]\n",
+            "    borders=[0, barrier_thick]\n",
             "    )\n",
             "\n",
-            "copper = F.Material(\n",
+            "tungsten = F.Material(\n",
             "    id=2,\n",
-            "    D_0=1.5e-7,\n",
-            "    E_D=0.15,\n",
-            "    S_0=3.14e24,\n",
-            "    E_S=0.57,\n",
-            "    borders=[0.5e-7, 1e-7]\n",
+            "    D_0=4.1e-7,\n",
+            "    E_D=0.39,\n",
+            "    S_0=1.87e24,\n",
+            "    E_S=1.04,\n",
+            "    borders=[barrier_thick, substrate_thick + barrier_thick]\n",
             "    )\n",
             "\n",
-            "tungsten_right = F.Material(\n",
+            "barrier_right = F.Material(\n",
             "    id=3,\n",
-            "    D_0=4.1e-7,\n",
+            "    D_0=1e-8,\n",
             "    E_D=0.39,\n",
-            "    S_0=1.87e24,\n",
+            "    S_0=1e22,\n",
             "    E_S=1.04,\n",
-            "    borders=[1e-7, 1.5e-7]\n",
+            "    borders=[substrate_thick + barrier_thick, substrate_thick + 2 * barrier_thick]\n",
             "    )\n",
             "\n",
-            "my_model.materials = [tungsten_left, copper, tungsten_right]"
+            "model_barrier.materials = [barrier_left, tungsten, barrier_right]"
          ]
       },
       {
-         "cell_type": "code",
-         "execution_count": null,
+         "attachments": {},
+         "cell_type": "markdown",
          "metadata": {},
-         "outputs": [],
          "source": [
-            "import numpy as np\n",
-            "\n",
-            "vertices = np.concatenate(\n",
-            "        [np.linspace(0, 0.5e-7, num=200),\n",
-            "        np.linspace(0.5e-7, 1e-7, num=100),\n",
-            "        np.linspace(1e-7, 1.5e-7, num=200)])\n",
-            "\n",
-            "my_model.mesh = F.MeshFromVertices(vertices)"
+            "To avoid cells overlapping the domains boundaries, we create 3 lists of vertices."
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 3,
          "metadata": {},
          "outputs": [],
          "source": [
-            "tungsten_density = 6.3e28 # m-3\n",
-            "\n",
-            "trap_tungsten = F.Trap(\n",
-            "    k_0=3.8e-17,\n",
-            "    E_k=0.39,\n",
-            "    p_0=8.4e12,\n",
-            "    E_p=1.2,\n",
-            "    density=1.3e-3*tungsten_density,\n",
-            "    materials=[tungsten_left, tungsten_right]\n",
-            ")\n",
+            "import numpy as np\n",
             "\n",
-            "copper_density = 8.43e28\n",
+            "vertices_left = np.linspace(0, barrier_thick, num=50)\n",
             "\n",
-            "trap_copper = F.Trap(\n",
-            "    k_0=6e-17,\n",
-            "    E_k=0.39,\n",
-            "    p_0=8e13,\n",
-            "    E_p=0.9,\n",
-            "    density=5e-5*copper_density,\n",
-            "    materials=[copper]\n",
-            ")\n",
+            "vertices_mid = np.linspace(\n",
+            "    barrier_thick, substrate_thick + barrier_thick, num=50)\n",
+            "\n",
+            "vertices_right = np.linspace(substrate_thick + barrier_thick,\n",
+            "                             substrate_thick + 2*barrier_thick, num=50)\n",
             "\n",
-            "my_model.traps = F.Traps([trap_tungsten, trap_copper])"
+            "vertices = np.concatenate([vertices_left, vertices_mid, vertices_right])\n",
+            "\n",
+            "model_barrier.mesh = F.MeshFromVertices(vertices)\n"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "The temperature is homogeneous across the domain."
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 4,
          "metadata": {},
          "outputs": [],
          "source": [
-            "my_model.T = F.Temperature(320)"
+            "model_barrier.T = F.Temperature(600)"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "A Sievert's boundary condition is applied on the left surface and the concentration is assumed to be zero on the right surface."
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 5,
          "metadata": {},
          "outputs": [],
          "source": [
-            "left_bc = F.DirichletBC(\n",
-            "    field=\"solute\",\n",
+            "left_bc = F.SievertsBC(\n",
             "    surfaces=1,\n",
-            "    value=1e20\n",
+            "    S_0=barrier_left.S_0,\n",
+            "    E_S=barrier_left.E_S,\n",
+            "    pressure=100\n",
             "    )\n",
             "\n",
-            "right_bc = F.RecombinationFlux(\n",
+            "right_bc = F.DirichletBC(\n",
+            "    field=\"solute\",\n",
             "    surfaces=2,\n",
-            "    Kr_0=2.9e-10,\n",
-            "    E_Kr=1,\n",
-            "    order=2\n",
+            "    value=0\n",
             "    )\n",
             "\n",
-            "my_model.boundary_conditions = [left_bc, right_bc]"
+            "model_barrier.boundary_conditions = [left_bc, right_bc]"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "For this task, we want to compute the permeation flux, that is the flux at the right surface.\n",
+            "\n",
+            "We will also export the concentration profiles at three different times"
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 6,
          "metadata": {},
          "outputs": [],
          "source": [
             "folder = 'outputs'\n",
             "\n",
-            "derived_quantities = F.DerivedQuantities(filename=\"{}/derived_quantities.csv\".format(folder))\n",
-            "derived_quantities.derived_quantities = [\n",
-            "    F.TotalVolume(field=\"retention\", volume=1),\n",
-            "    F.TotalVolume(field=\"retention\", volume=2),\n",
-            "    F.TotalVolume(field=\"retention\", volume=3),\n",
-            "    F.TotalVolume(field=\"1\", volume=1),\n",
-            "    F.TotalVolume(field=\"1\", volume=3),\n",
-            "    F.TotalVolume(field=\"2\", volume=2),\n",
-            "    F.SurfaceFlux(field=\"solute\", surface=1),\n",
-            "    F.SurfaceFlux(field=\"solute\", surface=2),\n",
-            "]\n",
+            "derived_quantities_with_barrier = F.DerivedQuantities()\n",
+            "derived_quantities_with_barrier.derived_quantities = [F.HydrogenFlux(surface=2)]\n",
             "\n",
             "txt_exports = F.TXTExports(\n",
-            "    fields=['1', '2', 'solute', 'retention'],\n",
-            "    labels=['trap1', 'trap2', 'mobile', 'retention'],\n",
-            "    times=[2000, 17000, 20000],\n",
+            "    fields=['solute'],\n",
+            "    labels=['mobile'],\n",
+            "    times=[100, 17000, 8e5],\n",
             "    folder=folder\n",
             "    )\n",
             "\n",
-            "my_model.exports = [derived_quantities] + txt_exports.exports"
+            "model_barrier.exports = [derived_quantities_with_barrier] + txt_exports.exports"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "In order to ensure the conservation of chemical potential at interfaces, the argument `chemical_pot=True` has to be specified.\n",
+            "\n",
+            "The reason it is fault by default is to save performance."
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 7,
          "metadata": {},
          "outputs": [],
          "source": [
-            "my_model.settings = F.Settings(\n",
-            "    absolute_tolerance=1e12,\n",
+            "model_barrier.settings = F.Settings(\n",
+            "    absolute_tolerance=1e0,\n",
             "    relative_tolerance=1e-09,\n",
-            "    final_time=2e4,\n",
+            "    final_time=8e5,\n",
             "    chemical_pot=True,\n",
-            "    traps_element_type=\"DG\",\n",
-            "    maximum_iterations=50\n",
             ")\n",
             "\n",
             "\n",
-            "my_model.dt = F.Stepsize(\n",
-            "    initial_value=50,\n",
-            "    stepsize_change_ratio=1.1,\n",
-            "    dt_min=1e-5)"
+            "model_barrier.dt = F.Stepsize(\n",
+            "    initial_value=5,\n",
+            "    stepsize_change_ratio=1.1\n",
+            ")"
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 8,
+         "metadata": {},
+         "outputs": [
+            {
+               "name": "stdout",
+               "output_type": "stream",
+               "text": [
+                  "Defining initial values\n",
+                  "Defining variational problem\n",
+                  "Defining source terms\n",
+                  "Defining boundary conditions\n",
+                  "Time stepping...\n",
+                  "100.0 %        8.0e+05 s    Ellapsed time so far: 1.6 s\n"
+               ]
+            }
+         ],
+         "source": [
+            "model_barrier.initialise()\n",
+            "model_barrier.run()"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
          "metadata": {},
-         "outputs": [],
          "source": [
-            "my_model.initialise()\n",
-            "my_model.run()"
+            "We can plot the concentration profiles at different times and notice the jump of concentrations at interfaces:"
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 9,
          "metadata": {},
-         "outputs": [],
+         "outputs": [
+            {
+               "data": {
+                  "image/png": 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",
+                  "text/plain": [
+                     "<Figure size 640x480 with 3 Axes>"
+                  ]
+               },
+               "metadata": {},
+               "output_type": "display_data"
+            }
+         ],
          "source": [
             "import matplotlib.pyplot as plt\n",
             "\n",
-            "t = derived_quantities.t\n",
-            "ret_cu = derived_quantities.filter(volumes=copper.id, fields=\"retention\").data\n",
-            "ret_w_left = derived_quantities.filter(volumes=tungsten_left.id, fields=\"retention\").data\n",
-            "ret_w_right = derived_quantities.filter(volumes=tungsten_right.id, fields=\"retention\").data\n",
+            "fig, axs = plt.subplots(nrows=1, ncols=3, sharey=True)\n",
             "\n",
-            "total = np.sum([ret_cu, ret_w_left, ret_w_right], axis=0)\n",
+            "for ax, xlim in zip(axs, [(0, barrier_thick * 1.2), (None, None), (substrate_thick, substrate_thick + 2*barrier_thick)]):\n",
+            "    plt.sca(ax)\n",
+            "    for time in txt_exports.times[::-1]:\n",
+            "        data = np.genfromtxt(folder + f'/mobile_{time:.1f}s.txt')\n",
+            "        data = data[data[:, 0].argsort()]  # make sure data is sorted\n",
+            "        plt.plot(data[:, 0], data[:, 1], label=f\"{time:.0f} s\")\n",
             "\n",
-            "plt.figure()\n",
-            "plt.plot(t, total, label=\"total\")\n",
-            "plt.plot(t, ret_w_left, label=\"W left\")\n",
-            "plt.plot(t, ret_w_right, label=\"W right\")\n",
-            "plt.plot(t, ret_cu, label=\"Cu\")\n",
+            "    plt.xlabel(\"Depth (m)\")\n",
+            "    plt.xlim(*xlim)\n",
             "\n",
+            "plt.sca(axs[0])\n",
+            "plt.title(\"zoom left\")\n",
             "plt.yscale(\"log\")\n",
-            "plt.xscale(\"log\")\n",
-            "plt.legend()\n",
-            "plt.ylabel(\"Inventory (H/m$^2$)\")\n",
-            "plt.xlabel(\"Time (s)\")"
+            "plt.ylim(bottom=1e12)\n",
+            "plt.ylabel(\"Mobile H concentration (H/m$^3$)\")\n",
+            "axs[2].set_title(\"zoom right\")\n",
+            "axs[2].legend()\n",
+            "plt.show()"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "## 2) Model without barrier\n",
+            "\n",
+            "We can also run the equivalent model without permeation barriers with bare tungsten.\n",
+            "Let's make a few modifications:"
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 10,
          "metadata": {},
-         "outputs": [],
+         "outputs": [
+            {
+               "name": "stdout",
+               "output_type": "stream",
+               "text": [
+                  "Defining initial values\n",
+                  "Defining variational problem\n",
+                  "Defining source terms\n",
+                  "Defining boundary conditions\n",
+                  "Time stepping...\n",
+                  "100.0 %        8.0e+05 s    Ellapsed time so far: 0.4 s\n"
+               ]
+            }
+         ],
          "source": [
-            "mobile_1 = np.genfromtxt(folder + '/mobile_2000.0s.txt')\n",
-            "mobile_2 = np.genfromtxt(folder + '/mobile_17000.0s.txt')\n",
+            "model_no_barrier = F.Simulation()\n",
             "\n",
-            "plt.figure()\n",
-            "plt.plot(mobile_1[:, 0], mobile_1[:, 1], linestyle=\"--\")\n",
-            "plt.plot(mobile_2[:, 0], mobile_2[:, 1], color=\"tab:blue\")\n",
-            "plt.yscale(\"log\")\n",
-            "plt.xlabel(\"$x$ (m)\")\n",
-            "plt.ylabel(\"solute concentration (H/m$^3$)\")"
+            "tungsten.id = 1\n",
+            "tungsten.borders = [0, 3e-3]\n",
+            "model_no_barrier.materials = [tungsten]\n",
+            "\n",
+            "# new mesh\n",
+            "model_no_barrier.mesh = F.MeshFromVertices(np.linspace(1e-6, 3e-3, num=50))\n",
+            "\n",
+            "# change the solubility of the Sievert's condition\n",
+            "left_bc.S_0 = tungsten.S_0\n",
+            "left_bc.E_S = tungsten.E_S\n",
+            "\n",
+            "model_no_barrier.T = model_barrier.T\n",
+            "model_no_barrier.boundary_conditions = model_barrier.boundary_conditions\n",
+            "\n",
+            "model_no_barrier.settings = model_barrier.settings\n",
+            "model_no_barrier.settings.chemical_pot = False  # no need for chemical potential anymore!\n",
+            "\n",
+            "model_no_barrier.dt = model_barrier.dt\n",
+            "\n",
+            "derived_quantities_without_barrier = F.DerivedQuantities([F.HydrogenFlux(surface=2)])\n",
+            "\n",
+            "model_no_barrier.exports = [derived_quantities_without_barrier]\n",
+            "\n",
+            "model_no_barrier.initialise()\n",
+            "model_no_barrier.run()"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "## 3) Calculate the PRF"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "We can plot the temporal evolution of permeation flux with or without permeation barriers:"
          ]
       },
       {
          "cell_type": "code",
-         "execution_count": null,
+         "execution_count": 11,
          "metadata": {},
-         "outputs": [],
+         "outputs": [
+            {
+               "data": {
+                  "image/png": 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",
+                  "text/plain": [
+                     "<Figure size 640x480 with 1 Axes>"
+                  ]
+               },
+               "metadata": {},
+               "output_type": "display_data"
+            }
+         ],
          "source": [
-            "solute_1_chemical_potential = np.genfromtxt(folder + '/mobile_2000.0s.txt')\n",
-            "solute_2_chemical_potential = np.genfromtxt(folder + '/mobile_17000.0s.txt')\n",
+            "t_with_barrier = derived_quantities_with_barrier.t\n",
+            "permeation_flux_with_barrier = derived_quantities_with_barrier.filter(surfaces=2, fields=\"solute\").data\n",
+            "permeation_flux_with_barrier = -np.array(permeation_flux_with_barrier)\n",
+            "\n",
+            "t_without_barrier = derived_quantities_without_barrier.t\n",
+            "permeation_flux_no_barrier = derived_quantities_without_barrier.filter(surfaces=2, fields=\"solute\").data\n",
+            "permeation_flux_no_barrier = -np.array(permeation_flux_no_barrier)\n",
             "\n",
             "plt.figure()\n",
-            "plt.plot(solute_1_chemical_potential[:, 0], solute_1_chemical_potential[:, 1], linestyle=\"--\")\n",
-            "plt.plot(solute_2_chemical_potential[:, 0], solute_2_chemical_potential[:, 1],\n",
-            "         color=\"tab:blue\", label=\"Chemical potential conservation\")\n",
             "\n",
-            "plt.yscale(\"log\")\n",
-            "plt.xlabel(\"$x$ (m)\")\n",
-            "plt.ylabel(\"solute concentration (H/m$^3$)\")\n",
-            "plt.legend()"
+            "plt.plot(t_without_barrier, permeation_flux_no_barrier, label=\"without barrier\")\n",
+            "plt.plot(t_with_barrier, permeation_flux_with_barrier, label=\"with barrier\")\n",
+            "\n",
+            "plt.xscale(\"log\")\n",
+            "plt.legend()\n",
+            "plt.xlabel(\"Time (s)\")\n",
+            "plt.ylabel(\"Permeation flux (H/m2/s)\")\n",
+            "plt.show()"
+         ]
+      },
+      {
+         "attachments": {},
+         "cell_type": "markdown",
+         "metadata": {},
+         "source": [
+            "Clearly, having the coating on both sides reduces the permeation flux!\n",
+            "\n",
+            "Moreover, it can be shown that the PRF of this configuration is:\n",
+            "\n",
+            "$$\\mathrm{PRF} = 1 + 2 \\alpha \\beta \\gamma$$\n",
+            "\n",
+            "With \n",
+            "\n",
+            "$$\\alpha = D_\\mathrm{substrate} / D_\\mathrm{barrier} $$\n",
+            "\n",
+            "$$\\beta = S_\\mathrm{substrate} / S_\\mathrm{barrier} $$\n",
+            "\n",
+            "$$\\gamma = e_\\mathrm{barrier} / e_\\mathrm{substrate} $$\n",
+            "\n",
+            "We can compare the computed PRF to the theory."
+         ]
+      },
+      {
+         "cell_type": "code",
+         "execution_count": 12,
+         "metadata": {},
+         "outputs": [
+            {
+               "name": "stdout",
+               "output_type": "stream",
+               "text": [
+                  "Theoretical PRF = 6.1113\n",
+                  "Computed PRF = 6.1135\n",
+                  "Error = 0.03%\n"
+               ]
+            }
+         ],
+         "source": [
+            "computed_PRF = permeation_flux_no_barrier[-1]/permeation_flux_with_barrier[-1]\n",
+            "\n",
+            "diff_ratio = tungsten.D_0/barrier_left.D_0\n",
+            "sol_ratio = tungsten.S_0/barrier_left.S_0\n",
+            "length_ratio = barrier_thick/substrate_thick\n",
+            "\n",
+            "theoretical_PRF = 1 + 2 * diff_ratio*sol_ratio*length_ratio\n",
+            "\n",
+            "print(f\"Theoretical PRF = {theoretical_PRF:.4f}\")\n",
+            "print(f\"Computed PRF = {computed_PRF:.4f}\")\n",
+            "print(f\"Error = {(computed_PRF - theoretical_PRF)/theoretical_PRF:.2%}\")"
          ]
       },
       {
@@ -320,8 +463,8 @@
          "cell_type": "markdown",
          "metadata": {},
          "source": [
-            "# Task\n",
-            "- Try altering the trap properties in each material and see how it affects the transport across the multi-material domain"
+            "# Question\n",
+            "- Will adding traps to the simulation change the value of the PRF?"
          ]
       }
    ],

From cc551b00dfd016f4cb564763cfa5fd4f3722ee42 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?R=C3=A9mi=20Delaporte-Mathurin?=
 <40028739+RemDelaporteMathurin@users.noreply.github.com>
Date: Mon, 3 Jul 2023 16:29:37 +0000
Subject: [PATCH 2/2] added solution

---
 tasks/task3.ipynb | 105 +++++++++++++---------------------------------
 1 file changed, 29 insertions(+), 76 deletions(-)

diff --git a/tasks/task3.ipynb b/tasks/task3.ipynb
index 885a4f6..327d8ee 100644
--- a/tasks/task3.ipynb
+++ b/tasks/task3.ipynb
@@ -24,7 +24,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 1,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -49,7 +49,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 2,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -96,7 +96,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 3,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -125,7 +125,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 4,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -142,7 +142,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 5,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -174,7 +174,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 6,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -205,7 +205,7 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 7,
+         "execution_count": null,
          "metadata": {},
          "outputs": [],
          "source": [
@@ -225,22 +225,9 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 8,
+         "execution_count": null,
          "metadata": {},
-         "outputs": [
-            {
-               "name": "stdout",
-               "output_type": "stream",
-               "text": [
-                  "Defining initial values\n",
-                  "Defining variational problem\n",
-                  "Defining source terms\n",
-                  "Defining boundary conditions\n",
-                  "Time stepping...\n",
-                  "100.0 %        8.0e+05 s    Ellapsed time so far: 1.6 s\n"
-               ]
-            }
-         ],
+         "outputs": [],
          "source": [
             "model_barrier.initialise()\n",
             "model_barrier.run()"
@@ -256,20 +243,9 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 9,
+         "execution_count": null,
          "metadata": {},
-         "outputs": [
-            {
-               "data": {
-                  "image/png": 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",
-                  "text/plain": [
-                     "<Figure size 640x480 with 3 Axes>"
-                  ]
-               },
-               "metadata": {},
-               "output_type": "display_data"
-            }
-         ],
+         "outputs": [],
          "source": [
             "import matplotlib.pyplot as plt\n",
             "\n",
@@ -308,22 +284,9 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 10,
+         "execution_count": null,
          "metadata": {},
-         "outputs": [
-            {
-               "name": "stdout",
-               "output_type": "stream",
-               "text": [
-                  "Defining initial values\n",
-                  "Defining variational problem\n",
-                  "Defining source terms\n",
-                  "Defining boundary conditions\n",
-                  "Time stepping...\n",
-                  "100.0 %        8.0e+05 s    Ellapsed time so far: 0.4 s\n"
-               ]
-            }
-         ],
+         "outputs": [],
          "source": [
             "model_no_barrier = F.Simulation()\n",
             "\n",
@@ -372,20 +335,9 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 11,
+         "execution_count": null,
          "metadata": {},
-         "outputs": [
-            {
-               "data": {
-                  "image/png": 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",
-                  "text/plain": [
-                     "<Figure size 640x480 with 1 Axes>"
-                  ]
-               },
-               "metadata": {},
-               "output_type": "display_data"
-            }
-         ],
+         "outputs": [],
          "source": [
             "t_with_barrier = derived_quantities_with_barrier.t\n",
             "permeation_flux_with_barrier = derived_quantities_with_barrier.filter(surfaces=2, fields=\"solute\").data\n",
@@ -431,19 +383,9 @@
       },
       {
          "cell_type": "code",
-         "execution_count": 12,
+         "execution_count": null,
          "metadata": {},
-         "outputs": [
-            {
-               "name": "stdout",
-               "output_type": "stream",
-               "text": [
-                  "Theoretical PRF = 6.1113\n",
-                  "Computed PRF = 6.1135\n",
-                  "Error = 0.03%\n"
-               ]
-            }
-         ],
+         "outputs": [],
          "source": [
             "computed_PRF = permeation_flux_no_barrier[-1]/permeation_flux_with_barrier[-1]\n",
             "\n",
@@ -464,7 +406,18 @@
          "metadata": {},
          "source": [
             "# Question\n",
-            "- Will adding traps to the simulation change the value of the PRF?"
+            "Will adding traps to the simulation change the value of the PRF?\n",
+            "\n",
+            "<details>\n",
+            "<summary>Show solution</summary>\n",
+            "<br>\n",
+            "No. The PRF is a measure of the flux of mobile particles and is computed at steady state.\n",
+            "\n",
+            "At steady state, the McNabb & Foster model states that the concentration of mobile particle is independent of the trapped concentration.\n",
+            "\n",
+            "Therefore, the steady state PRF is independent of trapping.\n",
+            "\n",
+            "</details>"
          ]
       }
    ],