{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# Imports & Constantes universelles\n",
    "%pylab inline\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "from ipywidgets import interact\n",
    "π = np.pi\n",
    "μ_0 = 4 * π * 10 ** (-7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "51eea72db3d546ecb70735d9d0c0b1e3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.2, description='E_0', max=0.6000000000000001, min=-0.2), IntSlider(v…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.effet_de_peau(E_0, f, γ, N, Z, duree)>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def effet_de_peau(E_0, f, γ, N, Z, duree):\n",
    "    \"\"\"\n",
    "    Anime l’évolution temporelle de la pénétration d’un champ dans un matériau:\n",
    "    - E_0: Amplitude du champ\n",
    "    - f: fréquence du champ\n",
    "    - γ: conductivité du matériau\n",
    "    - N: nombre de vecteurs à afficher\n",
    "    - Z: profondeur du dernier vecteur dans le matériau\n",
    "    - duree : intervale de temps écoulé entre deux images successives, en ms\n",
    "    \"\"\"\n",
    "    \n",
    "    def amplitude(t, z):\n",
    "        \"\"\"\n",
    "        Calcul de l’amplitude du champ à l’instant t et à une distance z de la surface\n",
    "        \"\"\"\n",
    "        ω = 2 * π * f  # Pulsation du champ, en rad/s\n",
    "        δ = sqrt(2 / (μ_0 * γ * ω))  # Épaisseur de peau, en m\n",
    "        return E_0 * exp(-z / δ) * cos(ω * t + z / δ)\n",
    "\n",
    "    def amplitudes(i, X):\n",
    "        \"\"\"\n",
    "        Calcule l’amplitude du champ à une liste de lieux de plus en plus profonds dans le matériau pour l’image i\n",
    "        \"\"\"\n",
    "        return [amplitude(i * duree / 1000, z) for z in X]\n",
    "\n",
    "    X = np.linspace(0, Z, N)  # Abscisses des vecteurs\n",
    "    Y = np.zeros(N)  # Ordonnées des vecteurs\n",
    "    U = np.zeros(N)  # Amplitude horizontale des vecteurs\n",
    "    V = amplitudes(0, X)  # Amplitude initiale verticale des vecteurs\n",
    "    fig, ax = plt.subplots()\n",
    "    Q = ax.quiver(X, Y, U, V, scale=1)\n",
    "\n",
    "    def update_quiver(i, Q):\n",
    "        V = amplitudes(i, X)\n",
    "        Q.set_UVC(U, V)\n",
    "        return Q,\n",
    "\n",
    "    anim = animation.FuncAnimation(fig, update_quiver, fargs=(Q,), interval=50, blit=False)\n",
    "    return HTML(anim.to_html5_video())\n",
    "\n",
    "\n",
    "interact(effet_de_peau, E_0=0.2, f=10, γ=60*10**6, N=10, Z=0.05, duree=1)"
   ]
  }
 ],
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