Tarea5y6_CVS.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3d1daf68-74f1-40f1-a5ad-23a796c46214",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import sklearn as sl\n",
    "\n",
    "import matplotlib as mpl\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "from matplotlib import cm\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf4c00ca-7c26-4ce5-a533-0432a50ce2c3",
   "metadata": {},
   "source": [
    "1. Escriba la ecuación de difusión para el tiempo  en coordenadas esféricas y asuma que  ya que por simetría esférica sólo dependerá de la posición radial respecto al centro de la gotica (Usar LaTex)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da2dc43f-5f82-46b8-80d4-64b84d05e68a",
   "metadata": {},
   "source": [
    "$$\\nabla^2\\tau=-\\frac{6\\pi\\eta a}{k_B T}$$\n",
    "$$\\nabla^2\\tau=\\frac{1}{r^2} \\frac{\\partial}{\\partial_r}(r^2 \\frac{\\partial_t}{\\partial_r})+ \\frac{1}{r^2 \\sin\\theta}\\frac{\\partial}{\\partial_\\theta}(\\sin\\theta \\frac{\\partial_t}{\\partial_\\theta})+\\frac{1}{r^2 \\sin\\theta}(\\frac{\\partial^2 t}{\\partial \\varphi^2})$$\n",
    "$$\\nabla^2\\tau=\\frac{1}{r^2} \\frac{\\partial}{\\partial_r}(r^2 \\frac{\\partial_t}{\\partial_r})+0+0$$\n",
    "$$\\frac{1}{r^2} \\frac{\\partial}{\\partial_r}(r^2 \\frac{\\partial_t}{\\partial_r})=-\\frac{6\\pi\\eta a}{k_B T}$$\n",
    "$$\\frac{1}{r^2}[(2r\\frac{\\partial_t}{\\partial_r}+r^2 \\frac{\\partial_t^2}{\\partial_r^2})]=-\\frac{6\\pi\\eta a}{k_B T}$$\n",
    "$$\\frac{\\partial_t^2}{\\partial_r^2}+\\frac{2\\partial_t}{r\\partial_r}=-\\frac{6\\pi\\eta a}{k_B T}$$\n",
    "$$\\frac{\\partial_t^2}{\\partial_r^2}+\\frac{2\\partial_t}{r\\partial_r}+\\frac{6\\pi\\eta a}{k_B T}=0$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2dd2301-ce64-4ca8-a5fc-f8844bcf86ce",
   "metadata": {},
   "source": [
    "2. Resuelva la ecuación diferencial para el tiempo de forma numérica y grafique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "242b83be-6ce1-4460-9484-a256aecb18c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 1*10**(-3)*(10**5)\n",
    "A = 1*10**(-7)\n",
    "D = (4.05*10**(-21))/(6*np.pi*E*A)\n",
    "R = 5*10**(-6)\n",
    "N = 200\n",
    "dr = (R)/(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "970233ce-56f3-442b-867a-477a4438b5df",
   "metadata": {},
   "outputs": [],
   "source": [
    "c0 = 0\n",
    "cN = 0\n",
    "r = np.arange(0, R, dr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8341b800-6388-4047-81c5-ec64ebcf8ddc",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = np.matrix([np.array([(r[i]-dr if j == i-1 and i > 0 else 0)for j in range(N)])for i in range(N) ]) # primera fila\n",
    "f = f + np.matrix([np.array([(-2*r[i] if j == i else 0)for j in range(N)])for i in range(N) ]) # primera fila\n",
    "f = f + np.matrix([np.array([(r[i]+dr if j == i+1 and i < N-1 else 0)for j in range(N)])for i in range(N) ]) # última fila\n",
    "\n",
    "f[0,:] = np.zeros(N)\n",
    "f[0,0] = 1\n",
    "f[0,1] = -1\n",
    "f[-1, -1] = 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "09c99953-262f-49da-b341-3aa82d9ccf36",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = (-r*(dr**2)/D)\n",
    "c[0] = c0\n",
    "c[-1] = cN\n",
    "c = np.matrix(c).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b52324a1-1e12-4e05-9780-26bfff9b3c7d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Tau = np.array((np.linalg.inv(f)*c).T).flatten()\n",
    "r1 = np.arange(0,5,5/N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "87454b94-6dde-4cea-af14-700fd904514e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Tau')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r1, Tau, label=\"Solucion\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"Tau\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f641725-7224-42d7-ac6b-5435317ed177",
   "metadata": {},
   "source": [
    "3. Si los viriones están distribuidos uniformemente, encuentre el tiempo que tardaría un virión en salir de la gota de aerosol."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "806949df-8bf9-45a2-a9e8-94e156394fba",
   "metadata": {},
   "outputs": [],
   "source": [
    "V = (4/3)*np.pi*(R**3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ec3b81d6-d1ee-4fe1-b28f-dd8fb87c5a76",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = sp.integrate.simpson(4*np.pi*Tau*(r**2)/V, r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "647f61d7-31dc-438d-bb43-a02cd117803d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "75650.1968281572\n"
     ]
    }
   ],
   "source": [
    "print (T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82661594-c46c-4900-8284-57eb0013b004",
   "metadata": {},
   "source": [
    "4. Las cadenas de Markov."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "879c069c-7ede-47d9-a088-10e6944ee4a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resumen:\n",
      "  alpha=8.59436692696235e-07\n",
      "  dx=5e-08\n",
      "  dt=0.0001\n"
     ]
    }
   ],
   "source": [
    "N = 100\n",
    "dx = R/N\n",
    "\n",
    "x = np.arange(0,R,dx)\n",
    "dt = 1e-4\n",
    "t = np.arange(0,T,dt)\n",
    "\n",
    "alpha = D*dt/dx**2\n",
    "\n",
    "assert alpha < 1/12\n",
    "\n",
    "print('Resumen:'\n",
    "     f'\\n  alpha={alpha}'\n",
    "     f'\\n  dx={dx}'\n",
    "     f'\\n  dt={dt}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "424ea633-9198-4e1f-be6e-75506b929b58",
   "metadata": {},
   "outputs": [],
   "source": [
    "def actualiza_objetos(n):\n",
    "    global alpha\n",
    "    # esta funcion me dice de n objetos cuantos van a la izquierda y cuantos a la derecha\n",
    "    v = np.random.uniform(size=n)\n",
    "    izq = sum(v<alpha)\n",
    "    der = sum(v<2*alpha) - izq\n",
    "    return (izq,der)\n",
    "\n",
    "def actualiza_phi(phi):\n",
    "    # calcular cuantos se van a la derecha y cuantos a la izquierda\n",
    "    dphi = np.array([actualiza_objetos(_phi) for _phi in phi]).T\n",
    "    # verificar cuantos hay.... reajustar cuantos se van: condiciones de frontera\n",
    "    dphi[0,0] = 0\n",
    "    dphi[1,-1] = 0\n",
    "    # sumar los q tenia phi0 + los q llegan - los q se van\n",
    "    dphi_izq = np.roll(dphi[0],-1)\n",
    "    dphi_der = np.roll(dphi[1], 1)\n",
    "    dphi = np.sum(dphi, axis=0)\n",
    "    return phi-dphi+dphi_izq+dphi_der"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "71d66881-c248-4acf-aec7-9ff80d470877",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1871e51e0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = np.zeros(N, dtype=np.uint32)\n",
    "# condiciones iniciales\n",
    "phi[0] = N*dx\n",
    "phi[N//2] = 15\n",
    "plt.scatter(x, phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "002ebd25-939e-4881-bee3-e2ff7f485c7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x187420910>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAEFCAYAAAD69rxNAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAAAO2UlEQVR4nO3df2ycB33H8c8H2wwnFFyUgzVOmQtiZlPZFnZCHdGY1lKSQdVG1ZBaUVS2SP5nY2Ub6RohDW3/gJSJgTRtk9dmBVGl29qQIcaaRqVVqVRKLz9KkroBVEpx0s1XVRl0jdQkfPeHn0yOa/vO9zx352/8fkmR7x7fPc/3UdW3Hj2+ex5HhAAA+byu3wMAADpDwAEgKQIOAEkRcABIioADQFKDvdzYunXrYmxsrJebBID0Dhw48GJE1OYv72nAx8bG1Gg0erlJAEjP9o8XWs4pFABIioADQFIEHACSIuAAkBQBB4CkevopFABYbfYeOqGd+47r5KnTWj8yrO2bx7V142gl6ybgANAlew+d0I49R3T6zDlJ0olTp7VjzxFJqiTinEIBgC7Zue/4/8f7vNNnzmnnvuOVrJ+AA0CXnDx1elnLl4uAA0CXrB8ZXtby5SLgANAl2zePa3ho4IJlw0MD2r55vJL180dMAOiS83+o5FMoAJDQ1o2jlQV7Pk6hAEBSBBwAkiLgAJAUAQeApAg4ACTVMuC2d9mesX10gd992nbYXted8QAAi2nnCPxuSVvmL7R9uaRrJT1f8UwAgDa0DHhEPCrppQV+9beSbpcUVQ8FAGito3Pgtq+XdCIinmrjtRO2G7YbzWazk80BABaw7IDbXiPpM5L+sp3XR8RkRNQjol6r1Za7OQDAIjo5An+npCskPWX7OUkbJB20/YtVDgYAWNqyr4USEUckvfX88yLi9Yh4scK5AAAttPMxwt2SHpc0bnva9rbujwUAaKXlEXhE3Nzi92OVTQMAaBvfxASApAg4ACRFwAEgKQIOAEkRcABIioADQFIEHACSIuAAkBQBB4CkCDgAJEXAASApAg4ASRFwAEiKgANAUgQcAJIi4ACQFAEHgKQIOAAk1c49MXfZnrF9dM6ynbafsf0921+zPdLVKQEAr9HOEfjdkrbMW7Zf0pUR8WuSvi9pR8VzAQBaaBnwiHhU0kvzlj0YEWeLp9+RtKELswEAllDFOfA/lPSfi/3S9oTthu1Gs9msYHMAAKlkwG1/RtJZSfcs9pqImIyIekTUa7Vamc0BAOYY7PSNtm+VdJ2kayIiqhsJANCOjgJue4ukv5D0OxHxSrUjAQDa0c7HCHdLelzSuO1p29sk/Z2kSyTtt33Y9j92eU4AwDwtj8Aj4uYFFt/VhVkAAMvANzEBICkCDgBJEXAASIqAA0BSBBwAkiLgAJAUAQeApAg4ACRFwAEgKQIOAEkRcABIioADQFIEHACSIuAAkBQBB4CkCDgAJEXAASCpdm6ptsv2jO2jc5a9xfZ+2z8ofl7a3TEBAPO1cwR+t6Qt85bdIemhiHiXpIeK5wCAHmoZ8Ih4VNJL8xbfIOnLxeMvS9pa7VgAgFY6PQf+toh4QZKKn29d7IW2J2w3bDeazWaHmwMAzNf1P2JGxGRE1COiXqvVur05AFg1Og34f9u+TJKKnzPVjQQAaEenAf+6pFuLx7dK+vdqxgEAtKudjxHulvS4pHHb07a3Sfq8pGtt/0DStcVzAEAPDbZ6QUTcvMivrql4FgDAMvBNTABIioADQFIEHACSIuAAkBQBB4CkCDgAJEXAASApAg4ASRFwAEiKgANAUgQcAJIi4ACQFAEHgKQIOAAkRcABICkCDgBJEXAASKpUwG3/qe1jto/a3m37DVUNBgBYWscBtz0q6U8k1SPiSkkDkm6qajAAwNLKnkIZlDRse1DSGkkny48EAGhHxwGPiBOS/kbS85JekPQ/EfHg/NfZnrDdsN1oNpudTwoAuECZUyiXSrpB0hWS1ktaa/uW+a+LiMmIqEdEvVardT4pAOACZU6hfFDSjyKiGRFnJO2R9P5qxgIAtFIm4M9Lusr2GtuWdI2kqWrGAgC0UuYc+BOS7pN0UNKRYl2TFc0FAGhhsMybI+Kzkj5b0SwAgGXgm5gAkBQBB4CkCDgAJEXAASApAg4ASRFwAEiKgANAUgQcAJIi4ACQFAEHgKQIOAAkRcABICkCDgBJEXAASIqAA0BSBBwAkiLgAJAUAQeApEoF3PaI7ftsP2N7yvZvVTUYAGBppe6JKelLkh6IiN+3/XpJayqYCQDQho4DbvtNkj4g6ROSFBGvSnq1mrEAAK2UOYXyDklNSf9s+5DtO22vnf8i2xO2G7YbzWazxOYAAHOVCfigpPdK+oeI2CjpfyXdMf9FETEZEfWIqNdqtRKbAwDMVSbg05KmI+KJ4vl9mg06AKAHOg54RPyXpJ/YHi8WXSPp6UqmAgC0VPZTKJ+UdE/xCZRnJf1B+ZEAAO0oFfCIOCypXs0oAIDl4JuYAJAUAQeApAg4ACRFwAEgKQIOAEkRcABIioADQFIEHACSIuAAkBQBB4CkCDgAJEXAASApAg4ASRFwAEiKgANAUgQcAJIi4ACQVOmA2x6wfcj2N6oYCADQniqOwG+TNFXBegAAy1Aq4LY3SPqIpDurGQcA0K6yR+BflHS7pJ8v9gLbE7YbthvNZrPk5gAA53UccNvXSZqJiANLvS4iJiOiHhH1Wq3W6eYAAPOUOQLfJOl6289JulfS1ba/WslUAICWOg54ROyIiA0RMSbpJknfiohbKpsMALAkPgcOAEkNVrGSiHhE0iNVrAsA0B6OwAEgKQIOAEkRcABIioADQFIEHACSIuAAkBQBB4CkCDgAJEXAASApAg4ASRFwAEiKgANAUgQcAJIi4ACQFAEHgKQIOAAkRcABIKkyd6W/3PbDtqdsH7N9W5WDAQCWVuaWamcl/XlEHLR9iaQDtvdHxNMVzQYAWEKZu9K/EBEHi8c/kzQlabSqwQAAS6vkHLjtMUkbJT1RxfoAAK2VDrjtN0q6X9KnIuKnC/x+wnbDdqPZbJbdHACgUCrgtoc0G+97ImLPQq+JiMmIqEdEvVarldkcAGCOMp9CsaS7JE1FxBeqGwkA0I4yR+CbJH1c0tW2Dxf/PlzRXACAFjr+GGFEPCbJFc4CAFgGvokJAEkRcABIioADQFIEHACSIuAAkBQBB4CkCDgAJEXAASApAg4ASRFwAEiKgANAUgQcAJIi4ACQFAEHgKQIOAAkRcABICkCDgBJEXAASKrjW6pJku0tkr4kaUDSnRHx+UqmmmPvoRPaue+4Tp46rTcPD8mWTr1ypq3H60eG9bvvrunhZ5odvb/bj1f6fJlmXenzZZp1pc+Xadb1I8PavnlcWzeOVp1GSZIjorM32gOSvi/pWknTkp6UdHNEPL3Ye+r1ejQajba3sffQCe3Yc0Snz5zraEYA6LfhoQF97sb3lIq47QMRUZ+/vMwplPdJ+mFEPBsRr0q6V9INJdb3Gjv3HSfeAFI7feacdu473pV1lwn4qKSfzHk+XSy7gO0J2w3bjWazuawNnDx1usR4ALAydKtlZQLuBZa95nxMRExGRD0i6rVabVkbWD8y3OlsALBidKtlZQI+LenyOc83SDpZbpwLbd88ruGhgSpXCQA9NTw0oO2bx7uy7jIBf1LSu2xfYfv1km6S9PVqxpq1deOoPnfjezQ6MixLGhke0qVrhtp+PDoyrFuuenvH7+/245U+X6ZZV/p8mWZd6fNlmnV0ZLj0HzCX0vHHCCPirO0/lrRPsx8j3BURxyqbrLB142jXdh4AMiv1OfCI+Kakb1Y0CwBgGfgmJgAkRcABICkCDgBJEXAASKrja6F0tDG7KenHHb59naQXKxwni9W436txn6XVud+rcZ+l5e/3L0XEa74J2dOAl2G7sdDFXC52q3G/V+M+S6tzv1fjPkvV7TenUAAgKQIOAEllCvhkvwfok9W436txn6XVud+rcZ+livY7zTlwAMCFMh2BAwDmIOAAkFSKgNveYvu47R/avqPf8/SC7V22Z2wf7fcsvWL7ctsP256yfcz2bf2eqdtsv8H2d20/VezzX/V7pl6xPWD7kO1v9HuWXrH9nO0jtg/bbv8GwYutb6WfA+/k5skXA9sfkPSypK9ExJX9nqcXbF8m6bKIOGj7EkkHJG29mP9b27aktRHxsu0hSY9Jui0ivtPn0brO9p9Jqkt6U0Rc1+95esH2c5LqEVHJl5cyHIF3/ebJK1FEPCrppX7P0UsR8UJEHCwe/0zSlBa4z+rFJGa9XDwdKv6t7KOqCtjeIOkjku7s9yyZZQh4WzdPxsXF9pikjZKe6PMoXVecSjgsaUbS/oi46PdZ0hcl3S7p532eo9dC0oO2D9ieKLuyDAFv6+bJuHjYfqOk+yV9KiJ+2u95ui0izkXEb2j2vrLvs31RnzKzfZ2kmYg40O9Z+mBTRLxX0u9J+qPiVGnHMgS86zdPxspRnAe+X9I9EbGn3/P0UkSckvSIpC39naTrNkm6vjgffK+kq21/tb8j9UZEnCx+zkj6mmZPEXcsQ8C7fvNkrAzFH/TukjQVEV/o9zy9YLtme6R4PCzpg5Ke6etQXRYROyJiQ0SMafb/529FxC19HqvrbK8t/jgv22slfUhSqU+ZrfiAR8RZSedvnjwl6V+7cfPklcb2bkmPSxq3PW17W79n6oFNkj6u2SOyw8W/D/d7qC67TNLDtr+n2YOV/RGxaj5Wt8q8TdJjtp+S9F1J/xERD5RZ4Yr/GCEAYGEr/ggcALAwAg4ASRFwAEiKgANAUgQcADpU9UXnbL/d9oPFBd2eLr6RvCgCDgCdu1vVfvHqK5J2RsSvaPZLPjNLvZiAA0CHFrronO132n6guN7Jt22/u5112f5VSYMRsb9Y98sR8cpS7yHgAFCtSUmfjIjflPRpSX/f5vt+WdIp23uK66TvLC6nvajBkoMCAArFhdjeL+nfZq8MIUn6heJ3N0r66wXediIiNmu2x7+t2atwPi/pXyR9QrOXl1gQAQeA6rxO0qni6pIXKC7OttQF2qYlHYqIZyXJ9l5JV2mJgHMKBQAqUlz++Ee2PyrNXqDN9q+3+fYnJV1qu1Y8v1rSknejIuAA0KFFLjr3MUnbiotWHVObdxCLiHOaPWf+kO0jmr0Xwj8tuX0uZgUAOXEEDgBJEXAASIqAA0BSBBwAkiLgAJAUAQeApAg4ACT1fwyD71pMQiv3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = np.zeros(N, dtype=np.uint32)\n",
    "# condiciones iniciales\n",
    "phi[0] = N*dx\n",
    "phi[N//-400] = 15\n",
    "plt.scatter(x, phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0dfd2a6c-d497-4bba-8198-d8bba9a97d12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x187484970>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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I7QOS/nXmyhCSpJ8pfnezpL+a423HI2KDZnr8G5q5CueLkv5Z0sc1c3mJORFwAKjPGySdLK4ueYHi4mwLXaDtmKQDEfG8JNneLekaLRBwDqEAQE2Kyx//wPbvSjMXaLP9K12+/WlJl9tuFM+vlbTg3agIOACUNM9F535P0ubiolVH1OUdxCLirGaOmT9i+5Bm7oXwjwuun4tZAUBO7IEDQFIEHACSIuAAkBQBB4CkCDgAJEXAASApAg4ASf0fADbzNow9VNgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = np.zeros(N, dtype=np.uint32)\n",
    "# condiciones iniciales\n",
    "phi[0] = N*dx\n",
    "phi[N//400] = 15\n",
    "plt.scatter(x, phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "820c95d2-44e0-4b44-9f90-a6596c1856af",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'L' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/g0/1krznd0j4xq2w7hp515svkb80000gp/T/ipykernel_46715/2253159197.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_xlim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_ylim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mphi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_ylim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mauto\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mphi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'L' is not defined"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "# First set up the figure, the axis, and the plot element we want to animate\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_xlim(( 0, L))\n",
    "ax.set_ylim((0, max(phi)))\n",
    "ax.set_ylim(auto=True, ymin=0, ymax=max(phi))\n",
    "\n",
    "line, = ax.plot([], [], 'o', lw=2)\n",
    "\n",
    "# initialization function: plot the background of each frame\n",
    "def init():\n",
    "    line.set_data([], [])\n",
    "    return (line,)\n",
    "\n",
    "# animation function. This is called sequentially\n",
    "def animate(i):\n",
    "    global phi\n",
    "    phi = actualiza_phi(phi)\n",
    "    line.set_data(x, phi)\n",
    "    return (line,)\n",
    "\n",
    "### call the animator. blit=True means only re-draw the parts that have changed.\n",
    "\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=200, interval=40, blit=True)\n",
    "\n",
    "# equivalent to rcParams['animation.html'] = 'html5'\n",
    "rc('animation', html='jshtml')\n",
    "rc\n",
    "tohtml = anim.to_jshtml()\n",
    "plt.clf()\n",
    "\n",
    "HTML(tohtml)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "faf70ae7-28db-4bbc-aebb-c3283f979f33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1894a8b3-bd36-461f-b118-e7a5210a8ba3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:fisi2028]",
   "language": "python",
   "name": "conda-env-fisi2028-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}