Experimento de Rutherford.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experimento de Rutherford"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ExperimentoRutherford import ExperimentoNumerico\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import multiprocessing\n",
    "import numpy as np\n",
    "import time\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parámetros de la función ExperimentoNumerico"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>N</b> <br>\n",
    "Número de partículas a simular en el experimento.\n",
    "\n",
    "<b>cpus(Parametro opcional)</b> <br>\n",
    "Número de nucleos que se usará para el computo. <br>\n",
    "(Default cpus=2)\n",
    "\n",
    "<b>tipo_cristal (Parametro opcional)</b><br>\n",
    "Tipo de cristal cúbico que se usará, disponibles \"pc\",\"bcc\",\"fcc\"<br>\n",
    "\"pc\" : primitive cube <br>\n",
    "\"bcc\": body centered cube <br>\n",
    "\"fcc\": face centerd cube <br>\n",
    "Aviso : Por el momento solo se tienen buenos resultados con \"fcc\" <br>\n",
    "(Default tipo_cristal=\"fcc\") <br>\n",
    "\n",
    "<b>z_a (Parametro opcional)</b>         \n",
    "Número atómico de elemento que conforman el blanco.<br>\n",
    "La opción de default es para el oro. <br> \n",
    "(Default: z_a = 79) <br>\n",
    "\n",
    "<b>num_laminas (Parametro opcional)</b><br>\n",
    "Número de láminas que compone al blanco. Cada lámina tiene 200 átomos de espesor. <br>\n",
    "(Default: num_laminas=2)\n",
    "\n",
    "<b> atom_radius (Parametro opcional)</b><br>\n",
    "Radio átomico del elemento que compone las laminas.<bt>\n",
    "El valor por default corresponde al del oro.<br>\n",
    "(Dafault: atom_radius = 1.44e-10)<br>\n",
    "    \n",
    "<b>diámetro_celda</b><br>\n",
    "Díametro de la celda unitaria.<br>\n",
    "El valor por default corresponde al del oro.<br>\n",
    "(Default:diámetro_celda4.07e-10)<br>\n",
    "\n",
    "<b>velocidad_inicial</b><br>\n",
    "Velocidad inicial de las partículas alfa.<br>\n",
    "(Default:velocidad_inicial=1.57e7)<br>\n",
    "\n",
    "<b>max_deslocacion</b><br>\n",
    "Añade aleatoridad a las posiciones de los átomos en la red cristalina.<br>Un valor mayor corresponde a la posibilidad de que el núcleo esté más lejos de su posición predeterminada. Se recomienda un valor de 0.5. <br>\n",
    "(Default:max_deslocacion= 0.5) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimento Angulos más Probables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aviso\n",
      "Tiempo aproximado  de los experimentos entre 5 a 15 minutos dependiendo de la maquina y los cpus ocupados.\n",
      "\n",
      "Iniciando experimento 1 ...\n",
      "Experimento 1 tardo 1.41 s en completarse\n",
      "Iniciando experimento 2 ...\n",
      "Experimento 2 tardo 2.89 s en completarse\n",
      "Iniciando experimento 3 ...\n",
      "Experimento 3 tardo 4.35 s en completarse\n",
      "Iniciando experimento 4 ...\n",
      "Experimento 4 tardo 10.49 s en completarse\n",
      "Iniciando experimento 5 ...\n",
      "Experimento 5 tardo 60.43 s en completarse\n",
      "Iniciando experimento 6 ...\n",
      "Experimento 6 tardo 101.52 s en completarse\n",
      "Iniciando experimento 7 ...\n",
      "Experimento 7 tardo 206.74 s en completarse\n",
      "Iniciando experimento 8 ...\n",
      "Experimento 8 tardo 540.05 s en completarse\n",
      "Iniciando experimento 9 ...\n",
      "Experimento 9 tardo 426.29 s en completarse\n",
      "\n",
      "Calculo numérico terminado !\n"
     ]
    }
   ],
   "source": [
    "print(\"Aviso\\nTiempo aproximado  de los experimentos entre 5 a 15 minutos dependiendo de la maquina y los cpus ocupados.\\n\")\n",
    "\n",
    "cpus            = 6\n",
    "max_deslocacion = 0.5\n",
    "\n",
    "experimento_laminas = [0.2,0.5,0.8,2,12,20,40,100,80]\n",
    "\n",
    "num_experimento = 0\n",
    "resultados      = []\n",
    "angulos         = []\n",
    "rebotes         = []\n",
    "\n",
    "for num_laminas in experimento_laminas:\n",
    "    num_experimento += 1\n",
    "    print(f\"Iniciando experimento {num_experimento} ...\")\n",
    "    inicio = time.time()\n",
    "    output = ExperimentoNumerico(N=30_000,\n",
    "                                 tipo_cristal=\"fcc\",\n",
    "                                 cpus=cpus,\n",
    "                                 num_laminas=num_laminas,\n",
    "                                 max_deslocacion = max_deslocacion)\n",
    "    resultados.append(output[\"datos\"])\n",
    "    x = output[\"datos\"][:,0]\n",
    "    y = output[\"datos\"][:,1]\n",
    "    z = output[\"datos\"][:,2]\n",
    "    pos      = output[\"datos\"][:,0:3]\n",
    "    pp       = np.sum(pos*np.array([0,1,0]),axis=1)\n",
    "    angulos.append(np.arccos(pp)*180 / math.pi)\n",
    "    final   = time.time()\n",
    "    tiempo   = round(final-inicio,2)\n",
    "    print(f\"Experimento {num_experimento} tardo {tiempo} s en completarse\")\n",
    "\n",
    "print(\"\\nCalculo numérico terminado !\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRAFICA 1 : Histograma muy pocas láminas.\n",
    "\n",
    "graficar_experimento = [0,1,2]\n",
    "lista_max_ang        = []\n",
    "for num_experimento in graficar_experimento:\n",
    "    num_laminas = experimento_laminas[num_experimento]\n",
    "    n,bins,_ = plt.hist(angulos[num_experimento],\n",
    "                        bins=60,\n",
    "                        density=True,\n",
    "                        range=(0,2),\n",
    "                        alpha=0.5,\n",
    "                        label=f\"{num_laminas} laminas\")\n",
    "    index   = np.argmax(n)\n",
    "    max_ang = bins[index]\n",
    "    lista_max_ang.append(max_ang)\n",
    "\n",
    "plt.title(\"Histograma de Probabilidad de Ángulos de Dispersión.\")\n",
    "plt.xlabel(\"Ángulo de desviación\")\n",
    "plt.ylabel(\"Densidad de probabilidad\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "##### GRAFICA 2 : Histograma muchas láminas.\n",
    "\n",
    "graficar_experimento = [3,4,5,6,7,8]\n",
    "for num_experimento in graficar_experimento:\n",
    "    num_laminas = experimento_laminas[num_experimento]\n",
    "    n,bins,_ = plt.hist(angulos[num_experimento],\n",
    "                        bins=60,\n",
    "                        density=True,\n",
    "                        range=(0,20),\n",
    "                        alpha=0.5,\n",
    "                        label=f\"{num_laminas} laminas\")\n",
    "    index   = np.argmax(n)\n",
    "    max_ang = bins[index]\n",
    "    lista_max_ang.append(max_ang)\n",
    "\n",
    "plt.title(\"Histograma de Probabilidad de Ángulos de Dispersión.\")\n",
    "plt.xlabel(\"Ángulo de desviación\")\n",
    "plt.ylabel(\"Densidad de probabilidad\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# GRAFICA 3 : GRAFICA ÁNGULOS MÁS PROBABLES.\n",
    "\n",
    "experimento_laminas_cm = np.copy(np.array(experimento_laminas))*0.038\n",
    "plt.plot(experimento_laminas_cm,lista_max_ang,\".\",c=\"firebrick\",markersize=15)\n",
    "plt.xlabel(\"Grosor del blanco en cm de aire\")\n",
    "plt.ylabel(\"Ángulo de dispersión más probable.\")\n",
    "#X = np.arange(0,100*0.038,0.01)\n",
    "#Y = 0.8*np.sqrt(X*0.038)\n",
    "#plt.plot(X,Y,\"--\",alpha=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Experimento Numéro de Partículas Rebotadas "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aviso\n",
      "Tiempo aproximado  de los experimentos entre 5 a 15 minutos dependiendo de la maquina y los cpus ocupados.\n",
      "\n",
      "Iniciando experimento 1 ...\n",
      "Experimento 1 tardo 9.45 s en completarse\n",
      "Iniciando experimento 2 ...\n",
      "Experimento 2 tardo 18.32 s en completarse\n",
      "Iniciando experimento 3 ...\n",
      "Experimento 3 tardo 28.19 s en completarse\n",
      "Iniciando experimento 4 ...\n",
      "Experimento 4 tardo 35.86 s en completarse\n",
      "Iniciando experimento 5 ...\n",
      "Experimento 5 tardo 45.44 s en completarse\n",
      "Iniciando experimento 6 ...\n",
      "Experimento 6 tardo 52.72 s en completarse\n",
      "Iniciando experimento 7 ...\n",
      "Experimento 7 tardo 66.73 s en completarse\n",
      "Iniciando experimento 8 ...\n",
      "Experimento 8 tardo 79.49 s en completarse\n",
      "\n",
      "Calculo numérico terminado !\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Partículas reflectadas')"
      ]
     },
     "execution_count": 10,
     "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": [
    "print(\"Aviso\\nTiempo aproximado  de los experimentos entre 5 a 15 minutos dependiendo de la maquina y los cpus ocupados.\\n\")\n",
    "\n",
    "cpus            = 8\n",
    "max_deslocacion = 0.5\n",
    "\n",
    "experimento_laminas = [10,12,14,16]\n",
    "\n",
    "num_experimento = 0\n",
    "resultados      = []\n",
    "angulos         = []\n",
    "rebotes         = []\n",
    "\n",
    "for num_laminas in experimento_laminas:\n",
    "    num_experimento += 1\n",
    "    print(f\"Iniciando experimento {num_experimento} ...\")\n",
    "    inicio = time.time()\n",
    "    output = ExperimentoNumerico(N=30_000,\n",
    "                                 tipo_cristal=\"fcc\",\n",
    "                                 cpus=cpus,\n",
    "                                 num_laminas=num_laminas,\n",
    "                                 max_deslocacion = max_deslocacion)\n",
    "    resultados.append(output[\"datos\"])\n",
    "    x = output[\"datos\"][:,0]\n",
    "    y = output[\"datos\"][:,1]\n",
    "    z = output[\"datos\"][:,2]\n",
    "    pos      = output[\"datos\"][:,0:3]\n",
    "    pp       = np.sum(pos*np.array([0,1,0]),axis=1)\n",
    "    angulos.append(np.arccos(pp)*180 / math.pi)\n",
    "    final   = time.time()\n",
    "    tiempo   = round(final-inicio,2)\n",
    "    print(f\"Experimento {num_experimento} tardo {tiempo} s en completarse\")\n",
    "\n",
    "print(\"\\nCalculo numérico terminado !\")\n",
    "\n",
    "# Contamos las partículas rebotadas.\n",
    "for experimento in resultados:\n",
    "    y           = experimento[:,1]\n",
    "    num_rebotes = y[y < 0]\n",
    "    num_rebotes = np.sum(num_rebotes)\n",
    "    rebotes.append(num_rebotes)\n",
    "\n",
    "# Plot\n",
    "a = experimento_laminas[:-2]\n",
    "b = rebotes[:-2]\n",
    "b = [abs(c) for c in b]\n",
    "a = [str(c) for c in a]\n",
    "plt.bar(a,b)\n",
    "plt.xlabel(\"Número de láminas\")\n",
    "plt.ylabel(\"Partículas reflectadas\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experimento a distintas velocidad de la partícula alfa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cpus = 6\n",
    "max_deslocacion = 0.5\n",
    "vel_base    = 1.57e7  \n",
    "num_laminas = 6\n",
    "velocidades = [0.4,0.6,0.8,1.0,1.2,1.4]\n",
    "\n",
    "num_experimento = 0\n",
    "resultados      = []\n",
    "angulos         = []\n",
    "\n",
    "for velocidad_inicial in velocidades:\n",
    "    num_experimento += 1\n",
    "    print(f\"Iniciando experimento {num_experimento} ...\")\n",
    "    inicio = time.time()\n",
    "    output = ExperimentoNumerico(N               = 30_000,\n",
    "                                 tipo_cristal    = \"fcc\",\n",
    "                                 cpus            = cpus,\n",
    "                                 num_laminas     = num_laminas,\n",
    "                                 max_deslocacion = max_deslocacion,\n",
    "                                 vel_inicial     = velocidad_inicial*vel_base)\n",
    "    resultados.append(output[\"datos\"])\n",
    "    x = output[\"datos\"][:,0]\n",
    "    y = output[\"datos\"][:,1]\n",
    "    z = output[\"datos\"][:,2]\n",
    "    pos      = output[\"datos\"][:,0:3]\n",
    "    pp       = np.sum(pos*np.array([0,1,0]),axis=1)\n",
    "    angulos.append(np.arccos(pp)*180 / math.pi)\n",
    "    final   = time.time()\n",
    "    tiempo   = round(final-inicio,2)\n",
    "    print(f\"Experimento {num_experimento} tardo {tiempo} s en completarse\")\n",
    "\n",
    "print(\"\\nCalculo numérico terminado !\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "graficar_experimento = [0,1,2,3,4,5]\n",
    "lista_max_ang        = []\n",
    "for num_experimento in graficar_experimento:\n",
    "    vel_inicial = velocidades[num_experimento]\n",
    "    n,bins,_    = plt.hist(angulos[num_experimento],\n",
    "                        bins=60,\n",
    "                        density=True,\n",
    "                        range=(0,15),\n",
    "                        alpha=0.5,\n",
    "                        label=f\"{vel_inicial} velocidad original\")\n",
    "    index   = np.argmax(n)\n",
    "    max_ang = bins[index]\n",
    "    lista_max_ang.append(max_ang)\n",
    "\n",
    "plt.title(\"Histograma de Probabilidad de Ángulos de Dispersión.\")\n",
    "plt.xlabel(\"Ángulo de desviación\")\n",
    "plt.ylabel(\"Densidad de probabilidad\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "plt.plot(velocidades,lista_max_ang,\".\",c=\"darkblue\",markersize=15)\n",
    "plt.xlabel(\"Velocidad relativa\")\n",
    "plt.ylabel(\"Ángulo de dispersión más probable.\")\n",
    "#plt.xlim(0,1.4)\n"
   ]
  }
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