Electrodynamics 2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "from matplotlib.pyplot import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dispersion1_D(M,k,a):\n",
    "    return sqrt(4/M)*(abs(sin((1/2)*k*a)))\n",
    "def optical(m1,m2,k,a):\n",
    "    return sqrt(((1)/(m1*m2))*(m1+m2+sqrt(m1**2+m2**2+2*m1*m2*cos(k*a))))\n",
    "def acoustical(m1,m2,k,a):\n",
    "    return sqrt(((1)/(m1*m2))*(m1+m2-sqrt(m1**2+m2**2+2*m1*m2*(cos(k*a)))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1\n",
    "M = 1\n",
    "m1 = 1\n",
    "m2 = 1\n",
    "k = linspace(-(pi/a),(pi/a),1000)\n",
    "omega = dispersion1_D(M,k,a)\n",
    "o = optical(1000000,0.000001,k,a)\n",
    "a1 = acoustical(1000000,0.000001,k,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(k,omega)\n",
    "show()\n",
    "plot(k,o)\n",
    "plot(k,a1)\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def optical(m1, m2, k, a):\n",
    "    return np.sqrt((1 / (m1 * m2)) * (m1 + m2 + np.sqrt(m1**2 + m2**2 + 2 * m1 * m2 * np.cos(k * a))))\n",
    "\n",
    "def acoustical(m1, m2, k, a):\n",
    "    return np.sqrt((1 / (m1 * m2)) * (m1 + m2 - np.sqrt(m1**2 + m2**2 + 2 * m1 * m2 * np.cos(k * a))))\n",
    "\n",
    "# Parameters\n",
    "k = np.pi / a  # Assuming 'a' is defined\n",
    "m1_over_m2_values = np.linspace(0.00001, 100, 100)  # Varying the ratio of m1/m2 from 1 to 10\n",
    "\n",
    "# Set a constant value for 'a'\n",
    "a = 1.0\n",
    "\n",
    "# Calculate frequency differences for each 'm1/m2'\n",
    "frequency_differences = []\n",
    "\n",
    "for m_ratio in m1_over_m2_values:\n",
    "    optical_frequencies = optical(m_ratio,0.000001, k, a)\n",
    "    acoustical_frequencies = acoustical(m_ratio, 0.000001, k, a)\n",
    "    frequency_difference = optical_frequencies - acoustical_frequencies\n",
    "    frequency_differences.append(frequency_difference)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(m1_over_m2_values, frequency_differences)\n",
    "plt.title('Difference between Optical and Acoustical Frequencies at k = pi/a')\n",
    "plt.xlabel('Mass Ratio (m1/m2)')\n",
    "plt.ylabel('Forbidden gap')\n",
    "plt.show()"
   ]
  }
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