{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# The Stoner-Wolfharth model for Magnetic Hysteresis\n",
    "Instructions:  \n",
    "\n",
    "After opening the file, run the Python 2 kernel. Wait for the kernel to start  \n",
    "The code sohuld autorun, but if it does not you can manually select the cells and run them  \n",
    "You can interact with the plot to change the parameters and it will auto-update  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "    // AUTORUN ALL CELLS ON NOTEBOOK-LOAD!\n",
       "    require(\n",
       "        ['base/js/namespace', 'jquery'], \n",
       "        function(jupyter, $) {\n",
       "            $(jupyter.events).on(\"kernel_ready.Kernel\", function () {\n",
       "                console.log(\"Auto-running all cells-below...\");\n",
       "                jupyter.actions.call('jupyter-notebook:run-all-cells-below');\n",
       "            });\n",
       "        }\n",
       "    );\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<script>\n",
    "    // AUTORUN ALL CELLS ON NOTEBOOK-LOAD!\n",
    "    require(\n",
    "        ['base/js/namespace', 'jquery'], \n",
    "        function(jupyter, $) {\n",
    "            $(jupyter.events).on(\"kernel_ready.Kernel\", function () {\n",
    "                console.log(\"Auto-running all cells-below...\");\n",
    "                jupyter.actions.call('jupyter-notebook:run-all-cells-below');\n",
    "            });\n",
    "        }\n",
    "    );\n",
    "</script>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "code_show=true; \n",
       "function code_toggle() {\n",
       " if (code_show){\n",
       " $('div.input').hide();\n",
       " } else {\n",
       " $('div.input').show();\n",
       " }\n",
       " code_show = !code_show\n",
       "} \n",
       "$( document ).ready(code_toggle);\n",
       "</script>\n",
       "The raw code for this IPython notebook is by default hidden for easier reading.\n",
       "To toggle on/off the raw code, click <a href=\"javascript:code_toggle()\">here</a>."
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('''<script>\n",
    "code_show=true; \n",
    "function code_toggle() {\n",
    " if (code_show){\n",
    " $('div.input').hide();\n",
    " } else {\n",
    " $('div.input').show();\n",
    " }\n",
    " code_show = !code_show\n",
    "} \n",
    "$( document ).ready(code_toggle);\n",
    "</script>\n",
    "The raw code for this IPython notebook is by default hidden for easier reading.\n",
    "To toggle on/off the raw code, click <a href=\"javascript:code_toggle()\">here</a>.''')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function __main__.SWplt>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Srrt9ROQLEflYRB4QkT0ARGQvXIvTt+u2q+pa4FVgcHzXQbgkNLnMh8CSpDLG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\nMzMzsxJOmMzMzMxKOGEyMzMzK/H/Sk40lEdp6BwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dc83731518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import *\n",
    "from IPython.display import display\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import *\n",
    "from scipy.optimize import brentq\n",
    "\n",
    "def SW(Ms, H, theta):\n",
    "    theta = theta/360.0*2.0*np.pi\n",
    "    phis1=[]\n",
    "    phis2=[]\n",
    "    ### Top part\n",
    "    for h in H: \n",
    "        F = lambda phi : 0.5*np.sin(2*(phi-theta)) + h*np.sin(phi) \n",
    "        phi = np.linspace(0, np.pi, points)\n",
    "        \n",
    "        phi_initial_guess = 0.8\n",
    "        \n",
    "        if max(F(phi)) > 0:\n",
    "                p = brentq(F, 0, phi[np.argmax(F(phi))])\n",
    "        else:\n",
    "            p = np.pi\n",
    "        phis1.append(p)\n",
    "    phis1 = np.array(phis1,dtype='float')\n",
    "    ### Bottom part          \n",
    "    for h in H:\n",
    "        F = lambda phi : 0.5*np.sin(2*(phi-theta)) + h*np.sin(phi) \n",
    "        phi = np.linspace(2*np.pi, np.pi, points)\n",
    "        \n",
    "        phi_initial_guess = 4.0\n",
    "        if max(F(phi)) > 0:\n",
    "                p = brentq(F, np.pi, phi[np.argmax(F(phi))])\n",
    "        else:\n",
    "            p = 0\n",
    "        phis2.append(p)\n",
    "    phis2 = np.array(phis2, dtype='float')\n",
    "    \n",
    "    for i in range(len(phis1)):\n",
    "        if H[i] < 0 and np.cos(phis2[i]) > np.cos(phis1[i]):\n",
    "            phis1[i] = phis2[i]\n",
    "    for i in range(len(phis2)):\n",
    "        if H[i] > 0 and np.cos(phis2[i]) > np.cos(phis1[i]):\n",
    "            phis2[i] = phis1[i]\n",
    "    return phis1, phis2\n",
    "points = 200\n",
    "H = np.linspace(-1.0,1.0,points)\n",
    "Ms=1752 #saturation of iron\n",
    "Ku=1.0e5 #anisotropy of iron\n",
    "theta0 = 45.0\n",
    "def SWplt(Ku, Ms, theta):\n",
    "    mu0 = 4*np.pi*1.0e-7 #V*s/(A*m)\n",
    "    points = 200\n",
    "    h = np.linspace(-1.0,1.0,points)\n",
    "    Hk = (2*Ku)/(Ms)\n",
    "    H = h*Hk*1.0e-3\n",
    "    \n",
    "    phis1, phis2 = SW(Ms, h, theta)\n",
    "    fig, ax = plt.subplots()\n",
    "    subplots_adjust(bottom=0.3)\n",
    "    \n",
    "    l, = plot(H, Ms*np.cos(phis1), 'b', linewidth=4)\n",
    "    k, = plot(H, Ms*np.cos(phis2), 'b', lw = 4)\n",
    "\n",
    "#     ax.set_ylim([-1.1,1.1])\n",
    "#     ax.set_xlim([-1.1,1.1])\n",
    "    ax.tick_params(axis='both', which='major', labelsize=10)\n",
    "    ax.set_xlabel('H (Oe)', fontsize=20)\n",
    "    ax.set_ylabel('M (emu/cc)',fontsize=20)\n",
    "    plt.grid(b=True, which='both')\n",
    "\n",
    "stheta = BoundedFloatText(value=theta0, min =0.0, max = 89.9, description= ''r'$\\theta$ (deg)' )\n",
    "Msbox = BoundedFloatText(value=Ms, min =0.2, max = 2000., description='M'r'$_s$ (T)' )\n",
    "Kubox = BoundedFloatText(value=Ku, min =0.2, max = 1.0e6, description='K'r'$_u$' )\n",
    "   \n",
    "interact(SWplt, Ku = Kubox, Ms = Msbox, theta=stheta)\n",
    "\n",
    "#h = μ0MsH/2Ku\n",
    "# H = h/mu0 / Ms*2*Ku\n",
    "\n"
   ]
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