{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IPython Notebook for turning in solutions to the problems in the Essentials of Paleomagnetism Textbook by L. Tauxe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem from Chapter 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 2.3: Use the dipole formula ($\\tan (I) = 2 \\tan (\\lambda)$ where $I$ is inclination and $\\lambda$ is latitude and calculate the GAD field at 36 $^{\\circ}$N.  Note that declination is always zero for a GAD field.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pmagpy.pmag as pmag # this imports the PmagPy module pmag\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "# This allows us to plot in the notebook environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   55.5\n"
     ]
    }
   ],
   "source": [
    "lat = np.radians(36.) # remember to convert to radians!\n",
    "inc = np.degrees(np.arctan(2.*np.tan(lat)))# and back! \n",
    "print '%7.1f'%(inc) # and print it out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use the pmag function dia_vgp.  First let's figure out what it does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    converts declination, inclination, alpha95 to VGP, dp, dm\n",
      "    takes input as (Decs, Incs, a95, Site latitudes, Site Longitudes).  \n",
      "    These can be lists or individual values.\n",
      "    Returns longitude, latitude, dp, dm\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print pmag.dia_vgp.__doc__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use it to convert our directions to VGPs. Note that alpha95 is require but is not given here so we supply a zero in its place. Note also that westward longitudes are indicated by minus signs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  130.6    75.1\n"
     ]
    }
   ],
   "source": [
    "vgp_lat,vgp_lon,dp,dp= pmag.dia_vgp(345,47,0.,36,-112) \n",
    "print '%7.1f %7.1f'%(vgp_lat,vgp_lon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems from Chapter 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.1a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the magnetostatic interaction energy for one Bohr magneton in a field of 40 $\\mu$T and plot for angles 0 $\\rightarrow$ 180. To do anything, we need to import numpy and matplotlib first. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the equation: $E=-m_b B \\cos(\\theta)$ for range of $\\theta$s. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1083d2790>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7EgFg4UI4/vgwNOigQbDmmklHJFK6MiYId38deN3M/ufun5pZM3dfmKsDu/sH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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d2ed90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mb=9.27e-24 # one Bohr magneton in Am^2\n",
    "B=40e-6 # field in tesla\n",
    "thetas=np.arange(0,180,1) # makes an array of thetas from 0 to 180\n",
    "Es=-mb*B*np.cos(np.radians(thetas)) # makes an array of energies\n",
    "plt.plot(thetas,Es) # make a nice plot\n",
    "plt.title(\"Magnetostatic energy versus angle\")\n",
    "plt.xlabel(\"Angle between moment and applied field\")\n",
    "plt.ylabel(\"Magnetostatic in Joules\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.1b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the rest of the problem we need to know the thermal energy (Bolzmann's constant $k=1.38 x 10^{-23}$ J/K and the absolute temperature $T=300$ Kelvin.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Thermal energy at room temperature is:  4.14e-21\n"
     ]
    }
   ],
   "source": [
    "k=1.38e-23\n",
    "T=300\n",
    "print 'Thermal energy at room temperature is: ',k*T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is a LOT bigger than the magnetostatic energy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.2a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We must find the induced  moment $m$ knowing that the magnetetization (moment per unit volume) is  $M=\\chi_p H$ for a paramagnetic substance.  For Fayalite $\\chi_p$ = = 4.4 x 10$^{-4}$ (cgs; per unit volume). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0088\n"
     ]
    }
   ],
   "source": [
    "chi_p=4.4e-4 # susceptibility of fayalite in cgs per volume\n",
    "B = 10. # applied field in Oersteds\n",
    "vol=2. # volume in cm^3\n",
    "M=chi_p*B # magnetization\n",
    "m=M*vol # moment in emu\n",
    "print m\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.2b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have to convert everything to SI. \n",
    "\n",
    "$\\chi_{SI} = 4\\pi\\chi_{cgs}$\n",
    "\n",
    "$H_{SI}={{H_{cgs}}\\over {4\\pi 10^{-3}}}$\n",
    "\n",
    "$vol_{SI}={{vol_{cgs}}*{10^{-6}}}$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Magnetization in A/m is:  4.4\n",
      "magnetic moment in Am^2 is:  8.8e-06\n"
     ]
    }
   ],
   "source": [
    "chi_SI=chi_p*4.*np.pi\n",
    "H_SI = B/(np.pi*4.*1e-3)\n",
    "vol_SI=vol*1e-6\n",
    "M_SI=H_SI*chi_SI\n",
    "m_SI=M_SI*vol_SI\n",
    "print 'Magnetization in A/m is: ',M_SI\n",
    "print 'magnetic moment in Am^2 is: ',m_SI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have to convert the $m$ in Am$^2$ to emu cm$^{-3}$ by muliplying by 10$^3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converted to cgs, m is:  0.0088\n"
     ]
    }
   ],
   "source": [
    "m_cgs=m_SI*1e3\n",
    "print 'converted to cgs, m is: ',m_cgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The governing equation here is the Curie Law of  paramagnetic susceptibility (Equation 3.6 in the text):\n",
    "$$\n",
    "\\chi_p={M\\over H} =  {{Nm^2\\mu_o}\\over{3kv}}\\cdot {1\\over T}.\n",
    "$$\n",
    "\n",
    "which shows that $\\chi_p$ is inversely related to temperature. We were given $\\chi_p$ at 273K, so at 773K, we have:\n",
    "$$\n",
    "\\chi_{773} = {\\chi_{273}} { 273\\over{773}} = { 4.4 \\times 10^{-4}  } { 273\\over{773}} = 1.6 \\times 10^{-4} { {\\hbox {emu}} \\over {\\hbox {cm}^3 \\hbox{oe}}}\n",
    "$$\n",
    "\n",
    "So if $H$ = 100 oe at T= 773K:  \n",
    "\n",
    "$$\n",
    "M = \\chi_{773} H = 1.6 \\times 10^{-2} { {\\hbox {emu}} \\over {\\hbox {cm}^3 }}\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here again we use the Curie Law of Paramagnetism:\n",
    "$$\n",
    "\\chi_p =  {N\\over v} m_b^2 { {\\mu_o}\\over {3kT}} .\n",
    "$$\n",
    "\n",
    "${N\\over v}$ is the number of atomic magnetic moments per unit volume.  The number of atoms was   given to us as 4 x 10$^{28}$ per m$^3$ and ${\\bf m_b}$ is their moment (the Bohr magneton).   Looking up from Figure 3.4 in the text we find that there are 5 unpaired spins for Mn$^{2+}$.   So ${N\\over v}$ is 20 x 10$^{28}$.    The other parameters are given in the text as $\\mu_o = 4 \\pi$ x 10$^{-7}$ Hm$^{-1}$,  $m_b$ = 9.27 x 10$^{-24}$ Am$^2$ and $k$ = 1.381 x 10$^{-23}$ JK$^{-1}$.   So,  $\\chi_p \\sim 1.7$ x 10$^{-3}$.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this problem, we need to find the data file curie\\_example.dat that is in the curie folder in the Datafiles folder that comes with PmagPy.  Copy it into the same folder that has this notebook.  Read it in and make a simple X,Y plot of the data.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x108e783d0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T/JlZb+ChdB3XZnYd8JS73xUdLwRGuHtVmmvVcS1SRNxhyBC47LKwxKkUp7x3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d6bd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data=np.loadtxt('curie_example.dat').transpose()\n",
    "plt.plot(data[0],data[1])\n",
    "plt.xlabel(r'Temperature ($^{\\circ}$C)')\n",
    "plt.ylabel('Magnetization (arbitrary units)')\n",
    "           "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now go to the command line in the same directory and try curie.py with the syntax curie.py -f curie\\_example.dat to see how the second derivative method works. You will see that the Curie Temperature is $\\sim$ 550$^{\\circ}$C."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}