{
 "cells": [
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   "cell_type": "markdown",
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    "editable": true,
    "slideshow": {
     "slide_type": ""
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   },
   "source": [
    "# Dynamics terms and dynamics equation\n",
    "\n",
    "There are several different dynamics terms that are implemented in `micromagneticmodel`. Here, we will provide a short list of them, together with some basic properties.\n",
    "\n",
    "## Dynamics terms\n",
    "\n",
    "### 1. Precession\n",
    "\n",
    "The main parameter required for the precession term is the gyrotropic ratio `gamma`. Optionally, `name` can be given to the dynamics term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import micromagneticmodel as mm\n",
    "\n",
    "precession = mm.Precession(gamma0=2.211e5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of its arguments are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "221100.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precession.gamma0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'precession'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precession.name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "String and LaTeX representations are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Precession(gamma0=221100.0)'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repr(precession)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{\\gamma_{0}}{1 + \\alpha^{2}} \\mathbf{m} \\times \\mathbf{H}_\\text{eff}$"
      ],
      "text/plain": [
       "Precession(gamma0=221100.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precession"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Damping\n",
    "\n",
    "Damping dynamics term requires Gilbert damping $\\alpha$ to be provided. Optionally, `name` can be given as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "damping = mm.Damping(alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of attributes are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "damping.alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'damping'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "damping.name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "String and LaTeX representations are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Damping(alpha=0.1)'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repr(damping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{\\gamma_{0} \\alpha}{1 + \\alpha^{2}} \\mathbf{m} \\times (\\mathbf{m} \\times \\mathbf{H}_\\text{eff})$"
      ],
      "text/plain": [
       "Damping(alpha=0.1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "damping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Zhang-Li term\n",
    "\n",
    "This dynamics term requires the non-adiabatic factor $\\beta$ and velocity vector $\\mathbf{u}$ to be passed. As before, `name` is optional as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "zhangli = mm.ZhangLi(u=1e6, beta=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The attributes are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000000.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zhangli.u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zhangli.beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "String and LaTeX representations are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ZhangLi(u=1000000.0, beta=0.5)'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repr(zhangli)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{1+\\alpha\\beta}{1+\\alpha^{2}} \\mathbf{m} \\times (\\mathbf{m} \\times (\\mathbf{u} \\cdot \\boldsymbol\\nabla)\\mathbf{m}) - \\frac{\\beta - \\alpha}{1+\\alpha^{2}} \\mathbf{m} \\times (\\mathbf{u} \\cdot \\boldsymbol\\nabla)\\mathbf{m}$"
      ],
      "text/plain": [
       "ZhangLi(u=1000000.0, beta=0.5)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zhangli"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For time-dependent current terms please refer to [this notebook](https://ubermag.github.io/documentation/ipynb/oommfc/timedependent-field-current.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamics equation\n",
    "\n",
    "Dynamics equation of the micromagnetic system is the sum of dynamics terms. For instance, if we sum two dynamics terms, we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "micromagneticmodel.dynamics.dynamics.Dynamics"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(precession + damping)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we assign this value to a separate variable, we can explore some of its properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "dynamics = precession + damping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The string representation is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Precession(gamma0=221100.0) + Damping(alpha=0.1)'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repr(dynamics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the LaTeX representation is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{\\gamma_{0}}{1 + \\alpha^{2}} \\mathbf{m} \\times \\mathbf{H}_\\text{eff}-\\frac{\\gamma_{0} \\alpha}{1 + \\alpha^{2}} \\mathbf{m} \\times (\\mathbf{m} \\times \\mathbf{H}_\\text{eff})$"
      ],
      "text/plain": [
       "Precession(gamma0=221100.0) + Damping(alpha=0.1)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dynamics equation consists of two dynamics term. To add another term to it `+=` operator can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "dynamics += zhangli"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dynamics equation is now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{\\gamma_{0}}{1 + \\alpha^{2}} \\mathbf{m} \\times \\mathbf{H}_\\text{eff}-\\frac{\\gamma_{0} \\alpha}{1 + \\alpha^{2}} \\mathbf{m} \\times (\\mathbf{m} \\times \\mathbf{H}_\\text{eff})-\\frac{1+\\alpha\\beta}{1+\\alpha^{2}} \\mathbf{m} \\times (\\mathbf{m} \\times (\\mathbf{u} \\cdot \\boldsymbol\\nabla)\\mathbf{m}) - \\frac{\\beta - \\alpha}{1+\\alpha^{2}} \\mathbf{m} \\times (\\mathbf{u} \\cdot \\boldsymbol\\nabla)\\mathbf{m}$"
      ],
      "text/plain": [
       "Precession(gamma0=221100.0) + Damping(alpha=0.1) + ZhangLi(u=1000000.0, beta=0.5)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Accesing individual dynamics terms from the dynamics equation\n",
    "\n",
    "There are two ways of retrieving an individual dynamics term from the dynamics equation. Let us say we want to change the value of the Gilbert damping constant $\\alpha$.\n",
    "\n",
    "If a dynamics term with name `mydynamicsterm` was added to the Hamiltonian, that term can be accessed by typing `hamiltonian.nydynamicsterm`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{\\gamma_{0} \\alpha}{1 + \\alpha^{2}} \\mathbf{m} \\times (\\mathbf{m} \\times \\mathbf{H}_\\text{eff})$"
      ],
      "text/plain": [
       "Damping(alpha=0.1)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dynamics.damping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dynamics.damping.alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "dynamics.damping.alpha = 5e-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dynamics.damping.alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the precession term is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
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    "tags": []
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{\\gamma_{0}}{1 + \\alpha^{2}} \\mathbf{m} \\times \\mathbf{H}_\\text{eff}$"
      ],
      "text/plain": [
       "Precession(gamma0=221100.0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dynamics.precession"
   ]
  }
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