{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.linspace(0,1,1000)\n",
    "y = 1 + x - 2*np.sqrt(x)\n",
    "\n",
    "plt.rc('font', size=20)\n",
    "plt.plot(x,y, lw=4)\n",
    "plt.xlabel(r'$T_c/T_h$')\n",
    "plt.ylabel(r'$W_{max}/T_hC$')\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1);\n",
    "plt.tight_layout();\n",
    "plt.savefig('htwork_plot.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def get_η(ξ,r):\n",
    "    if ξ==0:\n",
    "        return 1-r\n",
    "    else:\n",
    "        return (r + ξ*(1-np.sqrt(r)) - r/(1-ξ+ξ*np.sqrt(r))) / ξ / (1-np.sqrt(r))\n",
    "    \n",
    "ξ = np.linspace(0,1,1000)\n",
    "η = np.zeros(len(ξ))\n",
    "r = np.array([0.001, 0.2, 0.4, 0.6, 0.8, 0.999])\n",
    "\n",
    "plt.rc('font', size=14)\n",
    "for ri in r:\n",
    "    for i in range(len(ξ)):\n",
    "        η[i] = get_η(ξ[i], ri)\n",
    "    plt.plot(ξ, η/(1-ri))\n",
    "labels=[str(np.round(ri,3)) for ri in r]\n",
    "labels[0] = r'T$_c$/T$_h\\approx 0$'\n",
    "labels[-1] = r'$\\approx 1$'\n",
    "plt.legend(labels, frameon=False)\n",
    "plt.xlabel(r'$\\xi$: T$_h$ $\\rightarrow$ $\\sqrt{T_cT_h}$')\n",
    "plt.ylabel(r'η/(1-T$_c$/T$_h$)')\n",
    "plt.xlim([0,1])\n",
    "plt.ylim([0.5,1])\n",
    "plt.tight_layout();\n",
    "plt.savefig('htwork_plot2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
