Commit f0160f8a by dmar

### Adding the folder for the 4th exercise

parent 855d31e1
 { "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from ase.io import read\n", "from ase.visualize import view\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sigma = 3.405\n", "epsilon = 119.8*8.616733e-5 # eV" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def g_step(box, n_bin, d):\n", " box += 1\n", " box *= np.sqrt(2)/sigma\n", " del_bin = box/n_bin #width of a bin\n", " \n", " g = np.zeros([n_bin,n_bin])\n", " g[0] = np.linspace(0,box,n_bin)\n", " g[0]+= del_bin*0.5\n", " \n", " for i in range(len(d)):\n", " for j in range(i+1,len(d)):\n", " g_index = d[i][j]/(del_bin)\n", " g[1,g_index.astype(int)] += 2\n", " # we count both for i and j.\n", " \n", " \n", " #nomalized by number of particles\n", " g[1] /= len(d[0])\n", " #and by bin volume\n", " \n", " for k in range(len(g[1])):\n", " g[1][k] /= ((k+1)**3 -k**3)*del_bin**3\n", " \n", " #side of the optimized cell: 5,269\n", " vol = (5.269/sigma)**3\n", " rho = 4./vol\n", " g[1] /= np.pi*(4/3)*rho\n", " return g;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 38 atom" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "trajectory = read('production_38-pos-1.xyz', index='::2')\n", "N = len(trajectory[0]) #number of atoms\n", "n_step = len(trajectory) #number of step\n", "\n", "#create a distance array\n", "dist = np.empty([0,N,N])\n", "for frame in trajectory:\n", " dist = np.append(dist, [frame.get_all_distances()],axis=0)\n", "\n", "#Lennard Jones units\n", "\n", "dist /= sigma" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "#understand what the distance array is:\n", "\n", "#dist0 = trajectory[0].get_all_distances()\n", "# print(dist0.shape)\n", "# print(dist0)\n", "# print(dist0[0])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "ename": "IndexError", "evalue": "index 200 is out of bounds for axis 1 with size 200", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;31m#average during the thermalized part of the simulation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_step\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mg_38\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mg_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbox\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mn_bin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0mg_38\u001b[0m \u001b[0;34m/=\u001b[0m \u001b[0mn_step\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m\u001b[0m in \u001b[0;36mg_step\u001b[0;34m(box, n_bin, d)\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0mg_index\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdel_bin\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m \u001b[0mg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mg_index\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 14\u001b[0m \u001b[0;31m# we count both for i and j.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mIndexError\u001b[0m: index 200 is out of bounds for axis 1 with size 200" ] } ], "source": [ "n_bin = 200 #number of bin in the graph\n", "box = 25 #side of the bon in the simulation \n", "g_38 = np.zeros([n_bin,n_bin])\n", "\n", "#average during the thermalized part of the simulation\n", "for i in range(n_step):\n", " g_38 += g_step(box,n_bin,dist[i])\n", "g_38 /= n_step\n", "\n", "plt.plot(g_38[0],g_38[1])\n", "plt.xlim(0,box/(2*sigma))\n", "plt.xlabel('distance [ units of $\\sigma$]')\n", "plt.ylabel('radial distribution function')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 150 atoms" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "trajectory = read('production_150-pos-1.xyz', index='::2')\n", "N = len(trajectory[0]) #number of atoms\n", "n_step = len(trajectory) #number of step\n", "\n", "dist = np.empty([0,N,N])\n", "for frame in trajectory:\n", " dist = np.append(dist, [frame.get_all_distances()],axis=0)\n", "dist /= sigma\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'radial distribution function')" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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