{ "metadata": { "name": "", "signature": "sha256:c731e51cdd6285c8346172aa8a5e2cda3589bfc27694468f7455b81b0736a970" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# On Browniam motion and Diffusion coefficient\n", "\n", "> In this notebook we perform a mini Brownian motion simulation in 3D and check that the mean squared displacement (the variance of the instantaneous position) follows the theoretical equation\n", "> \n", "> For a general introduction on Brownian motion simulation see [Theory - Introduction to Brownian Motion simulation](Theory - Introduction to Brownian Motion simulation.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\langle|\\vec{r}(t)-\\vec{r}(t+\\tau)|^2\\rangle = \\sigma^2 = 2 D N \\tau$$\n", "\n", "- $\\vec{r}(t)$ position at time $t$\n", "- $N$ number of dimensions ($N$=3 for 3D simulations)\n", "- $D$ diffusion coefficient\n", "- $\\tau$ time interval." ] }, { "cell_type": "code", "collapsed": false, "input": [ "D = 1\n", "t = 1\n", "N = 3\n", "sigma = np.sqrt(2*N*D*t)\n", "sigma_1d = np.sqrt(2*D*t)\n", "sigma" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "2.4494897427831779" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "n_trajectories = 100\n", "n_time_steps = 1000" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(1)\n", "\n", "dx = sigma_1d*np.random.randn(n_time_steps, n_trajectories)\n", "dy = sigma_1d*np.random.randn(n_time_steps, n_trajectories)\n", "dz = sigma_1d*np.random.randn(n_time_steps, n_trajectories)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "x, y, z = np.cumsum(dx, 0), np.cumsum(dy, 0), np.cumsum(dz, 0)\n", "\n", "r_squared = x**2 + y**2 + z**2 # squared distance form the origin\n", "dr_squared = dx**2 + dy**2 + dz**2 # squared delta-distance " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a consistency check we fit the diffusion coefficient from the simulated data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "D_fitted = dr_squared.mean()/(2*N*t) # Fitted diffusion coefficient\n", "print 'Fitted diffusion coefficient: %.5f , True value %.5f' % (D_fitted, D)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Fitted diffusion coefficient: 0.99889 , True value 1.00000\n" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **NOTE:** To fit $D$ we are averaging the squared distance covered at each time step in each trajectory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we plot as a function of time:\n", "\n", "1. the squared distance $|\\vec{r}(t)|^2$ for all the simulated trajectories (*light blue lines*),\n", "2. the mean squared displacement $\\langle |\\vec{r}(t)|^2 \\rangle$(the variance of the distance), (*red line*)\n", "3. the theoretical mean-squared-displacement (*dashed black line*)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "time = np.arange(r_squared.shape[0])*t\n", "\n", "plot(time, r_squared, lw=1.5, alpha=0.1, color='b')\n", "plot(time, r_squared.mean(1), 'r', lw=3, alpha=0.7)\n", "plot(time, (2*N*D)*time, 'k', lw=4, ls='--', alpha=0.6);\n", "xlabel('Time')\n", "ylabel('Squared distance')\n", "grid(True);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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T9ee7AHwMwMn6PtfVt78PwBSA367v83EwESAO4CyAsfAg7r777trx48cv8BY8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mcJhXKa62AgzwVnNTmOHPuVK6o4wQmqg4GOpSYxI52W6zPZ0Et4b3ZWrhtHJ3yQXrf3sy4czY/A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\nzkzh+Sg19NPMBbIc5zw9dJOmj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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note that the simulated $\\langle |\\vec{r}(t)|^2 \\rangle$ follows the theoretical trend $2\\,D\\,N\\,t$." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 } ], "metadata": {} } ] }