{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Python and Jupyter 3: Random Walks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A random walk is a process of taking successive steps in a randomized way. Here we will study a one-dimensional (1D) random walk, but it is certainly interesting to extend these results to more spatial dimensions. Next week in lab you will start to study Brownian motion in 2D, which is closely related. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import math\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will imagine our walker moving along the $y$-axis in integer sized steps. The walker will take one step up the axis, one step down, or stay it is with equal probability. In this week's example I will start using comments within my code to explain what it does. \n", "\n", "First we define the parameters of the random walk:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "dim=1 #This will eventually allow you to change the dimension of your simulation\n", "steps=100\n", "stepset=[-1,0,1] #Walker can go +1,-1, or 0\n", "origin=np.zeros((1,dim)) #Location where the walker begins" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we write the simulation:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "stepArray_shape = (steps, dim) #This fixes the shape of the array that we will store the history of the walker in.\n", "stepVals=np.random.choice(a=stepset, size=stepArray_shape) #This fills the array with randomly chosen steps.\n", "path = np.concatenate([origin, stepVals]).cumsum(0) #This makes a path of those steps by cumulatively adding them up as the walker progresses.\n", "start = path[:1] #The starting point of the walk\n", "stop = path[-1:] #The ending point of the walk" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A good practice to make sure your simulation is working well is to plot it. Here's a code that does that. The starting point is marked with a red plus, the ending point with a black dot and all the steps inbetween with blue dashes." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,4),dpi=200)\n", "ax = fig.add_subplot(111)\n", "\n", "ax.scatter(np.arange(steps+1), path, c='blue',alpha=0.25,s=0.05);\n", "ax.plot(path,c='blue',alpha=0.5,lw=0.5,ls='-',);\n", "ax.plot(0, start, c='red', marker='+')\n", "ax.plot(steps, stop, c='black', marker='o')\n", "\n", "plt.title('1D Random Walk')\n", "plt.tight_layout(pad=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Starting next week in lab, it will be useful to have thought a little about random walks. \n", "\n", "Once you understand how the random walk works, choose a number of times steps to run it for and compute the displacement $x$ of the walker at the end of this run. Repeat this 10 times, each time saving the total displacement of the walker at the end of the run. After these 10 runs, compute the mean of the square of the 10 displacements, that is, compute $\\overline{x^2}$ for these 10 runs. Save that. \n", "\n", "Now increase the number of time steps and repeat the whole process 10 mores times. Do this for 7 different numbers of time steps. \n", "\n", "Finally, make a plot in this notebook of the mean squared displacement $\\overline{x^2}$ vs. the number of times steps that you used for each of your runs. What do you notice about this plot? Can you think of a way to model the relationship? If so, fit your results to your model and report the parameters of your fit. \n", "\n", "Repeat everything you've done here, but now instead of running your code 10 times for each of your chosen number of time steps, run it 1000 times for each of them. Of course, you will not want to do this by hand. Now the model you want to use should be clearer. " ] } ], "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }