{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "from matplotlib import animation\n", "from matplotlib.animation import PillowWriter\n", "plt.style.use(['science', 'notebook'])\n", "from itertools import combinations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define number of particles and get random positions (between 0 and 1) for each particle" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "n_particles = 16\n", "r = np.random.random((2,n_particles))\n", "# Color particles the start on either side\n", "ixr = r[0]>0.5 #right\n", "ixl = r[0]<=0.5 #left" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Give IDs to each particle (this will come in handy later)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "ids = np.arange(n_particles)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot initial configuration of particles" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(5,5))\n", "plt.scatter(r[0][ixr],r[1][ixr], color='r', s=6)\n", "plt.scatter(r[0][ixl],r[1][ixl], color='b', s=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obtain the initial velocities in the gas. We'll make the particles starting on the RHS move to the left at 500m/s and on the vice versa.\n", "\n", "* **Note**: We're using the assumption that particles in a gas move at approximately 500m/s, thanks google." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "v = np.zeros((2,n_particles))\n", "v[0][ixr] = -500\n", "v[0][ixl] = 500" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To run this simulation, we need to determine when two particles collide, and what the resulting final velocities will be.\n", "\n", "# Part 1: Distance Between all Pairs\n", "\n", "* To determine if two particles collide, we need to find the distance between **all pairs** of particles. If the distance is less than 2 times the radius of each particle, they collide. If there are $n$ particles, there are $n(n-1)/2$ pairs (combinatorics). To make this easier, we'll get pairs of particle IDs." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0, 1],\n", " [ 0, 2],\n", " [ 0, 3],\n", " [ 0, 4],\n", " [ 0, 5],\n", " [ 0, 6],\n", " [ 0, 7],\n", " [ 0, 8],\n", " [ 0, 9],\n", " [ 0, 10],\n", " [ 0, 11],\n", " [ 0, 12],\n", " [ 0, 13],\n", " [ 0, 14],\n", " [ 0, 15],\n", " [ 1, 2],\n", " [ 1, 3],\n", " [ 1, 4],\n", " [ 1, 5],\n", " [ 1, 6],\n", " [ 1, 7],\n", " [ 1, 8],\n", " [ 1, 9],\n", " [ 1, 10],\n", " [ 1, 11],\n", " [ 1, 12],\n", " [ 1, 13],\n", " [ 1, 14],\n", " [ 1, 15],\n", " [ 2, 3],\n", " [ 2, 4],\n", " [ 2, 5],\n", " [ 2, 6],\n", " [ 2, 7],\n", " [ 2, 8],\n", " [ 2, 9],\n", " [ 2, 10],\n", " [ 2, 11],\n", " [ 2, 12],\n", " [ 2, 13],\n", " [ 2, 14],\n", " [ 2, 15],\n", " [ 3, 4],\n", " [ 3, 5],\n", " [ 3, 6],\n", " [ 3, 7],\n", " [ 3, 8],\n", " [ 3, 9],\n", " [ 3, 10],\n", " [ 3, 11],\n", " [ 3, 12],\n", " [ 3, 13],\n", " [ 3, 14],\n", " [ 3, 15],\n", " [ 4, 5],\n", " [ 4, 6],\n", " [ 4, 7],\n", " [ 4, 8],\n", " [ 4, 9],\n", " [ 4, 10],\n", " [ 4, 11],\n", " [ 4, 12],\n", " [ 4, 13],\n", " [ 4, 14],\n", " [ 4, 15],\n", " [ 5, 6],\n", " [ 5, 7],\n", " [ 5, 8],\n", " [ 5, 9],\n", " [ 5, 10],\n", " [ 5, 11],\n", " [ 5, 12],\n", " [ 5, 13],\n", " [ 5, 14],\n", " [ 5, 15],\n", " [ 6, 7],\n", " [ 6, 8],\n", " [ 6, 9],\n", " [ 6, 10],\n", " [ 6, 11],\n", " [ 6, 12],\n", " [ 6, 13],\n", " [ 6, 14],\n", " [ 6, 15],\n", " [ 7, 8],\n", " [ 7, 9],\n", " [ 7, 10],\n", " [ 7, 11],\n", " [ 7, 12],\n", " [ 7, 13],\n", " [ 7, 14],\n", " [ 7, 15],\n", " [ 8, 9],\n", " [ 8, 10],\n", " [ 8, 11],\n", " [ 8, 12],\n", " [ 8, 13],\n", " [ 8, 14],\n", " [ 8, 15],\n", " [ 9, 10],\n", " [ 9, 11],\n", " [ 9, 12],\n", " [ 9, 13],\n", " [ 9, 14],\n", " [ 9, 15],\n", " [10, 11],\n", " [10, 12],\n", " [10, 13],\n", " [10, 14],\n", " [10, 15],\n", " [11, 12],\n", " [11, 13],\n", " [11, 14],\n", " [11, 15],\n", " [12, 13],\n", " [12, 14],\n", " [12, 15],\n", " [13, 14],\n", " [13, 15],\n", " [14, 15]])" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ids_pairs = np.asarray(list(combinations(ids,2)))\n", "ids_pairs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can obtain distances between particles in a similar fashion\n", "\n", "* First get the pairs of x-positions of all particles" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.49933565, 0.77561466],\n", " [0.49933565, 0.52699193],\n", " [0.49933565, 0.31364623],\n", " [0.49933565, 0.55463916],\n", " [0.49933565, 0.40926665],\n", " [0.49933565, 0.39123562],\n", " [0.49933565, 0.45682861],\n", " [0.49933565, 0.13379506],\n", " [0.49933565, 0.40710839],\n", " [0.49933565, 0.73873508],\n", " [0.49933565, 0.64314611],\n", " [0.49933565, 0.16580246],\n", " [0.49933565, 0.52967437],\n", " [0.49933565, 0.20286087],\n", " [0.49933565, 0.62540561],\n", " [0.77561466, 0.52699193],\n", " [0.77561466, 0.31364623],\n", " [0.77561466, 0.55463916],\n", " [0.77561466, 0.40926665],\n", " [0.77561466, 0.39123562],\n", " [0.77561466, 0.45682861],\n", " [0.77561466, 0.13379506],\n", " [0.77561466, 0.40710839],\n", " [0.77561466, 0.73873508],\n", " [0.77561466, 0.64314611],\n", " [0.77561466, 0.16580246],\n", " [0.77561466, 0.52967437],\n", " [0.77561466, 0.20286087],\n", " [0.77561466, 0.62540561],\n", " [0.52699193, 0.31364623],\n", " [0.52699193, 0.55463916],\n", " [0.52699193, 0.40926665],\n", " [0.52699193, 0.39123562],\n", " [0.52699193, 0.45682861],\n", " [0.52699193, 0.13379506],\n", " [0.52699193, 0.40710839],\n", " [0.52699193, 0.73873508],\n", " [0.52699193, 0.64314611],\n", " [0.52699193, 0.16580246],\n", " [0.52699193, 0.52967437],\n", " [0.52699193, 0.20286087],\n", " [0.52699193, 0.62540561],\n", " [0.31364623, 0.55463916],\n", " [0.31364623, 0.40926665],\n", " [0.31364623, 0.39123562],\n", " [0.31364623, 0.45682861],\n", " [0.31364623, 0.13379506],\n", " [0.31364623, 0.40710839],\n", " [0.31364623, 0.73873508],\n", " [0.31364623, 0.64314611],\n", " [0.31364623, 0.16580246],\n", " [0.31364623, 0.52967437],\n", " [0.31364623, 0.20286087],\n", " [0.31364623, 0.62540561],\n", " [0.55463916, 0.40926665],\n", " [0.55463916, 0.39123562],\n", " [0.55463916, 0.45682861],\n", " [0.55463916, 0.13379506],\n", " [0.55463916, 0.40710839],\n", " [0.55463916, 0.73873508],\n", " [0.55463916, 0.64314611],\n", " [0.55463916, 0.16580246],\n", " [0.55463916, 0.52967437],\n", " [0.55463916, 0.20286087],\n", " [0.55463916, 0.62540561],\n", " [0.40926665, 0.39123562],\n", " [0.40926665, 0.45682861],\n", " [0.40926665, 0.13379506],\n", " [0.40926665, 0.40710839],\n", " [0.40926665, 0.73873508],\n", " [0.40926665, 0.64314611],\n", " [0.40926665, 0.16580246],\n", " [0.40926665, 0.52967437],\n", " [0.40926665, 0.20286087],\n", " [0.40926665, 0.62540561],\n", " [0.39123562, 0.45682861],\n", " [0.39123562, 0.13379506],\n", " [0.39123562, 0.40710839],\n", " [0.39123562, 0.73873508],\n", " [0.39123562, 0.64314611],\n", " [0.39123562, 0.16580246],\n", " [0.39123562, 0.52967437],\n", " [0.39123562, 0.20286087],\n", " [0.39123562, 0.62540561],\n", " [0.45682861, 0.13379506],\n", " [0.45682861, 0.40710839],\n", " [0.45682861, 0.73873508],\n", " [0.45682861, 0.64314611],\n", " [0.45682861, 0.16580246],\n", " [0.45682861, 0.52967437],\n", " [0.45682861, 0.20286087],\n", " [0.45682861, 0.62540561],\n", " [0.13379506, 0.40710839],\n", " [0.13379506, 0.73873508],\n", " [0.13379506, 0.64314611],\n", " [0.13379506, 0.16580246],\n", " [0.13379506, 0.52967437],\n", " [0.13379506, 0.20286087],\n", " [0.13379506, 0.62540561],\n", " [0.40710839, 0.73873508],\n", " [0.40710839, 0.64314611],\n", " [0.40710839, 0.16580246],\n", " [0.40710839, 0.52967437],\n", " [0.40710839, 0.20286087],\n", " [0.40710839, 0.62540561],\n", " [0.73873508, 0.64314611],\n", " [0.73873508, 0.16580246],\n", " [0.73873508, 0.52967437],\n", " [0.73873508, 0.20286087],\n", " [0.73873508, 0.62540561],\n", " [0.64314611, 0.16580246],\n", " [0.64314611, 0.52967437],\n", " [0.64314611, 0.20286087],\n", " [0.64314611, 0.62540561],\n", " [0.16580246, 0.52967437],\n", " [0.16580246, 0.20286087],\n", " [0.16580246, 0.62540561],\n", " [0.52967437, 0.20286087],\n", " [0.52967437, 0.62540561],\n", " [0.20286087, 0.62540561]])" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_pairs = np.asarray(list(combinations(r[0],2)))\n", "x_pairs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Then take the difference to get $\\Delta x_{ij}$ of all pairs" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.27627901, 0.02765628, -0.18568942, 0.0553035 , -0.090069 ,\n", " -0.10810003, -0.04250704, -0.36554059, -0.09222727, 0.23939943,\n", " 0.14381046, -0.3335332 , 0.03033871, -0.29647478, 0.12606996,\n", " -0.24862273, -0.46196843, -0.2209755 , -0.36634801, -0.38437904,\n", " -0.31878605, -0.6418196 , -0.36850628, -0.03687958, -0.13246855,\n", " -0.60981221, -0.24594029, -0.57275379, -0.15020905, -0.2133457 ,\n", " 0.02764722, -0.11772528, -0.13575631, -0.07016332, -0.39319687,\n", " -0.11988355, 0.21174315, 0.11615418, -0.36118948, 0.00268243,\n", " -0.32413106, 0.09841368, 0.24099292, 0.09562042, 0.07758939,\n", " 0.14318238, -0.17985117, 0.09346215, 0.42508885, 0.32949987,\n", " -0.14784378, 0.21602813, -0.11078537, 0.31175938, -0.14537251,\n", " -0.16340354, -0.09781054, -0.4208441 , -0.14753077, 0.18409593,\n", " 0.08850695, -0.3888367 , -0.02496479, -0.35177829, 0.07076645,\n", " -0.01803103, 0.04756196, -0.27547159, -0.00215826, 0.32946843,\n", " 0.23387946, -0.24346419, 0.12040772, -0.20640578, 0.21613896,\n", " 0.06559299, -0.25744056, 0.01587277, 0.34749946, 0.25191049,\n", " -0.22543316, 0.13843875, -0.18837475, 0.23416999, -0.32303355,\n", " -0.04972023, 0.28190647, 0.18631749, -0.29102616, 0.07284575,\n", " -0.25396775, 0.168577 , 0.27331333, 0.60494002, 0.50935105,\n", " 0.0320074 , 0.39587931, 0.06906581, 0.49161055, 0.3316267 ,\n", " 0.23603772, -0.24130593, 0.12256598, -0.20424752, 0.21829722,\n", " -0.09558898, -0.57293263, -0.20906072, -0.53587422, -0.11332947,\n", " -0.47734365, -0.11347174, -0.44028524, -0.0177405 , 0.36387191,\n", " 0.03705841, 0.45960315, -0.3268135 , 0.09573124, 0.42254474])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dx_pairs = np.diff(x_pairs, axis=1).ravel()\n", "dx_pairs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The total distance is just $d_{ij}= \\sqrt{\\Delta x_{ij}^2 + \\Delta y_{ij}^2}$. Since there are $n(n-1)/2$ pairs, there will be $n(n-1)/2$ different values of $d_{ij}$." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.42012821, 0.10333724, 0.21472688, 0.26288666, 0.42410117,\n", " 0.12650135, 0.24589389, 0.39215166, 0.31908645, 0.24158027,\n", " 0.34956931, 0.48748727, 0.24673789, 0.54456236, 0.16075572,\n", " 0.32996453, 0.50691419, 0.61461081, 0.37920814, 0.45896655,\n", " 0.64325016, 0.78877069, 0.36867165, 0.35083957, 0.13248534,\n", " 0.90747045, 0.25616271, 0.58968118, 0.26372299, 0.21350559,\n", " 0.3576416 , 0.33614786, 0.1399162 , 0.34888757, 0.46147265,\n", " 0.23825774, 0.24949405, 0.24794098, 0.58100686, 0.14532269,\n", " 0.48235244, 0.09841384, 0.43724187, 0.32116255, 0.0882873 ,\n", " 0.37817433, 0.30782977, 0.21862324, 0.44761717, 0.39115482,\n", " 0.48637072, 0.2558265 , 0.36611811, 0.31186421, 0.68698749,\n", " 0.36171923, 0.09892568, 0.43627563, 0.58149724, 0.2904201 ,\n", " 0.58238608, 0.40112443, 0.50248984, 0.7957636 , 0.36369835,\n", " 0.34918872, 0.65833887, 0.62087937, 0.1089806 , 0.55515054,\n", " 0.25274282, 0.80752913, 0.20796382, 0.21070697, 0.38176102,\n", " 0.31480501, 0.33077939, 0.24028847, 0.36107856, 0.35696555,\n", " 0.47776082, 0.22641613, 0.43408317, 0.23663113, 0.33821564,\n", " 0.54991166, 0.35141037, 0.59094986, 0.31231562, 0.49247494,\n", " 0.74368399, 0.38123233, 0.52433199, 0.61478988, 0.68673425,\n", " 0.21591609, 0.55351844, 0.60274965, 0.54783132, 0.47341531,\n", " 0.23640376, 0.70366331, 0.13672964, 0.25419191, 0.29995995,\n", " 0.36378814, 0.65777734, 0.34723992, 0.72556803, 0.17407507,\n", " 0.82603151, 0.13533372, 0.46145507, 0.219592 , 0.70204985,\n", " 0.81315504, 0.64692062, 0.38950755, 0.17385305, 0.55319199])" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_pairs = np.asarray(list(combinations(r[0],2)))\n", "y_pairs = np.asarray(list(combinations(r[1],2)))\n", "dx_pairs = np.diff(x_pairs, axis=1).ravel()\n", "dy_pairs = np.diff(y_pairs, axis=1).ravel()\n", "d_pairs = np.sqrt(dx_pairs**2 + dy_pairs**2)\n", "d_pairs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 2: Velocities of a Collision" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So at each iteration of the simulation, we will evaluate `d_pairs`, and if any of the distances between particles is less than $2r$, then a collision occurs. What is the final velocity of each of the two spheres? In an elastic collision (conservation of energy + momentum + angular momentum), one can show\n", "\n", "$$\\vec{v}_1^{\\text{new}} = \\vec{v}_1 - \\frac{(\\vec{v}_1 - \\vec{v}_2) \\cdot (\\vec{r}_1 - \\vec{r}_2)}{|\\vec{r}_1 - \\vec{r}_2|^2} (\\vec{r}_1 - \\vec{r}_2)$$\n", "$$\\vec{v}_2^{\\text{new}} = \\vec{v}_2 - \\frac{(\\vec{v}_2 - \\vec{v}_1) \\cdot (\\vec{r}_2 - \\vec{r}_1)}{|\\vec{r}_1 - \\vec{r}_2|^2} (\\vec{r}_2 - \\vec{r}_1)$$" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0, 2],\n", " [ 2, 15],\n", " [ 3, 6],\n", " [ 4, 7],\n", " [ 5, 9]])" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "radius = 0.06\n", "ids_pairs_collide = ids_pairs[d_pairs < 2*radius]\n", "ids_pairs_collide" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will call all the particles in the left column \"1\" and the right column \"2\"" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "v1 = v[:,ids_pairs_collide[:,0]]\n", "v2 = v[:,ids_pairs_collide[:,1]]\n", "r1 = r[:,ids_pairs_collide[:,0]]\n", "r2 = r[:,ids_pairs_collide[:,1]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we can compute the new velocity:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "v1new = v1 - np.diag((v1-v2).T@(r1-r2))/np.sum((r1-r2)**2, axis=0) * (r1-r2)\n", "v2new = v2 - np.diag((v2-v1).T@(r2-r1))/np.sum((r2-r1)**2, axis=0) * (r2-r1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 3: Functions to Run the Simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we define some functions that will help make running the simulation easier." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "def get_delta_pairs(x):\n", " return np.diff(np.asarray(list(combinations(x,2))), axis=1).ravel()\n", "\n", "def get_deltad_pairs(r):\n", " return np.sqrt(get_delta_pairs(r[0])**2 + get_delta_pairs(r[1])**2)\n", "\n", "def compute_new_v(v1, v2, r1, r2):\n", " v1new = v1 - np.diag((v1-v2).T@(r1-r2))/np.sum((r1-r2)**2, axis=0) * (r1-r2)\n", " v2new = v2 - np.diag((v2-v1).T@(r2-r1))/np.sum((r2-r1)**2, axis=0) * (r2-r1)\n", " return v1new, v2new\n", "\n", "def motion(r, v, id_pairs, ts, dt, d_cutoff):\n", " rs = np.zeros((ts, r.shape[0], r.shape[1]))\n", " vs = np.zeros((ts, v.shape[0], v.shape[1]))\n", " # Initial State\n", " rs[0] = r.copy()\n", " vs[0] = v.copy()\n", " for i in range(1,ts):\n", " ic = id_pairs[get_deltad_pairs(r) < d_cutoff]\n", " v[:,ic[:,0]], v[:,ic[:,1]] = compute_new_v(v[:,ic[:,0]], v[:,ic[:,1]], r[:,ic[:,0]], r[:,ic[:,1]])\n", " \n", " v[0,r[0]>1] = -np.abs(v[0,r[0]>1])\n", " v[0,r[0]<0] = np.abs(v[0,r[0]<0])\n", " v[1,r[1]>1] = -np.abs(v[1,r[1]>1])\n", " v[1,r[1]<0] = np.abs(v[1,r[1]<0])\n", " \n", " r = r + v*dt\n", " rs[i] = r.copy()\n", " vs[i] = v.copy()\n", " return rs, vs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the radius and find the position of all particles as a function of time (3D array `rs` where each axis is $(t,x,y)$)." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "radius = 0.06\n", "rs, vs = motion(r, v, ids_pairs, ts=1000, dt=0.000008, d_cutoff=2*radius)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot red and blue circles, making sure each is the correct size." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(5,5))\n", "xred, yred = rs[0][0][ixr], rs[0][1][ixr]\n", "xblue, yblue = rs[0][0][ixl],rs[0][1][ixl]\n", "circles_red = [plt.Circle((xi, yi), radius=radius, linewidth=0) for xi,yi in zip(xred,yred)]\n", "circles_blue = [plt.Circle((xi, yi), radius=radius, linewidth=0) for xi,yi in zip(xblue,yblue)]\n", "cred = matplotlib.collections.PatchCollection(circles_red, facecolors='red')\n", "cblue = matplotlib.collections.PatchCollection(circles_blue, facecolors='blue')\n", "ax.add_collection(cred)\n", "ax.add_collection(cblue)\n", "ax.set_xlim(0,1)\n", "ax.set_ylim(0,1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make initial animation of the simulation" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(5,5))\n", "\n", "def animate(i):\n", " ax.clear()\n", " xred, yred = rs[i][0][ixr], rs[i][1][ixr]\n", " xblue, yblue = rs[i][0][ixl],rs[i][1][ixl]\n", " circles_red = [plt.Circle((xi, yi), radius=radius, linewidth=0) for xi,yi in zip(xred,yred)]\n", " circles_blue = [plt.Circle((xi, yi), radius=radius, linewidth=0) for xi,yi in zip(xblue,yblue)]\n", " cred = matplotlib.collections.PatchCollection(circles_red, facecolors='red')\n", " cblue = matplotlib.collections.PatchCollection(circles_blue, facecolors='blue')\n", " ax.add_collection(cred)\n", " ax.add_collection(cblue)\n", " ax.set_xlim(0,1)\n", " ax.set_ylim(0,1)\n", " \n", "ani = animation.FuncAnimation(fig, animate, frames=500, interval=50)\n", "ani.save('ani3.gif',writer='pillow',fps=30,dpi=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we're sure that it works, lets make a simulation containing many more particles" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "n_particles = 400\n", "r = np.random.random((2,n_particles))\n", "ixr = r[0]>0.5 \n", "ixl = r[0]<=0.5 \n", "ids = np.arange(n_particles)\n", "ids_pairs = np.asarray(list(combinations(ids,2)))\n", "v = np.zeros((2,n_particles))\n", "v[0][ixr] = -500\n", "v[0][ixl] = 500\n", "radius = 0.0015\n", "rs, vs = motion(r, v, ids_pairs, ts=1000, dt=0.000008, d_cutoff=2*radius)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make an animation" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(5,5))\n", "ani = animation.FuncAnimation(fig, animate, frames=500, interval=50)\n", "ani.save('ani3.gif',writer='pillow',fps=30,dpi=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the final velocity distribution of the particles and compare it to Maxwell-Boltzmann in 2 Dimensions:\n", "\n", "* $kT = KE_{avg} = \\frac{1}{2}m\\bar{v^2} \\implies \\boxed{\\frac{m}{kT} = \\frac{2}{\\bar{v^2}}}$\n", "* $\\boxed{f(v) = \\frac{m}{kT} v \\exp\\left(-\\frac{m}{kT}\\frac{v^2}{2} \\right)}$" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "v = np.linspace(0, 2000, 1000)\n", "a = 2/500**2\n", "fv = a*v*np.exp(-a*v**2 / 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the final histogram next to this curve:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '# Particles')" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "bins = np.linspace(0,1500,10)\n", "plt.figure()\n", "plt.hist(np.sqrt(np.sum(vs[400]**2, axis=0)), bins=bins, density=True)\n", "plt.plot(v,fv)\n", "plt.xlabel('Velocity [m/s]')\n", "plt.ylabel('# Particles')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can make an animation of the particles moving around and the histogram at the same time" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(20,10))\n", "\n", "def animate(i):\n", " [ax.clear() for ax in axes]\n", " ax = axes[0]\n", " xred, yred = rs[i][0][ixr], rs[i][1][ixr]\n", " xblue, yblue = rs[i][0][ixl],rs[i][1][ixl]\n", " circles_red = [plt.Circle((xi, yi), radius=4*radius, linewidth=0) for xi,yi in zip(xred,yred)]\n", " circles_blue = [plt.Circle((xi, yi), radius=4*radius, linewidth=0) for xi,yi in zip(xblue,yblue)]\n", " cred = matplotlib.collections.PatchCollection(circles_red, facecolors='red')\n", " cblue = matplotlib.collections.PatchCollection(circles_blue, facecolors='blue')\n", " ax.add_collection(cred)\n", " ax.add_collection(cblue)\n", " ax.set_xlim(0,1)\n", " ax.set_ylim(0,1)\n", " ax.tick_params(axis='x', labelsize=15)\n", " ax.tick_params(axis='y', labelsize=15)\n", " ax = axes[1]\n", " ax.hist(np.sqrt(np.sum(vs[i]**2, axis=0)), bins=bins, density=True)\n", " ax.plot(v,fv)\n", " ax.set_xlabel('Velocity [m/s]')\n", " ax.set_ylabel('# Particles')\n", " ax.set_xlim(0,1500)\n", " ax.set_ylim(0,0.006)\n", " ax.tick_params(axis='x', labelsize=15)\n", " ax.tick_params(axis='y', labelsize=15)\n", " fig.tight_layout()\n", " \n", " \n", "ani = animation.FuncAnimation(fig, animate, frames=500, interval=50)\n", "ani.save('ani.gif',writer='pillow',fps=30,dpi=100)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }