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random_walk.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- The above 3 meta tags *must* come first in the head; any other head content must come *after* these tags -->
<meta name="description" content="MD simulator.">
<meta name="author" content="Matt Hagy <[email protected]>">
<title>Browniwan Dynamics Simulation</title>
<style>
body { margin: 0; }
canvas { width: 100%; height: 100% }
</style>
<link rel="stylesheet"
href="https://stackpath.bootstrapcdn.com/bootstrap/3.4.1/css/bootstrap.min.css"
integrity="sha384-HSMxcRTRxnN+Bdg0JdbxYKrThecOKuH5zCYotlSAcp1+c8xmyTe9GYg1l9a69psu"
crossorigin="anonymous">
</head>
<body>
<h2>Random Walk in a Periodic Box</h2>
<div id="info">Info</div>
<div id="plot"></div>
<script src="https://fastcdn.org/three.js/73/three.min.js"></script>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<script src="https://code.jquery.com/jquery-1.12.4.min.js"
integrity="sha384-nvAa0+6Qg9clwYCGGPpDQLVpLNn0fRaROjHqs13t4Ggj3Ez50XnGQqc/r8MhnRDZ"
crossorigin="anonymous"></script>
<script>window.jQuery || document.write('<script src="../../assets/js/vendor/jquery.min.js"><\/script>')</script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/js/bootstrap.min.js"
integrity="sha384-JjSmVgyd0p3pXB1rRibZUAYoIIy6OrQ6VrjIEaFf/nJGzIxFDsf4x0xIM+B07jRM"
crossorigin="anonymous"></script>
<script>
window.onload = function() {
var boxSize = 1.0;
var steps=5000;
var cycleDuration = 5;
var scene = new THREE.Scene();
var camera = new THREE.PerspectiveCamera( 100, 1.2, 0.5, 10 );
camera.position.z = 1.5;
camera.position.x = 0.3;
camera.position.y = 0;
var renderer = new THREE.WebGLRenderer();
renderer.setSize(500, 500);
document.body.appendChild( renderer.domElement );
var halfBoxSize = boxSize / 2;
var geometry = new THREE.BoxGeometry( boxSize, boxSize, boxSize);
//var material = new THREE.MeshBasicMaterial(
// { color: 0x00ff00, opacity: 0.1, wireframe: true } );
var geo = new THREE.EdgesGeometry( geometry ); // or WireframeGeometry( geometry )
var mat = new THREE.LineBasicMaterial( { color: 0x00ff00, linewidth: 2 } );
var cube = new THREE.LineSegments( geo, mat );
//var cube = new THREE.Mesh( geometry, material );
scene.add( cube );
//cube.rotation.x = 3.14/16;
cube.position = new THREE.Vector3(-halfBoxSize, -halfBoxSize, -halfBoxSize);
var zeroVector = new THREE.Vector3(0, 0, 0)
var truePosition = zeroVector.clone();
var periodicPosition = zeroVector.clone();
function createSphere(color) {
var sphereGeometry = new THREE.SphereGeometry(0.025 * boxSize, 32, 32 );
var sphereMaterial = new THREE.MeshBasicMaterial( {color: color} );
var sphere = new THREE.Mesh(sphereGeometry, sphereMaterial);
scene.add(sphere);
return sphere;
}
var perioidicSphere = createSphere("teal");
var trueSphere = createSphere("orange");
function createLineGeo(n, color) {
var lineMaterial = new THREE.LineBasicMaterial({ color: color});
var lineGeo = new THREE.Geometry();
for (var i=0; i<n; i++) {
lineGeo.vertices.push(zeroVector.clone());
}
var line = new THREE.Line(lineGeo, lineMaterial);
scene.add(line);
return line;
}
var perioidLine = createLineGeo(steps, 0x0000ff);
var trueLine = createLineGeo(steps, 0xffff00);
var deltaLine = createLineGeo(2, 0xff0000);
function randomOffset() {
return 0.05 * boxSize * (Math.random() - 0.5);
}
function randomVector() {
return new THREE.Vector3(randomOffset(), randomOffset(), randomOffset());
}
function periodize(l) {
if (l < -halfBoxSize) {
return l + boxSize
} else if (l > halfBoxSize) {
return l - boxSize;
} else {
return l;
}
}
function periodizeVector(v) {
v.x = periodize(v.x);
v.y = periodize(v.y);
v.z = periodize(v.z);
return v;
}
function updateLine(i, line, position) {
line.geometry.vertices[i].copy(position);
line.geometry.verticesNeedUpdate = true
}
var tracePoints = {
x: [0],
y: [0],
name: 'Points',
type: 'scatter',
mode: 'markers',
marker: {
color: 'rgb(164, 194, 244)',
size: 5
}
};
var traceLine = {
x: [0],
y: [0],
name: 'Smoothed',
type: 'scatter',
mode: 'lines',
line: {
shape: 'spline',
color: 'rgb(255,127,80)',
width: 3
}
};
var layout = {
height: 300,
title: {
text:'Root Mean Sqaure Displacement of Tracer',
font: {
family: 'Courier New, monospace',
size: 18
},
xref: 'paper',
x: 0.05,
},
xaxis: {
title: {
text: 'Time, t (steps)',
font: {
family: 'Courier New, monospace',
size: 14,
color: '#7f7f7f'
}
},
},
yaxis: {
title: {
text: 'RMS Displacement',
font: {
family: 'Courier New, monospace',
size: 14,
color: '#7f7f7f'
}
}
}
};
function plot() {
Plotly.newPlot('plot', [tracePoints, traceLine],
layout,
{showSendToCloud: false});
}
plot();
var index=0;
var crossings = 0;
function animate() {
requestAnimationFrame( animate );
renderer.render( scene, camera );
index ++;
if (index >= steps) {
return;
}
for (var i=0; i<cycleDuration; i++) {
var delta = randomVector();
truePosition.add(delta);
var oldPeriodicPosition = periodicPosition.clone();
periodicPosition.add(delta);
periodizeVector(periodicPosition);
var periodicDelta = new THREE.Vector3();
periodicDelta.subVectors(periodicPosition, oldPeriodicPosition);
if (periodicDelta.length() > 1.2 * delta.length()) {
crossings ++;
}
}
trueSphere.position.copy(truePosition);
perioidicSphere.position.copy(periodicPosition);
updateLine(1, deltaLine, truePosition);
updateLine(index, trueLine, truePosition);
updateLine(index, perioidLine, periodicPosition);
var precision = 0.001;
var displacement = Math.floor(truePosition.length() / precision);
$("#info").text(
"Step: " + index +
" Displacement: " + displacement +
" Crossings: " + crossings);
tracePoints["x"].push(index);
tracePoints["y"].push(displacement);
if (index%100 == 0) {
traceLine["x"].push(index);
traceLine["y"].push(displacement);
}
if (index%10 == 0) {
plot();
}
}
animate();
}
</script>
</body>
</html>