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Brownian_Motion.html
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Brownian_Motion.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>demo_3_Brownian_Motion</title>
<style type="text/css">
h3 {
color:black;
text-align: left;}
p {color:black;}
.column {
text-align:center;
float:left;
}
.column.left {
width:750px;
}
.column.right {
width:550px;
}
.row:after {
content: "";
display: table;
clear: both;
}
input.quantity{
text-align: center;
width:60px;
}
table{
text-align: left;
}
button{
padding-top: 2.5px;
padding-bottom: 2.5px;
}
.row{
min-width: 1300px;
}
</style>
<script src="Chart.bundle.js"></script>
</head>
<body>
<div class="row">
<div class="column left">
<canvas id="myCanvas" width="600" height="600" style="border:1px solid #000000; position: absolute; left: 100px; top: 80px; z-index: 1;">CANVAS FOR SIMULATION</canvas>
<canvas id="myLayer" width="600" height="600" style="border:1px solid #000000; position: absolute; left: 100px; top: 80px; z-index: 0;">LAYER</canvas>
<div style="line-height: 150%;">
<button onclick="clearInterval(timer);clearCanvas('myCanvas');initialize();drawParticles();distplot();motion()" style="font-size: medium;"><b>Start!</b></button><br>
<button id="trajectoryControl" onclick="changeTrajectoryState()">Show Trajectory</button>
<button id="boundaryCondition" onclick="changeBoundaryCondition()">Rigid Boundary</button>
</div>
</div>
<div class="column right">
<!--设置参数-->
<h3>Change Parameters</h3>
<table>
<tr>
<td>Number of molecules:</td>
<td><input id="Number" type="number" class="quantity" min="100" max="1200"></td>
</tr>
<tr>
<td>Radius of molecules:</td>
<td><input id="lowerRadius" type="number" class="quantity" min="3" max="20"></td>
</tr>
<tr>
<td>Radius of pollen:</td>
<td><input id="upperRadius" type="number" class="quantity" min="3" max="50"></td>
</tr>
<tr>
<td>Initial velocity distribution:</td>
<td><input type="radio" name="IVD" value="uniform">uniform<input type="radio" name="IVD" value="gaussian" checked="checked">gaussian</td>
</tr>
<th colspan="2">
<button id="changeParticalNumber" onclick="changeParameter()">Submit and Restart!</button>
</th>
</table>
<h3>Velocity Distribution</h3>
<canvas id="myChart1"></canvas>
<h3 style="position: absolute; top: 550px;">Collision Point</h3>
<canvas id="myMonitor_layer1" width="120" height="120" style="border:1px solid #ADD8E6; position: absolute; left: 910px; top: 560px; z-index: 0;"></canvas>
<canvas id="myMonitor_layer2" width="120" height="120" style="border:1px solid #ADD8E6; position: absolute; left: 910px; top: 560px; z-index: 1;"></canvas>
<canvas id="myMonitor_layer3" width="120" height="120" style="border:1px solid #ADD8E6; position: absolute; left: 910px; top: 560px; z-index: 2;"></canvas>
</div>
</div>
<script>
var N=400;//total number of particles 400 or 900
var r=5;//particle radius in px 5 or 3
var m;
var R=40;//pollen size in px 30
var M;
var IVD;
var molecule=[];
var canvasSize=600;//in px 600
var dT=10;
var trajectoryState=false;
var periodicBoundary=true;
var timer;
var collision_x=[];
var collision_y=[];
var collision_count=0;
var collision_count_current=0;
var collision_count_limit=50;
document.getElementById("Number").value=N;
document.getElementById("lowerRadius").value=r;
document.getElementById("upperRadius").value=R;
var ctx_myLayer=document.getElementById("myLayer").getContext("2d");
var ctx_myCanvas=document.getElementById("myCanvas").getContext("2d");
function initialize(){
m=Math.pow(r,2);
M=Math.pow(R,2);
var v_0=[];
molecule=[];
v_0=randomNormalDistribution();
molecule[0]={
xvalue:canvasSize/2,
yvalue:canvasSize/2,
xvelocity:v_0[0]*Math.sqrt(m/M),
yvelocity:v_0[1]*Math.sqrt(m/M),
xclass:Math.floor(this.xvalue/(canvasSize/10)),
yclass:Math.floor(this.yvalue/(canvasSize/10))
};
for(var i=1;i<N+1;i++){
var position_x=Math.random()*canvasSize/Math.sqrt(N)+(i%Math.sqrt(N))*canvasSize/Math.sqrt(N);
var position_y=Math.random()*canvasSize/Math.sqrt(N)+Math.floor(i/Math.sqrt(N))*canvasSize/Math.sqrt(N);
var distance_to_pollen=Math.sqrt(Math.pow(position_x-molecule[0].xvalue,2)+Math.pow(position_y-molecule[0].yvalue,2));
while(distance_to_pollen<=(r+R)){
position_x=Math.random()*canvasSize;
position_y=Math.random()*canvasSize;
distance_to_pollen=Math.sqrt(Math.pow(position_x-molecule[0].xvalue,2)+Math.pow(position_y-molecule[0].yvalue,2));
}
var v=randomNormalDistribution();
molecule[i]={
xvalue:position_x,//in px
yvalue:position_y,//in px
xvelocity:(IVD)?(Math.random()*3.6-1.8):v[0],
yvelocity:(IVD)?(Math.random()*3.6-1.8):v[1],
xclass:Math.floor(this.xvalue/(canvasSize/10)),
yclass:Math.floor(this.yvalue/(canvasSize/10))
}
}
}
function randomNormalDistribution(){
var u=0.0, v=0.0, w=0.0, c=0.0;
do{
u=Math.random()*2-1.0;
v=Math.random()*2-1.0;//获得两个（-1,1）的独立随机变量
w=u*u+v*v;
}while(w==0.0||w>=1.0)
c=Math.sqrt((-2*Math.log(w))/w);//Box-Muller转换
return [u*c,v*c];//返回2个标准正态分布的随机数，封装进一个数组返回
}
function createCircle(x,y,r,cmap,ctx){
//var cs=document.getElementById(canvasName);
//var ctx=cs.getContext("2d");
ctx.fillStyle=cmap;//"#ADD8E6" for lightblue; "#CD5C5C" for indian red; "#87CEEB" for skyblue
ctx.beginPath();
ctx.arc(x,y,r,0,2*Math.PI);
ctx.closePath(); //关闭路径
ctx.fill();
}
function clearCanvas(canvasName){
var cs=document.getElementById(canvasName);
var ctx=cs.getContext("2d");
ctx.clearRect(0,0,cs.width,cs.height);
}
function drawParticles(){
clearCanvas("myCanvas");
for(var i=1;i<N+1;i++){
createCircle(molecule[i].xvalue,molecule[i].yvalue,r,"#00BFFF",ctx_myCanvas);
}
createCircle(molecule[0].xvalue,molecule[0].yvalue,R,"rgba(205,92,92,0.7)",ctx_myCanvas);
if(molecule[0].xvalue<R){
createCircle(molecule[0].xvalue+canvasSize,molecule[0].yvalue,R,"rgba(205,92,92,0.7)",ctx_myCanvas);
}
else if(molecule[0].xvalue>(canvasSize-R)){
createCircle(molecule[0].xvalue-canvasSize,molecule[0].yvalue,R,"rgba(205,92,92,0.7)",ctx_myCanvas);
}
if(molecule[0].yvalue<R){
createCircle(molecule[0].xvalue,molecule[0].yvalue+canvasSize,R,"rgba(205,92,92,0.7)",ctx_myCanvas);
}
else if(molecule[0].yvalue>(canvasSize-R)){
createCircle(molecule[0].xvalue,molecule[0].yvalue-canvasSize,R,"rgba(205,92,92,0.7)",ctx_myCanvas);
}
}
function drawTrajectory(){
createCircle(molecule[0].xvalue,molecule[0].yvalue,0.5,"rgba(143,188,143,0.6)",ctx_myLayer);
}
function move(){
for(var i=0;i<N+1;i++){
var radius_i=(i===0)?R:r;
var mass_i=(i===0)?M:m;
molecule[i].xvalue+=molecule[i].xvelocity;
molecule[i].yvalue+=molecule[i].yvelocity;
var x1=molecule[i].xvalue;
var y1=molecule[i].yvalue;
//周期性边界条件
if(periodicBoundary){
if(x1<0 || x1>canvasSize){
molecule[i].xvalue=(canvasSize+x1)%canvasSize;
}
if(y1<0 || y1>canvasSize){
molecule[i].yvalue=(canvasSize+y1)%canvasSize;
}
}
//非周期性边界条件
else{
if(x1<radius_i || x1>(canvasSize-radius_i)){
molecule[i].xvelocity=(-molecule[i].xvelocity);
if(x1<radius_i) molecule[i].xvalue=radius_i;
else molecule[i].xvalue=canvasSize-radius_i;
}//碰撞边界
if(y1<radius_i || y1>(canvasSize-radius_i)){
molecule[i].yvelocity=(-molecule[i].yvelocity);
if(y1<radius_i) molecule[i].yvalue=radius_i;
else molecule[i].yvalue=canvasSize-radius_i;
}//碰撞边界*/
}
molecule[i].xclass=Math.floor(molecule[i].xvalue/(canvasSize/10));
molecule[i].yclass=Math.floor(molecule[i].yvalue/(canvasSize/10));
if(i!=0){//液体分子去碰撞别的粒子（包括pollen）
for(var j=0;j<N+1 && j!=i;j++){
var radius_j=(j===0)?R:r;
var mass_j=(j===0)?M:m;
var x1=molecule[i].xvalue;
var x2=molecule[j].xvalue;
var y1=molecule[i].yvalue;
var y2=molecule[j].yvalue;
var check1=false;
var xclass_2=molecule[j].xclass;
var xclass_1=molecule[i].xclass;
var yclass_2=molecule[j].yclass;
var yclass_1=molecule[i].yclass;
//判断是否需要考虑碰撞可能
if(periodicBoundary){
if(Math.abs(xclass_2-xclass_1)<=1 && Math.abs(yclass_2-yclass_1)<=1){
check1=true;
}
else if(j===0){
if(Math.abs(yclass_2-yclass_1)<=1 && Math.abs(xclass_1-xclass_2)===9){
check1=true;
x2+=(canvasSize*Math.sign(xclass_1-xclass_2));
}
else if(Math.abs(xclass_2-xclass_1)<=1 && Math.abs(yclass_1-yclass_2)===9){
check1=true;
y2+=(canvasSize*Math.sign(yclass_1-yclass_2));
}
else if(Math.abs(xclass_1-xclass_2)==9 && Math.abs(yclass_1-yclass_2)===9){
check1=true;
x2+=(canvasSize*Math.sign(xclass_1-xclass_2));
y2+=(canvasSize*Math.sign(yclass_1-yclass_2));
}
}
}
else{
check1=(Math.abs(xclass_2-xclass_1)<=1 && Math.abs(yclass_2-yclass_1)<=1);
}
if(check1){//判断是否需要考虑碰撞可能
var distance=Math.sqrt(Math.pow((x1-x2),2)+Math.pow((y1-y2),2));
if(distance<=(radius_i+radius_j)){//判断是否有碰撞可能，是则进入循环
var totalMass=mass_i+mass_j;
//relative to central mass
var v_x_relative_to_c_i=(molecule[i].xvelocity-molecule[j].xvelocity)*mass_j/totalMass;
var v_y_relative_to_c_i=(molecule[i].yvelocity-molecule[j].yvelocity)*mass_j/totalMass;
//normalized to unit vector
var v_relative_to_c_i_magnitude=Math.sqrt(Math.pow(v_x_relative_to_c_i,2)+Math.pow(v_y_relative_to_c_i,2));
var v_x_relative_to_c_i_normalized=v_x_relative_to_c_i/v_relative_to_c_i_magnitude;
var v_y_relative_to_c_i_normalized=v_y_relative_to_c_i/v_relative_to_c_i_magnitude;
//central mass
var v_x_c=(mass_i*molecule[i].xvelocity+mass_j*molecule[j].xvelocity)/totalMass;
var v_y_c=(mass_i*molecule[i].yvelocity+mass_j*molecule[j].yvelocity)/totalMass;
//判断是否碰撞
var dotProduct=v_y_relative_to_c_i_normalized*(y2-y1)+v_x_relative_to_c_i_normalized*(x2-x1);
if(dotProduct>0){
if(j===0){
collision_x[collision_count]=(x1-x2)/distance;
collision_y[collision_count]=(y1-y2)/distance;
collision_count_current=collision_count;
collision_count=(collision_count+1)%collision_count_limit;
}
var b=(v_x_relative_to_c_i_normalized*(y2-y1)-v_y_relative_to_c_i_normalized*(x2-x1));
var theta=2*Math.acos(b/(radius_i+radius_j));//scatter angle from 0 to 2*pi; 逆时针为正
var alpha;
if(v_y_relative_to_c_i_normalized>=0){
alpha=Math.acos(v_x_relative_to_c_i_normalized);
}//from 0 to pi
else{
alpha=2*Math.PI-Math.acos(v_x_relative_to_c_i_normalized);
}//from pi to 2*pi
var alpha_new=alpha-theta;
//velocity change after scatter
var v_x_relative_to_c_i_scatter=v_relative_to_c_i_magnitude*Math.cos(alpha_new);
var v_y_relative_to_c_i_scatter=v_relative_to_c_i_magnitude*Math.sin(alpha_new);
molecule[i].xvelocity=v_x_c+v_x_relative_to_c_i_scatter;
molecule[i].yvelocity=v_y_c+v_y_relative_to_c_i_scatter;
molecule[j].xvelocity=v_x_c-v_x_relative_to_c_i_scatter*mass_i/mass_j;
molecule[j].yvelocity=v_y_c-v_y_relative_to_c_i_scatter*mass_i/mass_j;
molecule[i].xvalue+=molecule[i].xvelocity;
molecule[i].yvalue+=molecule[i].yvelocity;
molecule[j].xvalue+=molecule[j].xvelocity;
molecule[j].yvalue+=molecule[j].yvelocity;//速度改变之后就分开了
//drawParticles();
molecule[i].xclass=Math.floor(molecule[i].xvalue/(canvasSize/10));
molecule[i].yclass=Math.floor(molecule[i].yvalue/(canvasSize/10));
molecule[j].xclass=Math.floor(molecule[j].xvalue/(canvasSize/10));
molecule[j].yclass=Math.floor(molecule[j].yvalue/(canvasSize/10));
}
}
}
}
}
}
}
function motion(){
var count=0;
collision_count=0;
createMonitorBG();
timer=setInterval(function(){
var collision_last_count=collision_count;
count+=1;
move();
drawParticles();
if(trajectoryState) drawTrajectory();
if(count%100==0){
distplot();
}
if(collision_count===collision_last_count){
collision_x[collision_count]=undefined;
collision_y[collision_count]=undefined;
collision_count_current=collision_count;
collision_count=(collision_count+1)%collision_count_limit;
}
createMonitor();
},dT);
}
function changeTrajectoryState(){
trajectoryState=(!trajectoryState);
if(trajectoryState===false){
clearCanvas('myLayer');
document.getElementById("trajectoryControl").innerHTML="Show Trajectory";
}
else{
document.getElementById("trajectoryControl").innerHTML="Hide Trajectory";
}
}
function changeBoundaryCondition(){
periodicBoundary=(!periodicBoundary);
document.getElementById("boundaryCondition").innerHTML=(periodicBoundary)?"Rigid Boundary":"Periodic Boundary";
}
function changeParameter(){
var trialN=Number(document.getElementById('Number').value);
var trialR=Number(document.getElementById('upperRadius').value);
var trialr=Number(document.getElementById('lowerRadius').value);
if(trialN<100 || trialN>1200){
alert('N is not in the range of [100,1200]')
}
else if(trialR<3 || trialR>50){
alert('R is not in the range of [3,50]')
}
else if(trialr<3 || trialr>20){
alert('r is not in the range of [3,20]')
}
else{
clearInterval(timer);
clearCanvas("myCanvas");
clearCanvas("myLayer");
N=Number(document.getElementById("Number").value);
R=Number(document.getElementById("upperRadius").value);
r=Number(document.getElementById("lowerRadius").value);
IVD=document.getElementsByName("IVD");
IVD=(IVD[0].checked===true);
initialize();
drawParticles();
distplot();
//document.getElementById("show").innerHTML=N;
motion();
}
}
var MC1 = document.getElementById('myChart1');
var MC2 = document.getElementById('myChart2');
var dataValues_X = [];
var dataValues_Y = [];
var dataValues_line=[];
var dataLabels = [];
var bins=30;
var start=-3;
var end=3;
var delta=(end-start)/bins;
delta=delta.toPrecision(1);
function distplot(){
for(var i=0;i<bins;i++){
dataLabels[i]=(start+i*delta).toPrecision(2);
dataValues_X[i]=0;
dataValues_Y[i]=0;
dataValues_line[i]=1/Math.sqrt(2*Math.PI)*Math.exp(-Math.pow(dataLabels[i],2)/2)*N*delta;
}
for(var i=1;i<N+1;i++){
var x=Math.floor((molecule[i].xvelocity-start)/delta);
var y=Math.floor((molecule[i].yvelocity-start)/delta);
dataValues_X[x]+=1;
dataValues_Y[y]+=1;
}
var barChartData={
labels: dataLabels,
datasets:[{
label: 'velocity along x axis',
backgroundColor: 'rgba(106,90,205,0.5)',
data: dataValues_X
}, {
label: 'velocity along y axis',
backgroundColor: 'rgba(154,205,50,0.7)',
data: dataValues_Y
},{
label:'Maxwell\'s velocity distribution',
data:dataValues_line,
type:'line',
borderColor:'rgba(211,211,211,0.5)',
backgroundColor:'rgba(211,211,211,0.5)',
fill:false
}]
};
var myChart1 = new Chart(MC1, {
type: 'bar',
data: barChartData,
options: {
hover: {
animationDuration: 0 // duration of animations when hovering an item
},
responsiveAnimationDuration: 0 ,// animation duration after a resize
animation: {
duration: 0 // general animation time
},
scales: {
barPercentage:1,
xAxes: [{
display: true,
ticks: {
autoSkip: false,
min:-2,
max:2
},
scaleLabel:{
display: true,
labelString: 'velocity'
}
}],
yAxes: [{
//stacked:true,
ticks: {
beginAtZero:true,
min:0,
max:Math.floor(N/80)*10
},
scaleLabel:{
display:true,
labelString:'count'
}
}]
}
}
});
/*var myChart2 = new Chart(MC2, {
type: 'bar',
data: {
labels: dataLabels,
datasets: [{
label: 'velocity along y axis',
data: dataValues_Y,
backgroundColor: 'rgba(54, 162, 235, 0.2)',
}]
},
options: {
animation: {
duration: 200 // general animation time
},
scales: {
xAxes: [{
display: true,
ticks: {
autoSkip: false,
min:-2,
max:2
},
barPercentage:1
}],
yAxes: [{
ticks: {
beginAtZero:true,
min:0,
max:100
}
}]
}
}
});*/
}
function createMonitorBG(){
clearCanvas("myMonitor_layer1");
clearCanvas("myMonitor_layer3");
//底层
var cs_monitor_1=document.getElementById("myMonitor_layer1");
var ctx_monitor_1=cs_monitor_1.getContext("2d");
ctx_monitor_1.fillStyle="rgba(205,92,92,0.7)";
ctx_monitor_1.beginPath();
ctx_monitor_1.arc(60,60,R,0,2*Math.PI);
ctx_monitor_1.closePath();
ctx_monitor_1.fill();
//上层
var cs_monitor_3=document.getElementById("myMonitor_layer3");
var ctx_monitor_3=cs_monitor_3.getContext("2d");
ctx_monitor_3.fillStyle="#ffffff";
ctx_monitor_3.arc(60,60,100,0,2*Math.PI,false);
ctx_monitor_3.arc(60,60,R+1,0,2*Math.PI,true);
ctx_monitor_3.fill();
}
function createMonitor(){
//中层
clearCanvas("myMonitor_layer2");
var cs_monitor_2=document.getElementById("myMonitor_layer2");
var ctx_monitor_2=cs_monitor_2.getContext("2d");
for(var i=0;i<collision_count_limit;i++){
ctx_monitor_2.fillStyle="#FFFF00";
if(i<=collision_count_current) ctx_monitor_2.globalAlpha=(1-Math.pow((collision_count_current-i)/collision_count_limit,2));
else ctx_monitor_2.globalAlpha=(1-Math.pow((collision_count_current+collision_count_limit-i)/collision_count_limit,2));
ctx_monitor_2.beginPath();
ctx_monitor_2.arc(60+collision_x[i]*R,60+collision_y[i]*R,r,0,2*Math.PI);
ctx_monitor_2.closePath(); //关闭路径
ctx_monitor_2.fill();
}
}
</script>
</body>
</html>