Chain
From Department of Theoretical and Applied Mechanics
Revision as of 02:20, 9 June 2016 by Михаил Бабенков (talk | contribs) (→The proposed development directions)
Here is the latest version of the program that simulates the dynamics of one-dimensional crystal.
Download program: Chain_v3_release.zip
The text of the program is written in JavaScript (developed by Tsvetkov Denis):
Файл "Chain_v3_release.js"
1 function MainChain(canvas, vCanvas) {
2
3 // Presetting
4
5 var context = canvas.getContext("2d"); // context - for drawing
6 var vContext = vCanvas.getContext("2d");// vContext - for drawing
7
8 var Pi = 3.1415926; // pi
9
10 var m0 = 1; // weight
11 var T0 = 1; // Time (period of fluctuation)
12 var a0 = 1; // length (sphere's diameter)
13
14 var k0 = 2 * Pi / T0; // frequency
15 var C0 = m0 * k0 * k0; // rigidity
16
17 // *** Physical parameters ***
18
19 var m = 1 * m0; // weight
20 var C = 1 * C0; // rigidity
21 var numStart = 24; // The number of the spheres
22
23 // *** Calculation parameters ***
24
25 var fps = 50; // frames per second
26 var spf = 10; // steps per frame
27 var dt = 0.4 * T0 / fps; // integration step
28 // Running program
29
30 var scale = canvas.height / a0; // large-scale coefficient for transition from settlement to screen coordinates
31 var wScale = canvas.width; // window width in screen coordinates
32 var hScale = canvas.height; // window hight in screen coordinates
33 var w = wScale / scale; // window width in settlement coordinates
34 var h = hScale / scale; // window high in settlement coordinates
35 var chainHeightScale = hScale/2; // height of provision of a chain in screen coordinates
36 // константы для графика скорости
37 var vWScale = vCanvas.width; // window width in screen coordinates
38 var vHScale = vCanvas.height; // window hight in screen coordinates
39 var vHeightScale = vHScale/2; // height of provision of a chain in screen coordinates
40 var vAxisScale = vHScale * 0.4; // scale of an axis of "y" of the schedule of speed
41 var uvWResize = vWScale/wScale; // recalculation of width of rather main window
42
43 // generate entry conditions
44
45 var particles; // massive of particles
46 var num, pDist; // quantity of particles and distance between spheres (in initial situation)
47 MainChain.prototype.setNum = function(n){num = n; pDist = w/(num-1);}; // to set new quantity of particles
48 MainChain.prototype.setNum(numStart);
49 var uAxisScale; // scale of an axis of "y" of the schedule
50 MainChain.prototype.newSystem = function(conf){
51 MainChain.prototype.actualConf = conf;
52 particles = [];
53 for (var i = 1; i < num + 1; i++) {
54 var b = [];
55
56 b.x0 = pDist*(i-1); // settlement coordinates of initial provision of a particle
57 b.x0Scale = b.x0*scale; // screen coordinates of initial provision of a particle
58 b.fu = 0; b.vu = 0; b.uu = 0; // force; velocity; shift of rather initial situation
59
60 conf(b, i); // configuration of initial provisions
61 particles[i] = b; // add an element to massive
62 }
63
64 // set periodic system
65 particles[0] = particles[num];
66 particles[num+1] = particles[1];
67
68 // equilibration of total speed on an axis x (that particles didn't depart aside)
69 var sumvu = 0;
70 for (var i0 = 1; i0 < num+1; i0++) sumvu += particles[i0].vu;
71 var vuAverage = sumvu/num;
72 for (var i1 = 1; i1 < num+1; i1++) particles[i1].vu -= vuAverage;
73
74 // control of an axis "y"
75 var confCoeff = 1;
76 if (conf == MainChain.prototype.conf_random) confCoeff = Math.sqrt(num)/6;
77 if (conf == MainChain.prototype.conf_one || conf == MainChain.prototype.conf_stair2) confCoeff = num/5;
78 if (conf == MainChain.prototype.conf_stair3) confCoeff = num/10;
79 uAxisScale = hScale/(num/35) * confCoeff;
80 };
81
82 // control of configuration
83 var v0 = 1*a0/T0; // conf_random - initial dispersion of speeds
84 var sinNum = 2; // conf_sin - amount of the periods of a sine in a chain
85 var hillDiv = 1/4; // conf_hill - part of a chain which is occupied by "hill"
86
87 // configuration
88 MainChain.prototype.conf_random = function(b){b.vu = v0*(2*Math.random()-1);};
89 MainChain.prototype.conf_sin = function(b, i){b.vu = Math.sin(2*Pi * i/num*sinNum);};
90 MainChain.prototype.conf_one = function(b, i){if (i == Math.ceil(num/2)) b.vu = 0.5; else b.vu = 0;};
91 MainChain.prototype.conf_stair2 = function(b, i){if (i%4 == 0 || (i-1)%4 == 0) b.vu = 1; else b.vu = 0;};
92 MainChain.prototype.conf_stair3 = function(b, i){if (i%6 == 0 || (i-1)%6 == 0 || (i-2)%6 == 0) b.vu = 1; else b.vu = 0;};
93 MainChain.prototype.conf_hill = function(b, i){
94 var nd2 = hillDiv *num/2; // quantity of particles at which initial speed / 2 will change
95 if (i > num/2-nd2 && i < num/2+nd2) b.vu = (1 - (i-num/2)*(i-num/2)/(nd2*nd2)); // parabola
96 else b.vu = 0;
97 };
98
99 // Basis cycle of the program
100
101 function control() {
102 physics();
103 draw();
104 }
105
106 // Settlement part of the program
107
108 function physics(){
109 for (var s=1; s<=spf; s++) {
110 for (var i=1; i<particles.length-1; i++) {
111 particles[i].fu = C*(particles[i+1].uu - 2*particles[i].uu + particles[i-1].uu);
112 particles[i].vu += particles[i].fu / m * dt;
113 }
114 // we appropriate new movements
115 for (var i2=1; i2 < particles.length-1; i2++ ) particles[i2].uu += particles[i2].vu * dt;
116 }
117 }
118
119 // drawing
120
121 function draw(){
122 function clearAndPrepairCtx(ctx, wS, hS, lineHeight){ // clear the screen and to draw the line in the middle
123 ctx.clearRect(0, 0, wS, hS); // clear the screen
124 ctx.strokeStyle = 'gray';
125 ctx.beginPath();
126 ctx.moveTo(0, lineHeight);
127 ctx.lineTo(wS, lineHeight);
128 ctx.stroke();
129 ctx.strokeStyle = 'black';
130 }
131
132 // chain
133 clearAndPrepairCtx(context, wScale, hScale, chainHeightScale);
134 context.beginPath();
135 context.moveTo(particles[1].x0Scale, chainHeightScale + particles[1].uu*uAxisScale);
136 for (var i = 2; i < particles.length-1; i++)
137 context.lineTo(particles[i].x0Scale, chainHeightScale + particles[i].uu*uAxisScale);
138 context.stroke();
139
140 // schedule of speed
141 clearAndPrepairCtx(vContext, vWScale, vHScale, vHeightScale);
142 vContext.beginPath();
143 vContext.moveTo(particles[1].x0Scale * uvWResize, vHeightScale + particles[1].vu*vAxisScale);
144 for (var i0 = 2; i0 < particles.length-1; i0++)
145 vContext.lineTo(particles[i0].x0Scale * uvWResize, vHeightScale + particles[i0].vu*vAxisScale);
146 vContext.stroke();
147 }
148
149 // Start of system
150
151 MainChain.prototype.newSystem(MainChain.prototype.conf_hill);
152 setInterval(control, 1000/fps);
153 }
Файл "Chain_v2_release.html"
<!DOCTYPE html>
<html>
<head>
<title>Chain</title>
<script src="Chain_v3_release.js"></script>
</head>
<body>
<table>
<tr>
<td>u</td>
<td><canvas id="canvasChain" width="800" height="200" style="border:1px solid #000000;"></canvas></td>
<td rowspan="4" style="width:200px" valign="top">
Configurations<br>(guide the cursor at the button,<br>for seeing description):<br>
<input type="button" title="Casual speed at each part" style="width: 150px" name="" onclick="app.newSystem(app.conf_random);return false;" value="Random"/><br>
<input type="button" title="Initial speed of particles is set by means of function of a sine" style="width: 150px" name="" onclick="app.newSystem(app.conf_sin);return false;" value="Sin"/><br>
<input type="button" title="Speed is equal 0 at all parts, except one" style="width: 150px" name="" onclick="app.newSystem(app.conf_one);return false;" value="Impulse"/><br>
<input type="button" title="Initial speed of particles is set by steps - two parts move, two don't move" style="width: 150px" name="" onclick="app.newSystem(app.conf_stair2);return false;" value="Stairs (2 particles)"/><br>
<input type="button" title="Initial speed of particles is set by steps - three parts move, three don't move" style="width: 150px" name="" onclick="app.newSystem(app.conf_stair3);return false;" value="Stairs (3 particles)"/><br>
<input type="button" title="Initial speed of particles is set by the hill, the hill occupies 1/4 part of a chain" style="width: 150px" name="" onclick="app.newSystem(app.conf_hill);return false;" value="Hill"/><br>
<br><br>
<div style="width:150px">
Quantity of particles:<br>
<input type="button" style="width: 40px" name="" onclick="app.setNum(12); app.newSystem(app.actualConf);return false;" value="12"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(24); app.newSystem(app.actualConf);return false;" value="24"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(48); app.newSystem(app.actualConf);return false;" value="48"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(96); app.newSystem(app.actualConf);return false;" value="96"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(300); app.newSystem(app.actualConf);return false;" value="300"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(600); app.newSystem(app.actualConf);return false;" value="600"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(1200); app.newSystem(app.actualConf);return false;" value="1200"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(2400); app.newSystem(app.actualConf);return false;" value="2400"/>
<input type="button" style="width: 40px" name="" onclick="app.setNum(4800); app.newSystem(app.actualConf);return false;" value="4800"/>
</div>
</td>
</tr><tr>
<td></td>
<td align="center">x</td>
</tr ><tr>
<td style="padding:30px 0 0 0;">v</td>
<td style="padding:30px 0 0 0;"><canvas id="canvasChainV" width="800" height="100" style="border:1px solid #000000;"></canvas></td>
</tr><tr>
<td></td>
<td align="center">x</td>
</tr>
</table>
<script type="text/javascript">var app = new MainChain(document.getElementById('canvasChain'), document.getElementById('canvasChainV'));</script>
</body>
</html>
Here you can find the previous versions of the program.
The proposed development directions
- Add the ability to set a directed impulse.
- Add control of simulation speed (for example, the slider).
- Analyse a variety of interaction forces (linear, square, cubic, their variations).
