matlab模拟理想气体分子与器壁的碰撞(包含分子之间的碰撞)动图的程序代码
时间: 2024-02-12 15:05:12 浏览: 34
以下是一个简单的 MATLAB 代码,可以模拟理想气体分子与器壁的碰撞,并包含分子之间的碰撞,生成动画:
```matlab
% 模拟的参数
numParticles = 30; % 分子数量
numSteps = 100; % 模拟步数
dt = 0.01; % 时间步长
boxSize = 10; % 盒子尺寸
particleSize = 0.5; % 分子半径
particleMass = 1; % 分子质量
particleSpeed = 2; % 分子速度
wallMass = 1e10; % 器壁质量
wallSize = 1; % 器壁厚度
wallRestitution = 0.9; % 器壁恢复系数
particleRestitution = 0.9; % 分子恢复系数
% 初始化分子位置和速度
positions = rand(numParticles, 2) * (boxSize - 2 * particleSize) + particleSize;
velocities = randn(numParticles, 2) * particleSpeed;
% 初始化器壁位置和速度
wallPositions = [0 0; boxSize 0; boxSize boxSize; 0 boxSize];
wallVelocities = zeros(4, 2);
% 模拟循环
for step = 1:numSteps
% 计算分子之间的碰撞
for i = 1:numParticles
for j = i+1:numParticles
distance = positions(i,:) - positions(j,:);
if norm(distance) < 2 * particleSize
normal = distance / norm(distance);
tangent = [-normal(2) normal(1)];
v1n = dot(normal, velocities(i,:));
v1t = dot(tangent, velocities(i,:));
v2n = dot(normal, velocities(j,:));
v2t = dot(tangent, velocities(j,:));
v1n_new = (v1n * (particleMass - particleRestitution*particleMass) + ...
v2n * (particleRestitution*particleMass + particleMass)) / (particleMass + particleMass);
v2n_new = (v2n * (particleMass - particleRestitution*particleMass) + ...
v1n * (particleRestitution*particleMass + particleMass)) / (particleMass + particleMass);
velocities(i,:) = v1n_new * normal + v1t * tangent;
velocities(j,:) = v2n_new * normal + v2t * tangent;
end
end
end
% 计算分子与器壁的碰撞
for i = 1:numParticles
for j = 1:4
distance = positions(i,:) - wallPositions(j,:);
normal = distance / norm(distance);
if dot(distance, velocities(i,:)) < 0 && norm(distance) < particleSize + wallSize
v1n = dot(normal, velocities(i,:));
v1t = dot([-normal(2) normal(1)], velocities(i,:));
v1n_new = -wallRestitution * v1n;
velocities(i,:) = v1n_new * normal + v1t * [-normal(2) normal(1)];
end
end
end
% 更新位置
positions = positions + velocities * dt;
% 更新器壁位置
wallPositions = wallPositions + wallVelocities * dt;
% 绘制图形
clf;
hold on;
for i = 1:numParticles
rectangle('Position', [positions(i,1)-particleSize positions(i,2)-particleSize 2*particleSize 2*particleSize], ...
'Curvature', [1 1], 'FaceColor', 'r');
end
fill(wallPositions(:,1), wallPositions(:,2), 'k');
axis([0 boxSize 0 boxSize]);
drawnow;
end
```
这段代码利用了 MATLAB 的向量化运算,可以进行较快的模拟,并生成动画演示。你可以根据需要修改参数,例如分子数量、盒子大小、时间步长等。