defining boxes that reflects particles of electron

I wrote a code to display particles of electron but now I want to add inner rectangular bottle-necks boundaries to the plot. This will be done by defining boxes that will reflect particles whenever it hits the boundary of the boxes.

The code I wrote below does not relect the particles instead it passes behind the boxes.

Please some to help me. Thanks

LR = 200e-9; %Length of region
BR = 100e-9; %Breadth of region
numParticles = 1000;% no of particles
numSteps = 2;
x = zeros(numParticles, numSteps);
y = zeros(numParticles, numSteps);
xx = 0:0.2e-9:200e-9;
yy = 0:0.1e-9:100e-9;
size_x = numel(xx);
size_y = numel(yy);

            xindex_Particles = randi(size_x,[numParticles,2]);
            yindex_Particles = randi(size_y,[numParticles,2]);
            x_Particles = xx(xindex_Particles)';
            y_Particles = yy(yindex_Particles)';
            
            figure
            plot(x_Particles, y_Particles)
            title('Sample Particle trajectories')
  
% Define extent of the boxes
xv = [0.8e-7 0.8e-7 1.2e-7 1.2e-7 0.8e-7 NaN 0.8e-7 0.8e-7 1.2e-7 1.2e-7 0.8e-7];
yv = [0.0e-7 0.4e-7 0.4e-7 0.0e-7 0.1e-7 NaN 0.6e-7 1.0e-7 1.0e-7 0.6e-7 0.6e-7];

%Determine whether each particles lies inside or on the edge of the polygon area.
[in, on] = inpolygon(x_Particles, y_Particles,xv,yv);

Pinx = x_Particles(~in);
Piny = y_Particles(~in);
f1 = [Pinx(1:838,:),Pinx(839:1676,:)]';
f2 = [Piny(1:838,:),Piny(839:1676,:)]';

%Plot the polygon and the query points. Display the points inside the polygon with a red plus. Display the points outside the polygon with a blue circle.
figure
plot(xv,yv,'k') % polygon

hold on
% plot(x_Particles(in&~on),y_Particles(in&~on),'r+') % points strictly inside
% plot(x_Particles(on)',y_Particles(on)','r*') % points on edge
plot(f1,f2) % points outside
hold off
title('Sample Particles trajectories with Bottle neck')

rectangle('Position',[0.8e-7,0.0e-7,0.4e-7,0.4e-7],'FaceColor',[1 1 1],'EdgeColor','k',...
    'LineWidth',2)
rectangle('Position',[0.8e-7,0.6e-7,0.4e-7,0.4e-7],'FaceColor',[1 1 1],'EdgeColor','k',...
    'LineWidth',2)

Answer 1

[Samhitha]

Hi @ELUFISAN PAUL TOMILOLA,

The current code does not reflect the particles off the bottle-neck boundaries. It only plots the boxes and checks if particles are inside, but it does not update their trajectories when they hit the boxes.To make particles reflect off the bottle-neck boundaries, you need to:

1. At each simulation step, check if a particle will enter a box
2. If a particle hits a box, reverse its velocity component perpendicular to the wall to reflect it.

LR = 200e-9; % Length of region
BR = 100e-9; % Breadth of region
numParticles = 1000;
numSteps = 50; % Increase for visible trajectories
dt = 1e-14; % Time step

% Particle properties
x = rand(numParticles,1) * LR;
y = rand(numParticles,1) * BR;
theta = 2*pi*rand(numParticles,1);
v = 1e5; % m/s, arbitrary constant speed
vx = v * cos(theta);
vy = v * sin(theta);

% Obstacles (bottle-neck rectangles)
boxes = [0.8e-7 0.0e-7 0.4e-7 0.4e-7;   % [x y width height]
         0.8e-7 0.6e-7 0.4e-7 0.4e-7];

% For plotting trajectories
x_traj = zeros(numParticles, numSteps);
y_traj = zeros(numParticles, numSteps);

for t = 1:numSteps
    % Save trajectory
    x_traj(:,t) = x;
    y_traj(:,t) = y;

    % Update positions
    x_new = x + vx*dt;
    y_new = y + vy*dt;

    % Reflect off region boundaries
    outX = (x_new<0) | (x_new>LR);
    outY = (y_new<0) | (y_new>BR);
    vx(outX) = -vx(outX);
    vy(outY) = -vy(outY);

    % Update positions after boundary reflection
    x_new(outX) = x(outX) + vx(outX)*dt;
    y_new(outY) = y(outY) + vy(outY)*dt;

    % Reflect off boxes
    for b = 1:size(boxes,1)
        bx = boxes(b,1); by = boxes(b,2); bw = boxes(b,3); bh = boxes(b,4);
        inBoxX = (x_new > bx) & (x_new < bx+bw);
        inBoxY = (y_new > by) & (y_new < by+bh);
        inBox = inBoxX & inBoxY;
        % Find which wall was crossed
        crossedLeft   = (x <= bx)   & (x_new > bx)   & inBoxY;
        crossedRight  = (x >= bx+bw)& (x_new < bx+bw)& inBoxY;
        crossedBottom = (y <= by)   & (y_new > by)   & inBoxX;
        crossedTop    = (y >= by+bh)& (y_new < by+bh)& inBoxX;
        % Reflect velocities
        vx(crossedLeft | crossedRight) = -vx(crossedLeft | crossedRight);
        vy(crossedBottom | crossedTop) = -vy(crossedBottom | crossedTop);
        % Update positions after box reflection
        x_new(crossedLeft | crossedRight) = x(crossedLeft | crossedRight) + vx(crossedLeft | crossedRight)*dt;
        y_new(crossedBottom | crossedTop) = y(crossedBottom | crossedTop) + vy(crossedBottom | crossedTop)*dt;
    end

    % Update positions for next step
    x = x_new;
    y = y_new;
end

% Plot
figure;
hold on;
for i = 1:numParticles
    plot(x_traj(i,:), y_traj(i,:));
end
for b = 1:size(boxes,1)
    rectangle('Position', boxes(b,:), 'FaceColor', [1 1 1], 'EdgeColor', 'k', 'LineWidth', 2);
end

The Figure looks like this:

Hope this helps!