Simulating random walkers which can not collide into each other in Matlab - matlab

Question

I have written a code to simulate the motion of circular particles in a 2d box. Whenever they move out of the box, I put them inside the box and near the wall. I want to add the diameter (2R) of particles in the code, which means when the distance between the center of two circles become less than 2R, they separate along the line connecting their centers so that the distance between the centers of the circles becomes equal to 2R.
Could anyone suggest a code to perevent the overlapping of particles?
This is my code in which overlap is not considered:
clear all
close all
l = 224; nn = 800; %number of particles
time = 1000; dd = 1;
x= l*rand(1,nn);
y= l*rand(1,nn);
for t = 1:time;
x= x + rand(1,nn)-0.5* ones(1,nn);
y=y+rand(1,nn)-0.5* ones (1,nn);
index = (x < 0); x(index) = abs(normrnd(0,1,1,nnz(index)));
index = (y < 0); y(index) = abs(normrnd(0,1,1,nnz(index)));
index = (x > l); x(index) = l-abs(normrnd(0,1,1,nnz(index)));
index = (y > l); y(index) = l-abs(normrnd(0,1,1,nnz(index)));
end

Answer 1

Here is some commented code which does what you want. Notably:
psize is some defined particle size for interaction.
point-to-point distances found using pdist2.
points that are too close are moved away from each other by some amount (dp times their current distances, if dp=1/2 then their x and y distances double) until there are no clashes.
See comments for details.
clear; close all;
l = 224; nn = 800; % number of particles
time = 100;
x = l*rand(1,nn); y = l*rand(1,nn);
psize = 2; % Particle size for interaction
dp = 0.1;
figure; hold on; axis([0 l 0 l]);
for t = 1:time;
% Random movement
movement = 2*rand(2,nn)-1;
x = x + movement(1,:);
y = y + movement(2,:);
index = (x < 0); x(index) = abs(normrnd(0,1,1,nnz(index)));
index = (y < 0); y(index) = abs(normrnd(0,1,1,nnz(index)));
index = (x > l); x(index) = l-abs(normrnd(0,1,1,nnz(index)));
index = (y > l); y(index) = l-abs(normrnd(0,1,1,nnz(index)));
% Particle interaction. Loop until there are no clashes. For
% robustness, some max iteration counter should be added!
numclash = 1;
while numclash > 0
dists = pdist2([x;y]', [x;y]'); % Distances between all particles
dists(dists < psize) = NaN; % Those too close are assigned NaN
tooclose = isnan(tril(dists,-1)); % All NaNs identified by logical
[clash1,clash2] = find(tooclose); % Get particles which are clashing
numclash = numel(clash1); % Get number of clashes
% All points where there was a clash, move away from each other
x(clash1) = x(clash1) + (x(clash1)-x(clash2))*dp;
x(clash2) = x(clash2) - (x(clash1)-x(clash2))*dp;
y(clash1) = y(clash1) + (y(clash1)-y(clash2))*dp;
y(clash2) = y(clash2) - (y(clash1)-y(clash2))*dp;
end
% Plot to visualise results. Colour fade from dark to bright green over time
scatter(x,y,'.','markeredgecolor',[0.1,t/time,0.4]);
drawnow;
end
hold off
Result:
Edit:
For a clearer diagram, you could initialise some colour matrix C = rand(nn,3); and plot using
scatter(x,y,[],C*(t/time),'.'); % the (t/time) factor makes it fade from dark to light
This would give each particle a different colour, which also fade from dark to light, rather than just fading from dark to light as before. The result would be something like this: