How do i apply an open boundary so that any particle that leaves my matrix will just disappear.

How do i apply an open boundary so that any particle that leaves my matrix will just disappear. Random diffusion occurs in my code. However when a particle leaves i don not want it to be able to return. How might i implement this?

tic

% Clear Workspace clear all; close all; clc;

% Define the "physical" system dimensions = 2; boxSize = 400;

domain = zeros(boxSize,boxSize); domain(180:220,180:220) = 1;

% Write image file mkdir('./lapse') imwrite(domain,['./lapse/_',num2str(0),'.png'])

% Generate Position Arrays [particlePosition(:,1), particlePosition(:,2)] = ind2sub([boxSize boxSize],find(domain)); particleIndex = sub2ind( [boxSize boxSize], particlePosition(:,1), particlePosition(:,2));

for time = 1:1000;

    for i = 1:length( particlePosition )
        %Select from +/- dir for each spatial dimention   
        switch ceil( 2 * dimensions * rand )
            case 1
                % Displacement Vector
                dR = [-1  0]; % 0];
                % Where we want to move
                tempPosition = particlePosition(i,:) + dR;
                % Periodic Boundary Conditions
                tempPosition(tempPosition>boxSize) = tempPosition(tempPosition>boxSize) - boxSize;
                tempPosition(tempPosition<1) = tempPosition(tempPosition<1) + boxSize;
                % Convert to indicies for speedy search
                moveIndex = sub2ind( [boxSize boxSize], tempPosition(1), tempPosition(2));
                % If where we want to move is empty, move
                if ~sum(ones(length(particleIndex),1)*moveIndex == particleIndex)
                    particlePosition(i,:) = tempPosition;
                    particleIndex(i) = moveIndex;
                end
            case 2
                dR = [+1  0];%  0];
                tempPosition = particlePosition(i,:) + dR;
                tempPosition(tempPosition>boxSize) = tempPosition(tempPosition>boxSize) - boxSize;
                tempPosition(tempPosition<1) = tempPosition(tempPosition<1) + boxSize;
                moveIndex = sub2ind( [boxSize boxSize], tempPosition(1), tempPosition(2));
                if ~sum(ones(length(particleIndex),1)*moveIndex == particleIndex)
                    particlePosition(i,:) = tempPosition;
                    particleIndex(i) = moveIndex;
                end
            case 3
                dR = [ 0 -1];%  0];
                tempPosition = particlePosition(i,:) + dR;
                tempPosition(tempPosition>boxSize) = tempPosition(tempPosition>boxSize) - boxSize;
                tempPosition(tempPosition<1) = tempPosition(tempPosition<1) + boxSize;
                moveIndex = sub2ind( [boxSize boxSize], tempPosition(1), tempPosition(2));
                if ~sum(ones(length(particleIndex),1)*moveIndex == particleIndex)
                    particlePosition(i,:) = tempPosition;
                    particleIndex(i) = moveIndex;
                end
            case 4
                dR = [ 0 +1];%  0];
                tempPosition = particlePosition(i,:) + dR;
                tempPosition(tempPosition>boxSize) = tempPosition(tempPosition>boxSize) - boxSize;
                tempPosition(tempPosition<1) = tempPosition(tempPosition<1) + boxSize;
                moveIndex = sub2ind( [boxSize boxSize], tempPosition(1), tempPosition(2));
                if ~sum(ones(length(particleIndex),1)*moveIndex == particleIndex)
                    particlePosition(i,:) = tempPosition;
                    particleIndex(i) = moveIndex;
                end
        end

    end

    % Update Domain Image
    domain = zeros(boxSize,boxSize);
    domain(particleIndex) = 1;

    % Write Image File at some rate
    if mod(time,1) == 0
        imwrite(domain,['./lapse/_',num2str(time),'.png'])
    end

    % Print to Screen at some other rate
    if mod(time,10) == 0
        fprintf(1,'Time is %d \n', time )
    end

end

% Show final image and total time figure; imshow(domain) toc