Why do i receive error in line 36:Index in position 1 is invalid. Array indices must be positive integers or logical values.

%start by defining the parameters
N = 50; % Number of particles
domainSize = 99; % Size of the simulation domain
s = 3/5; % Probability to move South
w = 1/5; % Probability to move West
e = 1/5; % Probability to move East
% Initialize variables to store particle positions and results
particlePositions = zeros(N, 2); % Each row stores [row, column] position
reachedBottom = zeros(N, 1); % 1 if particle reached the bottom, 0 otherwise
% Loop over particles and simulate biased walks
for i = 1:N
    % Choose start position
    if rand < 0.5
        startColumn = 1; % Particle starts at column 1 (P = 1)
    else
        startColumn = randi(domainSize); % Random start position (rand)
    end
    
    particlePositions(i, :) = [1, startColumn]; % Initialize particle position
    
    % Simulate biased walk
    while particlePositions(i, 1) < domainSize % While particle not at bottom row
        % Choose direction with probabilities
        direction = rand();
        if direction < s
            particlePositions(i, 1) = particlePositions(i, 1) + 1; % Move South
        elseif direction < s + w
            particlePositions(i, 2) = mod(particlePositions(i, 2) - 2, domainSize) + 1; % Move West
        else
            particlePositions(i, 2) = mod(particlePositions(i, 2), domainSize) + 1; % Move East
        end
        
        % Check if particle's next position is occupied
        if particlePositions(i, 1) < domainSize && ...
                particlePositions(i, 2) == particlePositions(i -1, 2) && ...
                particlePositions(i, 1) == particlePositions(i -1, 1) + 1
            reachedBottom(i) = 1; % Particle reached bottom row
            break;
        end
    end
end

Index in position 1 is invalid. Array indices must be positive integers or logical values.

% Calculate statistics
reachedBottomN50 = sum(reachedBottom);
reachedBottomPctN50 = reachedBottomN50 / N * 100;
% Display results
fprintf('For N = %d particles:\n', N);
fprintf('Number of particles reaching bottom row: %d\n', reachedBottomN50);
fprintf('Percentage of particles reaching bottom row: %.2f%%\n', reachedBottomPctN50);

Answer 1

[Walter Roberson]

for i = 1:N

i starts at 1.

            % Check if particle's next position is occupied

Inside the for loop, i has not been reassigned anything by the time you reach this line. On the first iteration, i will still be 1.

            if particlePositions(i, 1) < domainSize && ...
                particlePositions(i, 2) == particlePositions(i -1, 2) && ...
                particlePositions(i, 1) == particlePositions(i -1, 1) + 1

On the first iteration, when i is 1, is there any reason why particlePositions(i,1) should definitely be >= domainSize so that the test fails immediately? Because if the test does not fail immediately and you proceed to the next clause, then particlePositions(i -1,2) is used for the calculation, but when i is 1, that is particlePositions(1-1,2) which is particlePositions(0,2) which is not a valid index.

[Sophie]

This is actually my first time using matlab and i have mostly used variations of script given to me from lectures, so im not 100% certain on any of it. I think the test fails imdeiantly as the particles are not allowed to occupy the same space, however i am unsure whether this is correst in the script.

[Walter Roberson]

    particlePositions(i, :) = [1, startColumn]; % Initialize particle position
    

when i is 1, you are initializing the first column of particlePositions(1,:) to be 1.

    domainSize = 99; % Size of the simulation domain

1 is < 99 so

        while particlePositions(i, 1) < domainSize % While particle not at bottom row

starts out true

            if direction < s
              particlePositions(i, 1) = particlePositions(i, 1) + 1; % Move South

that random selection might not be true, but if it is then the position would increment from 1 to 2; if it is false, the position stays where it is. Going through the first iteration, after the end of that if and all elseif and else we know the position will be either 1 or 2.

        if particlePositions(i, 1) < domainSize && ...
                particlePositions(i, 2) == particlePositions(i -1, 2) && ...
                particlePositions(i, 1) == particlePositions(i -1, 1) + 1

1 and 2 are both < 99, so the first part of the test will be true, and you proceed with the rest of the test, which is trying to loop at the previous particle position... but there is no previous particle position.

By the way, I would suggest that you consider code such as

        just_moved_south = false;
        if direction < s
              particlePositions(i, 1) = particlePositions(i, 1) + 1; % Move South
              just_moved_south = true;
        elseif etc
        end
        if particlePositions(i, 1) < domainSize && ...
                particlePositions(i, 2) == particlePositions(i -1, 2) && ...
                just_moved_south

if that is what your code is intending by the third part of that test.