I understand that you want to visualize heat diffusion in the spherical coordinate system,
Here's an outline on how to implement the same,
- Define the neutron diffusion equation in spherical coordinates, considering parameters like absorption and fission cross-sections.
- Generate a grid representing the spherical domain and initialize it with initial conditions and parameters.
- Iterate over time steps, solving the diffusion equation numerically for each step.
- Visualize the results as a heatmap using MATLAB's plotting functions, such as "surf".
- Implement sliders or input parameters to dynamically adjust absorption and fission cross-sections, allowing for the visualization of different diffusion intensities.
Here's an example implementation you may refer to,
% Define parameters
radius = 1; % Radius of the sphere
num_points = 100; % Number of points in each dimension
time_steps = 100; % Number of time steps
% Create spherical grid
theta = linspace(0, pi, num_points);
phi = linspace(0, 2*pi, num_points);
[Theta, Phi] = meshgrid(theta, phi);
% Initialize heat distribution
heat = zeros(num_points, num_points, time_steps);
heat(:,:,1) = sin(Theta) .* cos(Phi); % Example initial condition
% Define diffusion parameters
absorption_cross_section = 0.1; % Example absorption cross-section
fission_cross_section = 0.05; % Example fission cross-section
% Perform simulation
for t = 2:time_steps
% Apply diffusion equation
heat(:,:,t) = heat(:,:,t-1) + absorption_cross_section * heat(:,:,t-1) - fission_cross_section * heat(:,:,t-1);
end
% Visualize heat distribution
for t = 1:time_steps
% Plot heatmap
surf(Theta, Phi, heat(:,:,t));
shading interp;
colormap('hot');
colorbar;
title(['Heatmap at Time Step ', num2str(t)]);
xlabel('\theta');
ylabel('\phi');
zlabel('Heat');
pause(0.1); % Pause to visualize each time step
end
This code initializes a spherical grid, sets initial conditions for heat distribution, iterates over time steps to simulate heat diffusion, and visualizes the results as a heatmap. You can adjust parameters like absorption and fission cross-sections to observe different diffusion behaviors.
Note: You can modify the equations and code according to your specifications.
You can also refer to the following odcumentation links for more information,
Hope this helps!
