How to create a better 3D Discrete Plot?
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Athanasios Paraskevopoulos
le 10 Mar 2024
Commenté : Voss
le 10 Mar 2024
I am study the Discrete Klein-Gordon Equation.
By interpreting the equation in this way, we can relate the dynamics described by the discrete Klein - Gordon equation to the behavior of DNA molecules within a biological system . This analogy allows us to understand the behavior of DNA in terms of concepts from physics and mathematical modeling . Is ti possivle to I create a nicer 3D plot than the following?
% Parameters
numBases = 100; % Number of base pairs
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient
% Initial conditions
initialPositions = 0.01 + (0.02 - 0.01) * rand(numBases, 1);
initialVelocities = zeros(numBases, 1);
% Time span for the simulation
tSpan = [0 50];
% Differential equations function
odeFunc = @(t, y) [y(numBases+1:end); ... % velocities
kappa * ([y(2); y(3:numBases); 0] - 2 * y(1:numBases) + [0; y(1:numBases-1)]) + ...
omegaD^2 * (y(1:numBases) - beta * y(1:numBases).^3)]; % accelerations
% Solve the system numerically
[T, Y] = ode45(odeFunc, tSpan, [initialPositions; initialVelocities]);
% Specific time points for visualization
timePoints = [0, 10, 20, 30, 40, 50];
% Initialize the figure for 3D plot
figure;
hold on;
% Plotting the dynamics in 3D
for i = 1:length(timePoints)
time = timePoints(i);
[~, timeIndex] = min(abs(T - time)); % Find the index of the closest time in T
displacements = Y(timeIndex, 1:numBases); % Displacement values at this time point
% Plotting each base pair displacement as a line in 3D space
plot3(1:numBases, repmat(time, 1, numBases), displacements, 'LineWidth', 2);
end
hold off;
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
view(3); % Adjust the view to see the plot in 3D
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Voss
le 10 Mar 2024
Maybe a surface? Something like this:
% Parameters
numBases = 100; % Number of base pairs
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient
% Initial conditions
initialPositions = 0.01 + (0.02 - 0.01) * rand(numBases, 1);
initialVelocities = zeros(numBases, 1);
% Time span for the simulation
tSpan = [0 50];
% Differential equations function
odeFunc = @(t, y) [y(numBases+1:end); ... % velocities
kappa * ([y(2); y(3:numBases); 0] - 2 * y(1:numBases) + [0; y(1:numBases-1)]) + ...
omegaD^2 * (y(1:numBases) - beta * y(1:numBases).^3)]; % accelerations
% Solve the system numerically
[T, Y] = ode45(odeFunc, tSpan, [initialPositions; initialVelocities]);
% Specific time points for visualization
timePoints = [0, 10, 20, 30, 40, 50];
% Initialize the figure for 3D plot
figure;
% Plotting the dynamics in 3D
[~, timeIndex] = min(abs(T - timePoints),[],1); % Find the index of the closest time in T
surf(1:numBases, repmat(timePoints(:), 1, numBases), Y(timeIndex, 1:numBases), ...
'EdgeColor', 'none', 'FaceColor', 'interp')
box on;
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
view(3); % Adjust the view to see the plot in 3D
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