Hello everyone, I am trying to obtain the following graph using the explanations below, but I am getting a different result. I would really appreciate it if you could help me find the error.
explanations:

my code:
clear all
clc

% Parameters
epsilon0 = 8.85e-12;
epsilon_m = 79;
CM = 0.5;
k_B = 1.38e-23;
R = 1e-6;
gamma = 1.88e-8;
q = 1e-14;
dt = 1e-3;
T = 300;
x0 = 10e-6;
num_steps = 1000;
N = 100000;

epsilon = 1e-9;
k = 1 / (4 * pi * epsilon_m);

% **Creating matrices to store FDEP force and positions**
x_dep = zeros(num_steps, N);
x_diff = zeros(num_steps, N);
FDEP = zeros(num_steps, N);

% **Initial Positions**
x_dep(1, = x0;
x_diff(1, = x0;

% **Generating random numbers for Brownian motion**
rng(0);

% **Loop for 100,000 Simulations (Each Simulation Runs Independently!)**
for sim = 1:N
% **Generate random Gaussian noise for each particle**
W = randn(num_steps, 1);

for i = 1:num_steps-1
% **Calculate FDEP separately for each particle**
FDEP(i, sim) = 4 * pi * R^3 * epsilon0 * epsilon_m * CM * (-2 * k^2 * q^2) / ((abs(x_dep(i, sim) – x0) + epsilon)^5);

% **Motion under the effect of FDEP (Used for Correct Simulation)**
x_dep(i+1, sim) = x_dep(i, sim) + (FDEP(i, sim) / gamma) * dt + sqrt(2 * k_B * T / gamma) * sqrt(dt) * W(i);

% **Pure diffusion (without DEP force)**
x_diff(i+1, sim) = x_diff(i, sim) + sqrt(2 * k_B * T / gamma) * sqrt(dt) * W(i);
end
end

% **Calculate Mean Positions**
x_mean_dep = mean(x_dep, 2);
x_mean_diff = mean(x_diff, 2);

% **Plot the Graph**
figure;
plot((0:num_steps-1) * dt, x_mean_dep * 1e6, ‘b’, ‘LineWidth’, 1.5);
hold on;
plot((0:num_steps-1) * dt, x_mean_diff * 1e6, ‘r–‘, ‘LineWidth’, 1.5);
xlabel(‘Time (s)’);
ylabel(‘Position (μm)’);
title(‘Particle Motion Under the Effect of Dielectrophoretic Force’);
legend(‘Diffusion under F_{DEP}’, ‘Pure diffusion’);
grid on;
hold off;Hello everyone, I am trying to obtain the following graph using the explanations below, but I am getting a different result. I would really appreciate it if you could help me find the error.
explanations:

my code:
clear all
clc

% Parameters
epsilon0 = 8.85e-12;
epsilon_m = 79;
CM = 0.5;
k_B = 1.38e-23;
R = 1e-6;
gamma = 1.88e-8;
q = 1e-14;
dt = 1e-3;
T = 300;
x0 = 10e-6;
num_steps = 1000;
N = 100000;

epsilon = 1e-9;
k = 1 / (4 * pi * epsilon_m);

% **Creating matrices to store FDEP force and positions**
x_dep = zeros(num_steps, N);
x_diff = zeros(num_steps, N);
FDEP = zeros(num_steps, N);

% **Initial Positions**
x_dep(1, = x0;
x_diff(1, = x0;

% **Generating random numbers for Brownian motion**
rng(0);

% **Loop for 100,000 Simulations (Each Simulation Runs Independently!)**
for sim = 1:N
% **Generate random Gaussian noise for each particle**
W = randn(num_steps, 1);

for i = 1:num_steps-1
% **Calculate FDEP separately for each particle**
FDEP(i, sim) = 4 * pi * R^3 * epsilon0 * epsilon_m * CM * (-2 * k^2 * q^2) / ((abs(x_dep(i, sim) – x0) + epsilon)^5);

% **Motion under the effect of FDEP (Used for Correct Simulation)**
x_dep(i+1, sim) = x_dep(i, sim) + (FDEP(i, sim) / gamma) * dt + sqrt(2 * k_B * T / gamma) * sqrt(dt) * W(i);

% **Pure diffusion (without DEP force)**
x_diff(i+1, sim) = x_diff(i, sim) + sqrt(2 * k_B * T / gamma) * sqrt(dt) * W(i);
end
end

% **Calculate Mean Positions**
x_mean_dep = mean(x_dep, 2);
x_mean_diff = mean(x_diff, 2);

% **Plot the Graph**
figure;
plot((0:num_steps-1) * dt, x_mean_dep * 1e6, ‘b’, ‘LineWidth’, 1.5);
hold on;
plot((0:num_steps-1) * dt, x_mean_diff * 1e6, ‘r–‘, ‘LineWidth’, 1.5);
xlabel(‘Time (s)’);
ylabel(‘Position (μm)’);
title(‘Particle Motion Under the Effect of Dielectrophoretic Force’);
legend(‘Diffusion under F_{DEP}’, ‘Pure diffusion’);
grid on;
hold off; Hello everyone, I am trying to obtain the following graph using the explanations below, but I am getting a different result. I would really appreciate it if you could help me find the error.
explanations:

my code:
clear all
clc

% Parameters
epsilon0 = 8.85e-12;
epsilon_m = 79;
CM = 0.5;
k_B = 1.38e-23;
R = 1e-6;
gamma = 1.88e-8;
q = 1e-14;
dt = 1e-3;
T = 300;
x0 = 10e-6;
num_steps = 1000;
N = 100000;

epsilon = 1e-9;
k = 1 / (4 * pi * epsilon_m);

% **Creating matrices to store FDEP force and positions**
x_dep = zeros(num_steps, N);
x_diff = zeros(num_steps, N);
FDEP = zeros(num_steps, N);

% **Initial Positions**
x_dep(1, = x0;
x_diff(1, = x0;

% **Generating random numbers for Brownian motion**
rng(0);

% **Loop for 100,000 Simulations (Each Simulation Runs Independently!)**
for sim = 1:N
% **Generate random Gaussian noise for each particle**
W = randn(num_steps, 1);

for i = 1:num_steps-1
% **Calculate FDEP separately for each particle**
FDEP(i, sim) = 4 * pi * R^3 * epsilon0 * epsilon_m * CM * (-2 * k^2 * q^2) / ((abs(x_dep(i, sim) – x0) + epsilon)^5);

% **Motion under the effect of FDEP (Used for Correct Simulation)**
x_dep(i+1, sim) = x_dep(i, sim) + (FDEP(i, sim) / gamma) * dt + sqrt(2 * k_B * T / gamma) * sqrt(dt) * W(i);

% **Pure diffusion (without DEP force)**
x_diff(i+1, sim) = x_diff(i, sim) + sqrt(2 * k_B * T / gamma) * sqrt(dt) * W(i);
end
end

% **Calculate Mean Positions**
x_mean_dep = mean(x_dep, 2);
x_mean_diff = mean(x_diff, 2);

% **Plot the Graph**
figure;
plot((0:num_steps-1) * dt, x_mean_dep * 1e6, ‘b’, ‘LineWidth’, 1.5);
hold on;
plot((0:num_steps-1) * dt, x_mean_diff * 1e6, ‘r–‘, ‘LineWidth’, 1.5);
xlabel(‘Time (s)’);
ylabel(‘Position (μm)’);
title(‘Particle Motion Under the Effect of Dielectrophoretic Force’);
legend(‘Diffusion under F_{DEP}’, ‘Pure diffusion’);
grid on;
hold off; mathematics, signal processing, signal, graph, graphics, matrices, matlab, differential equations MATLAB Answers — New Questions

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