% equation number 11 code

% Define the equation

theta = linspace(0, 2*pi, 1000);

E = linspace(Delta(0), 10, 1000); % Assuming a range for E values

Delta_0 = 1; % Assuming a value for Delta(0)

n = 1; % Assuming a value for n

n_s_T = 1; % Assuming a value for n_s(T)

% Calculate the integrals

cos_theta = cos(theta).^4;

integral_theta = trapz(theta, cos_theta);

integral_E = zeros(size(E));

for i = 1:length(E)

if E(i) > Delta_0

integral_E(i) = E(i) / sqrt(E(i)^2 - Delta_0^2);

end

end

integral_E = trapz(E, integral_E);

% Calculate bx

bx = -2/3 * Delta_0^2 * (n / n_s_T)^3 * integral_theta * integral_E;

% Plot the equation

figure;

plot(E, bx * ones(size(E)), 'LineWidth', 2);

xlabel('E');

ylabel('b_x');

title('Plot of b_x');

grid on;

% % % % % % % % % % % % % % % % %

%Make sure to adjust the default values for variables like Delta(0), n, and

%n_s(T) based

% % % % % % % % % % % % % % % % % %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% equation number 12 code

% Define constants and functions

Delta_0 = 1; % Assuming a value for Delta(0)

n_s_T = 1; % Assuming a value for n_s(T)

n_s_0 = 1; % Assuming a value for n_s(0)

theta_i = pi/4; % Assuming a value for theta_i

% Define theta range

theta = linspace(0, 2*pi, 1000);

% Calculate the first integral

cos_theta = cos(theta).^4;

integral_theta = trapz(theta, cos_theta) / (2*pi);

% Define E range

E = linspace(Delta_0, 10, 1000); % Assuming a range for E values

% Calculate the second integral

integral_E = zeros(size(E));

for i = 1:length(E)

if E(i) > Delta_0

integral_E(i) = E(i) / (E(i)^2 - Delta_0^2)^(3/2);

end

end

integral_E = trapz(E, integral_E);

% Calculate b_xy

b_xy = -1/3 * Delta_0^2 * (n_s_T / n_s_0)^3 * integral_theta + ...

3 * cos(theta_i)^2 * sin(theta_i)^2 * integral_E;

% Plot the equation

figure;

plot(theta, b_xy * ones(size(theta)), 'LineWidth', 2);

xlabel('Theta (θ)');

ylabel('b_{xy}');

title('Plot of b_{xy}');

grid on;

% % % % % % % % % % % % % % % % %

% Make sure to adjust the default values for variables like Delta(0), n_s(T),

% n_s(0), and theta_i based on your actual values.

% % % % % % % % % % % % % % % % % %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%