Circular vortex with spin vectors

Question

Sateesh Kandukuri 2023-7-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1999798-circular-vortex-with-spin-vectors

编辑： Bruno Luong 2023-7-31

I need help to create a circular vortex with different polarizations like converging, diverging and clockwise etc.,

I attached an image for reference.

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Dyuman Joshi 2023-7-24

Please show what you have attempted yet.

Sateesh Kandukuri 2023-7-24

在 MATLAB Online 中打开

% Parameters

numPoints = 100; % Number of points in the vortex

spinMagnitude = 0.5; % Magnitude of the spin vectors

radius = 1; % Radius of the vortex

% Generate theta values

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

% Generate x and y coordinates

x = radius * cos(theta);

y = radius * sin(theta);

% Generate spin vectors

spinVectors = spinMagnitude * ones(size(x));

% Plot the vortex

figure;

quiver(x, y, spinVectors.*cos(theta), spinVectors.*sin(theta), 'b');

axis equal;

title('Circular Diverging Vortex');

xlabel('X');

ylabel('Y');

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Answer 1

Dyuman Joshi 2023-7-24

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1999798-circular-vortex-with-spin-vectors#answer_1277688

在 MATLAB Online 中打开

% Parameters

numPoints = 50; % Number of points in the vortex

spinMagnitude = 0.5; % Magnitude of the spin vectors

r1 = 1; % Radius of the outer vortex

r2 = 0.5; %Radius of the inner vortex

% Generate theta values

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

% Generate x and y coordinates

x = cos(theta);

y = sin(theta);

% Generate spin vectors

spinVectors = spinMagnitude * ones(size(x));

%%Radially outward arrows

figure;

quiver(r1*x, r1*y, spinVectors.*x, spinVectors.*y, 'b');

hold on

quiver(r2*x, r2*y, spinVectors.*x, spinVectors.*y, 'b');

axis equal;

xlabel('X');

ylabel('Y');

%%Radially outward arrows leaning in a counter clockwise direction

figure

quiver(r1*(x+y), r1*(y-x), spinVectors.*x, spinVectors.*y, 'b');

hold on

quiver(r2*(x+y), r2*(y-x), spinVectors.*x, spinVectors.*y, 'b');

axis equal;

xlabel('X');

ylabel('Y');

4 个评论
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Dyuman Joshi 2023-7-31

Do you only have these images to work with? or do you have any data or any other piece of information?

Sateesh Kandukuri 2023-7-31

Actually, the polarization of the system is defined by P = (cosφ, sinφ, 0), where φ = tan-1(y/x) +Ψ and (x,y) are the spatial coordinates in the system plane with the origin at the centre. The angle Ψ determines the polarization orientation. For Ψ = 0, it gives diverging vortex. I hope this piece of information helpful.

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Answer 2

Bruno Luong 2023-7-31

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1999798-circular-vortex-with-spin-vectors#answer_1280962

编辑：Bruno Luong 2023-7-31

在 MATLAB Online 中打开

[x,y] = ndgrid(linspace(-1,1,10));

x = x(:)';

y = y(:)';

xy = [x; y];

r = vecnorm(xy, 2, 1);

r(r > 1) = NaN;

xyn = xy ./ r;

for k=1:12

Psi = 2*pi*rand();

R = [cos(Psi), -sin(Psi);

sin(Psi), cos(Psi)];

V = R * xyn;

vx = V(1,:);

vy = V(2,:);

subplot(3,4,k);

quiver(x, y, vx, vy, 'linewidth', 2);

set(gca, 'visible', 'off')

end

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Sateesh Kandukuri 2023-7-31

Dear @Bruno Luong, I want to define these normalized spin vectors on a 200-unit diameter circular geometry with a unit vector spacing, and I need it in a separate image based on the angle Psi.