Circular vortex with spin vectors

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

I attached an image for reference.

[Dyuman Joshi]

Please show what you have attempted yet.

[Sateesh Kandukuri]

% 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');

Answer 1

[Dyuman Joshi]

% 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');

[Dyuman Joshi]

In case you want Radially outward arrows which are leaning clockwise, try this -

% 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 leaning in a clockwise direction
figure
quiver(r1*(x-y), r1*(x+y), spinVectors.*x, spinVectors.*y, 'b');
    hold on
quiver(r2*(x-y), r2*(x+y), spinVectors.*x, spinVectors.*y, 'b');
axis equal;
xlabel('X');
ylabel('Y');

[Sateesh Kandukuri]

Dear @Dyuman Joshi, thank you so much for your response. Actually, I am looking for a pattern something like as below.

Let's consider a 200-unit dia circular geometry with a unit vector spacing. I want to define my base geometry with normalized spin vectors with different in-plane possible orientations. Could you please help me in this wasy?

[Dyuman Joshi]

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

[Sateesh Kandukuri]

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.

Answer 2

[Bruno Luong]

[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

[Sateesh Kandukuri]

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.

[Bruno Luong]

Feel free to adapt my code to your need.

I gave you a recipe of the cake, if you want strawberry flavor, you need to adapt my recipe and make your own cake.