Circular vortex with spin vectors

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Sateesh Kandukuri
Sateesh Kandukuri 2023-7-24
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.
  2 个评论
Dyuman Joshi
Dyuman Joshi 2023-7-24
Please show what you have attempted yet.
Sateesh Kandukuri
Sateesh Kandukuri 2023-7-24
Ran in:
% 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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回答（2 个）

Dyuman Joshi
Dyuman Joshi 2023-7-24
Ran in:
% 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
显示 2更早的评论
Dyuman Joshi
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
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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Bruno Luong
Bruno Luong 2023-7-31
编辑：Bruno Luong 2023-7-31
Ran in:
[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
  2 个评论
Sateesh Kandukuri
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.
Bruno Luong
Bruno Luong 2023-7-31
编辑：Bruno Luong 2023-7-31
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.

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