How do I convert a T dependent Mexican hat plot to a surface plot.

I have created this code to create a gif of a temperature dependent potential.

clear all
clc
clf

lam=0.5;
phi=linspace(-7,7,1000);
eta=3;
init=7;

filename = 'Nachos.gif';
for n = init:-init/100:-init           %Allows me to cycle through values of T, 
                                       %from the initial value to zero and back.
    T=sqrt(n^2); 
    V=0.25*lam.*(phi.^2-eta^2).^2+0.5*lam*T^2.*phi.^2;          %T dependant potential

      plot(phi,V)
      axis([-8 8 0 15])

     drawnow                            %Adds current plot as a frame in the gif.
      frame = getframe(1);
      im = frame2im(frame);
      [imind,cm] = rgb2ind(im,256);
      if n == init;
          imwrite(imind,cm,filename,'gif', 'Loopcount',inf);
      else
          imwrite(imind,cm,filename,'gif','WriteMode','append');
      end
end

I would like to create the equivalent for the 3D surface plot :

But can't seem to get it to work, would anybody be able to help?

Answer 1

[Star Strider]

This will give you what appears to be the surface plot your animated plot traces:

lam=0.5;
phi=linspace(-7,7,1000);
eta=3;
init=7;
fin=0.1;
n=1;
n = init:-14/100:-init;

[T,P] = meshgrid(n, phi);

Vfcn = @(phi,T) 0.25*lam.*(phi.^2-eta^2).^2+0.5*lam*T.^2.*phi.^2;

V = Vfcn(P,T);

figure(1)
meshc(T, P, V)
grid on
axis([-8  8  ylim   0  15])

It’s not the plot you posted as what you want, but it does reproduce the plot in your animation. I’ll let you sort that. You might want to consider using cart2pol or pol2cart since I’m not certain what you’re doing.

[Stephen Cripps]

Sorry that didn't really help, I've tried clearing up the code above.

This is the current output, but I'd like to create the 3D version of this.

[Star Strider]

My code does create a 3D version of your plot. If you want it to be like the one you pictured, you have to define it in terms of the matrices the meshgrid function produces. I can’t follow what you’re doing so I came up with a simple example:

[X,Y] = meshgrid(-5:0.1:+5);

Z = -(X.^2 + Y.^2).*exp(-0.3*(X.^2 + Y.^2));

figure(3)
mesh(X, Y, Z)
grid on