3D surface plot help

I am trying to plot a 3d surface of a function vs two variables. Simply, I would like to plot R2 as a function of mu_eff and tau_e with fixed values of the others.

R2=((2/15)*((mu0/(4*pi))^2)*((gamma_H^2)*(mu_eff^2)/(r^6)))*...
          ((2*(1/((1/tau_r)+(1/tau_e))))+(  (13/2)*(1/((1/tau_r)+(1/tau_e)))/(1+(omega_e^2)*((1/((1/tau_r)+(1/tau_e)))^2)))+((3/2)*(1/((1/tau_r)+(1/tau_e)))/(1+(omega_H^2)*((1/((1/tau_r)+(1/tau_e)))^2))))+...
 ((2/5)*((mu0/(4*pi))^2)*((omega_H^2)*(mu_eff^4)/(((3*k*T)^2)*(r^6)))*((2*tau_r)+(((3/2)*tau_r)/(1+(omega_H^2)*(tau_r^2)))));

The others variables are fixed as

   tau_r = 345;
r = 6.6;
B = 3
mu0=4*pi*1e-7;  % J/Tesla
r=r*1e-10;
mu_eff=mu_eff*9.274e-24;
tau_r=tau_r*1e-12;
tau_e=tau_e*1e-12;
gamma_H=2.6753e8;    % (rad/s)/Tesla
gamma_e=1.760860e11; % (rad/s)/Tesla
k=1.3806503e-23;
T=295;
omega_H=gamma_H*B;
omega_e=gamma_e*B;

I've set mu_eff and tau_e to vary and made a meshgrid

mu_eff = linspace(8,12,100);
tau_e = linspace(0,1,100);
[X, Y] = meshgrid (mu_eff, tau_e);

I believe I then need to replace all the instances of mu_eff and tau_r in the original R2 equation (which I've now called Z) with X. and Y. as

Z=((2/15)*((mu0/(4*pi))^2)*((gamma_H^2)*(X^2)/(r^6)))*...
            (  (2*(1/((1/tau_r)+(1/Y.))))+(  (13/2)*(1/((1/tau_r)+(1/Y.)))/(1+(omega_e^2)*((1/((1/tau_r)+(1/Y.)))^2))   )+((3/2)*(1/((1/tau_r)+(1/Y.)))/(1+(omega_H^2)*((1/((1/tau_r)+(1/Y.)))^2))))+...
   (     (2/5)*((mu0/(4*pi))^2)*((omega_H^2)*(X.^4)/(((3*k*T)^2)*(r^6)))*(   (2*tau_r)   +  (     ((3/2)*tau_r)/(1+(omega_H^2)*(tau_r^2))   )   )  );

surf(X, Y, Z)

I am just getting bracket errors back in the new Z equation that I cannot seem to fix.

Error: File: test2.m Line: 25 Column: 38 Unbalanced or unexpected parenthesis or bracket.

Sorry if this is a simple question.

Thanks,

Answer 1

[Abraham Boayue]

It's difficult to figure out the the exact expression for R2 among those parenthesis. Can you post the equation instead?

Answer 2

[Alice Harnden]

Sorry, should have done this previously, the code isn't the most user friendly.

Answer 3

[Abraham Boayue]

This is what I came up with. I hope this helps.

clear variables
close all
% Define parameters
tau_r    =  345e-12;
r        =  6.6e-10;
b        =  3;
muo      =  4*pi*1e-7;           
gamma_N  =  2.6753e8; 
we       =  b*1.760860e11;
wN       =  b*2.6753e8;
k        =  1.3806503e-23;
T        =  295;
% Define constants
C1 = (1/15)*(gamma_N^2/r^6)*(muo/4*pi)^2;
C2 = (1/5*r^6)*(muo/4*pi)^2*(wN/3*k*T)^2;
% Define variables and function
mu_eff = linspace(8,12,200)*9.274e-24;
tau_e  = linspace(0,1,200)*1e-12;
[x,y] = meshgrid(mu_eff,tau_e);
tau_c  = 1./(1/r +1./y);
A = (13*tau_c)./(1+(we*tau_c).^2);
B = (3*tau_c)./(1+(wN*tau_c).^2);
C = (3*tau_r)/(1+(wN.*tau_r)^2);
R2 = C1*(x.^2).*(4*tau_c + A + B )+ C2*(x.^4).*(4*tau_r + C);
surf(x,y,R2)