double summation in matlab

Plotting j_z/j_o against beta_1 = {0,...,10}; and beta_2 = 1, This is what I have done (check the code below) using symsum but for days now it is still running and want to find out whether there are different methods to that. Thanks in advance ;

clc;
b = 0.142e-9; gammao = 3.0; m = 101;
hbar = 1; e = -1; 
K = 8.617e-16; T = 287.5;
a = ((3*b)/(2*hbar)); Pz = ((2*pi*hbar)/(3*b));
beta2 = 1; beta1 = linspace(0,10, 30); % However many you want.
Wcnzz = sqrt(3);
jo = ((8*e*Wcnzz*gammao)/(3*hbar*m*b));
%%
syms q s 
B1 = q.*beta1; B2 = q.*beta2; v = ((pi.*s)./m); h = (a.*Pz);
z = (2.*(pi.^2).*s.*sqrt(3).*(a./(2*pi)));
Eqszz = (a./(2*pi)).*((1+(4.*cos(h).*cos(v))+(4.*((cos(v)).^2))).^0.5);
Fqszz = ((a.^2).*m)./((z.*((1+(4.*cos(h).*cos(v))+(4.*((cos(v)).^2))).^0.5))./(K.*T));
J1 = besselj(0,B1); J2 = besselj(0,B2);
J = q.*Fqszz.*Eqszz.*J1.*J2;
X = symsum(J,s,1,m);
jz = symsum(X,q,1,inf);
j = jz./jo; 
fplot(beta1, j, 'r-', 'LineWidth', 2 );
drawnow;
grid on;
fontSize = 20;
xlabel('\beta_1', 'FontSize', fontSize)
ylabel('j_z/j_o', 'FontSize', fontSize)
hold on
%%
b = 0.142e-9; gammao = 3.0; m = 101;
hbar = 1; e = -1; 
K = 8.617e-16; T = 287.5;
a = ((3*b)/(2*hbar)); Pz = ((2*pi*hbar)/(3*b));
beta2 = 1; beta1 = linspace(0,10, 30); % However many you want.
Wcnac = 1; t = sqrt(3); n = 1e-9;
jo = ((8*e*Wcnac*gammao)/(3*hbar*m*b));
%%
syms q s 
B1 = q.*beta1; B2 = q.*beta2; u = ((a.*Pz)./t); g = ((pi.*s.*t)./n);
y = (2.*(pi.^2).*s.*t);
Eqsac = ((1+(4.*cos(g).*cos(u))+(4.*((cos(u)).^2))).^0.5);
Fqsac = ((a.^2).*n)./((y.*((1+(4.*cos(g).*cos(u))+(4.*((cos(u)).^2))).^0.5))./(K.*T));
J1 = besselj(0,B1); J2 = besselj(0,B2);
J = q.*Fqsac.*Eqsac.*J1.*J2;
X1 = symsum(J,s,1,m);
jz = symsum(X1,q,1,inf);
j = jz./jo;
fplot(beta1, j, 'b-', 'LineWidth', 2);
drawnow;
grid on; 
fontSize = 20;
xlabel('\beta_1', 'FontSize', fontSize)
ylabel('j_z/j_o', 'FontSize', fontSize)
title('j_x/j_o vs.  \beta_1', 'FontSize', fontSize)
legend('zigzig CNs','armchair CNs','Location','Best');
% Maximize the figure window.
hFig.WindowState = 'maximized';

[darova]

Look similar. Mistake?

[Samuel Suakye]

not a mistake.

[darova]

It's strangle because it can be simplified

Answer 1

[darova]

Here is numerical approach

clc,clear

% alignComments
b      = 0.142e-9;
gammao = 3.0;
m      = 101;
hbar   = 1;
e      = -1;
K      = 8.617e-16;
T      = 287.5;
a      = 3*b/(2*hbar);
Pz     = 2*pi*hbar/(3*b);
beta2  = 1;
beta1  = linspace(0,10, 100); % However many you want.
Wcnzz  = sqrt(3);
jo     = 8*e*Wcnzz*gammao/(3*hbar*m*b);

[q,s] = meshgrid(1:0.1:3,1:m);  % 1:0.1:3 span for 'q'
cps   = cos(pi.*s./m);
cap   = cos(a.*Pz);
Eqszz = a/2/pi*sqrt(1 + 4*cap.*cps + 4*cps.^2);
Fqszz = a^2*m*K*T ./ (2*pi^2*s.*sqrt(3).*Eqszz);

for i = 1:length(beta1)
    B1 = q.*beta1(i);
    B2 = q.*beta2;    
    J1 = besselj(0,q.*B1);
    J2 = besselj(0,q.*B2);    
    tmp = q.*Fqszz.*Eqszz.*J1.*J2;
    J(i) = sum(tmp(:));
end

plot(beta1,J)

I don't know if q value can be float number but the result looks nices

[Samuel Suakye]

q is to infinity, and the float number depends

but am expecting something like the graph below