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double summation in matlab
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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';
3 Commenti
Risposte (1)
darova
il 21 Apr 2020
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
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/286270/image.png)
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