double summation in matlab

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Samuel Suakye
Samuel Suakye 2020-4-21
编辑： darova 2020-4-21
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';

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回答（1 个）

darova
darova 2020-4-21
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
  1 个评论
Samuel Suakye
Samuel Suakye 2020-4-21
编辑：darova 2020-4-21
q is to infinity, and the float number depends
but am expecting something like the graph below

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