Math Forum Discussions

Francesco Perrone

Posts: 38
Registered: 5/2/12

Construct this function!
Posted: Jan 15, 2013 10:06 AM

Plain Text

Hi everybody,

starting from this code:

clc, clear all, close all
tic

k1 = 0.01:0.1:100;
k2 = 0.01:0.1:100;
k3 = 0.01:0.1:100;

k = sqrt(k1.^2 + k2.^2 + k3.^2);

c = 1.476;
gamma = 3.9;

colors = {'cyan'};
Ek = (1.453*k.^4)./((1 + k.^2).^(17/6));
E = @(k) (1.453*k.^4)./((1 + k.^2).^(17/6));
E_int = zeros(1,numel(k1));
E_int(1) = 1.5;

for i = 2:numel(k)
E_int(i) = E_int(i-1) - integral(E,k(i-1),k(i));
end

beta = c*gamma./(k.*sqrt(E_int));

F_11 = zeros(1,numel(k1));
F_22 = zeros(1,numel(k1));
F_33 = zeros(1,numel(k1));

count = 0;
for i = 1:numel(k1)
count = count + 1;
phi_11 = @(k2,k3) phi_11_new(k1,k2,k3,beta,i);
phi_22 = @(k2,k3) phi_22_new(k1,k2,k3,beta,i);
phi_33 = @(k2,k3) phi_33_new(k1,k2,k3,beta,i);
F_11(count) = integral2(phi_11,-100,100,-100,100);
F_22(count) = integral2(phi_22,-100,100,-100,100);
F_33(count) = integral2(phi_33,-100,100,-100,100);
end

figure
hold on
plot(k1,F_11,'b')
plot(k1,F_22,'cyan')
plot(k1,F_33,'magenta')
hold off

where

function phi_11 = phi_11_new(k1,k2,k3,beta,i)
k = sqrt(k1(i).^2 + k2.^2 + k3.^2);
k30 = k3 + beta(i).*k1(i);
k0 = sqrt(k1(i).^2 + k2.^2 + k30.^2);
E_k0 = 1.453.*k0.^4./((1 + k0.^2).^(17/6));
C1 = (beta(i).*k1(i).^2).*(k1(i).^2 + k2.^2 - k3.*k30)./(k.^2.*(k1(i).^2 + k2.^2));
C2 = k2.*k0.^2./((k1(i).^2 + k2.^2).^(3/2)).*atan2((beta(i).*k1(i).*sqrt(k1(i).^2 + k2.^2)),(k0.^2 - k30.*k1(i).*beta(i)));
xhsi1 = C1 - k2./k1(i).*C2;
xhsi1_q = xhsi1.^2;
phi_11 = E_k0./(4.*pi.*k0.^4).*(k0.^2 - k1(i).^2 - 2.*k1(i).*k30.*xhsi1 + (k1(i).^2 + k2.^2).*xhsi1_q);
end

function phi_22 = phi_22_new(k1,k2,k3,beta,i)
k = sqrt(k1(i).^2 + k2.^2 + k3.^2);
k30 = k3 + beta(i).*k1(i);
k0 = sqrt(k1(i).^2 + k2.^2 + k30.^2);
E_k0 = 1.453.*k0.^4./((1 + k0.^2).^(17/6));
C1 = (beta(i).*k1(i).^2).*(k1(i).^2 + k2.^2 - k3.*k30)./(k.^2.*(k1(i).^2 + k2.^2));
C2 = k2.*k0.^2./((k1(i).^2 + k2.^2).^(3/2)).*atan2((beta(i).*k1(i).*sqrt(k1(i).^2 + k2.^2)),(k0.^2 - k30.*k1(i).*beta(i)));
xhsi2 = k2./k1(i).*C1 + C2;
xhsi2_q = xhsi2.^2;
phi_22 = E_k0./(4.*pi.*k0.^4).*(k0.^2 - k2.^2 - 2.*k2.*k30.*xhsi2 + (k1(i).^2 + k2.^2).*xhsi2_q);
end

function phi_33 = phi_33_new(k1,k2,k3,beta,i)
k = sqrt(k1(i).^2+k2.^2+k3.^2);
k30 = k3 + beta(i).*k1(i);
k0 = sqrt(k1(i).^2+k2.^2+k30.^2);
E_k0 = (1.453.*k0.^4./((1+k0.^2).^(17/6)));
phi_33 = (E_k0./(4*pi.*(k.^4))).*(k1(i).^2+k2.^2);
end

This procedure is leading me to results not matching some others coming from a study.
I believe that the flaw may reside in the definition of beta outside the function phi_11_new (and phi_22_new).

May any of you suggest how to calculate beta within phi_11_new(and phi_22_new) instead than the way I currently do?

I thank you all in advance for supporting.

Best Regards,
fpe