Simple Integration equation HELP

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sese
sese on 4 Aug 2013
Dear friends, i am really in trable, i am trying to find the specific attenuation due to rain but i have problem in my code and i am asking you your help. My problem is in the last command which is an integration operation, and i am sure you will do your best for helping me. The link below is for the equations and it's followed by the code.
radius = 1;
nMax = 40; % maximum mode number
No=8*10^3; %m^ -4
R1=140; %rainfall rate=1mm/hr
AS1=8.2*R1^-0.21;
N1D=No*exp(-AS1*radius*1e-3);
% mode numbers
mode = 1:nMax;
frequency = 6e9;
% speed of light
c = 299792458.0;
lambda = c / ( frequency ) ;
for n=1:10;
n2 = (2*n+1);
% radian frequency
w = 2.0*pi*frequency;
% wavenumber
k = w/c;
% conversion factor between cartesian and spherical Bessel/Hankel function
s = sqrt(0.5*pi/(k*radius));
% compute spherical bessel, hankel functions
[J(mode)] = besselj(mode + 1/2, k*radius); J = J*s;
[H(mode)] = besselh(mode + 1/2, 2, k*radius); H = H*s;
[J2(mode)] = besselj(mode + 1/2 - 1, k*radius); J2 = J2*s;
[H2(mode)] = besselh(mode + 1/2 - 1, 2, k*radius); H2 = H2*s;
% derivatives of spherical bessel and hankel functions
% Recurrence relationship, Abramowitz and Stegun Page 361
kaJ1P(mode) = (k*radius*J2 - mode .* J );
kaH1P(mode) = (k*radius*H2 - mode .* H );
% Ruck, et. al. (3.2-1)
An = -((1i).^mode) .* ( J ./ H ) .* (2*mode + 1) ./ (mode.*(mode + 1));
% Ruck, et. al. (3.2-2), using derivatives of bessel functions
Bn = ((1i).^(mode+1)) .* (kaJ1P ./ kaH1P) .* (2*mode + 1) ./ (mode.*(mode + 1));
Qt = (lambda^2/2*pi)*sum(n2).*sum(real(An + Bn));
end
Co1=4.343*No;
==============================================================
NOW HOW TO FIND THE INTEGRATION OF "k", where k=integration of (Qt*N1D)
  7 Comments
Jan
Jan on 6 Aug 2013
I got 5 emails today with questions which belongs to the forum. Two of them were double posts also. It seems to be the day of the nervous askers.

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Answers (1)

Walter Roberson
Walter Roberson on 5 Aug 2013
Change
n2 = (2*n+1);
to
n2(n) = (2*n+1);
Change
An = -((1i).^mode) .* ( J ./ H ) .* (2*mode + 1) ./ (mode.*(mode + 1));
% Ruck, et. al. (3.2-2), using derivatives of bessel functions
Bn = ((1i).^(mode+1)) .* (kaJ1P ./ kaH1P) .* (2*mode + 1) ./ (mode.*(mode + 1));
Qt = (lambda^2/2*pi)*sum(n2).*sum(real(An + Bn));
end
to
An(n) = -((1i).^mode) .* ( J ./ H ) .* (2*mode + 1) ./ (mode.*(mode + 1));
% Ruck, et. al. (3.2-2), using derivatives of bessel functions
Bn(n) = ((1i).^(mode+1)) .* (kaJ1P ./ kaH1P) .* (2*mode + 1) ./ (mode.*(mode + 1));
end
Qt = (lambda^2/2*pi)*sum(n2 .* real(An + Bn));
end
Also, in theory you should change
for n=1:10;
to
for n=1:inf
but you are unlikely to have an infinite amount of memory or an infinite amount of time to wait.
Now in addition to all of this, you should not be setting "radius" to 1.0, or frequency to 6e9 or running mode over 1:40 : you should be bundling everything into a function that takes radius and lambda and the mode number as parameters. You would then be invoking that function from within integrate() or quadgk(), using parameterization to pass in one specific lambda and mode number, such as
this_frequency = 6e9;
this_lambda = c ./ this_frequency;
this_mode_number = 5;
low_r = 0;
high_r = 173;
k = integrate(@(r) compute_Qt(r, this_lambda, this_mode_number), [low_r, high_r]);
Please review the equations and notice that only one mode number (m) is used, not a range of mode numbers. If for some reason you want to compute for different mode numbers, that should be done by a series of integrals.
  1 Comment
sese
sese on 5 Aug 2013
Edited: sese on 5 Aug 2013
Hi Walter, i appreciate your help so much, God bless you. When i applied what you explained to me i got the following error
In an assignment A(I) = B, the number of elements in B and I must be the same.
Error in mathworkss (line 64) An(n) = -((1i).^mode) .* ( J ./ H ) .* (2*mode + 1) ./ (mode.*(mode + 1));
What should i do

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