Simple Integration equation HELP

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.

http://www.mediafire.com/view/u7ktl5tj5jy700u/nnnn.png

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)

[Jan]

What exactly is your question?

[sese]

Tnx Jan for your reply, my question is to find the "k" factor in the equation number 9 here in this link http://www.mediafire.com/view/u7ktl5tj5jy700u/nnnn.png

where k=integration of (Qt*N1D)

Regards

[Jan]

I see a grey page with some blue and white icons. Perhaps the service wants me to enable JavaScript, but I'm not willing to reduce the security level of my browser. It would be kind, if you post your question completely here instead of storing a file on a foreign hoster.

[sese]

Here are the equations

K=integration of (Qt(raduis,lambda,m)*N1D(radius) dr)

N1D=No*exp(-AS1*radius)

K=4.343* No integration of (Qt(raduis,lambda,m) exp(-AS1*radius) dr)

Qt = (lambda^2/2*pi)*sum(n2).*sum(real(An + Bn));

Where An and Bn are Mie scattering coefficients, which are complex function of raduis, lambda and m

My question is to find the integration to get K

Appreciate it

[Jan]

Please do not send me questions by email, but insert all important information into the question, where readers expect them. Hiding them in comments or trying to push the contributors is a bad idea.

Did you read my profile while you've sent your question through the profiles interface?

[Mike Hosea]

This question is a repeat of

http://www.mathworks.com/matlabcentral/answers/83917-integration-help-mie-scattering

[Jan]

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.

Answer 1

[Walter Roberson]

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.

[sese]

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