How to code a certain part of this equation?
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Angshuman Podder
on 17 May 2022
Edited: Angshuman Podder
on 18 May 2022
I am trying to write a code for solving population based equations (PBEs) using cell average technique (CAT) by Kumar et al. (2006). Link to the paper: PAPER
However, I am stucking with interpreting a certain part of the whole formulation (mathematical notation) which I have circled in red in the figure. Can anyone help me in correcting me or explaining it? My attempt is somewhat as follows:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1001315/image.png)
clear
close all;
clc;
% ======== User handle starts ==================
%% Initializing
v_max = 100.0; % Maximum size/volume
v_min = 1e-5; % Minimum size/volume
r = 2; % Geometric ratio
% v0 = 0.01; % Initial average size
% N0 = 1; % Initial total number
% tspan = [0 20]; % time span for integration
%% Generating discretized grid
disp('Creating the geometric grid..')
m = ceil(log(v_max/v_min)/log(r)); % Number of pivots
mv = m + 1; % Number of volume boundaries
vi = zeros(mv,1);
vi(1) = v_min;
for i = 2:mv
vi(i) = vi(i-1)*r; %cell edges
end
x = zeros(m,1); % Creating pivots
w = zeros(m,1); % Bin width
for i = 1:m
x(i) = (vi(i) + vi(i+1))/2; %cell centers/pivots
w(i) = vi(i+1) - vi(i); % width
end
p = 1; %fixed pivot
for j = 1: m
for k = 1:j
v = x(j) + x(k) ;
for i = 1:m-1
if v < x(i+1) && v >= x(i)
itvl(p,:) = [x(j), x(k)] ;
Z(i,j,k) = 1;
p = p +1;
break;
end
end
end
end
p = 1; %CAT
for j = 1: m
for k = 1:j
v = x(j) + x(k) ;
for i = 1:mv-1
if v < vi(i+1) && v >= vi(i)
itvl(p,:) = [x(j), x(k)] ;
Z(i,j,k) = 1;
p = p +1;
end
end
end
end
return
%%%%%%%% i-th equation %%%%%%%%%%%%
for i = 1:m
for j = 1:m
for k = 1:j
B(i) = (1 - (1/2)*Z(i,j,k)*dirac_delta(i,j))*beta(j,k)*N(j)*N(k) ;
end
end
end
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Accepted Answer
Torsten
on 17 May 2022
for i = 1:m-1
xmhalf = x(i);
xphalf = x(i+1);
B_agg(i) = 0.0;
for k=1:m
for j=k:m
if vi(j) + vi(k) < xphalf && vi(j) + vi(k) >= xmhalf
B_agg(i) = B_agg(i) + (1-0.5*dirac_delta(j,k))*beta(j,k)*N(j)*N(k);
end
end
end
end
Not sure about the loop limits - recheck !
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