Help Defining Variable Contained Within Summation Notation, and Using this Variable for Plot

Hi all,

I am having trouble defining and using a variable in my code. In my code (shown below), I would like to establish a variable "t" that varies from 0 to 1e6, only containing integer values. Therefore, I would like my SumFe56 term to be a function that finds the sum from n=1 to n=1e7 for t=0, and then from n=1 to n=1e7 for t=1, and so on, until my code provides values for SumFe56 from n=1 to n=1e7 for t=1e6. I would then like to use the SumFe56 function in a larger function, BulkFe56, before finally making a plot that shows BulkFe56 values on the y-axis, and t on the x-axis, with the t values varying on this plot from t=0 to t=1e6. Can anyone please tell me the code that would be capable of doing this?

Here is my code, currently:

n = 1:1e7;
t = 0:1e6;
r = .002;
DFe56 = 1e-12;
SumFe56 = sum((1./n.^2).*exp(-n.^2*pi^2*DFe56*t/r^2));
BulkFe56 = (20*.9175)+((6*.9175*(9-20))/pi^2)*SumFe56;

Thanks,

Jonathan

Answer 1

[fred ssemwogerere]

Hello, you could use nested for loop. But i envision this running into an "Out of memory" problem sheerly based on the length of "n" and "t".

[Jonathan Pinko]

Hi Fred,

Thanks for your response. I'm pretty new to this, so could you provide more detail as to what the nested for loop would look like?

I've provided what I've changed below, choosing to modify the t values at intervals of 100000 at this step so the code takes less time to run. I've also provided the answers for BulkFe56 that I'm getting farther below. Here's the thing: I'm generating the correct values of BulkFe56, although when I try to plot them, there is nothing that is appearing on my plots. I'm assuming that my data is overwriting itself with every new point I get for BulkFe56, and this is why there are no lines appearing on my plot.

Thus, what would my code look like for creating a nested loop so that my data does not overwrite itself, and I can plot the values of t vs. BulkFe56?

n = 1:1e7;

r = .002;

DFe56 = 1e-12;

for t = 0:100000:1e6

SumFe56 = sum((1./n.^2).*exp(-n.^2*pi^2*DFe56*t/r^2));

BulkFe56 = (20*.9175)+((6*.9175*(9-20))/pi^2)*SumFe56;

end

plot(t,BulkFe56)

set(gca,'XScale','log')

BulkFe56 =

8.2575

BulkFe56 =

12.9024

BulkFe56 =

14.3830

BulkFe56 =

15.3430

BulkFe56 =

16.0336

BulkFe56 =

16.5522

BulkFe56 =

16.9498

BulkFe56 =

17.2577

BulkFe56 =

17.4971

BulkFe56 =

17.6839

BulkFe56 =

17.8296

[fred ssemwogerere]

Hello, by nested for loop, i meant something like this;

n = 1:1e7;
r = .002;
DFe56 = 1e-12;
t = 0:100000:1e6;
% pre-allocate a temporary variable to store output from the nested loop. Let me call this variable: "v"
v=zeros(length(t),length(n));
for i=1:numel(t)
    for j=1:numel(n)
        % storing output in variable "v"
        v(i,j)=(1/n(j)^2)*exp(-n(j)^2*pi^2*DFe56*t(i)/r^2); 
    end
end
SumFe56=sum(v,2); % taking sum along the rows (this computes sum for each value of "t")
clear v % Since there is no further use for the temporary variable "v", it is best to clear it from memory with this line
BulkFe56=(20*.9175)+((6*.9175*(9-20))/pi^2).*SumFe56;
% plot your data
figure;handl=plot(t,BulkFe56);handl.Parent.XScale='log';

[Jonathan Pinko]

This was a lot of help.

Thank you.