How to write integral equation ?

2020 9 5
4 个回答
回答已采纳
更新时间：2020 9 10
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I like to check if my code represent the equation. Please help

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David Hill
David Hill 2020-9-5
What is your function D(c)? Or is it an array? Depending on what D(c) is, and assuming you want a numerical solution, it should not be a hard problem.
Michael Crown
Michael Crown 2020-9-5
It should return a single value. Not an array
David Hill
David Hill 2020-9-5
What is your function D with respect to c? For example:
D=@(c)5*c.^2+4*c-10;
Michael Crown
Michael Crown 2020-9-5
That is why I need help. If I have your email address, I can send the entire code to you. I am a novice with this. Thanks.
Michael Crown
Michael Crown 2020-9-5
My email: miki7as@gmail.com You can send me a mail and I will reply with the code if you aren’t comfortable sharing email here
Walter Roberson
Walter Roberson 2020-9-5
It looks to me as if you should be using trapz()
Michael Crown
Michael Crown 2020-9-5
If you don’t mind, can I send the full code? I need help.
David Hill
David Hill 2020-9-5
Yes, attach full code and ask a specific question.
Michael Crown
Michael Crown 2020-9-5
attached @David Hill
All i need is to calculate DaveA and DaveB using the attached equation. I am not sure what i have i right.

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 采纳的回答

David Hill
David Hill 2020-9-5

0 个投票

Not sure if your Ca is sorted. Yes, you have a stream of data that is being integrated. The proper function is trapz(). Providing your full code helped significantly. I assume you want your data sorted before integrating.
[Ca,idx]=sort(dataB(:,1));
Da=dataB(:,2);
Da=Da(idx);%aligns Da to sorted Ca
DaveA=trapz(Ca,Da)/(Ca(end)-Ca(1));

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David Hill
David Hill 2020-9-5
The above is all you need if you have dataB. It will calculate DaveA per the equation you provided.
David Hill
David Hill 2020-9-6
编辑：David Hill 2020-9-6
I do not know what matanoIndex is, so you will have to code that.
time = 501*60*60;
[pos,idx]=sort(data(:,1).*3e2);
c=data(:,2);
c=d(idx);
c=smooth(d,.2);
cMax=c(end);
cMin=c(1);
pos=smooth(c,.2);
matanoPos= pos(matanoIndex);
posn =(pos - matanoPos);
slope = 1/2*diff(posn(1:end-1))./diff(c(1:end-1))+diff(posn(2:end))./diff(c(2:end));
i= cumsum(1/2*movsum(posn(2:end),2,'Endpoints','discard').*diff(c(1:end-1)));
c=c(2:end-1);
d=-1/(2*time).*slope.*i;
DaveM=trapz(c,d)/(cMax-cMin);
Michael Crown
Michael Crown 2020-9-6
Please check, D was calculated in the code and not given in input file like DA. I get error code: “x must be a vector” when I used this code for DaveM
Michael Crown
Michael Crown 2020-9-6
I realised that it retuned an answer without error now but it messed up my plot for D vrs C
David Hill
David Hill 2020-9-6
You will have to figure it out from here. conc was not needed (only the transpose of c). d is calculated in your code. I vectorized and eliminated your loops. Keep in mind, you smoothed for DaveM but did not smooth for DaveA. Also cMax and cMin were calculated before the elimination of the two end-points for the integration. I would suggest determining cMax and cMin just before integration.
Michael Crown
Michael Crown 2020-9-6
Is there another way in such that DaveM is calculated from the value I got for D vz c? This code you shared messed the plots.
Michael Crown
Michael Crown 2020-9-6
Hello, if you don’t mind, help modify code such that DaveM will be calculated from the already obtained D vrs c from my data without sorting . The one you sent to me isn’t working.

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更多回答（3 个）

Michael Crown
Michael Crown 2020-9-5

0 个投票

Forgive me for too many requests. Please can you put the modification in the code and send back. I am not clear

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Michael Crown
Michael Crown 2020-9-5
Hello David, I am not able to calcualte DaveM. can you help check?

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Michael Crown
Michael Crown 2020-9-6
编辑：Walter Roberson 2020-9-6

0 个投票

Now, i am totally confused, it didnt run
time = 223*60*60; % diffusion time in seconds
data = load ('File 223.txt'); % read in data
dataB = load ('File 2233.txt');
[pos,idx]=sort(data(:,1));
c=data(:,2 );
D= D(idx );
c=smooth(c,.2 );
D = smooth(D, .2);
cMax=c(end );
cMin=c(1 );
pos=smooth(c,.2 );
matanoPos= pos(matanoIndex );
posn =(pos - matanoPos );
slope = 1/2*diff(posn(1:end-1))./diff(c(1:end-1))+diff(posn(2:end))./diff(c(2:end ));
i= cumsum(1/2*movsum(posn(2:end),2,'Endpoints','discard').*diff(c(1:end-1 )));
c=c(2:end-1 );
D=-1/(2*time).*slope.*i ;
DaveM=trapz(c,d)/(cMax-cMin);
[cA,idx] = sort(dataB(:,1));
DA=DA(idx);
DaveA = trapz(cA,DA)/(cAMax-cAMin); %cAMax = cA(end), cAMin = cA(1)
semilogy (c,D,'r*') %create a plot using a base 10 logarithmic scale for y-axis and a linear scale for x-axis
hold on
semilogy(cA,DA, 'k*')
title('D of the Cu–Zn binary system at 700degC, 501hrs')
xlabel('Concentration, Zn(at.%)')
ylabel('Interdiffusion Coefficient (m2/s)')
legend('Mike','','Author')
Michael Crown
Michael Crown 2020-9-10

0 个投票

Hello Walter Roberson,
I still need your help on my codes. Attahced codes; mainBMFull and mainSF are written for two methods of calcualting 'D'
My mainSF code works well and gives me exactly what i want. However, mainBMFull is not accurate. Please, can you help check this?
let me know what else you need to help me.

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