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Diffusion with reflecting boundary

1 vote

What I have tried:

https://imgur.com/a/ESWy1k5 (sorry but I did not manage to use imgur as you instructed).

Note that my question is that how is it possible that I get $t = \infty$. It does not make sense for me (physically speaking). Where did I get wrong?

Please if there is information you require let me know.

asked Nov 14 in Physics Problems by JD_PM (500 points)
edited Nov 15 by JD_PM
How are you getting PasteBoard to work (1st image)? It is not working for me!

Why didn't you get PasteBoard to work for the 2nd image?
You have obtained a quartic equation in $z$. This has 4 solutions, not 1. Find some more solutions! Then check which one describes the situation you are trying to find.

In fact there is one other real solution and 2 imaginary solutions. Probably you should solve numerically (this is a physics question, not maths). eg Make a first guess $z$ then reiterate $z'=\frac12 (z^4+1)$. Or apply Newton-Raphson Method.
I do not why PasteBoard works with computers connected to the uni server. I did not use it again because the pic was yielded horizontally all the time.
You are right, there is another real solution. Taking logarithms came to my mind:

$$lnz = -\frac{x_0}{4Dt}$$

$$ t = -\frac{-x_0}{4Dlnz}$$

But this gives a negative time so it is not a reliable path to take...

You wrote about reiteration and Newton-Raphson Method. I am not acquainted with those; may you delve into it?

The quartic equation gives you a value of $z$ which is less than 1, so its logarithm is -ve. The corresponding value of time in your formula is +ve.
Oops... I have to think more before asking.

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