# I Using Separation of Variables to Modify Neutron Density Diff

1. Oct 26, 2016

### tasm

I was overlooking page 47 of "The Physics of the Manhattan Project" 2.2 Critical Mass: Diffusion Theory, and author Bruce Cameron Reed reported that:

Can anyone explain how Bruce Cameron Reed got from (2.18) to (2.19)

I tried plugging $N(r,t) = N(r) N(t)$ into (2.18) to get (2.19), but it just does not make any sense to me on how there is a fraction of $\frac{1}{N_r}$ multiplied to the second term after the equals sign

Assuming $N$ in the first term after the equals sign is $N(r,t)$ I cannot see how using algebra would allow a person to arrive to (2.19)

I have also tried to take advantage of the relationship

$\Big (\frac{\partial N(r,t)}{\partial t} \Big)_t = N'(t) N(r)$ but even taking advantage of this I still could not figure out how Reed transformed (2.18) to (2.19)

Last edited by a moderator: Oct 27, 2016
2. Oct 27, 2016

### tasm

BY THE WAY, I FORGOT TO GIVE A LINK TO THE PDF OF THE BOOK. HERE IT IS: