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I Using Separation of Variables to Modify Neutron Density Diff

  1. Oct 26, 2016 #1
    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. jcsd
  3. Oct 27, 2016 #2
    BY THE WAY, I FORGOT TO GIVE A LINK TO THE PDF OF THE BOOK. HERE IT IS:

    http://download.springer.com/static...2238b065b3a347a0078d2a4cc041f0781d563e9739e2a
     
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