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Undoing Similarity Transforms

  1. Jun 30, 2015 #1

    joshmccraney

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    Gold Member

    Hi PF!

    I am wondering how to bring boundary conditions through a similarity transform. The transform is as follows $$h(z,\tau) = \tau^a F(\eta)\\ \eta = C_2 z \tau^b\\L=\eta_{tip} C_2^{-1}\tau^{-b}$$ Before I continue, I have a pdf of a tex doc I made for this, but since I don't have the same syntax as these forums it would be easier if I could pm someone with the problem.

    If not, please let me know, as I am totally fine with posting all of the work. I just want someone to check and see if my work is okay.

    Thanks so much!

    Actually, for ease I'll post my work for one here now so you get a better idea of what I'm talking about. The first boundary condition is ##F^+(\eta^+)=0## where ##\eta^+=1## so essentially ##F^+(1)=0##. I should say ##F^+\lambda^2=F## and ##\eta^+ \lambda = \eta##. Now we have ##F^+(1)=0 \implies \lambda^{-2} F(1)=0 \implies F(1)=0##.

    From here ##\eta=1\implies z=C_2^{-1} \tau^{-b}## and thus ##h(C_2^{-1} \tau^{-b},\tau) = \tau^a F(1) = 0##.
     
    Last edited: Jun 30, 2015
  2. jcsd
  3. Jul 5, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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