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Homework Help: Rescaling Variables

  1. May 19, 2015 #1
    1. The problem statement, all variables and given/known data

    Suppose I have the following expression:
    [tex] (v \frac {\partial}{\partial r} ) f(r,v)[/tex]

    I want to obtain:

    [tex] \frac {\partial \hat{f}(z,x)}{\partial z} [/tex]

    2. Relevant equations

    [tex] x \rightarrow v/v0 [/tex]
    [tex] z \rightarrow (r-r0)/H [/tex]
    [tex] H \rightarrow \frac{k_{b} T} {m g } [/tex]
    [tex] \hat{f}(z,x) = x^2 f(r,v) [/tex]

    3. The attempt at a solution

    [tex] x v0 \frac {\partial}{\partial (zH+r0)} \frac{1}{x^2} \hat{f}(z,x) [/tex]

    is this possible?
  2. jcsd
  3. May 19, 2015 #2


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    Where does the x2 come from?

    Assuming H and r0 are constant, you can simplify the derivative.
  4. May 19, 2015 #3

    It was just a given a change of variable. I am trying to verify it.
    [tex] f(r,v) = f( zH+r0, xv0) [/tex]

    Can you show me explicitly?
  5. May 19, 2015 #4


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    The equations look good apart from that x2. Where does it come from?
  6. May 20, 2015 #5
    What do you mean?

    I am trying to show

    [tex] (v \frac {\partial}{\partial r} ) f(r,v) \rightarrow

    \frac {\partial \hat{f}(z,x)}{\partial z} [/tex]
  7. May 21, 2015 #6


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    Staff: Mentor

    There is an x2 in your equations. Why? What did you calculate that let this factor appear in the equation?

    Edit: This one: ##\hat{f}(z,x) = x^2 f(r,v)##
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