1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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

    mfb

    User Avatar
    2016 Award

    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)##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rescaling Variables
  1. Random variable (Replies: 2)

  2. Change of Variables (Replies: 1)

  3. Change of Variables (Replies: 2)

Loading...