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A Collision integral approximation in boltzmann equation

  1. Dec 11, 2017 #1

    Hi, as you can see at the end of the picture/attached file collision integral is approximated to a discrete sum. Could you express how this approximation is derived????

    Attached Files:

  2. jcsd
  3. Dec 11, 2017 #2


    Staff: Mentor

    @mertcan what reference (book/article/web page/whatever) is this taken from?
  4. Dec 11, 2017 #3
  5. Dec 11, 2017 #4
    It is not really an approximation of the integral from a purely mathematical point-of-view I think, it rather seems a mather of intuitive common sense.

    It is reasonable to suppose that the velocity change of component alpha depends linearly on the differences with the velocities of the other components beta. I don't think there is much more in it than that.
  6. Dec 12, 2017 #5
    thanks for response @thephystudent ,@PeterDonis you have not given any answers, what is your response about my question???
  7. Dec 12, 2017 #6


    Staff: Mentor

    I don't have one, at least not at the moment. I asked you for a reference because that's part of moderating the forum, and to hopefully help other possible responders.
  8. Dec 12, 2017 #7
    Last edited: Dec 12, 2017
  9. Dec 13, 2017 #8
    Seems related indeed, where the $\langle \nu_{\alpha\beta}$ coefficient captures the average of some remaining coefficients. Difference of velocities= the relative velocity of particle beta when travelling along particle alpha.
  10. Dec 13, 2017 #9
    thanks for responses but, I need some mathematical demonstration to learn better, could you help me about where relative velocity comes from that????
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