# A Collision integral approximation in boltzmann equation

1. Dec 11, 2017

### mertcan

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????

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2. Dec 11, 2017

### Staff: Mentor

@mertcan what reference (book/article/web page/whatever) is this taken from?

3. Dec 11, 2017

### mertcan

4. Dec 11, 2017

### thephystudent

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.

5. Dec 12, 2017

### mertcan

thanks for response @thephystudent ,@PeterDonis you have not given any answers, what is your response about my question???

6. Dec 12, 2017

### 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.

7. Dec 12, 2017

### mertcan

Last edited: Dec 12, 2017
8. Dec 13, 2017

### thephystudent

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.

9. Dec 13, 2017

### mertcan

thanks for responses but, I need some mathematical demonstration to learn better, could you help me about where relative velocity comes from that????