Timeline for What is the relation between the Boltzmann distribution and Boltzmann equation?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2016 at 23:58 | comment | added | Thomas | Any book on kinetic theory will do the trick. Also, slightly more advanced text books on stat mech, e.g. Kerson Huang. | |
| Jun 28, 2016 at 23:48 | comment | added | Syntax_ErrorX00 | @Thomas: I do not really understand what you are talking about!, what kind of mathematics behind it? what should I learn to understand that? | |
| Jun 28, 2016 at 23:38 | history | edited | Thomas | CC BY-SA 3.0 |
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| Jun 28, 2016 at 23:35 | comment | added | anon01 | @Thomas this is a good answer. Maybe you could explain some of the variables in your collision operator? | |
| Jun 28, 2016 at 23:30 | comment | added | Thomas | You don't have to solve the Boltzmann equation to show that $C[f^{eq}]=0$. I added a short proof to my answer. For the BGK kernel the collision term obviously vanishes by definition, $C_{BGK}[f^{eq}]=(f^{eq}-f^{eq})/\tau=0$. | |
| Jun 28, 2016 at 23:27 | history | edited | Thomas | CC BY-SA 3.0 |
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| Jun 28, 2016 at 22:28 | comment | added | Syntax_ErrorX00 | the collision operator is a function of $f$,so the equation will be an-integro-differential which is difficult to solve. therfore I need to use the BGKW approximation of the collision operator as follows: $$\Omega = \dfrac 1\tau \left(f^{eq}-f \right)$$ | |
| Jun 28, 2016 at 22:22 | comment | added | Thomas | That's my point. You have to include the collision term. Then, only $f\sim \exp(-v^2)$ is a solution. | |
| Jun 28, 2016 at 22:01 | comment | added | Syntax_ErrorX00 | but if any function for example $f(v) = v^2$ is also a solution based on your answer. | |
| Jun 28, 2016 at 20:58 | history | answered | Thomas | CC BY-SA 3.0 |