# Differences

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boltzmann_equation [2014/06/26 14:46] nikolaj |
boltzmann_equation [2015/06/15 17:48] (current) nikolaj |
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at the fixed point velocity ${\bf v}$. The second term is more involved, since it doesn't represent the loss at ${\bf v}$, but the gain: It's the sum of processes of pairs particles with velocities ${\bf v'},{\bf v'}_1$, which end up with particles having the velocity ${\bf v}$ and any other velocity ${\bf v}_1$. | at the fixed point velocity ${\bf v}$. The second term is more involved, since it doesn't represent the loss at ${\bf v}$, but the gain: It's the sum of processes of pairs particles with velocities ${\bf v'},{\bf v'}_1$, which end up with particles having the velocity ${\bf v}$ and any other velocity ${\bf v}_1$. | ||

+ | === Note === | ||

+ | <code> | ||

+ | $Assumptions = {kT > 0, n > -1, \[CapitalTheta] > 0}; | ||

+ | |||

+ | f[EE_] = E^(-(EE/kT))* | ||

+ | E^(-(EE^2/\[CapitalTheta]^2))/(E^(\[CapitalTheta]^2/(2 kT)^2) | ||

+ | Sqrt[\[Pi]] /2 \[CapitalTheta] Erfc[\[CapitalTheta]/(2 kT)]); | ||

+ | |||

+ | Integrate[f[EE] EE^n, {EE, 0, \[Infinity]}] | ||

+ | </code> | ||

=== Reference === | === Reference === | ||

Wikipedia: | Wikipedia: |