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boltzmann_equation [2014/06/26 14:46]
nikolaj
boltzmann_equation [2015/06/15 17:48]
nikolaj
Line 44: Line 44:
 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: ​
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