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macroscopic_observables_from_kinetic_theory [2014/02/22 17:13] nikolaj |
macroscopic_observables_from_kinetic_theory [2014/02/22 17:14] nikolaj |
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| @#AADDEE: $ \langle A \rangle({\bf x},t) \equiv \int\ A({\bf v})\ f({\bf x},{\bf v},t)\ \mathrm d^3v$ | | | @#AADDEE: $ \langle A \rangle({\bf x},t) \equiv \int\ A({\bf v})\ f({\bf x},{\bf v},t)\ \mathrm d^3v$ | | ||
| @#AADDEE: $ v({\bf v}):={\bf v} $ | | | @#AADDEE: $ v({\bf v}):={\bf v} $ | | ||
+ | |||
+ | | @#FFFDDD: $i,j\in\{1,2,3\}$ | | ||
| @#FFBB00: $ n := \langle \mathrm{1} \rangle $ | | | @#FFBB00: $ n := \langle \mathrm{1} \rangle $ | | ||
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| @#FFBB00: $ e := \rho \frac{1}{2}V^2 $ | | | @#FFBB00: $ e := \rho \frac{1}{2}V^2 $ | | ||
| @#FFBB00: $ E := \rho \frac{1}{2}C^2 $ | | | @#FFBB00: $ E := \rho \frac{1}{2}C^2 $ | | ||
- | |||
- | | @#FFBB00: $ T := E/\left(\frac{3}{2}n\ k_B\right) $ | | ||
- | |||
- | | @#FFFDDD: $i,j\in\{1,2,3\}$ | | ||
| @#FFBB00: $ q_i := \rho \frac{1}{2}\langle v^2\ v_i\rangle $ | | | @#FFBB00: $ q_i := \rho \frac{1}{2}\langle v^2\ v_i\rangle $ | | ||
| @#FFBB00: $ Q_i := \rho \frac{1}{2}\langle c^2\ c_i\rangle $ | | | @#FFBB00: $ Q_i := \rho \frac{1}{2}\langle c^2\ c_i\rangle $ | | ||
+ | | @#FFBB00: $ T := E/\left(\frac{3}{2}n\ k_B\right) $ | | ||
==== Discussion ==== | ==== Discussion ==== |