Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
transport_coefficients [2013/11/10 22:14] nikolaj |
transport_coefficients [2013/11/10 23:10] nikolaj |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ===== Macroscopic observables from kinetic theory ===== | + | ===== Transport coefficients ===== |
| ==== Definition ==== | ==== Definition ==== | ||
| | @#88DDEE: $ n,u,Q,T,\mathrm{P},K $ ... density, mean velocity, heat flux, pressure tensor, temperature, external force | | | @#88DDEE: $ n,u,Q,T,\mathrm{P},K $ ... density, mean velocity, heat flux, pressure tensor, temperature, external force | | ||
| Line 5: | Line 5: | ||
| | @#FFBB00: $ \langle D,\kappa,p,\eta,\zeta \rangle $ | | | @#FFBB00: $ \langle D,\kappa,p,\eta,\zeta \rangle $ | | ||
| - | | @#DDDDDD: $ \Lambda_{ik} = \frac{1}{2}\left( \frac{\partial}{\partial x_k}u_i + \frac{\partial}{\partial x_i}u_k \right) $ | | + | These are matrices or numbers, and they might even depend on any other quantities. |
| | @#55EE55: $ u = - D\ \frac{\nabla n}{n} $ | | | @#55EE55: $ u = - D\ \frac{\nabla n}{n} $ | | ||
| + | |||
| | @#55EE55: $ Q = - \kappa\ \nabla T $ | | | @#55EE55: $ Q = - \kappa\ \nabla T $ | | ||
| + | |||
| + | | @#DDDDDD: $ \Lambda_{ik} = \frac{1}{2}\left( \frac{\partial}{\partial x_k}u_i + \frac{\partial}{\partial x_i}u_k \right) $ | | ||
| | @#55EE55: $ P = p\ I - 2\ \eta\ \Lambda - (\zeta+\frac{2}{3}\eta)\ \nabla u $ | | | @#55EE55: $ P = p\ I - 2\ \eta\ \Lambda - (\zeta+\frac{2}{3}\eta)\ \nabla u $ | | ||
