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transport_coefficients [2013/11/10 23:10] nikolaj |
transport_coefficients [2014/03/21 11:11] (current) |
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| ===== Transport coefficients ===== | ===== Transport coefficients ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ n,u,Q,T,\mathrm{P},K $ ... density, mean velocity, heat flux, pressure tensor, temperature, external force | | + | | @#55CCEE: context | @#55CCEE: $ n,u,Q,T,\mathrm{P},K $ ... density, mean velocity, heat flux, pressure tensor, temperature, external force | |
| - | | @#FFBB00: $ \langle D,\kappa,p,\eta,\zeta \rangle $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle D,\kappa,p,\eta,\zeta \rangle $ | |
| These are matrices or numbers, and they might even depend on any other quantities. | These are matrices or numbers, and they might even depend on any other quantities. | ||
| - | | @#55EE55: $ u = - D\ \frac{\nabla n}{n} $ | | + | | @#55EE55: postulate | @#55EE55: $ u = - D\ \frac{\nabla n}{n} $ | |
| - | | @#55EE55: $ Q = - \kappa\ \nabla T $ | | + | | @#55EE55: postulate | @#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) $ | | + | | @#DDDDDD: range | @#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: postulate | @#55EE55: $ P = p\ I - 2\ \eta\ \Lambda - (\zeta+\frac{2}{3}\eta)\ \nabla u $ | |
| - | | @#55EE55: $ u = \mu\ K $ | | + | | @#55EE55: postulate | @#55EE55: $ u = \mu\ K $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Macroscopic observables from kinetic theory]] | [[Macroscopic observables from kinetic theory]] | ||
