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 transport_coefficients [2013/11/10 23:09]nikolaj transport_coefficients [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/11/10 23:10 nikolaj 2013/11/10 23:09 nikolaj 2013/11/10 23:09 nikolaj 2013/11/10 22:14 nikolaj 2013/11/10 22:13 nikolaj 2013/11/10 22:13 nikolaj 2013/11/10 22:11 nikolaj 2013/11/10 21:49 nikolaj 2013/11/10 21:48 nikolaj 2013/11/10 21:48 nikolaj 2013/11/10 21:42 nikolaj 2013/11/10 21:40 nikolaj 2013/11/10 21:40 nikolaj old revision restored (2013/11/10 21:08) Next revision Previous revision 2013/11/10 23:10 nikolaj 2013/11/10 23:09 nikolaj 2013/11/10 23:09 nikolaj 2013/11/10 22:14 nikolaj 2013/11/10 22:13 nikolaj 2013/11/10 22:13 nikolaj 2013/11/10 22:11 nikolaj 2013/11/10 21:49 nikolaj 2013/11/10 21:48 nikolaj 2013/11/10 21:48 nikolaj 2013/11/10 21:42 nikolaj 2013/11/10 21:40 nikolaj 2013/11/10 21:40 nikolaj old revision restored (2013/11/10 21:08) Line 1: Line 1: ===== 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: $\langle D,​\kappa,​p,​\eta,​\zeta \rangle$ | - | @#55EE55: $u = - D\ \frac{\nabla n}{n}$ | + These are matrices or numbers, and they might even depend on any other quantities. - | @#55EE55: $Q = - \kappa\ \nabla ​T$ | + | @#55EE55: postulate ​  | @#55EE55: $u = - D\ \frac{\nabla ​n}{n}$ | - | @#DDDDDD: $\Lambda_{ik} = \frac{1}{2}\left( \frac{\partial}{\partial x_k}u_i + \frac{\partial}{\partial x_i}u_k \right)$ | + | @#55EE55: postulate ​  | @#55EE55: $Q = - \kappa\ \nabla ​T$ | - | @#55EE55: $P = p\ I - 2\ \eta\ \Lambda - (\zeta+\frac{2}{3}\eta)\ \nabla ​u$ | + - | @#55EE55: $u = \mu\ K$ | + | @#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: postulate ​  | @#55EE55: $P = p\ I - 2\ \eta\ \Lambda - (\zeta+\frac{2}{3}\eta)\ \nabla u$ | + + | @#55EE55: postulate ​  | @#55EE55: $u = \mu\ K$ | ==== Discussion ==== ==== Discussion ==== Line 18: Line 20: ==== Parents ==== ==== Parents ==== - === Requirements ​=== + === Context ​=== [[Macroscopic observables from kinetic theory]] [[Macroscopic observables from kinetic theory]] 