Download A Non-Equilibrium Statistical Mechanics: Without the by Tian-Quan Chen PDF

Mathematical Physics

By Tian-Quan Chen

This e-book provides the development of an asymptotic method for fixing the Liouville equation, that's to a point an analogue of the Enskog–Chapman strategy for fixing the Boltzmann equation. as the assumption of molecular chaos has been given up on the outset, the macroscopic variables at some extent, outlined as mathematics technique of the corresponding microscopic variables inside of a small local of the purpose, are random ordinarily. they're the simplest applicants for the macroscopic variables for turbulent flows. the end result of the asymptotic method for the Liouville equation finds a few new phrases exhibiting the difficult interactions among the velocities and the inner energies of the turbulent fluid flows, that have been misplaced within the classical idea of BBGKY hierarchy.

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Example text

2), and that the subsystems are statistically independent. m|u„P)] s = (*i,s 2 ,*3). 33) and the convex linear combinations of several local Gibbs distributions with different parameters are special cases of the turbulent Gibbs distributions. Actually any convex linear combinations of turbulent Gibbs distributions themselves are turbulent Gibbs distributions too. 33) is a subset of the set of the turbulent Gibbs distributions and the latter is far much wider than the former. 2. OUTLINE OF THE BOOK 23 linear combinations of local Gibbs distributions should be included in the class of the distributions describing turbulence phenomena (of inviscid flows).

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Of course, the angular momentum density might play a role in the definition of turbulent Gibbs distribution too. But the size K of the cube is negligibly small in comparison with the macroscopic length scale, the total angular momentum of the molecules in the cube is approximately equal to the vector product of a constant vector and the total momentum. Thus the angular momentum density can be (approximately) expressed as a function in momentum density of the molecules in the cube. Hence it is redundant to include the angular momentum density of the molecules in the cube as an argument of 22 CHAPTER 1.

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