Numerical evidence for divergent Burnett coefficients

Abstract

In previous papers [Phys. Rev. A 41, 4501 (1990); Phys. Rev. E 18, 3178 (1993)], simple equilibrium expressions were obtained for nonlinear Burnett coefficients. A preliminary calculation of a 32-particle Lennard-Jones fluid was presented in the previous papers. Now, sufficient resources have become available to address the question of whether nonlinear Burnett coefficients are finite for soft spheres. The hard sphere case is known to have infinite nonlinear Burnett coefficients (i.e., a nonanalytic constitutive relation) from mode-coupling theory. This paper reports a molecular dynamics caclulation of the third order nonlinear Burnett coefficient of a Lennard-Jones fluid undergoing color flow, which indicates that this term diverges in the thermodynamic limit.

Beyond the Navier–Stokes equations: Burnett hydrodynamics

“…However, notice should be made about the results from molecular dynamics for shock waves in dense fluids and in particular to the work done recently [173] that apparently exhibits a contradiction with Fourier's Law. Furthermore, for dense fluids evidence for divergent Burnett coefficients has been provided [174,175]. 17 For the dilute gas 17 In our opinion the goal is to have a theory that can be applied to different situations.…”

Physical origin of nonequilibrium fluctuation-induced forces in fluids

“…Here κ NL is a kinetic coefficient commonly referred to as a nonlinear Burnett coefficient [33,34]. As has been discussed elsewhere [35][36][37][38], it is well known that κ NL diverges linearly in the large system size, L, due to longtime-tails effects. To take this divergence into account we wrote in our previous publications [29,30]…”

Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation

“…Worse still, it is well-known that the higher-order corrections in the gradient expansion to the Navier-Stokes equations are ill-posed and many questions about the meaningfulness of the Chapman-Enskog solutions to the Boltzmann equations have been raised (Cercignani 1975;Ernst et al 1978). Mode-coupling theories (Ernst & Dorfman 1975;Ernst et al 1978) and computer simulations (Standish 1999) have revealed that the transport coefficients corresponding to the Burnett and super-Burnett terms actually diverge in the thermodynamic limit, indicating non-analytic (in the gradients) corrections.…”