A Langevin Description for Driven Granular Gases

Abstract

Abstract. The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one-and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also studied.

Linear hydrodynamics for driven granular gases

“…In fact, the functions ξ 1 and ξ 2 have been previously identified in Refs. [33,34,43], where they were used to study the fluctuations of quantities like the total energy in the stationary state. There, it was also proven thatξ 1 andξ 2 are eigenfunctions of the adjoint operator of the linearized collision operator, + , associated to the null eigenvalue.…”

The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

“…All these systems exhibit a reach phenomenology and striking differences to the gases studied in the framework of the "standard" BBGKY theory [19]. The kinetic approaches are under investigation, see [20,21,22,23,24,25,26,27,28,29] for granular gas dynamics. We believe that alternative approaches and/or techniques are still on the agenda because of the strong complexity of these systems.…”