Heat flux of a granular gas with homogeneous temperature

Abstract

A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position-dependent force or by enclosing the grains inside a curved twodimensional silo. At a macroscopic level, the state is identified with one solution to the inelastic Navier-Stokes equations, due to the coupling between the heat flux induced by the density gradient and the external force. On the contrary, at the mesoscopic level, by exactly solving a BGK model or the inelastic Boltzmann equation in an approximate way, a one-parametric family of solutions is found. Molecular dynamics simulations of the system in the quasi-elastic limit are in agreement with the theoretical results.

Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases

“…The function φ can be expanded using the Sonine Polynomials {S n } n≥1 , see Appendix B of [76], as ] . where the terms of order a 2 2 have been neglected.…”

Unified hydrodynamic description for driven and undriven inelastic Maxwell mixtures at low density

“…Since ξ * (t) ∝ T(t) −3/2 , we can take ξ * instead of the (scaled) time t/t 0 (t 0 being an arbitrary unit of time) to analyze the time-dependence of the temperature ratios. Thus, the solution to equation (32) provides the dependence of the temperature ratios χ i (x 1 , ω * , ξ * ) on the reduced noise strength ξ * . Note first that equation (32) reduces to that of the undriven case when ξ * → 0 but keeping ω * finite (which is equivalent to γ b → 0 and…”

“…Thus, the solution to equation (32) provides the dependence of the temperature ratios χ i (x 1 , ω * , ξ * ) on the reduced noise strength ξ * . Note first that equation (32) reduces to that of the undriven case when ξ * → 0 but keeping ω * finite (which is equivalent to γ b → 0 and…”

“…Beyond the homogeneous cooling state, another type of reference states can be chosen when, for instance, the granular gas is strongly sheared [18,[27][28][29] or subjected to strong temperature gradients [30][31][32]. Another relevant situation is when the granular gas is driven by the action of an external driving force or thermostat [33].…”

Unified hydrodynamic description for driven and undriven inelastic Maxwell mixtures at low density

“…Beyond the homogeneous cooling state, another type of reference states can be chosen when, for instance, the granular gas is strongly sheared [18,[29][30][31] or subjected to strong temperature gradients [32][33][34]. Another relevant situation is when the granular gas is driven by the action of an external driving force.…”