Third and fourth degree collisional moments for inelastic Maxwell models

Abstract

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\ge 2$.

15 pages, 3 figures; v2: addition of two new references

References in corpus (8)

• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions
• Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails
• Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
• Breakdown of the Sonine expansion for the velocity distribution of Granular Gases
• Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis
• The Boltzmann equation for driven systems of inelastic soft spheres
• Shear-rate dependent transport coefficients for inelastic Maxwell models

Cited by in corpus (18)

• Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
• Hydrodynamics of inelastic Maxwell models
• Impurity in a sheared inelastic Maxwell gas
• Granular gas of inelastic and rough Maxwell particles
• An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux
• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model
• Moment theories for a d-dimensional dilute granular gas of Maxwell molecules
• Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state
• Anomalous transport of impurities in inelastic Maxwell gases
• Navier-Stokes transport coefficients for driven inelastic Maxwell models
• High-degree collisional moments of inelastic Maxwell mixtures. Application to the homogeneous cooling and uniform shear flow states
• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
• Inelastic Maxwell models for monodisperse gas-solid flows
• Monotonicity in the averaging process
• Kinetic model for transport in granular mixtures
• Polydispersity and optimal relaxation in the hard sphere fluid
• Finite-time consensus in a compromise process