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Related papers: Hydrodynamics for inelastic Maxwell mixtures: Some…

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In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system…

Analysis of PDEs · Mathematics 2022-05-04 Ricardo J. Alonso , Bertrand Lods , Isabelle Tristani

A recent model for monodisperse granular suspensions is used to analyze transport properties in spatially inhomogeneous states close to the simple (or uniform) shear flow. The kinetic equation is based on the inelastic Boltzmann (for low…

Statistical Mechanics · Physics 2017-06-30 Vicente Garzó

The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…

Statistical Mechanics · Physics 2015-06-24 J. Javier Brey , James W. Dufty , M. J. Ruiz-Montero

The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the…

Statistical Mechanics · Physics 2025-02-05 Maciej Łebek , Miłosz Panfil

The Euler and Navier-Stokes fluid mechanics equations are derived using a modified statistical mechanical approach using theory taken from the Chapman-Enskog perturbation analysis used to support the lattice Boltzmann method. Additional…

Fluid Dynamics · Physics 2021-07-06 Charles Cook

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic…

Statistical Mechanics · Physics 2009-11-10 Nikolai Brilliantov , Thorsten Poeschel

We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic…

Statistical Mechanics · Physics 2007-05-23 Francois Coppex , Michel Droz , Emmanuel Trizac

Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and…

Nuclear Theory · Physics 2015-06-11 Radoslaw Ryblewski

A linear stability analysis of the Navier-Stokes (NS) granular hydrodynamic equations is performed to determine the critical length scale for the onset of vortices and clusters instabilities in granular dense binary mixtures. In contrast to…

Statistical Mechanics · Physics 2014-02-19 Peter P. Mitrano , Vicente Garzó , Christine M. Hrenya

Transport coefficients associated with the mass flux of a binary mixture of Maxwell molecules under uniform shear flow are exactly determined from the Boltzmann kinetic equation. A normal solution is obtained via a Chapman--Enskog-like…

Statistical Mechanics · Physics 2009-11-13 Vicente Garzo

The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport…

Statistical Mechanics · Physics 2009-11-10 James W. Dufty , J. Javier Brey

A numerical study is presented to analyze the thermal mechanisms of unsteady, supersonic granular flow, by means of hydrodynamic simulations of the Navier-Stokes granular equations. For this purpose a paradigmatic problem in granular…

Fluid Dynamics · Physics 2015-06-04 Lidia Almazán , José A. Carrillo , Clara Salueña , Vicente Garzó , Thorsten Poeschel

Granular systems confined in a shallow box and driven by vertical vibration provide a simple geometry to study fluidized granular media. Grains gain kinetic energy vertically through collisions with the walls and redistribute it…

Soft Condensed Matter · Physics 2026-04-21 Ricardo Brito , Rodrigo Soto , Vicente Garzó

A hydrodynamic description for an $s$-component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In…

Statistical Mechanics · Physics 2009-11-13 V. Garzo , J. W. Dufty , C. M. Hrenya

The basis for a hydrodynamic description of granular gases is discussed for a low density gas of smooth, inelastic hard spheres. The more fundamental mesoscopic description is taken to be the nonlinear Boltzmann kinetic equation. Two…

Statistical Mechanics · Physics 2007-05-23 James W. Dufty , J. Javier Brey

Segregation induced by a thermal gradient of an impurity in a driven low-density granular gas is studied. The system is enclosed between two parallel walls from which we input thermal energy to the gas. We study here steady states occurring…

Statistical Mechanics · Physics 2014-05-15 Francisco Vega Reyes , Vicente Garzó , Nagi Khalil

The hydrodynamics for a gas of hard-spheres which sometimes experience inelastic collisions resulting in the loss of a fixed, velocity-independent, amount of energy $\Delta $ is investigated with the goal of understanding the coupling…

Soft Condensed Matter · Physics 2007-05-23 James F. Lutsko

A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a…

Analysis of PDEs · Mathematics 2026-03-31 Kazuo Aoki , Niclas Bernhoff

We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…

Analysis of PDEs · Mathematics 2025-12-30 Andrea Giorgini , Jingning He , Hao Wu

We analyze the transport properties of a low density ensemble of identical macroscopic particles immersed in an active fluid. The particles are modeled as inelastic hard spheres (granular gas). The non-homogeneous active fluid is modeled by…

Soft Condensed Matter · Physics 2017-10-17 Francisco Vega Reyes , Antonio Lasanta