Eur. Phys. J. E (2015) 38: 16
https://doi.org/10.1140/epje/i2015-15016-5

Regular Article

Anomalous transport of impurities in inelastic Maxwell gases

¹ Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071, Badajoz, Spain
² Departamento de Didáctica de las Matemáticas, Universidad de Sevilla, 41080, Sevilla, Spain
³ Laboratoire de Physique Théorique et Modèles Statistiques (CNRS UMR 8626), Université Paris-Sud, Bâtiment 100, 91405, Orsay cedex, France

^* e-mail: vicenteg@unex.es
^** e-mail: nagi@us.es

Received: 8 September 2014
Revised: 22 January 2015
Accepted: 3 February 2015
Published online: 17 March 2015

Abstract

A mixture of dissipative hard grains generically exhibits a breakdown of kinetic energy equipartition. The undriven and thus freely cooling binary problem, in the tracer limit where the density of one species becomes minute, may exhibit an extreme form of this breakdown, with the minority species carrying a finite fraction of the total kinetic energy of the system. We investigate the fingerprint of this non-equilibrium phase transition, akin to an ordering process, on transport properties. The analysis, performed by solving the Boltzmann kinetic equation from a combination of analytical and Monte Carlo techniques, hints at the possible failure of hydrodynamics in the ordered region. As a relevant byproduct of the study, the behaviour of the second- and fourth-degree velocity moments is also worked out.