Collisional statistics of the hard-sphere gas

Paolo Visco (1, 2) , Frédéric van Wijland (3) , Emmanuel Trizac (1)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 SUPA School of Physics and Astronomy [Edinburgh]
3 MSC - Matière et Systèmes Complexes

We investigate the probability distribution function of the free flight time and of the number of collisions in a hard sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex et al., Phys. Rev. E 69 11303 (2004)]. We exploit this analogy to construct a Monte-Carlo like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are confronted against the results of Molecular Dynamics simulations and Direct Simulation Monte Carlo technique. An excellent agreement is reported.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Matière Molle [cond-mat.soft]

Paolo Visco, Frédéric van Wijland, Emmanuel Trizac. Collisional statistics of the hard-sphere gas. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 77 (4), pp.041117. ⟨10.1103/PhysRevE.77.041117⟩. ⟨hal-00303734⟩