title: Collision densities and mean residence times for d-dimensional exponential flights.
abstract: In this paper we analyze some aspects of exponential flights, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical or biological species migration, and electron motion. We introduce a general framework for d-dimensional setups and emphasize that exponential flights represent a deceivingly simple system, where in most cases closed-form formulas can hardly be obtained. We derive a number of exact (where possible) or asymptotic results, among which are the stationary probability density for two-dimensional systems, a long-standing issue in physics, and the mean residence time in a given volume. Bounded or unbounded domains as well as scattering or absorbing domains are examined, and Monte Carlo simulations are performed so as to support our findings.
authors: Commissariat à l'Energie Atomique et aux Energies Alternatives, Direction de l'Energie Nucléaire, Département de Modélisation des Systèmes et Structures, Service d'Etudes des Réacteurs et de Mathématiques Appliquées, CEA-Saclay, F-91191 Gif-sur-Yvette, France. andrea.zoia@cea.fr
authors: A
authors: A
authors: Zoia
authors: E
authors: E
authors: Dumonteil
authors: A
authors: A
authors: Mazzolo