Rare events and their impact on velocity diffusion in a stochastic Fermi-Ulam model

Karlis, A. K.; Diakonos, F. K.; Constantoudis, V.; Schmelcher, P.

Abstract

A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards. © 2008 The American Physical Society.

• Journal Article Type: Article
• Acceptance Date: Oct 21, 2008
• Publication Date: Oct 21, 2008
• Deposit Date: May 2, 2018
• Journal: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 78
• Issue: 4
• Pages: 046213
• DOI: https://doi.org/10.1103/PhysRevE.78.046213
• Keywords: rare events, impact, velocity, diffusion, stochastic, Fermi-Ulam model
• Public URL: https://uwe-repository.worktribe.com/output/1008175
• Publisher URL: https://doi.org/10.1103/PhysRevE.78.046213
• Contract Date: May 2, 2018