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Updated: Oct 21, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Inertial Lévy flights in bounded domains
Karol Capała1, Bartłomiej Dybiec1
1Institute of Theoretical Physics, and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland.
Abstract:
The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by Lévy noise from a bounded domain, restricted by two absorbing boundaries. The presence of two absorbing boundaries assures that the escape process can be characterized by the finite mean first passage time. The detailed analysis of escape kinetics shows that properties of the mean first passage time for the integrated Ornstein-Uhlenbeck process driven by Lévy noise are closely related to properties of the integrated Lévy motions, which, in turn, are close to properties of the integrated Wiener process. The extensive studies of the mean first passage time were complemented by examination of the escape velocity and energy along with their sensitivity to initial conditions.
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