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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Related Experiment Video

Updated: Oct 21, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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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.

Chaos (Woodbury, N.Y.)
|September 2, 2021
PubMed
Summary

This study analyzes how inertial particles escape bounded domains using Lévy noise. The mean first passage time properties resemble those of integrated Wiener processes.

Area of Science:

  • Statistical Physics
  • Stochastic Processes Theory

Background:

  • Escape from a domain is a fundamental problem in physics.
  • Inertial particles in bounded domains with absorbing boundaries are studied.

Purpose of the Study:

  • To explore the escape properties of inertial particles driven by Lévy noise from a bounded domain.
  • To analyze the mean first passage time, escape velocity, and energy.

Main Methods:

  • Analysis of escape kinetics for an integrated Ornstein-Uhlenbeck process driven by Lévy noise.
  • Examination of mean first passage time, escape velocity, and energy.

Main Results:

  • Escape kinetics are characterized by finite mean first passage time due to absorbing boundaries.

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  • Mean first passage time properties are closely related to integrated Lévy motions and integrated Wiener processes.

    • Conclusions:

    • The study provides insights into escape dynamics influenced by Lévy noise.
    • Findings relate to fundamental problems in statistical physics and stochastic processes.