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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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Related Experiment Video

Updated: Nov 29, 2025

Spot Variation Fluorescence Correlation Spectroscopy for Analysis of Molecular Diffusion at the Plasma Membrane of Living Cells
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Diffusion and escape times in the open-leaky standard map.

L Lugosi1, T Kovács1

  • 1Eötvös Loránd University, Institute of Physics, H-1117 Budapest, Pázmány P. s. 1/A, Hungary.

Physical Review. E
|November 20, 2020
PubMed
Summary

This study explores transport phenomena and escape rates in a 2D standard map. Diffusion analysis reveals non-exponential escape statistics, particularly with strong perturbation, challenging standard models.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Chaos theory

Background:

  • The standard map is a fundamental model for studying chaotic dynamics.
  • Understanding particle escape and diffusion is crucial in various physical systems.
  • Open phase space dynamics require careful analysis of transport and escape phenomena.

Purpose of the Study:

  • To investigate the relationship between transport phenomena and escape rate statistics.
  • To analyze diffusion coefficients based on escape region properties.
  • To examine the influence of perturbation strength on escape dynamics.

Main Methods:

  • Simulating particle trajectories in a two-dimensional standard map with an open phase space.
  • Defining artificial escape regions (holes) in the momentum coordinate.

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Last Updated: Nov 29, 2025

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  • Analyzing the ensemble of survived particles to study diffusion.
  • Varying escape region size/position and perturbation strength.

    • Main Results:

    • Diffusion coefficient is dependent on the size and position of escape regions.
    • Short-time escape statistics deviate from exponential decay, especially at high perturbation strengths.
    • Particles can escape after long excursions in remote phase space regions, bypassing direct leaks.

    Conclusions:

    • The study highlights complex escape dynamics in open chaotic systems.
    • Non-exponential escape statistics indicate deviations from simple diffusion models under certain conditions.
    • Perturbation strength significantly alters transport and escape behaviors in the standard map.