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Aging ballistic Lévy walks.

Marcin Magdziarz1, Tomasz Zorawik1

  • 1Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.

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Summary
This summary is machine-generated.

Aging in physical systems is affected by observation delays. Standard Lévy walks show weak aging effects, while jump models exhibit drastic changes in probability distributions and mean square displacement (MSD).

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Aging phenomena are prevalent in diverse physical systems.
  • Statistical properties like probability distributions and mean square displacement (MSD) are time-dependent.
  • The delay in observation (t_a) can influence these aging dynamics.

Purpose of the Study:

  • To investigate the aging properties of ballistic Lévy walks.
  • To analyze two related jump models: wait-first and jump-first.
  • To compare the impact of observation delay (t_a) on these different models.

Main Methods:

  • Explicit calculation of probability distributions.
  • Explicit calculation of mean square displacement (MSD).
  • Analysis of aging effects based on the observation delay (t_a).

Main Results:

  • Standard Lévy walks exhibit weak changes in probability density function and MSD due to aging.
  • Jump models show significant alterations in probability density function shape.
  • The wait-first jump model displays distinct MSD behaviors for t_a << t and t_a >> t.

Conclusions:

  • Ballistic Lévy walks and jump models respond differently to aging and observation delays.
  • Jump models are more sensitive to aging effects than standard Lévy walks.
  • The wait-first jump model presents unique aging characteristics impacting MSD.