Lévy walk dynamics in non-static media

@article{Zhou2021LvyWD,
  title={L{\'e}vy walk dynamics in non-static media},
  author={Tianci Zhou and Pengbo Xu and Weihua Deng},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={55}
}
  • T. Zhou, Pengbo Xu, Weihua Deng
  • Published 13 October 2021
  • Physics
  • Journal of Physics A: Mathematical and Theoretical
Almost all the media the particles move in are non-static, one of which is the most common expanding or contracting (by a scale factor) non-static medium discussed in this paper. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement caused by the non-static media, sometimes the non-static behaviors of the media can not be ignored. In this paper, we build the model describing Lévy walks in one-dimension uniformly non-static media, where the physical… 

References

SHOWING 1-10 OF 112 REFERENCES
Continuous-time random-walk model for anomalous diffusion in expanding media.
TLDR
The analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions.
Lévy Walk with Multiple Internal States
  • P. Xu, W. Deng
  • Physics, Mathematics
    Journal of Statistical Physics
  • 2018
Lévy walk with multiple internal states can effectively model the motion of particles that don’t immediately move back to the directions or areas which they come from. When the Lévy walk behaves
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking.
TLDR
This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion, and pays special attention to the ergodicity breaking parameters for the different anomalous stochastic processes.
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Abstract The subject of this paper is the evolution of Brownian particles in disordered environments. The “Ariadne's clew” we follow is understanding of the general statistical mechanisms which may
Langevin equations for continuous time Lévy flights.
  • Fogedby
  • Mathematics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
TLDR
This analysis is a formulation in terms of coupled Langevin equations which allows in a natural way for the inclusion of external force fields and finds that this result is independent of the presence of weak quenched disorder.
Towards deterministic equations for Lévy walks: the fractional material derivative.
  • I. Sokolov, R. Metzler
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
A generalized dynamical formulation is derived for Lévy walks, in which the fractional equivalent of the material derivative occurs, which is expected to be useful for the dynamical formulations of LÉvy walks in an external force field or in phase space.
Bayesian inference of Lévy walks via hidden Markov models
The Lévy walk (LW) is a non-Brownian random walk model that has been found to describe anomalous dynamic phenomena in diverse fields ranging from biology over quantum physics to ecology. Recurrently
Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions
We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that
One-dimensional stochastic Levy-lorentz gas
  • Barkai, Fleurov, Klafter
  • Mathematics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
TLDR
A Levy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line is introduced and it is shown that under certain conditions the mean square displacement of the particle obeys <x(2)(t)>>/=Ct3-gamma for 1<gamma<2.
Anomalous transport in the crowded world of biological cells.
TLDR
A large body of recent experimental evidence for anomalous transport in crowded biological media is reported on in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions.
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4
5
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