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Continuous-time random walks that alter environmental transport properties
1School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. c.angstmann@unsw.edu.au
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
Transmogrifying continuous-time random walks (TCTRWs) can exhibit transient anomalous diffusion. These walks alter environmental properties, leading to subdiffusion or superdiffusion without complex waiting-time or step-length distributions.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Continuous-time random walks (CTRWs) are fundamental models for diffusion.
- Anomalous diffusion deviates from standard Brownian motion.
- Environmental interactions can modify diffusion dynamics.
Purpose of the Study:
- Introduce and analyze transmogrifying continuous-time random walks (TCTRWs).
- Investigate the generation of transient anomalous diffusion in TCTRWs.
- Explore how walkers alter environmental transport properties.
Main Methods:
- Derivation of master equations for TCTRW probability density functions.
- Comparison of theoretical results with Monte Carlo simulations.
- Analysis of TCTRWs with specific waiting-time and step-length distributions.
Main Results:
- TCTRWs can produce transient subdiffusion and superdiffusion.
- This occurs without requiring truncated or tempered power-law densities.
- Transient diffusion depends on alterations in average waiting times.
Conclusions:
- TCTRWs offer a novel mechanism for transient anomalous diffusion.
- Environmental modification by walkers is key to observed diffusion behaviors.
- The model provides insights into complex transport phenomena.
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