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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

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Published on: January 31, 2020

Continuous-time random walks that alter environmental transport properties.

C Angstmann¹, B I Henry

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.

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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.