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Related Experiment Video

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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

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Published on: January 31, 2020

Hopping transport in hostile reaction-diffusion systems.

Andrew R Missel¹, Karin A Dahmen

¹Physics Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. missel@uiuc.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 28, 2009

Summary

This study models population dynamics in patchy environments. We found that population spread between "oases" can be estimated using first passage time calculations, predicting overall system crossing times.

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Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

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Area of Science:

Complex Systems
Mathematical Biology
Statistical Physics

Background:

Reaction-diffusion models simulate population dynamics in spatially heterogeneous environments.
Previous work applied these models to bacterial and plankton populations.
Understanding transport in disordered systems is crucial for ecological and biological studies.

Purpose of the Study:

To investigate particle transport in a disordered reaction-diffusion model with birth, death, and competition.
To determine the first passage time probability density function for transport between two oases.
To estimate the time for a population to cross a large system.

Main Methods:

Analysis of a disordered reaction-diffusion model with specific reaction terms (2A-->A, A-->2A, A-->0).
Application of first passage time processes in the high growth rate limit.
Utilizing hopping conduction theory from doped semiconductors for system-wide transport estimation.

Main Results:

The transport between two oases, in the high growth rate limit, is characterized as a first passage process.
The first passage time probability density function was determined for large oasis separations.
An estimation for the population's time to cross a large system was derived.

Conclusions:

The study provides a framework for understanding population spread in patchy, disordered environments.
First passage time analysis is a powerful tool for modeling transport in such systems.
The findings have implications for predicting population dynamics and colonization times in ecological contexts.