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Continuous-time random walks on networks with vertex- and time-dependent forcing.

C N Angstmann¹, I C Donnelly, B I Henry

¹School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia.

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

|September 17, 2013

Summary

Forced particle transport on networks can lead to unique pair-aggregation patterns. This self-chemotactic-like forcing drives particles to form concentrated pairs on adjacent network vertices, unlike random walks.

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Area of Science:

Statistical Physics
Network Science
Complex Systems

Background:

Particle transport on networks is fundamental to many physical and biological processes.
Understanding how external forces influence particle dynamics is crucial for predicting system behavior.
Continuous time random walks (CTRWs) provide a framework for modeling stochastic transport.

Purpose of the Study:

To investigate particle transport on networks under vertex- and time-dependent forcing.
To derive and analyze the generalized master equations governing this forced transport.
To explore the emergence of pattern formation due to self-chemotactic-like forcing.

Main Methods:

Derivation of generalized master equations using continuous time random walks (CTRWs).
Incorporation of forcing via vertex- and time-dependent bias in jump densities.
Algebraic and numerical studies to analyze steady-state behavior and pattern formation.

Main Results:

Forced particle transport exhibits unique pair-aggregation patterns not seen in unforced random walks.
Steady states show high concentrations of particles on isolated pairs of adjacent vertices.
The observed pair aggregation is a direct consequence of the self-chemotactic-like forcing.

Conclusions:

Self-chemotactic-like forcing can induce significant pattern formation in particle transport on networks.
Pair aggregation serves as a potential signature of such forcing mechanisms.
The findings offer insights into collective behavior driven by local interactions in networked systems.