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.
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.
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