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Continuous-time random walks on bounded domains
1Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523-1874, USA. burch@math.colostate.edu
Summary
This study introduces a generalized master equation for continuous-time random walks in bounded domains. Numerical solutions accurately model anomalous diffusion, offering a powerful research tool.
Area of Science:
- Physics
- Physical Chemistry
- Statistical Mechanics
Background:
- Anomalous diffusion processes are often studied using continuous-time random walks (CTRWs).
- Generalized master equations (GMEs) are associated with CTRWs, providing a framework for analysis.
Purpose of the Study:
- To derive GMEs for CTRWs confined to a bounded domain.
- To compare numerical solutions of these GMEs with simulation-based estimates.
Main Methods:
- Derivation of GMEs for bounded CTRWs.
- Numerical solution of the derived GMEs.
- Kernel-density estimation of probability density functions from simulations.
Main Results:
- Numerical solutions of the GMEs align well with simulation data.
- The derived GMEs effectively describe CTRWs in bounded domains.
Conclusions:
- The numerical solution of GMEs is a potent method for studying CTRWs on bounded domains.
- This approach enhances the understanding of anomalous diffusion in confined systems.
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