Dissertation
STOCHASTIC PURSUIT MODELS: THEORY AND APPLICATIONS
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000005466
Handle:
https://hdl.handle.net/2376/119164
Abstract
Recent years have seen an increase of evidence of systems driven by diffusive processes that exhibit mixed linear and anomalous diffusive regimes, typically in the form of an anomalous to normal transition in time. Despite showing many characteristics reminiscent of anomalous diffusion, the density profiles of these systems seem to carry over exponential tails in strong contrast to power-laws. Inspired by the simple idea of a driven particle undergoing Brownian diffusion while simultaneously pursuing another diffusive particle, we develop a model of stochastic pursuit that exhibits transient anomalous features while maintaining key normal diffusive components. Specifically, we show: a) the model is capable of capturing transient sub-diffusion, super-diffusion and pure super-diffusion depending on the parameters, b) the orientation auto-correlation function of the model exhibits stretched-exponential behavior, c) hitting (catching) times are Inverse-Gaussian distributed, and d) the distance between the two particles satisfies the dry friction equation. Extensions of the model to higher dimensions are also presented, where the properties of the model are shown to have strong dimension dependence. As an application, we apply the stochastic pursuit-evasion model to foraging theory, and show how the model fits well with experimental data from cell-motility.
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Details
- Title
- STOCHASTIC PURSUIT MODELS: THEORY AND APPLICATIONS
- Creators
- Kellan Ray Toman
- Contributors
- Nikolaos K Voulgarakis (Advisor)Kevin R Vixie (Committee Member)Charles N Moore (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 87
- Identifiers
- 99900592362101842
- Language
- English
- Resource Type
- Dissertation