Competition between slow and fast regimes for extreme first passage times of diffusion
| Autor: | Jacob B. Madrid, Sean D. Lawley |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Diffusion (acoustics) Computer science General Physics and Astronomy FOS: Physical sciences 01 natural sciences Quantitative Biology - Quantitative Methods 010305 fluids & plasmas Competition (economics) 0103 physical sciences FOS: Mathematics Statistical physics Limit (mathematics) Physics - Biological Physics 010306 general physics Extreme value theory Mathematical Physics Brownian motion Quantitative Methods (q-bio.QM) Narrow escape problem Probability (math.PR) Statistical and Nonlinear Physics Biological Physics (physics.bio-ph) Modeling and Simulation FOS: Biological sciences 60G70 92B05 92C05 First-hitting-time model Large group Mathematics - Probability |
| Popis: | Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the target is small (the narrow escape problem) or if the searcher must escape a potential well. However, many systems depend on the first time a searcher finds the target out of a large group of searchers, which is the so-called extreme FPT. Since this extreme FPT vanishes in the limit of many searchers, the prohibitively slow FPTs of diffusive search can be negated by deploying enough searchers. However, the notion of "enough searchers" is poorly understood. How can one determine if a system is in the slow regime (dominated by small targets or a deep potential, for example) or the fast regime (dominated by many searchers)? How can one estimate the extreme FPT in these different regimes? In this paper, we answer these questions by deriving conditions which ensure that a system is in either regime and finding approximations of the full distribution and all the moments of the extreme FPT in these regimes. Our analysis reveals the critical effect that initial searcher distribution and target reactivity can have on extreme FPTs. 38 pages, 5 figures |
| Databáze: | OpenAIRE |
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