Journal ArticleDOI
Asymptotic Analysis of First Passage Time Problems Inspired by Ecology
TLDR
The hybrid approach has the advantage of eliminating the difficulty with resolving small spatial scales in a full numerical treatment of the partial differential equation (PDE).About:
This article is published in Bulletin of Mathematical Biology.The article was published on 2015-01-01. It has received 80 citations till now. The article focuses on the topics: First-hitting-time model & Singular perturbation.read more
Citations
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Redundancy principle and the role of extreme statistics in molecular and cellular biology.
TL;DR: The physical models, the mathematical analysis and the new paradigm of setting the scale to be the shortest time for activation that clarifies the role of population redundancy in selecting and accelerating transient cellular search processes are reviewed.
Posted Content
Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries
TL;DR: In this article, the mean first-passage times for random walks in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a sphere, were investigated.
Journal ArticleDOI
First passage time distribution of multiple impatient particles with reversible binding.
Sean D. Lawley,Jacob B. Madrid +1 more
TL;DR: This paper approximate the full distribution of the FPT for any N ≥ K ≥ 1 in a broad class of domains in any space dimension and proves that the approximation is exact in the limit that the target and/or binding rate is small and is an upper bound in any parameter regime.
Journal ArticleDOI
Distribution of extreme first passage times of diffusion.
TL;DR: In this paper, the authors apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion, which can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT.
Journal ArticleDOI
Navigating the flow: individual and continuum models for homing in flowing environments.
Kevin J. Painter,Thomas Hillen +1 more
TL;DR: This paper forms an individual-based model for navigation within a flowing field and applies scaling to derive its corresponding macroscopic and continuous model, which is applied to various movement classes, from drifters that simply go with the flow to navigators that respond to environmental orienteering cues.
References
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Book
Random walks in biology
TL;DR: This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know.
Journal ArticleDOI
Random dispersal in theoretical populations.
TL;DR: In this paper, the authors used the random walk problem as a starting point for the analytical study of dispersal in living organisms and applied the law of diffusion to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats.
Book
Potential theory in the complex plane
TL;DR: Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity.