Diffusion and multiplication in random media

P. L. Krapivsky, K. Mallick

Type: Article

Publication Date: 2011-01-14

Citations: 3

DOI: https://doi.org/10.1088/1742-5468/2011/01/p01015

Abstract

We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication.Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of nutrients.We focus on the situation where the distribution of nutrients is a stationary quenched random variable, and show that the population exhibits a super-exponential growth whenever the nutrient distribution is unbounded.We elucidate a huge difference between the average and typical asymptotic growths and emphasize the role played by the spatial correlations in the nutrient distribution.

Locations

Journal of Statistical Mechanics Theory and Experiment - View
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
DataCite API - View

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Works Cited by This (35)

Action	Title	Year	Authors
+	Advanced mathematical methods for scientists and engineers	1978	Carl M. Bender Steven A. Orszag
+	Random multiplication in a diffusive medium	1989	M. N. Rosenbluth
+ PDF Chat	Self-trapping of a single bacterium in its own chemoattractant	2004	Yoav Tsori P. G. de Gennes
+	Statistics of a polymer in a random potential, with implications for a nonlinear interfacial growth model	1988	M. E. Cates R. C. Ball
+	Complex patterns formed by motile cells of Escherichia coli	1991	Elena O. Budrene Howard C. Berg
+	Diffusion and reaction in random media and models of evolution processes	1984	W. Ebeling A. Engel B. Esser Rainer Feistel
+	Random multiplicative processes: An elementary tutorial	1990	S. Redner
+	Experimental Investigation on the Validity of Population Dynamics Approach to Bacterial Colony Formation	1994	Jun-ichi Wakita Kenji Komatsu Akio Nakahara Tohey Matsuyama Mitsugu Matsushita
+	Partition function of a particle subject to Gaussian noise	1983	Eugene P. Gross
+	Path-integral approach to diffusion in random media	1991	R. Tao