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Aggregation-fragmentation-diffusion model for trail dynamics

Kawagoe, Kyle; Huber, Greg; Pradas, Marc; Wilkinson, Michael; Pumir, Alain and Ben-Naim, Eli (2017). Aggregation-fragmentation-diffusion model for trail dynamics. Physical Review E, 96, article no. 012142.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1103/PhysRevE.96.012142
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Abstract

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)~w for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. The exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.

Item Type: Journal Item
Copyright Holders: 2017 American Physical Society
ISSN: 1550-2376
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetPHY1125915National Science Foundation
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 50435
Depositing User: Marc Pradas
Date Deposited: 10 Aug 2017 14:32
Last Modified: 01 May 2019 17:34
URI: http://oro.open.ac.uk/id/eprint/50435
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