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Title: Aggregation-fragmentation-diffusion model for trail dynamics

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 –γ for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. In conclusion, 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.

Authors:
 [1];  [2];  [3];  [3];  [4]; ORCiD logo [5]
  1. Univ. of California, Santa Barbara, CA (United States); Univ. of Chicago, Chicago, IL (United States)
  2. Univ. of California, Santa Barbara, CA (United States)
  3. The Open Univ., Milton Keynes (England); Univ. of California, Santa Barbara, CA (United States)
  4. Univ. de Lyon, Lyon (France); Univ. of California, Santa Barbara, CA (United States)
  5. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1375177
Report Number(s):
LA-UR-17-23902
Journal ID: ISSN 2470-0045; PLEEE8
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats

Kawagoe, Kyle, Huber, Greg, Pradas, Marc, Wilkinson, Michael, Pumir, Alain, and Ben-Naim, Eli. Aggregation-fragmentation-diffusion model for trail dynamics. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.012142.
Kawagoe, Kyle, Huber, Greg, Pradas, Marc, Wilkinson, Michael, Pumir, Alain, & Ben-Naim, Eli. Aggregation-fragmentation-diffusion model for trail dynamics. United States. doi:10.1103/PhysRevE.96.012142.
Kawagoe, Kyle, Huber, Greg, Pradas, Marc, Wilkinson, Michael, Pumir, Alain, and Ben-Naim, Eli. Fri . "Aggregation-fragmentation-diffusion model for trail dynamics". United States. doi:10.1103/PhysRevE.96.012142. https://www.osti.gov/servlets/purl/1375177.
@article{osti_1375177,
title = {Aggregation-fragmentation-diffusion model for trail dynamics},
author = {Kawagoe, Kyle and Huber, Greg and Pradas, Marc and Wilkinson, Michael and Pumir, Alain and Ben-Naim, Eli},
abstractNote = {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–γ for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. In conclusion, 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.},
doi = {10.1103/PhysRevE.96.012142},
journal = {Physical Review E},
number = 1,
volume = 96,
place = {United States},
year = {2017},
month = {7}
}

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