• shareshare
  • link
  • cite
  • add
auto_awesome_motion View all 5 versions
Publication . Article . Preprint . 2017 . Embargo end date: 01 Jan 2017

Aggregation-fragmentation-diffusion model for trail dynamics

Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;
Open Access

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 $P(w) \sim w^{-\gamma}$ for small weight $w$. We obtain the exponent $\gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare.

Comment: 8 pages, 8 figures

Subjects by Vocabulary

Microsoft Academic Graph classification: Asymptotic distribution Range (statistics) Physics Exponent Combinatorics Limit (mathematics) Diffusion (business) Steady state Fragmentation (computing) Statistical physics Stochastic process


Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Condensed Matter - Statistical Mechanics