Flux-conserving directed percolation
Disordered Systems and Neural Networks
2023-10-04 v1
Abstract
We discuss a model for directed percolation in which the flux of material along each bond is a dynamical variable. The model includes a physically significant limiting case where the total flux of material is conserved. We show that the distribution of fluxes is asymptotic to a power law at small fluxes. We give an implicit equation for the exponent, in terms of probabilities characterising site occupations. In one dimension the site occupations are exactly independent, and the model is exactly solvable. In two dimensions, the independent-occupation assumption gives a good approximation. We explore the relationship between this model and traditional models for directed percolation.
Keywords
Cite
@article{arxiv.2310.01933,
title = {Flux-conserving directed percolation},
author = {Barto Cucurull and Greg Huber and Kyle Kawagoe and Marc Pradas and Alain Pumir and Michael Wilkinson},
journal= {arXiv preprint arXiv:2310.01933},
year = {2023}
}
Comments
30 pages, 16 figures