Flux-conserving directed percolation

Author:

Barto Cucurull, Greg Huber, Kyle Kawagoe, Marc Pradas, Alain Pumir, Michael Wilkinson

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

date:

2023-10-02 16:00:00

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.

PDF: Flux-conserving directed percolation.pdf