Nonequilibrium roughening transition in a simple model of fungal growth in 1+1 dimensions

TL;DR

This paper presents a simple 1+1 dimensional model of fungal colony growth that exhibits a continuous nonequilibrium roughening transition, with critical exponents derived via directed percolation mapping, aligning with experimental observations.

Contribution

The study introduces a minimal model capturing the nonequilibrium roughening transition in fungal growth, providing analytical insights through directed percolation mapping.

Findings

Identifies a continuous roughening transition in the model

Calculates critical exponents at the transition point

Reproduces experimental roughening behavior in fungi

Abstract

We introduce a simple model of yeast-like growth of fungi colonies, which exhibits a continuous roughening transition far from equilibrium from a smooth ($\alpha = 0$) to rough phase ($\alpha = 1/2$) in 1+1 dimensions. At the transition some scaling exponents are calculated by mapping the problem onto a directed percolation process. The model reproduces the roughening transition observed in some experiments of fungal growth