Continuum model for radial interface growth

TL;DR

This paper introduces a stochastic PDE model for radial interface growth, analyzing deterministic solutions and numerical simulations to understand surface roughness scaling, with implications for Eden growth processes.

Contribution

It presents a continuum stochastic PDE model for radial growth, identifying stable symmetric solutions and analyzing surface roughness scaling.

Findings

Polygon solutions are unstable compared to symmetric solutions.

Surface width scaling matches that of substrate growth.

Numerical simulations confirm the scaling exponent.

Abstract

A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions are identified in the deterministic limit. The polygon solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise limit, are unstable in the continuum in favour of the symmetric solutions. The asymptotic surface width scaling for stochastic radial interface growth is investigated through numerical simulations and found to be characterized by the same scaling exponent as that for stochastic growth on a substrate.