Roughening Interfaces in Deterministic Dynamics

Abstract

Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface. I. INTRODUCTION Dynamics of growing and roughening interfaces have been intensively investigated recently[1]. This phenomenon is of importance in deposition, crystal growth, two-phase flow in porous media, etc. The universal equation governing the motion of the interface was derived by Kardar, Parisi and Zhang (KPZ)[2]: @H @t = 2 ( @H ..