Phase growth in bistable systems with impurities

TL;DR

This study investigates how impurities affect phase growth in bistable systems, revealing that increased impurities slow domain growth and reduce domain size, with implications for controlling phase dynamics in nonuniform media.

Contribution

It introduces a model of coupled chaotic bistable maps with impurities, analyzing how inhomogeneities influence phase domain growth and stability, providing a phase diagram and growth transition boundary.

Findings

Impurities slow down phase domain growth.

Higher impurity density reduces average domain size.

A phase diagram delineates regimes of pattern formation.

Abstract

A system of coupled chaotic bistable maps on a lattice with randomly distributed impurities is investigated as a model for studying the phenomenon of phase growth in nonuniform media. The statistical properties of the system are characterized by means of the average size of spatial domains of equivalent spin variables that define the phases. It is found that the rate at which phase domains grow becomes smaller when impurities are present and that the average size of the resulting domains in the inhomogeneous state of the system decreases when the density of impurities is increased. The phase diagram showing regions where homogeneous, heterogeneous, and chessboard patterns occur on the space of parameters of the system is obtained. A critical boundary that separates the regime of slow growth of domains from the regime of fast growth in the heterogeneous region of the phase diagram is calculated. The transition between these two growth regimes is explained in terms of the stability properties of the local phase configurations. Our results show that the inclusion of spatial inhomogeneities can be used as a control mechanism for the size and growth velocity of phase domains forming in spatiotemporal systems.