Properties of nano-pattern formation in reaction-diffusion systems with hyperbolic transport and multiplicative noise

TL;DR

This paper investigates nano-pattern formation in reaction-diffusion systems incorporating hyperbolic transport and multiplicative noise, revealing how noise can induce re-entrant patterns and analyzing stable nano-sized structures through analytical and simulation methods.

Contribution

It introduces a stochastic model with hyperbolic transport and noise, demonstrating noise-induced pattern formation and analyzing stable nano-patterns with analytical and simulation approaches.

Findings

Noise can induce re-entrant pattern formation.

Stable nano-sized patterns are identified and analyzed.

Analytical results agree with computer simulations.

Abstract

We study nano-pattern formation in a stochastic model for adsorption-desorption processes with interacting adsorbate and hyperbolic transport caused by memory effects. It is shown that at early stages the system manifests pattern selection processes. Stationary stable patterns of nano-size are analyzed. It was found that multiplicative noise satisfying fluctuation-dissipation relation can induce re-entrant pattern formation related to non-equilibrium transitions. According to obtained Fokker-Planck equation kinetics of island sizes in a quasi-stationary limit is discussed. Analytical results are compared with computer simulations.