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

Source: [Properties of nano-pattern formation in reaction-diffusion systems with hyperbolic transport and multiplicative noise](<https://www.sota2.com/research/paper/68fa2e921e209131ce863fb0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:01:05.449Z

Authors: Dmitrii O.Kharchenko, Vasyl O.Kharchenko, Sergei V.Kokhan

Published: 2011-01-17T11:56:13.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1101.3189>)

[PDF](<https://arxiv.org/pdf/1101.3189.pdf>)