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We study nano-pattern formation in a stochastic model foradsorption-desorption processes with interacting adsorbate and hyperbolictransport caused by memory effects. It is shown that at early stages the systemmanifests pattern selection processes. Stationary stable patterns of nano-sizeare analyzed. It was found that multiplicative noise satisfyingfluctuation-dissipation relation can induce re-entrant pattern formationrelated to non-equilibrium transitions. According to obtained Fokker-Planckequation kinetics of island sizes in a quasi-stationary limit is discussed.Analytical results are compared with computer simulations.

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