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

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.