Nano-pattern stabilization by multiplicative noise

Within the reaction–diffusion framework, a one-component system was confined by means of a multiplicative noise into the attraction basin of a patterning attractor in its (infinite-dimensional) configuration space. In this way, inhomogeneities that otherwise would have been “expelled” from this basin, and subsequently eliminated through the diffusive process, were stabilized. For the present study, a model describing the physics of adsorbed particles on a metallic surface has been used. In particular, an underlying deterministic inhomogeneity-building mechanism was exploited, that acts driven by lateral interactions among the adsorbed particles. This process cannot by itself sustain and stabilize the inhomogeneities, but together with the contribution of a particular form of multiplicative noise, it is able to confine the system into the region of configuration space where this mechanism is enabled, hence stabilizing the pattern. Although the proposal could be applied to more general situations, for the particular model studied here we have found that nanopatterns that without the indicated noise source would be eliminated by diffusion, under its effect can grow and be stabilized.