Localized excitations in a vertically vibrated granular layer

Abstract

THE formation of two-dimensional patterns in biological, chemical and physical systems is often described by the nonlinear interaction of plane waves¹. An alternative approach views patterns as ensembles of interacting localized objects, analogous to the assembly of crystals from atoms. For macroscopic pattern-forming systems, one objection to the latter approach is that no 'atoms' exist; however spatially localized excitations can play an analogous role. One-dimensional localized states are observed in many systems—for example, solitary waves in water^2–4 and optical fibres⁵—and can organize into simple patterns^6,7. But few examples of two-dimensional localized states are known, and these tend to be unstable and/or do not show simple pattern-forming interactions^8–11. Here we report the observation of stable, two-dimensional localized excitations zin a vibrating layer of sand. These excitations, which we term 'oscillons', have a propensity to assemble into 'molecular' and 'crystalline' structures. Our experimental results, together with the observation of similar localized excitations in model differential equations^12–14, indicate a crucial, cooperative role for hysteresis and dissipation in the formation of oscillons, and suggest that similar behaviour may occur in continuous media.