Nearest pattern interaction and global pattern formation

Abstract

We studied the effect of nearest pattern interaction on a global pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of a periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective of the experimentally observed pattern dynamics such as oscillon and stripe formations, skew-varicose and crossroll instabilities, and also a kink formation and decoration.

A fluid-like model of vibrated granular layers: Linear stability, kinks, and oscillons

“…Given the sensitivity to bottom impact, a change in layer thickness, e.g., a small perturbation on the antiplane solutions, is expected to significantly affect the localized solutions found above. More importantly, varicosity is obviously implicated in the spatially extended waves that are much more prevalent in experiment and simulation (De Bruyn et al, 1998;Clément and Labous, 2000;Jeong et al, 2000). For example, the 2D particledynamics simulation shown in Fig.…”

“…Among the possible benefits, the present effort may pave the way to a sound mechanical foundation for certain phenomenological dynamical-systems (DS) models (Aranson and Tsimring, 1998;Rothman, 1998;Venkataramani and Ott, 1998;Jeong and Moon, 1999;Jeong et al, 2000;Blair et al, 2000), models that have been remarkably successful in capturing several qualitative aspects of granular-layer dynamics. With a similar motivation, Eggers and Riecke (1999) offer a model with a more evident mechanical content, but it still relies on a phenomenological ''granular diffusion", whose mechanical origins are not obvious to us.…”