Nonlinear, Statistical and Applied Physics of Solitary Wave-like Objects in Granular Systems

Abstract

We consider a simple problem that of a horizontal alignment of identical grains, and insure that the grains are in gentle mutual contact and held between two rigid fixed end walls. Grain‐grain interactions are intrinsically nonlinear according to the Hertz law and hence no sound waves can propagate through this alignment. The discussions here concern the solitary wave nature of propagation of any perturbation and its subsequent dispersion in the same vein as we probe the dispersion of a perturbation in linear response theory in statistical physics. We show that a perturbed granular alignment exhibits both decaying and growing solitary waves and can indeed reach an equilibrium‐like state. We suggest that this equilibrium‐like state may not be the equilibrium state commonly reached in thermodynamics and statistical physics. Moving beyond the effort to develop a deeper understanding of the energy transport problem in granular systems, we discuss a new application of a granular alignment system, that of driven granular alignments that show rich nonlinear dynamics and can turn out to be technologically meaningful entities.