Lattice Dynamics and Melting of a Nonequilibrium Pattern.pdf

Lattice Dynamics and Melting of a Nonequilibrium Pattern Daniel I. Goldman,∗ M. D. Shattuck, Sung Joon Moon, J. B. Swift, and Harry L. Swinney Center for Nonlinear Dynamics, The University of Texas at Austin, Austin, TX 78712 (Dated: February 8, 2008) We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for different driving frequencies (f ) and accelerations. The d amplitude of a mode can be further excited by either frequency modulation of fd or reduction of friction between the grains and the plate. When the mode amplitude becomes large, the lattice melts (disorders), in accord with the Lindemann criterion for melting in two-dimensions. 3 0 Systems driven away from thermodynamic equilibrium A B 0T 0 often form patterns when forced beyond a critical thresh- (a) (b) (c) 2 r old. Close to this bifurcation, the dynamics of the 8T p nonequilibrium patterns are well described by partial A A differential equations called amplitude equations, whose a 16T