title: Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices.
abstract: Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. The transition between these two types of propagation is explored.
authors: Department of Mechanical and Process Engineering (D-MAVT), ETH-Zurich, 8092 Zurich, Switzerland.|Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USA.
authors: C
authors: C
authors: Chong
authors: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
authors: P G
authors: PG
authors: Kevrekidis
authors: Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, Colorado 80309-0526, USA.
authors: M J
authors: MJ
authors: Ablowitz
authors: Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, Colorado 80309-0526, USA.
authors: Yi-Ping
authors: YP
authors: Ma