Journal
PHYSICAL REVIEW E
Volume 93, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.93.012909
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Funding
- ETH Zurich Foundation [ESC-A 06-14]
- NSF [DMS-1310200]
- US Department of Energy
- US AFOSR [FA9550-12-1-0332]
- ERC under FP7, Marie Curie Actions, People, International Research Staff Exchange Scheme [IRSES-605096]
- [BSF-2010239]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1310200] Funding Source: National Science Foundation
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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, conicalwave 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.
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