{"paper":{"title":"Dispersion of waves in two and three-dimensional periodic media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.app-ph"],"primary_cat":"math.AP","authors_text":"Boris Vainberg, Yuri A. Godin","submitted_at":"2019-05-29T15:26:38Z","abstract_excerpt":"We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the radius $a$ of inclusions is small. A new approach is suggested to derive the complete asymptotic expansions of the dispersion relations in two and three-dimensional cases as $a \\to 0$ and evaluate explicitly several first terms. Our method is based on the reduction of the original singularly perturbed (by inclusions) problem to the regular one. The Neumann, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12529","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}