{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:34:14Z","timestamp":1787236454863,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>High-frequency homogenization is applied herein to develop asymptotics for waves propagating along line defects in lattices; the approaches developed are anticipated to be of wide application to many other systems that exhibit surface waves created or directed by microstructure. With the aim being to create a long-scale continuum representation of the line defect that nonetheless accurately incorporates the microscale information, this development uses the microstructural information embedded within, potentially high-frequency, standing wave solutions. A two-scaled approach is utilized for a simple line defect and demonstrated versus exact solutions for quasi-periodic systems and versus numerical solutions for line defects that are themselves perturbed or altered. In particular, Rayleigh--Bloch states propagating along the line defect, and localized defect states, are identified both asymptotically and numerically. Additionally, numerical simulations of large-scale lattice systems illustrate the physics underlying the propagation of waves through the lattice at different frequencies.<\/jats:p>","DOI":"10.1137\/120872401","type":"journal-article","created":{"date-parts":[[2013,8,20]],"date-time":"2013-08-20T12:11:36Z","timestamp":1377000696000},"page":"871-889","source":"Crossref","is-referenced-by-count":9,"title":["Asymptotics for Rayleigh--Bloch Waves along Lattice Line Defects"],"prefix":"10.1137","volume":"11","author":[{"given":"L. M.","family":"Joseph","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. V.","family":"Craster","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,8,20]]},"reference":[{"key":"atypb1","unstructured":"J. D. 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