{"id":"https://openalex.org/W1990947082","doi":"https://doi.org/10.1137/060677689","title":"Multiscale Modeling of Elastic Waves: Theoretical Justification and Numerical Simulation of Band Gaps","display_name":"Multiscale Modeling of Elastic Waves: Theoretical Justification and Numerical Simulation of Band Gaps","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1990947082","doi":"https://doi.org/10.1137/060677689","mag":"1990947082"},"language":"en","primary_location":{"id":"doi:10.1137/060677689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060677689","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3267920","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025119410","display_name":"Andr\u00e9s I. \u00c1vila","orcid":"https://orcid.org/0000-0001-7180-1479"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. \u00c1vila","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049669767","display_name":"Georges Griso","orcid":"https://orcid.org/0000-0001-6819-353X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Griso","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062798078","display_name":"Bernadette Miara","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Miara","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001528015","display_name":"Eduard Rohan","orcid":"https://orcid.org/0000-0002-0300-4600"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. Rohan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5025119410"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7216,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.92547743,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/long-wavelength-limit","display_name":"Long wavelength limit","score":0.7444671392440796},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.617605447769165},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.5812508463859558},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.577009916305542},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5280571579933167},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5086113214492798},{"id":"https://openalex.org/keywords/wavelength","display_name":"Wavelength","score":0.5062534213066101},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.46285855770111084},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4421711564064026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4385341703891754},{"id":"https://openalex.org/keywords/wave-propagation","display_name":"Wave propagation","score":0.43594563007354736},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3354518413543701},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.319966197013855},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.18836799263954163},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18620195984840393},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.17550814151763916},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.1353902816772461}],"concepts":[{"id":"https://openalex.org/C2777144786","wikidata":"https://www.wikidata.org/wiki/Q41364","display_name":"Long wavelength limit","level":2,"score":0.7444671392440796},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.617605447769165},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.5812508463859558},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.577009916305542},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5280571579933167},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5086113214492798},{"id":"https://openalex.org/C6260449","wikidata":"https://www.wikidata.org/wiki/Q41364","display_name":"Wavelength","level":2,"score":0.5062534213066101},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.46285855770111084},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4421711564064026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4385341703891754},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.43594563007354736},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3354518413543701},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.319966197013855},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.18836799263954163},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18620195984840393},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.17550814151763916},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.1353902816772461},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060677689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060677689","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:americanae.aecid.es:3267920","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3267920","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MULTISCALE MODELING & SIMULATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/139597","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/139597","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MULTISCALE MODELING & SIMULATION (PRINT)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3267920","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3267920","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MULTISCALE MODELING & SIMULATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1967203031","https://openalex.org/W1972892940","https://openalex.org/W1999011963","https://openalex.org/W2007371871","https://openalex.org/W2016163205","https://openalex.org/W2017836087","https://openalex.org/W2027239222","https://openalex.org/W2029816817","https://openalex.org/W2039954719","https://openalex.org/W2049129866","https://openalex.org/W2063187679","https://openalex.org/W2116801612","https://openalex.org/W2148020016"],"related_works":["https://openalex.org/W1598955744","https://openalex.org/W4384111961","https://openalex.org/W2127985649","https://openalex.org/W2529287984","https://openalex.org/W2058166223","https://openalex.org/W2144602163","https://openalex.org/W2412659219","https://openalex.org/W2146284271","https://openalex.org/W2032422937","https://openalex.org/W2206177520"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,53],"three-dimensional":[3],"composite":[4],"material":[5],"made":[6],"of":[7,30,39,67,72,80],"small":[8],"inclusions":[9],"periodically":[10],"embedded":[11],"into":[12],"an":[13],"elastic":[14,81],"matrix;":[15],"the":[16,27,37,40,45,65,95],"whole":[17],"structure":[18,48],"presents":[19],"strong":[20],"heterogeneities":[21],"between":[22],"its":[23],"different":[24],"components.":[25],"In":[26,83],"general":[28],"framework":[29],"linearized":[31],"elasticity":[32],"we":[33,59,85],"show":[34,86],"that,":[35],"when":[36],"size":[38],"microstructures":[41],"tends":[42],"to":[43,62,88],"zero,":[44],"limit":[46],"homogeneous":[47],"presents,":[49],"for":[50],"some":[51,99],"wavelengths,":[52],"negative":[54],"\u201cmass":[55],"density\u201d":[56],"tensor.":[57],"Hence":[58],"are":[60],"able":[61],"rigorously":[63],"justify":[64],"existence":[66],"forbidden":[68],"bands,":[69],"i.e.,":[70],"intervals":[71],"frequencies":[73],"in":[74],"which":[75],"there":[76],"is":[77],"no":[78],"propagation":[79],"waves.":[82],"particular,":[84],"how":[87],"compute":[89],"these":[90],"band":[91],"gaps":[92],"and":[93],"illustrate":[94],"theoretical":[96],"results":[97],"with":[98],"numerical":[100],"simulations.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-23T07:41:27.035349","created_date":"2025-10-10T00:00:00"}