{"id":"https://openalex.org/W3214944642","doi":"https://doi.org/10.1137/21m1398410","title":"Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains","display_name":"Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3214944642","doi":"https://doi.org/10.1137/21m1398410","mag":"3214944642"},"language":"en","primary_location":{"id":"doi:10.1137/21m1398410","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1398410","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022835152","display_name":"Guo Deng","orcid":"https://orcid.org/0000-0002-6055-2013"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo Deng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014200379","display_name":"Christopher J. Lustri","orcid":"https://orcid.org/0000-0001-9504-277X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher J. Lustri","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9504-277X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058684689","display_name":"Mason A. Porter","orcid":"https://orcid.org/0000-0002-5166-0717"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mason A. Porter","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5166-0717","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9409,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.74327064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"4","first_page":"2412","last_page":"2449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.6635233163833618},{"id":"https://openalex.org/keywords/diatomic-molecule","display_name":"Diatomic molecule","score":0.6391309499740601},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5742618441581726},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.541619598865509},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4402415156364441},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37845349311828613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2967836260795593},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24713563919067383},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14107924699783325}],"concepts":[{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.6635233163833618},{"id":"https://openalex.org/C111806078","wikidata":"https://www.wikidata.org/wiki/Q1751859","display_name":"Diatomic molecule","level":3,"score":0.6391309499740601},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5742618441581726},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.541619598865509},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4402415156364441},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37845349311828613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2967836260795593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24713563919067383},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14107924699783325},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1398410","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1398410","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4583096896","display_name":"A new asymptotic toolbox for nonlinear discrete systems and particle chains","funder_award_id":"DP190101190","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":100,"referenced_works":["https://openalex.org/W32505504","https://openalex.org/W572613202","https://openalex.org/W1591737370","https://openalex.org/W1599623497","https://openalex.org/W1648724192","https://openalex.org/W1655919780","https://openalex.org/W1958971842","https://openalex.org/W1964630443","https://openalex.org/W1971892010","https://openalex.org/W1973365196","https://openalex.org/W1979400409","https://openalex.org/W1979722387","https://openalex.org/W1982388251","https://openalex.org/W1983031318","https://openalex.org/W1983519722","https://openalex.org/W1984262071","https://openalex.org/W1986904823","https://openalex.org/W1987052298","https://openalex.org/W1989107818","https://openalex.org/W1994664602","https://openalex.org/W1999089726","https://openalex.org/W2001532260","https://openalex.org/W2007391507","https://openalex.org/W2013013264","https://openalex.org/W2021974737","https://openalex.org/W2024717204","https://openalex.org/W2027193995","https://openalex.org/W2028109377","https://openalex.org/W2030349113","https://openalex.org/W2032034145","https://openalex.org/W2032667778","https://openalex.org/W2032741615","https://openalex.org/W2037092024","https://openalex.org/W2039513402","https://openalex.org/W2040353725","https://openalex.org/W2041902442","https://openalex.org/W2043334136","https://openalex.org/W2048275247","https://openalex.org/W2056390447","https://openalex.org/W2057711075","https://openalex.org/W2058989020","https://openalex.org/W2060924778","https://openalex.org/W2065010069","https://openalex.org/W2066147095","https://openalex.org/W2067648566","https://openalex.org/W2070351788","https://openalex.org/W2070691428","https://openalex.org/W2071466496","https://openalex.org/W2073646445","https://openalex.org/W2078823160","https://openalex.org/W2083209220","https://openalex.org/W2086297854","https://openalex.org/W2087002348","https://openalex.org/W2087920936","https://openalex.org/W2094704991","https://openalex.org/W2113023087","https://openalex.org/W2115890772","https://openalex.org/W2119391724","https://openalex.org/W2128216632","https://openalex.org/W2139131426","https://openalex.org/W2142666280","https://openalex.org/W2150901097","https://openalex.org/W2152652011","https://openalex.org/W2167107473","https://openalex.org/W2169597393","https://openalex.org/W2187636587","https://openalex.org/W2313064426","https://openalex.org/W2322419622","https://openalex.org/W2323178299","https://openalex.org/W2324196768","https://openalex.org/W2340547177","https://openalex.org/W2369574689","https://openalex.org/W2396922055","https://openalex.org/W2399798088","https://openalex.org/W2490792505","https://openalex.org/W2521794926","https://openalex.org/W2562705434","https://openalex.org/W2583304575","https://openalex.org/W2593064165","https://openalex.org/W2617632021","https://openalex.org/W2750807505","https://openalex.org/W2786771202","https://openalex.org/W2803736456","https://openalex.org/W2884781943","https://openalex.org/W2893257945","https://openalex.org/W2943271495","https://openalex.org/W2952971403","https://openalex.org/W2963341933","https://openalex.org/W2966277930","https://openalex.org/W2982006093","https://openalex.org/W3014141305","https://openalex.org/W3014824328","https://openalex.org/W3044568403","https://openalex.org/W3100403934","https://openalex.org/W3101109967","https://openalex.org/W3101844390","https://openalex.org/W3103638457","https://openalex.org/W3104424556","https://openalex.org/W3199435061","https://openalex.org/W4244319576"],"related_works":["https://openalex.org/W1040118206","https://openalex.org/W2391145968","https://openalex.org/W2361826783","https://openalex.org/W2067229394","https://openalex.org/W2016660140","https://openalex.org/W2054021433","https://openalex.org/W2354611255","https://openalex.org/W1591139189","https://openalex.org/W2032004148","https://openalex.org/W2333147276"],"abstract_inverted_index":{"We":[0,45,68,127,151],"study":[1],"\u201cnanoptera,\u201d":[2],"which":[3,98,162],"are":[4,25,62],"nonlocalized":[5],"solitary":[6,170,189],"waves":[7,190],"with":[8,20,42,109,208],"exponentially":[9,147],"small":[10,148],"but":[11,228],"nondecaying":[12,120],"oscillations,":[13],"in":[14,64,87,123,191],"two":[15,23,145,164],"singularly":[16,89],"perturbed":[17,90],"Hertzian":[18,34,40,135,193,206],"chains":[19,27,41,194],"precompression.":[21,196],"These":[22],"systems":[24,32],"woodpile":[26,91,125],"(which":[28],"we":[29,138],"model":[30],"as":[31,56],"of":[33,77,132,158,225,235],"particles":[35],"and":[36,38,54,137,178,200],"springs)":[37],"diatomic":[39,134,192,205],"alternating":[43],"masses.":[44],"demonstrate":[46,152],"that":[47,84,113,140,153,181,186,211,239],"nanoptera":[48],"arise":[49],"from":[50,71],"the":[51,65,78,102,119,218,236],"Stokes":[52,60,96],"phenomenon":[53],"appear":[55],"special":[57],"curves":[58],"(called":[59],"curves)":[61],"crossed":[63],"complex":[66],"plane.":[67],"use":[69],"techniques":[70],"exponential":[72,213],"asymptotics":[73],"to":[74,167,231,241],"obtain":[75],"approximations":[76],"oscillation":[79,219],"amplitudes.":[80],"Our":[81],"analysis":[82,131],"demonstrates":[83],"traveling-wave":[85],"solutions":[86],"a":[88,94,124,129,133,156,204,222],"chain":[92,207],"have":[93],"single":[95],"curve,":[97],"generates":[99],"oscillations":[100],"behind":[101],"wave":[103],"front.":[104],"Comparing":[105,197],"these":[106,163],"asymptotic":[107,115,199,214],"predictions":[108],"numerical":[110,179,201],"simulations":[111],"reveals":[112,210],"our":[114,198,212],"approximation":[116],"accurately":[117,216],"describes":[118],"oscillatory":[121,149],"behavior":[122],"chain.":[126],"perform":[128],"similar":[130],"chain,":[136],"show":[139],"each":[141],"nanopteron":[142],"solution":[143],"has":[144],"distinct":[146],"contributions.":[150],"there":[154,182],"exists":[155],"set":[157],"mass":[159,184,237],"ratios":[160,185],"for":[161,203,221],"contributions":[165],"cancel":[166],"produce":[168],"localized":[169,188,242],"waves.":[171],"This":[172],"result":[173],"builds":[174],"on":[175],"prior":[176],"experimental":[177],"observations":[180],"exist":[183],"support":[187],"without":[195],"results":[202],"precompression":[209],"approach":[215],"predicts":[217],"amplitude":[220],"wide":[223],"range":[224],"system":[226],"parameters,":[227],"it":[229],"fails":[230],"identify":[232],"several":[233],"values":[234],"ratio":[238],"correspond":[240],"solitary-wave":[243],"solutions.":[244]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
