{"id":"https://openalex.org/W1998776178","doi":"https://doi.org/10.1017/s0956792500000516","title":"Experimental and theoretical investigation of an equation of dendritic crystal growth","display_name":"Experimental and theoretical investigation of an equation of dendritic crystal growth","publication_year":1991,"publication_date":"1991-09-01","ids":{"openalex":"https://openalex.org/W1998776178","doi":"https://doi.org/10.1017/s0956792500000516","mag":"1998776178"},"language":"en","primary_location":{"id":"doi:10.1017/s0956792500000516","doi":"https://doi.org/10.1017/s0956792500000516","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0956792500000516","pdf_url":null,"source":{"id":"https://openalex.org/S8839896","display_name":"European Journal of Applied Mathematics","issn_l":"0956-7925","issn":["0956-7925","1469-4425"],"is_oa":false,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"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/A5113672476","display_name":"J. N. Dewynne","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J. N. Dewynne","raw_affiliation_strings":["Mathematics Faculty, Southampton University, Southampton SO9 5NH, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Faculty, Southampton University, Southampton SO9 5NH, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044626996","display_name":"F.N.H. Robinson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"F. N. H. Robinson","raw_affiliation_strings":["Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"3","first_page":"199","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.37380000948905945,"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"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.37380000948905945,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.3237000107765198,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.10599999874830246,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dendrite-growth","display_name":"dendritic growth","score":0.9860000014305115},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"equations of motion","score":0.3930000066757202},{"id":"https://openalex.org/keywords/dissipative-terms","display_name":"dissipative terms","score":0.8240000009536743},{"id":"https://openalex.org/keywords/periodic-solutions","display_name":"periodic solutions","score":0.6539999842643738},{"id":"https://openalex.org/keywords/harmonic-balance-method","display_name":"harmonic balance method","score":0.5479999780654907},{"id":"https://openalex.org/keywords/method-of-multiple-scales","display_name":"method of multiple scales","score":0.9330000281333923},{"id":"https://openalex.org/keywords/attractors","display_name":"attractors","score":0.3880000114440918},{"id":"https://openalex.org/keywords/nonlinear-dynamics","display_name":"nonlinear dynamics","score":0.33500000834465027}],"concepts":[{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.783223032951355},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.7710897326469421},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6666408777236938},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.48580336570739746},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.483309268951416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39001360535621643},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36986014246940613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35913586616516113},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.23241016268730164},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2253563404083252},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11581400036811829},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0956792500000516","doi":"https://doi.org/10.1017/s0956792500000516","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0956792500000516","pdf_url":null,"source":{"id":"https://openalex.org/S8839896","display_name":"European Journal of Applied Mathematics","issn_l":"0956-7925","issn":["0956-7925","1469-4425"],"is_oa":false,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-b","jufo-1","norway-1","oarl","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1481616730","https://openalex.org/W1968393164","https://openalex.org/W2033142051","https://openalex.org/W2033840645","https://openalex.org/W2078100674","https://openalex.org/W2089740930","https://openalex.org/W2089876099","https://openalex.org/W2517468947","https://openalex.org/W2739685101","https://openalex.org/W3016843226","https://openalex.org/W3041070869"],"related_works":["https://openalex.org/W2166097318","https://openalex.org/W2005931916","https://openalex.org/W3167571383","https://openalex.org/W7117248134","https://openalex.org/W2284334979","https://openalex.org/W2587263501","https://openalex.org/W1554253216","https://openalex.org/W1231420362","https://openalex.org/W2069217083","https://openalex.org/W6903806173"],"abstract_inverted_index":{"An":[0],"experimental":[1,57,101],"study":[2],"using":[3,86,125],"an":[4],"analogue":[5],"electronic":[6],"model":[7],"of":[8,22,73,81,89,107,112,128],"the":[9,20,46,66,79,87,100,113,126],"equation":[10],"x\u2034":[11],"+":[12],"x\u2032":[13],"=":[14,69],"\u0454":[15,35],"sin":[16],"x,":[17],"modified":[18],"by":[19,124],"addition":[21],"small":[23],"terms":[24,40],"ax\u2033":[25],"and":[26,92,110],"\u03b2x":[27],"with":[28,99],"0":[29],"<":[30,32],"\u03b2":[31],"\u03b1":[33],"\u226b":[34],"shows":[36],"that":[37],"these":[38],"dissipative":[39],"have":[41],"a":[42,61,82,104],"profound":[43],"effect":[44],"on":[45],"solutions":[47,58,121],"for":[48,103],"large":[49],"time.":[50],"If":[51],"\u2208":[52],"is":[53,122],"not":[54],"too":[55],"large,":[56],"tend":[59],"to":[60,96],"simple":[62,83],"periodic":[63,76,120],"form,":[64],"unlike":[65],"case":[67],"\u03b1=\u03b2":[68],"0.":[70],"The":[71,115],"existence":[72],"this":[74,93],"limiting":[75,119],"form":[77],"suggests":[78],"possibility":[80],"analytic":[84],"treatment":[85,94],"method":[88,127],"harmonic":[90],"balance,":[91],"leads":[95],"excellent":[97],"agreement":[98],"results":[102],"wide":[105],"range":[106],"initial":[108],"conditions":[109],"values":[111],"parameters.":[114],"approach":[116],"towards":[117],"attracting":[118],"analysed":[123],"multiple":[129],"scales.":[130]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}