{"id":"https://openalex.org/W2058660613","doi":"https://doi.org/10.1137/110849687","title":"Discrete and Continuum Relaxation Dynamics of Faceted Crystal Surface in Evaporation Models","display_name":"Discrete and Continuum Relaxation Dynamics of Faceted Crystal Surface in Evaporation Models","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2058660613","doi":"https://doi.org/10.1137/110849687","mag":"2058660613"},"language":"en","primary_location":{"id":"doi:10.1137/110849687","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110849687","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 &amp; Simulation","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/A5084889375","display_name":"Kanna Nakamura","orcid":"https://orcid.org/0009-0003-7051-9705"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kanna Nakamura","raw_affiliation_strings":["Department of Mathematics, University of Maryland, College Park, MD 20742-4015"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Maryland, College Park, MD 20742-4015","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051899167","display_name":"Dionisios Margetis","orcid":"https://orcid.org/0000-0001-9058-502X"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dionisios Margetis","raw_affiliation_strings":["Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742-4015"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742-4015","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084889375"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":0.2445,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57657356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"1","first_page":"244","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.996999979019165,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.996999979019165,"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/T10402","display_name":"Phase Equilibria and Thermodynamics","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10474","display_name":"Material Dynamics and Properties","score":0.9937000274658203,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5036632418632507},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4880301058292389},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4630363881587982},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3981863558292389},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36738622188568115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35309725999832153},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3214508593082428}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5036632418632507},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4880301058292389},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4630363881587982},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3981863558292389},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36738622188568115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35309725999832153},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3214508593082428}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110849687","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110849687","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 &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.259.8689","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.259.8689","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cscamm.umd.edu/publications/Nakamura-Margetis-MMS-_CS-12-12.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.87","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.87","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-users.math.umd.edu/%7Edio/Nakamura-Margetis-Evap_Facet.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.5,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G7911934013","display_name":"CAREER: Thermodynamic and kinetic approaches for epitaxial material systems","funder_award_id":"0847587","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W42072607","https://openalex.org/W89907685","https://openalex.org/W91764347","https://openalex.org/W390897399","https://openalex.org/W1020649356","https://openalex.org/W1515555908","https://openalex.org/W1547666981","https://openalex.org/W1548377147","https://openalex.org/W1578478808","https://openalex.org/W1601100443","https://openalex.org/W1605771617","https://openalex.org/W1965571863","https://openalex.org/W1965691857","https://openalex.org/W1966539836","https://openalex.org/W1968253930","https://openalex.org/W1977578154","https://openalex.org/W1981479913","https://openalex.org/W1987639561","https://openalex.org/W1987867371","https://openalex.org/W1993917000","https://openalex.org/W2014523663","https://openalex.org/W2020168202","https://openalex.org/W2024233310","https://openalex.org/W2029928672","https://openalex.org/W2034976587","https://openalex.org/W2036841093","https://openalex.org/W2048976031","https://openalex.org/W2053247976","https://openalex.org/W2057391982","https://openalex.org/W2060073240","https://openalex.org/W2060814680","https://openalex.org/W2063324480","https://openalex.org/W2067265108","https://openalex.org/W2068728923","https://openalex.org/W2069792251","https://openalex.org/W2072599949","https://openalex.org/W2075139044","https://openalex.org/W2077550649","https://openalex.org/W2078022532","https://openalex.org/W2081338783","https://openalex.org/W2082068401","https://openalex.org/W2089076027","https://openalex.org/W2089133017","https://openalex.org/W2099302759","https://openalex.org/W2101950721","https://openalex.org/W2155315887","https://openalex.org/W2430365524","https://openalex.org/W2481493153","https://openalex.org/W3035721348","https://openalex.org/W3081913446","https://openalex.org/W3092667176","https://openalex.org/W3141151088","https://openalex.org/W4240139632","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4249341887","https://openalex.org/W3095645108","https://openalex.org/W1603681120","https://openalex.org/W2379016242","https://openalex.org/W585736820","https://openalex.org/W1998200799","https://openalex.org/W2051519054","https://openalex.org/W2488633177","https://openalex.org/W2043702156","https://openalex.org/W2352708639"],"abstract_inverted_index":{"We":[0,69,191],"study":[1,186],"linkages":[2],"of":[3,9,27,52,62,137,142,195,204,207,216],"two":[4,72],"scales":[5],"in":[6,16,91,115,134],"the":[7,25,39,42,44,50,53,66,81,88,95,130,143,167,188,193,196,205,212],"relaxation":[8],"an":[10,100],"axisymmetric":[11],"crystal":[12],"with":[13,38,125,159],"a":[14,121,155,160,178,217],"facet":[15,131,197],"evaporation-condensation":[17],"kinetics.":[18],"The":[19],"macroscale":[20],"evolution":[21],"is":[22,47,84,97],"driven":[23],"by":[24,99],"motion":[26],"concentric":[28],"circular,":[29],"repulsively":[30],"interacting":[31],"line":[32],"defects":[33],"(steps)":[34],"which":[35,184],"exchange":[36],"atoms":[37],"vapor.":[40],"At":[41,166],"microscale,":[43],"step":[45,55,67,73,170],"velocity":[46],"proportional":[48,86],"to":[49,59,87,174,211],"variation":[51],"total":[54],"free":[56],"energy,":[57],"leading":[58],"large":[60],"systems":[61],"differential":[63,182],"equations":[64],"for":[65,163,177],"radii.":[68],"focus":[70],"on":[71],"flow":[74],"models.":[75],"In":[76],"one":[77],"model":[78,93],"(called":[79],"M1)":[80],"discrete":[82,117,209],"mobility":[83,96],"simply":[85],"upper-terrace":[89],"width;":[90],"another":[92],"(M2)":[94],"altered":[98],"extra":[101],"geometric":[102],"factor.":[103],"By":[104],"invoking":[105],"self-similarity":[106],"at":[107,129],"long":[108],"time,":[109],"we":[110,185],"numerically":[111],"demonstrate":[112],"that":[113],"(i)":[114],"M1,":[116],"slopes":[118],"follow":[119],"closely":[120],"continuum":[122,145,156],"thermodynamics":[123],"approach":[124],"\u201cnatural":[126],"boundary":[127,157],"conditions\u201d":[128],"edge;":[132],"(ii)":[133],"contrast,":[135],"predictions":[136],"M2":[138],"deviate":[139],"from":[140],"results":[141],"above":[144],"approach;":[146],"and":[147,201],"(iii)":[148],"this":[149],"discrepancy":[150],"can":[151],"be":[152],"eliminated":[153],"via":[154,187],"condition":[158],"geometry-induced":[161],"jump":[162],"top-step":[164],"collapses.":[165],"macroscale,":[168],"both":[169],"models":[171],"give":[172],"rise":[173],"free-boundary":[175],"problems":[176],"second-order,":[179],"parabolic":[180],"partial":[181],"equation,":[183],"subgradient":[189],"formalism.":[190],"discuss":[192],"interpretation":[194],"height":[198],"as":[199],"shock":[200],"prove":[202],"convergence":[203],"solution":[206,215],"each":[208],"scheme":[210],"(weak)":[213],"entropy":[214],"conservation":[218],"law":[219],"if":[220],"steps":[221],"do":[222],"not":[223],"interact.":[224]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
