{"id":"https://openalex.org/W3041219455","doi":"https://doi.org/10.3390/sym12071155","title":"Numerical Simulation of Dendritic Pattern Formation in an Isotropic Crystal Growth Model on Curved Surfaces","display_name":"Numerical Simulation of Dendritic Pattern Formation in an Isotropic Crystal Growth Model on Curved Surfaces","publication_year":2020,"publication_date":"2020-07-11","ids":{"openalex":"https://openalex.org/W3041219455","doi":"https://doi.org/10.3390/sym12071155","mag":"3041219455"},"language":"en","primary_location":{"id":"doi:10.3390/sym12071155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071155","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1155/pdf?version=1595173853","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/7/1155/pdf?version=1595173853","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068886926","display_name":"Sungha Yoon","orcid":"https://orcid.org/0000-0002-9122-1612"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sungha Yoon","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032971929","display_name":"Jintae Park","orcid":"https://orcid.org/0000-0002-3648-2967"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jintae Park","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100370326","display_name":"Jian Wang","orcid":"https://orcid.org/0000-0001-5130-300X"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101566848","display_name":"Chaeyoung Lee","orcid":"https://orcid.org/0000-0002-1120-2455"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Chaeyoung Lee","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Korea"],"raw_orcid":"https://orcid.org/0000-0002-1120-2455","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100698865","display_name":"Junseok Kim","orcid":"https://orcid.org/0000-0002-0484-9189"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Junseok Kim","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Korea"],"raw_orcid":"https://orcid.org/0000-0002-0484-9189","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100698865"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5701,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.60303285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"12","issue":"7","first_page":"1155","last_page":"1155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9997000098228455,"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":0.9997000098228455,"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/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/discretization","display_name":"Discretization","score":0.5948813557624817},{"id":"https://openalex.org/keywords/computer-simulation","display_name":"Computer simulation","score":0.5586442351341248},{"id":"https://openalex.org/keywords/fuselage","display_name":"Fuselage","score":0.5281386971473694},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5040084719657898},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.49933552742004395},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.45933830738067627},{"id":"https://openalex.org/keywords/dendrite","display_name":"Dendrite (mathematics)","score":0.4326099157333374},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.40470778942108154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3288804292678833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3125898838043213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2985115647315979},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22760829329490662},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.17599982023239136},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13915923237800598},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.09248948097229004}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5948813557624817},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.5586442351341248},{"id":"https://openalex.org/C113556839","wikidata":"https://www.wikidata.org/wiki/Q1110579","display_name":"Fuselage","level":2,"score":0.5281386971473694},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5040084719657898},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.49933552742004395},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.45933830738067627},{"id":"https://openalex.org/C84248122","wikidata":"https://www.wikidata.org/wiki/Q5256671","display_name":"Dendrite (mathematics)","level":2,"score":0.4326099157333374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.40470778942108154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3288804292678833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3125898838043213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2985115647315979},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22760829329490662},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.17599982023239136},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13915923237800598},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.09248948097229004},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12071155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071155","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1155/pdf?version=1595173853","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9d3722cc58c8459db96ea06300e94efd","is_oa":true,"landing_page_url":"https://doaj.org/article/9d3722cc58c8459db96ea06300e94efd","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 7, p 1155 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/7/1155/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12071155","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12071155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071155","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1155/pdf?version=1595173853","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2726159061","display_name":null,"funder_award_id":"201808260026","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G6542542020","display_name":null,"funder_award_id":"2019R1A6A3A13094308","funder_id":"https://openalex.org/F4320311687","funder_display_name":"Ministry of Education"}],"funders":[{"id":"https://openalex.org/F4320311687","display_name":"Ministry of Education","ror":"https://ror.org/03m01yf64"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3041219455.pdf","grobid_xml":"https://content.openalex.org/works/W3041219455.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1562896382","https://openalex.org/W1626653188","https://openalex.org/W1964716185","https://openalex.org/W1977032047","https://openalex.org/W1991076983","https://openalex.org/W2004073007","https://openalex.org/W2010014688","https://openalex.org/W2010982693","https://openalex.org/W2092886188","https://openalex.org/W2111628784","https://openalex.org/W2135073078","https://openalex.org/W2283269714","https://openalex.org/W2316888830","https://openalex.org/W2530980628","https://openalex.org/W2542505516","https://openalex.org/W2550726378","https://openalex.org/W2804973738","https://openalex.org/W2806693976","https://openalex.org/W2808039348","https://openalex.org/W2890217004","https://openalex.org/W2900798261","https://openalex.org/W2910738463","https://openalex.org/W2926865354","https://openalex.org/W2949037765","https://openalex.org/W2964381117","https://openalex.org/W2972626412"],"related_works":["https://openalex.org/W4248245130","https://openalex.org/W1527563262","https://openalex.org/W1966616960","https://openalex.org/W4312554538","https://openalex.org/W1982444000","https://openalex.org/W3130756715","https://openalex.org/W2039210922","https://openalex.org/W4312342900","https://openalex.org/W2058313026","https://openalex.org/W3121468381"],"abstract_inverted_index":{"In":[0,88],"this":[1,138],"paper,":[2],"we":[3,118,136],"present":[4],"several":[5,120],"numerical":[6,121,143],"simulation":[7,93,144],"results":[8,94],"of":[9,130,140],"dendritic":[10,83],"pattern":[11],"formation":[12],"using":[13],"an":[14],"isotropic":[15],"crystal":[16,91],"growth":[17,84,92,115],"model,":[18],"which":[19,43],"is":[20,32,59],"based":[21],"on":[22,25,67,71,85,95,132,145],"phase-field":[23],"modeling,":[24],"curved":[26,101],"surfaces.":[27,87,134,147],"An":[28],"explicit":[29],"time-stepping":[30],"method":[31,38,80],"used":[33],"and":[34,77],"the":[35,40,45,52,78,109],"direct":[36],"computing":[37],"to":[39,107,112,124,142],"Laplace\u2013Beltrami":[41],"operator,":[42],"employs":[44],"point":[46],"centered":[47],"triangulation":[48],"approximating":[49],"Laplacian":[50],"over":[51],"discretized":[53],"surface":[54],"with":[55,74],"a":[56,126],"triangular":[57],"mesh,":[58],"adopted.":[60],"Numerical":[61],"simulations":[62],"are":[63,103],"performed":[64],"not":[65],"only":[66],"simple":[68,133],"but":[69],"also":[70],"complex":[72,86,146],"surfaces":[73,102],"various":[75],"curvatures,":[76],"proposed":[79],"can":[81],"simulate":[82],"particular,":[89],"ice":[90],"aircraft":[96],"fuselage":[97],"or":[98],"metal":[99],"bell-shaped":[100],"provided":[104],"in":[105],"order":[106],"demonstrate":[108],"practical":[110],"relevance":[111],"our":[113],"dendrite":[114],"model.":[116],"Furthermore,":[117],"perform":[119],"parameter":[122],"tests":[123],"obtain":[125],"best":[127],"fitted":[128],"set":[129,139],"parameters":[131,141],"Finally,":[135],"apply":[137]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}