{"id":"https://openalex.org/W7167790482","doi":"https://doi.org/10.1137/25m1753152","title":"Self-Assembly of Triblock Copolymers Under Soft Confinement: Solution Landscape, Bifurcation Diagram,\u00a0and Heatmap","display_name":"Self-Assembly of Triblock Copolymers Under Soft Confinement: Solution Landscape, Bifurcation Diagram,\u00a0and Heatmap","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W7167790482","doi":"https://doi.org/10.1137/25m1753152"},"language":"en","primary_location":{"id":"doi:10.1137/25m1753152","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1753152","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","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/A5137331800","display_name":"LongJing Li","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longjing Li","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0009-0000-0869-5511","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People\u2019s Republic of China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068462779","display_name":"Guanghua Ji","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghua Ji","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0001-9157-025X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People\u2019s Republic of China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103206674","display_name":"Zhen Yuan Xu","orcid":"https://orcid.org/0000-0001-9357-5409"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Xu","raw_affiliation_strings":["Corresponding author. School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100124, China"],"raw_orcid":"https://orcid.org/0000-0001-9357-5409","affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100124, China","institution_ids":["https://openalex.org/I37796252","https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.75245126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"86","issue":"4","first_page":"1609","last_page":"1631"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11471","display_name":"Block Copolymer Self-Assembly","score":0.9728999733924866,"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/T11471","display_name":"Block Copolymer Self-Assembly","score":0.9728999733924866,"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/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10405","display_name":"Advanced Polymer Synthesis and Characterization","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7932999730110168},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5393999814987183},{"id":"https://openalex.org/keywords/copolymer","display_name":"Copolymer","score":0.5203999876976013},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.507099986076355},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5008000135421753},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4255000054836273},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.414000004529953},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.38350000977516174},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.3686999976634979}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7932999730110168},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5871999859809875},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C15920480","wikidata":"https://www.wikidata.org/wiki/Q421281","display_name":"Copolymer","level":3,"score":0.5203999876976013},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.507099986076355},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5008000135421753},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.38350000977516174},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36079999804496765},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.36010000109672546},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3244999945163727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32249999046325684},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.31850001215934753},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C521977710","wikidata":"https://www.wikidata.org/wiki/Q81163","display_name":"Polymer","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C45594756","wikidata":"https://www.wikidata.org/wiki/Q5282784","display_name":"Dissipative particle dynamics","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C196503311","wikidata":"https://www.wikidata.org/wiki/Q145623","display_name":"Molar mass","level":3,"score":0.26829999685287476},{"id":"https://openalex.org/C155673373","wikidata":"https://www.wikidata.org/wiki/Q1648886","display_name":"Structural stability","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C59593255","wikidata":"https://www.wikidata.org/wiki/Q901663","display_name":"Molecular dynamics","level":2,"score":0.25529998540878296}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/25m1753152","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1753152","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5185680389404297}],"awards":[{"id":"https://openalex.org/G4794130641","display_name":null,"funder_award_id":"12471363","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7340443643","display_name":null,"funder_award_id":"12201021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W655790194","https://openalex.org/W1511572470","https://openalex.org/W1601132577","https://openalex.org/W1967424713","https://openalex.org/W1967676806","https://openalex.org/W1978713033","https://openalex.org/W1986614779","https://openalex.org/W1988720110","https://openalex.org/W1999513324","https://openalex.org/W2004751437","https://openalex.org/W2011095781","https://openalex.org/W2020559913","https://openalex.org/W2051142108","https://openalex.org/W2063867437","https://openalex.org/W2065376268","https://openalex.org/W2079563227","https://openalex.org/W2086147404","https://openalex.org/W2095436347","https://openalex.org/W2113404900","https://openalex.org/W2159603314","https://openalex.org/W2167035284","https://openalex.org/W2172949807","https://openalex.org/W2282959781","https://openalex.org/W2313368352","https://openalex.org/W2331044883","https://openalex.org/W2966076368","https://openalex.org/W2975220792","https://openalex.org/W2983275660","https://openalex.org/W2999060662","https://openalex.org/W3008343542","https://openalex.org/W3011861497","https://openalex.org/W3045682917","https://openalex.org/W3110042095","https://openalex.org/W3123799039","https://openalex.org/W3213118245","https://openalex.org/W4213199372","https://openalex.org/W4230344563","https://openalex.org/W4297998095","https://openalex.org/W4309002127","https://openalex.org/W4319786844","https://openalex.org/W4362519055","https://openalex.org/W4362659078","https://openalex.org/W4383067194","https://openalex.org/W4388252586","https://openalex.org/W4395673297","https://openalex.org/W4406039582"],"related_works":[],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"investigate":[2],"the":[3,41,46,66,110,116,131,137,141],"self-assembly":[4],"of":[5,45,74,112,118,133,140],"triblock":[6,14],"copolymers":[7],"under":[8],"soft":[9],"confinement":[10],"with":[11,23,121],"a":[12,31,58,72,122],"multicomponent":[13],"homopolymer-copolymer":[15],"(THC)":[16],"model.":[17,68],"To":[18],"address":[19],"computational":[20],"challenges":[21],"associated":[22],"multiple":[24],"components":[25],"and":[26,39,61,91,101,115],"mass":[27],"conservation,":[28],"we":[29,53,70,108,126],"develop":[30],"novel":[32,103],"accelerated":[33],"projection":[34],"saddle":[35],"dynamics":[36],"(A-PSD)":[37],"method":[38],"prove":[40],"linear":[42],"stability":[43],"theory":[44],"continuous":[47],"A-PSD":[48],"rigorously.":[49],"With":[50],"this":[51],"algorithm,":[52],"numerically":[54],"construct":[55],"solution":[56],"landscapes,":[57],"bifurcation":[59,123],"diagram,":[60],"heatmaps":[62,128],"to":[63,129],"systematically":[64],"study":[65],"THC":[67],"First,":[69],"derive":[71],"multitude":[73],"extreme":[75],"points,":[76],"which":[77],"can":[78],"be":[79],"categorized":[80],"into":[81],"several":[82],"classes,":[83],"including":[84],"Layer":[85],"class,":[86,88],"Flower":[87],"Circle":[89],"class":[90],"Core-Shell":[92],"class.":[93],"The":[94],"connections":[95],"between":[96],"these":[97],"classes":[98],"are":[99,105],"established":[100],"some":[102],"structures":[104],"observed.":[106],"Next,":[107],"illustrate":[109],"emergence":[111],"critical":[113],"points":[114],"impact":[117,132],"domain":[119],"size":[120],"diagram.":[124],"Finally,":[125],"employ":[127],"visualize":[130],"volume":[134],"fractions":[135],"on":[136],"morphological":[138],"behavior":[139],"system.":[142]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-07-10T00:00:00"}