{"id":"https://openalex.org/W2594179311","doi":"https://doi.org/10.1137/060656711","title":"Boundary\u2010Roughness Effects in Nematic Liquid Crystals","display_name":"Boundary\u2010Roughness Effects in Nematic Liquid Crystals","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2594179311","doi":"https://doi.org/10.1137/060656711","mag":"2594179311"},"language":"en","primary_location":{"id":"doi:10.1137/060656711","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060656711","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/A5069257948","display_name":"Paolo Biscari","orcid":"https://orcid.org/0000-0001-9299-6340"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Biscari","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030749427","display_name":"Stefano Turzi","orcid":"https://orcid.org/0000-0003-1245-3800"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Turzi","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":0.1813,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.54654965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"2","first_page":"447","last_page":"463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"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/T10306","display_name":"Liquid Crystal Research Advancements","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/liquid-crystal","display_name":"Liquid crystal","score":0.8717008233070374},{"id":"https://openalex.org/keywords/anchoring","display_name":"Anchoring","score":0.7354037761688232},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.7219316363334656},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.6612316966056824},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5582408905029297},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5309005975723267},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.5232987999916077},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.515491783618927},{"id":"https://openalex.org/keywords/tilt","display_name":"Tilt (camera)","score":0.5142800211906433},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5071313381195068},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.49276331067085266},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4574517607688904},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.40493321418762207},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.35220569372177124},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32256096601486206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21430659294128418},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18932035565376282}],"concepts":[{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.8717008233070374},{"id":"https://openalex.org/C18483071","wikidata":"https://www.wikidata.org/wiki/Q168432","display_name":"Anchoring","level":2,"score":0.7354037761688232},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.7219316363334656},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.6612316966056824},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5582408905029297},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5309005975723267},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.5232987999916077},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.515491783618927},{"id":"https://openalex.org/C2779844322","wikidata":"https://www.wikidata.org/wiki/Q2919140","display_name":"Tilt (camera)","level":2,"score":0.5142800211906433},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5071313381195068},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.49276331067085266},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4574517607688904},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.40493321418762207},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.35220569372177124},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32256096601486206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21430659294128418},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18932035565376282},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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":2,"locations":[{"id":"doi:10.1137/060656711","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060656711","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"},{"id":"pmh:oai:re.public.polimi.it:11311/552386","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/552386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.44999998807907104,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1547666981","https://openalex.org/W1579689348","https://openalex.org/W1595032093","https://openalex.org/W1600845614","https://openalex.org/W1657347807","https://openalex.org/W1972893601","https://openalex.org/W1973015446","https://openalex.org/W1977290919","https://openalex.org/W1978143610","https://openalex.org/W1983538842","https://openalex.org/W1983592130","https://openalex.org/W1985099834","https://openalex.org/W1986811768","https://openalex.org/W2006323578","https://openalex.org/W2014354725","https://openalex.org/W2016295415","https://openalex.org/W2018423786","https://openalex.org/W2024880000","https://openalex.org/W2024888583","https://openalex.org/W2030193543","https://openalex.org/W2035837671","https://openalex.org/W2048399166","https://openalex.org/W2052060375","https://openalex.org/W2055777092","https://openalex.org/W2064075386","https://openalex.org/W2064097274","https://openalex.org/W2065355206","https://openalex.org/W2071991233","https://openalex.org/W2078783586","https://openalex.org/W2080560411","https://openalex.org/W2092269985","https://openalex.org/W2108489387","https://openalex.org/W2136216669","https://openalex.org/W3102511473"],"related_works":["https://openalex.org/W2978614239","https://openalex.org/W4313425019","https://openalex.org/W2071637480","https://openalex.org/W1972893601","https://openalex.org/W4247655891","https://openalex.org/W1965151300","https://openalex.org/W2001926133","https://openalex.org/W2065836647","https://openalex.org/W2009004747","https://openalex.org/W3132999871"],"abstract_inverted_index":{"We":[0,86,101],"study":[1],"the":[2,18,25,33,46,50,53,57,63,89,97,104,109,114,139],"equilibrium":[3],"configuration":[4],"of":[5,17,27,49,60,80,116,141],"a":[6,12,21,37,71],"nematic":[7,58],"liquid":[8],"crystal":[9],"bounded":[10],"by":[11,108],"rough":[13],"surface.":[14],"The":[15],"wrinkling":[16],"surface":[19,91],"induces":[20],"partial":[22],"melting":[23],"in":[24,78],"degree":[26,59,115,140],"orientation.":[28,117],"This":[29],"softened":[30],"region":[31],"penetrates":[32],"bulk":[34],"up":[35],"to":[36,43,70,96,135],"length":[38,93],"scale":[39],"which":[40,74],"turns":[41],"out":[42],"coincide":[44],"with":[45,144],"characteristic":[47],"wavelength":[48],"corrugation.":[51],"Within":[52],"boundary":[54,110],"layer":[55],"where":[56],"orientation":[61,142],"decreases,":[62],"tilt":[64],"angle":[65],"steepens":[66],"and":[67],"gives":[68],"rise":[69],"nontrivial":[72],"structure,":[73],"may":[75,132],"be":[76,133],"interpreted":[77],"terms":[79],"an":[81,145],"effective":[82,90],"weak":[83],"anchoring":[84,99],"potential.":[85],"determine":[87],"how":[88,138],"extrapolation":[92],"is":[94],"related":[95],"microscopic":[98],"parameters.":[100],"also":[102],"analyze":[103],"crucial":[105],"role":[106],"played":[107],"conditions":[111],"assumed":[112],"on":[113,123],"Quite":[118],"different":[119],"features":[120,131],"emerge":[121],"depending":[122],"whether":[124],"they":[125],"are":[126],"Neumann\u2010":[127],"or":[128],"Dirichlet\u2010like.":[129],"These":[130],"useful":[134],"ascertain":[136],"experimentally":[137],"interacts":[143],"external":[146],"boundary.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
