{"id":"https://openalex.org/W3096294275","doi":"https://doi.org/10.1137/19m1307019","title":"Toroidal Vortex Filament Knots and Links: Existence, Stability and Dynamics","display_name":"Toroidal Vortex Filament Knots and Links: Existence, Stability and Dynamics","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3096294275","doi":"https://doi.org/10.1137/19m1307019","mag":"3096294275"},"language":"en","primary_location":{"id":"doi:10.1137/19m1307019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1307019","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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/A5015774352","display_name":"Th\u00e9odore Kolokolnikov","orcid":"https://orcid.org/0000-0002-7179-4325"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theodore Kolokolnikov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060684045","display_name":"Christopher Ticknor","orcid":"https://orcid.org/0000-0001-9972-4524"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chris Ticknor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054719860","display_name":"P. G. Kevrekidis","orcid":"https://orcid.org/0000-0002-7714-3689"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panayotis Kevrekidis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"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":0.12312512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"4","first_page":"2403","last_page":"2427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T12612","display_name":"Strong Light-Matter Interactions","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/toroid","display_name":"Toroid","score":0.8358650207519531},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7990376949310303},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.6854948401451111},{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.6475411653518677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6393851637840271},{"id":"https://openalex.org/keywords/protein-filament","display_name":"Protein filament","score":0.5304279327392578},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.5142821669578552},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.45852652192115784},{"id":"https://openalex.org/keywords/vortex-ring","display_name":"Vortex ring","score":0.4449288845062256},{"id":"https://openalex.org/keywords/twist","display_name":"Twist","score":0.43943536281585693},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4326602518558502},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.41989511251449585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40351590514183044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3491666316986084},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3465127944946289},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3316870927810669},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26056545972824097},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14054325222969055},{"id":"https://openalex.org/keywords/plasma","display_name":"Plasma","score":0.11329951882362366}],"concepts":[{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.8358650207519531},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7990376949310303},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.6854948401451111},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.6475411653518677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6393851637840271},{"id":"https://openalex.org/C14228908","wikidata":"https://www.wikidata.org/wiki/Q2920483","display_name":"Protein filament","level":2,"score":0.5304279327392578},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5142821669578552},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.45852652192115784},{"id":"https://openalex.org/C168475990","wikidata":"https://www.wikidata.org/wiki/Q1030571","display_name":"Vortex ring","level":3,"score":0.4449288845062256},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.43943536281585693},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4326602518558502},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.41989511251449585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40351590514183044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3491666316986084},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3465127944946289},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3316870927810669},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26056545972824097},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14054325222969055},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.11329951882362366},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1307019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1307019","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1946301069","https://openalex.org/W1986111505","https://openalex.org/W1986740750","https://openalex.org/W2003991760","https://openalex.org/W2012680925","https://openalex.org/W2028573294","https://openalex.org/W2030876368","https://openalex.org/W2049905703","https://openalex.org/W2053086469","https://openalex.org/W2060610526","https://openalex.org/W2065687171","https://openalex.org/W2068737563","https://openalex.org/W2091748216","https://openalex.org/W2107927762","https://openalex.org/W2108701202","https://openalex.org/W2111061190","https://openalex.org/W2111843081","https://openalex.org/W2118860521","https://openalex.org/W2133509236","https://openalex.org/W2150724445","https://openalex.org/W2153559928","https://openalex.org/W2154421583","https://openalex.org/W2154596449","https://openalex.org/W2166111281","https://openalex.org/W2176364383","https://openalex.org/W2214602817","https://openalex.org/W2222612219","https://openalex.org/W2273945324","https://openalex.org/W2281994713","https://openalex.org/W2316644885","https://openalex.org/W2342363147","https://openalex.org/W2342970744","https://openalex.org/W2619721235","https://openalex.org/W2770006776","https://openalex.org/W2783371810","https://openalex.org/W2791310229","https://openalex.org/W2809706169","https://openalex.org/W2912253299","https://openalex.org/W2919995148","https://openalex.org/W2952783912","https://openalex.org/W2963409875","https://openalex.org/W2963890672","https://openalex.org/W2964275983","https://openalex.org/W3098789577","https://openalex.org/W3099071241","https://openalex.org/W3101076207","https://openalex.org/W3103631081","https://openalex.org/W3104441364","https://openalex.org/W3121703172","https://openalex.org/W3124784800","https://openalex.org/W4234274421"],"related_works":["https://openalex.org/W2116932386","https://openalex.org/W2136809508","https://openalex.org/W1610769317","https://openalex.org/W2113101158","https://openalex.org/W2113978471","https://openalex.org/W6624980","https://openalex.org/W2903571211","https://openalex.org/W1970443200","https://openalex.org/W4318001898","https://openalex.org/W1982391239"],"abstract_inverted_index":{"Using":[0],"the":[1,52,138,142,153,159,162],"Klein--Majda--Damodaran":[2,139],"model":[3,140],"of":[4,30,38,70,80],"nearly":[5],"parallel":[6],"vortex":[7,11,31],"filaments,":[8],"we":[9,55],"construct":[10],"knots":[12],"and":[13,22,42,67,95,113,124,161],"links":[14,66],"on":[15,99],"a":[16,27,35,71,78,92,100],"torus":[17],"involving":[18],"periodic":[19],"boundary":[20],"conditions":[21],"analyze":[23],"their":[24,40,60],"stability.":[25],"For":[26],"special":[28],"class":[29],"knots---toroidal":[32],"knots---we":[33],"give":[34],"full":[36,143],"characterization":[37],"both":[39],"energetic":[41],"dynamical":[43],"stabilities.":[44],"In":[45,102],"addition":[46,103],"to":[47,104,116,136,151],"providing":[48],"explicit":[49,57],"expressions":[50],"for":[51,59,120,128],"relevant":[53],"waveforms,":[54],"derive":[56],"formulas":[58],"stability":[61],"boundaries.":[62],"These":[63],"include":[64],"simple":[65],"different":[68],"realizations":[69],"trefoil":[72],"knot.":[73],"It":[74],"is":[75],"shown":[76],"that":[77],"ring":[79],"more":[81],"than":[82],"7":[83],"filaments":[84,98],"can":[85],"potentially":[86],"be":[87,117],"stablized":[88],"by":[89],"giving":[90],"it":[91],"slight":[93],"twist":[94],"connecting":[96],"neighboring":[97],"torus.":[101],"rings,":[105],"(helical)":[106],"filament":[107],"lattice":[108],"configurations":[109],"are":[110,114,134,166],"also":[111,125,167],"considered":[112],"found":[115],"dynamically":[118],"stable":[119,127],"all":[121],"rotation":[122],"frequencies":[123],"energetically":[126],"sufficiently":[129],"fast":[130],"rotations.":[131],"Numerical":[132],"simulations":[133],"used":[135],"compare":[137],"with":[141],"three-dimensional":[144],"(3D)":[145],"Gross--Pitaevskii":[146],"equations":[147],"as":[148,150],"well":[149],"confirm":[152],"analytical":[154],"theory.":[155],"Potential":[156],"differences":[157],"between":[158],"quasi-one-dimensional":[160],"fully":[163],"3D":[164],"description":[165],"discussed.":[168]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
