{"id":"https://openalex.org/W1979918070","doi":"https://doi.org/10.1142/s0218127411028350","title":"ACOUSTIC RAY STABILITY FOR LONG-RANGE SOUND SPEED PROFILE TRANSITION SCENARIOS","display_name":"ACOUSTIC RAY STABILITY FOR LONG-RANGE SOUND SPEED PROFILE TRANSITION SCENARIOS","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1979918070","doi":"https://doi.org/10.1142/s0218127411028350","mag":"1979918070"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411028350","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028350","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5021460820","display_name":"Tam\u00e1s B\u00f3dai","orcid":"https://orcid.org/0000-0002-3049-107X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"TAM\u00c1S B\u00d3DAI","raw_affiliation_strings":["Green Ocean Energy Limited, Osborne House, 28 Carden Place, Aberdeen, AB10 1UP, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Green Ocean Energy Limited, Osborne House, 28 Carden Place, Aberdeen, AB10 1UP, UK","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024727666","display_name":"Marian Wiercigroch","orcid":"https://orcid.org/0000-0002-2706-9150"},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"MARIAN WIERCIGROCH","raw_affiliation_strings":["Centre for Applied Dynamics Research, School of Engineering, Kings College, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Applied Dynamics Research, School of Engineering, Kings College, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, UK","institution_ids":["https://openalex.org/I195460627"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2793,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61939809,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"01","first_page":"177","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11698","display_name":"Underwater Acoustics Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11698","display_name":"Underwater Acoustics Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"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/T11459","display_name":"Arctic and Antarctic ice dynamics","score":0.9973999857902527,"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/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quasistatic-process","display_name":"Quasistatic process","score":0.6513004899024963},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6489360332489014},{"id":"https://openalex.org/keywords/speed-of-sound","display_name":"Speed of sound","score":0.6428448557853699},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5625090599060059},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.5574672222137451},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5560457706451416},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5318721532821655},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5317505598068237},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4890657365322113},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.47817450761795044},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4693295359611511},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.43843764066696167},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.42675620317459106},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.36417847871780396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36020374298095703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35883629322052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2828202247619629},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20186331868171692},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.16209200024604797},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10131236910820007}],"concepts":[{"id":"https://openalex.org/C4708273","wikidata":"https://www.wikidata.org/wiki/Q900222","display_name":"Quasistatic process","level":2,"score":0.6513004899024963},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6489360332489014},{"id":"https://openalex.org/C200351514","wikidata":"https://www.wikidata.org/wiki/Q124003","display_name":"Speed of sound","level":2,"score":0.6428448557853699},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5625090599060059},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5574672222137451},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5560457706451416},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5318721532821655},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5317505598068237},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4890657365322113},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.47817450761795044},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4693295359611511},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.43843764066696167},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.42675620317459106},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.36417847871780396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36020374298095703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35883629322052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2828202247619629},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20186331868171692},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.16209200024604797},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10131236910820007},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127411028350","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028350","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8899999856948853}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320359","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W847839542","https://openalex.org/W937144718","https://openalex.org/W1496798092","https://openalex.org/W1510864383","https://openalex.org/W1964320077","https://openalex.org/W1964492337","https://openalex.org/W1968351646","https://openalex.org/W1968656950","https://openalex.org/W1985437019","https://openalex.org/W1988143666","https://openalex.org/W2003705331","https://openalex.org/W2007084925","https://openalex.org/W2018089264","https://openalex.org/W2029176179","https://openalex.org/W2031890315","https://openalex.org/W2036547145","https://openalex.org/W2047459555","https://openalex.org/W2049000326","https://openalex.org/W2051314738","https://openalex.org/W2080762500","https://openalex.org/W2093346900","https://openalex.org/W2104201352","https://openalex.org/W2121919769","https://openalex.org/W2129769146","https://openalex.org/W2129838748","https://openalex.org/W2171647245","https://openalex.org/W2488397002","https://openalex.org/W2567736332","https://openalex.org/W2953735919","https://openalex.org/W4214819286","https://openalex.org/W4238057673"],"related_works":["https://openalex.org/W2127887854","https://openalex.org/W2552606849","https://openalex.org/W15730607","https://openalex.org/W1982572960","https://openalex.org/W1516195074","https://openalex.org/W2085740305","https://openalex.org/W2370864161","https://openalex.org/W2898039612","https://openalex.org/W2162630464","https://openalex.org/W3214520723"],"abstract_inverted_index":{"Range-dependency":[0],"in":[1,54,64,70,81],"the":[2,49,55,71,82,88,95,106],"background":[3],"sound":[4,31],"speed":[5,32],"structure":[6],"for":[7,39,87],"deep":[8],"ocean":[9],"propagation":[10],"scenarios":[11],"is":[12,18,22,42,45,61],"typical.":[13],"Here":[14],"a":[15,23,78,91,98,109],"special":[16],"case":[17],"considered":[19],"when":[20],"there":[21],"gradual":[24],"transition":[25],"between":[26],"single":[27],"and":[28],"double":[29],"minimum":[30],"profiles.":[33],"Ray":[34],"stability,":[35],"an":[36,101],"important":[37],"measure":[38],"many":[40],"applications,":[41],"analyzed.":[43],"It":[44],"done":[46],"by":[47],"studying":[48],"unperturbed":[50],"autonomous":[51],"ray":[52,99],"equations":[53],"quasistatic":[56],"limit.":[57],"The":[58],"wave":[59,84],"guide":[60],"mapped":[62],"out":[63],"terms":[65],"of":[66,74,94,97,108],"constant":[67],"action":[68,96],"curves":[69],"vertical":[72],"plane":[73],"propagation,":[75],"which":[76],"reveals":[77],"bifurcation":[79],"effect":[80,102],"studied":[83],"guides.":[85],"Conditions":[86],"constancy":[89],"or":[90],"sudden":[92],"change":[93],"trajectory,":[100],"that":[103],"impacts":[104],"on":[105],"\"use\"":[107],"ray,":[110],"are":[111],"given.":[112]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}