{"id":"https://openalex.org/W2092257181","doi":"https://doi.org/10.1137/s0036139996304081","title":"An Analytic Solution for Low-Frequency Scattering by Two Soft Spheres","display_name":"An Analytic Solution for Low-Frequency Scattering by Two Soft Spheres","publication_year":1998,"publication_date":"1998-04-01","ids":{"openalex":"https://openalex.org/W2092257181","doi":"https://doi.org/10.1137/s0036139996304081","mag":"2092257181"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139996304081","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996304081","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/A5021443418","display_name":"Antonios Charalambopoulos","orcid":"https://orcid.org/0000-0002-9505-0830"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Charalambopoulos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057085378","display_name":"George Dassios","orcid":"https://orcid.org/0000-0002-1738-1693"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Dassios","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041569942","display_name":"\u039caria Hadjinicolaou","orcid":"https://orcid.org/0000-0002-6055-5775"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Hadjinicolaou","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021443418"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.695,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.69780088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"2","first_page":"370","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11757","display_name":"Seismic Waves and Analysis","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"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/T11757","display_name":"Seismic Waves and Analysis","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"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/T11312","display_name":"Soil Moisture and Remote Sensing","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11698","display_name":"Underwater Acoustics Research","score":0.9836000204086304,"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/rayleigh-scattering","display_name":"Rayleigh scattering","score":0.6908954381942749},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.6845459938049316},{"id":"https://openalex.org/keywords/scattering-amplitude","display_name":"Scattering amplitude","score":0.6569987535476685},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.6182208061218262},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6144105195999146},{"id":"https://openalex.org/keywords/discrete-dipole-approximation","display_name":"Discrete dipole approximation","score":0.5630021095275879},{"id":"https://openalex.org/keywords/scattering-length","display_name":"Scattering length","score":0.5069451332092285},{"id":"https://openalex.org/keywords/codes-for-electromagnetic-scattering-by-spheres","display_name":"Codes for electromagnetic scattering by spheres","score":0.49449488520622253},{"id":"https://openalex.org/keywords/dipole","display_name":"Dipole","score":0.49294447898864746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.491534560918808},{"id":"https://openalex.org/keywords/optical-theorem","display_name":"Optical theorem","score":0.4750423729419708},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.46815088391304016},{"id":"https://openalex.org/keywords/cross-section","display_name":"Cross section (physics)","score":0.4378509819507599},{"id":"https://openalex.org/keywords/magnetic-monopole","display_name":"Magnetic monopole","score":0.4329715967178345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35156238079071045},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.34388744831085205},{"id":"https://openalex.org/keywords/light-scattering","display_name":"Light scattering","score":0.2313160002231598},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21616774797439575},{"id":"https://openalex.org/keywords/mie-scattering","display_name":"Mie scattering","score":0.1255563199520111}],"concepts":[{"id":"https://openalex.org/C46244369","wikidata":"https://www.wikidata.org/wiki/Q193709","display_name":"Rayleigh scattering","level":2,"score":0.6908954381942749},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.6845459938049316},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.6569987535476685},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6182208061218262},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6144105195999146},{"id":"https://openalex.org/C49874194","wikidata":"https://www.wikidata.org/wiki/Q5282045","display_name":"Discrete dipole approximation","level":3,"score":0.5630021095275879},{"id":"https://openalex.org/C37196565","wikidata":"https://www.wikidata.org/wiki/Q4118602","display_name":"Scattering length","level":3,"score":0.5069451332092285},{"id":"https://openalex.org/C173225287","wikidata":"https://www.wikidata.org/wiki/Q5140168","display_name":"Codes for electromagnetic scattering by spheres","level":5,"score":0.49449488520622253},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.49294447898864746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.491534560918808},{"id":"https://openalex.org/C115710402","wikidata":"https://www.wikidata.org/wiki/Q1136262","display_name":"Optical theorem","level":4,"score":0.4750423729419708},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.46815088391304016},{"id":"https://openalex.org/C52234038","wikidata":"https://www.wikidata.org/wiki/Q17128025","display_name":"Cross section (physics)","level":2,"score":0.4378509819507599},{"id":"https://openalex.org/C149298590","wikidata":"https://www.wikidata.org/wiki/Q219708","display_name":"Magnetic monopole","level":2,"score":0.4329715967178345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35156238079071045},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34388744831085205},{"id":"https://openalex.org/C120456961","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Light scattering","level":3,"score":0.2313160002231598},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21616774797439575},{"id":"https://openalex.org/C63688654","wikidata":"https://www.wikidata.org/wiki/Q901737","display_name":"Mie scattering","level":4,"score":0.1255563199520111},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139996304081","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139996304081","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1517670975","https://openalex.org/W1523113578","https://openalex.org/W1573761753","https://openalex.org/W1971318657","https://openalex.org/W2069938029","https://openalex.org/W2072907579"],"related_works":["https://openalex.org/W2040852018","https://openalex.org/W1525004701","https://openalex.org/W76618410","https://openalex.org/W2043044156","https://openalex.org/W2889919121","https://openalex.org/W105730666","https://openalex.org/W3131160574","https://openalex.org/W2102935281","https://openalex.org/W2914057215","https://openalex.org/W2093790492"],"abstract_inverted_index":{"A":[0],"plane":[1],"wave":[2],"is":[3,32,49,64,70,165],"scattered":[4],"by":[5],"two":[6,60,84,140,154],"small":[7],"spheres":[8,141,155],"of":[9,23,87,125,179],"not":[10],"necessarily":[11],"equal":[12,157],"radii.":[13],"Low-frequency":[14],"theory":[15],"reduces":[16],"this":[17,145,180],"scattering":[18,90,96,174,181],"problem":[19],"to":[20,51,150],"a":[21,113,126,131,148],"sequence":[22],"potential":[24,55],"problems":[25,56],"which":[26],"can":[27],"be":[28],"solved":[29],"iteratively.":[30],"It":[31,63],"shown":[33,65,166],"that":[34,42,66,167],"there":[35],"exists":[36],"exactly":[37],"one":[38],"bispherical":[39],"coordinate":[40],"system":[41],"fits":[43],"the":[44,54,58,67,74,78,88,95,105,109,139,153],"given":[45],"geometry.":[46],"Then":[47],"R-separation":[48],"utilized":[50],"solve":[52],"analytically":[53],"governing":[57],"leading":[59,83],"low-frequency":[61],"approximations.":[62],"Rayleigh":[68,102],"approximation":[69,76,178],"azimuthal":[71,79],"independent,":[72],"while":[73,116],"first-order":[75,172],"involves":[77],"angle":[80],"explicitly.":[81],"The":[82,101,134],"nonvanishing":[85],"approximations":[86,103,120],"normalized":[89],"amplitude":[91,106],"as":[92,94,128,130],"well":[93,129],"cross-section":[97,110],"are":[98,121,156],"also":[99],"provided.":[100],"for":[104,108,168],"and":[107,144],"involve":[111],"only":[112],"monopole":[114,127],"term,":[115],"their":[117],"next":[118],"order":[119],"expressed":[122],"in":[123],"terms":[124],"dipole":[132,135],"term.":[133],"term":[136],"disappears":[137],"whenever":[138],"become":[142],"equal,":[143],"observation":[146],"provides":[147],"way":[149],"determine":[151],"whether":[152],"or":[158],"not,":[159],"from":[160],"far-field":[161],"measurements.":[162],"Finally,":[163],"it":[164],"all":[169],"practical":[170],"purposes,":[171],"multiple":[173],"yields":[175],"an":[176],"excellent":[177],"process.":[182]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}