{"id":"https://openalex.org/W7222441282","doi":"https://doi.org/10.48550/arxiv.2610.21258","title":"Rigidity for formally determined point source scattering for an anisotropic acoustic medium","display_name":"Rigidity for formally determined point source scattering for an anisotropic acoustic medium","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222441282","doi":"https://doi.org/10.48550/arxiv.2610.21258"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.21258","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21258","pdf_url":"https://arxiv.org/pdf/2610.21258","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.21258","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123991453","display_name":"Pradipta Chatterjee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Chatterjee, Pradipta","raw_affiliation_strings":["Centre for Applicable Mathematics , Tata Institute of Fundamental Research , Bangalore , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Applicable Mathematics , Tata Institute of Fundamental Research , Bangalore , India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122896580","display_name":"Rakesh","orcid":"https://orcid.org/0000-0003-1293-5113","observed_orcids":["https://orcid.org/0000-0003-1293-5113"]},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rakesh","raw_affiliation_strings":["Department of Mathematical Sciences , University of Delaware , Newark DE , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , University of Delaware , Newark DE , USA","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061664911","display_name":"Abhilash Tushir","orcid":"https://orcid.org/0009-0001-2870-0979","observed_orcids":["https://orcid.org/0009-0001-2870-0979"]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tushir, Abhilash","raw_affiliation_strings":["Centre for Applicable Mathematics , Tata Institute of Fundamental Research , Bangalore , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Applicable Mathematics , Tata Institute of Fundamental Research , Bangalore , India","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.8715999722480774,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.8715999722480774,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.05570000037550926,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.006800000090152025,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/inverse-problems","display_name":"inverse problems","score":0.593999981880188},{"id":"https://openalex.org/keywords/rigidity","display_name":"rigidity","score":0.6850000023841858},{"id":"https://openalex.org/keywords/riemannian-metrics","display_name":"Riemannian metrics","score":0.796999990940094},{"id":"https://openalex.org/keywords/sound-velocity","display_name":"sound velocity","score":0.7120000123977661},{"id":"https://openalex.org/keywords/boundary-measurements","display_name":"boundary measurements","score":0.5659999847412109},{"id":"https://openalex.org/keywords/diffeomorphisms","display_name":"diffeomorphisms","score":0.597000002861023},{"id":"https://openalex.org/keywords/plane-waves","display_name":"plane waves","score":0.4740000069141388},{"id":"https://openalex.org/keywords/three-dimensional-scattering","display_name":"three-dimensional scattering","score":0.32199999690055847}],"concepts":[{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6222000122070312},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5526000261306763},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5522000193595886},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5408999919891357},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5246000289916992},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.492900013923645},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C204723758","wikidata":"https://www.wikidata.org/wiki/Q3882459","display_name":"Acoustic wave","level":2,"score":0.4722000062465668},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4659000039100647},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4408999979496002},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C68115822","wikidata":"https://www.wikidata.org/wiki/Q1068172","display_name":"Sound pressure","level":2,"score":0.4034999907016754},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C103783831","wikidata":"https://www.wikidata.org/wiki/Q2552709","display_name":"Point source","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.36730000376701355},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.3578999936580658},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.32910001277923584},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2720000147819519},{"id":"https://openalex.org/C145589544","wikidata":"https://www.wikidata.org/wiki/Q4674723","display_name":"Acoustic wave equation","level":3,"score":0.26109999418258667}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.21258","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21258","pdf_url":"https://arxiv.org/pdf/2610.21258","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2610.21258","doi":"https://doi.org/10.48550/arxiv.2610.21258","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.21258","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.21258","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21258","pdf_url":"https://arxiv.org/pdf/2610.21258","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2082259293","display_name":"The inverse backscattering problem and the inverse fixed angle scattering problem","funder_award_id":"2307800","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306227","display_name":"Arthritis National Research Foundation","ror":"https://ror.org/03abbex33"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320768","display_name":"Department of Atomic Energy, Government of India","ror":"https://ror.org/02m388s04"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222441282.pdf","grobid_xml":"https://content.openalex.org/works/W7222441282.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3113016109","https://openalex.org/W4403345523","https://openalex.org/W7123345384","https://openalex.org/W1578641501","https://openalex.org/W2157787958","https://openalex.org/W2108283493","https://openalex.org/W7213327559","https://openalex.org/W2115466198","https://openalex.org/W7098096749","https://openalex.org/W4242719340"],"abstract_inverted_index":{"Consider":[0],"an":[1,71],"acoustic":[2,31],"medium,":[3],"occupying":[4],"three":[5],"dimensional":[6],"space,":[7],"whose":[8],"anisotropic":[9],"sound":[10],"speed":[11],"is":[12,19,28,49,77,85],"modeled":[13],"by":[14,30,34],"a":[15,22,35,57,81],"Riemannian":[16],"metric":[17,73,76],"which":[18],"Euclidean":[20,72,78],"outside":[21,43],"compact":[23],"region":[24],"$D$.":[25],"The":[26],"medium":[27,47],"probed":[29],"waves":[32,96,107],"generated":[33],"finite":[36,58],"number":[37],"(dimension":[38],"dependent)":[39],"of":[40,54,70,98,105],"point":[41,99,102],"sources":[42,103],"$D$":[44,55],"and":[45],"the":[46,52,75,88],"response":[48],"measured":[50],"on":[51],"boundary":[53],"for":[56],"time":[59],"period.":[60],"We":[61],"show":[62],"that":[63,69],"if":[64],"these":[65],"measurements":[66],"agree":[67],"with":[68,112],"then":[74],"up":[79],"to":[80,87],"diffeomorphism.":[82],"This":[83],"result":[84,89],"similar":[86],"in":[90,113],"\\cite{ORS26a}":[91],"where":[92],"they":[93],"used":[94],"plane":[95,106],"instead":[97,104],"sources.":[100],"Using":[101],"presents":[108],"new":[109],"difficulties,":[110],"dealt":[111],"this":[114],"article.":[115]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-17T00:00:00"}
