{"id":"https://openalex.org/W2329099558","doi":"https://doi.org/10.3390/mi7040055","title":"An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method","display_name":"An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method","publication_year":2016,"publication_date":"2016-03-29","ids":{"openalex":"https://openalex.org/W2329099558","doi":"https://doi.org/10.3390/mi7040055","mag":"2329099558","pmid":"https://pubmed.ncbi.nlm.nih.gov/30407428"},"language":"en","primary_location":{"id":"doi:10.3390/mi7040055","is_oa":true,"landing_page_url":"https://doi.org/10.3390/mi7040055","pdf_url":"https://www.mdpi.com/2072-666X/7/4/55/pdf?version=1459247500","source":{"id":"https://openalex.org/S96702057","display_name":"Micromachines","issn_l":"2072-666X","issn":["2072-666X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Micromachines","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2072-666X/7/4/55/pdf?version=1459247500","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100444409","display_name":"Wen Zhang","orcid":"https://orcid.org/0000-0002-8934-3346"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen Zhang","raw_affiliation_strings":["State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100323420","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0002-1803-3148"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000038694","display_name":"Shijiu Jin","orcid":"https://orcid.org/0000-0002-8910-5161"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shijiu Jin","raw_affiliation_strings":["State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051637055","display_name":"Zhoumo Zeng","orcid":"https://orcid.org/0000-0001-8220-598X"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhoumo Zeng","raw_affiliation_strings":["State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100323420"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2905,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.56947617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"4","first_page":"55","last_page":"55"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10727","display_name":"Ultrasound Imaging and Elastography","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10369","display_name":"Advanced MEMS and NEMS Technologies","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/capacitive-micromachined-ultrasonic-transducers","display_name":"Capacitive micromachined ultrasonic transducers","score":0.883306622505188},{"id":"https://openalex.org/keywords/deflection","display_name":"Deflection (physics)","score":0.7299335598945618},{"id":"https://openalex.org/keywords/membrane","display_name":"Membrane","score":0.7177340388298035},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.6276057958602905},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5902125835418701},{"id":"https://openalex.org/keywords/capacitive-sensing","display_name":"Capacitive sensing","score":0.5640279054641724},{"id":"https://openalex.org/keywords/frequency-response","display_name":"Frequency response","score":0.5567792057991028},{"id":"https://openalex.org/keywords/monolayer","display_name":"Monolayer","score":0.5273593068122864},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.527326762676239},{"id":"https://openalex.org/keywords/transducer","display_name":"Transducer","score":0.5083834528923035},{"id":"https://openalex.org/keywords/ritz-method","display_name":"Ritz method","score":0.4769686162471771},{"id":"https://openalex.org/keywords/ultrasonic-sensor","display_name":"Ultrasonic sensor","score":0.4602346420288086},{"id":"https://openalex.org/keywords/residual-stress","display_name":"Residual stress","score":0.41222232580184937},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.33431476354599},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.3341129422187805},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.24542149901390076},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1512804627418518},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13902857899665833},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12028300762176514},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.09336388111114502},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.08246681094169617},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.08234202861785889}],"concepts":[{"id":"https://openalex.org/C58772458","wikidata":"https://www.wikidata.org/wiki/Q5034480","display_name":"Capacitive micromachined ultrasonic transducers","level":3,"score":0.883306622505188},{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.7299335598945618},{"id":"https://openalex.org/C41625074","wikidata":"https://www.wikidata.org/wiki/Q176088","display_name":"Membrane","level":2,"score":0.7177340388298035},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.6276057958602905},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5902125835418701},{"id":"https://openalex.org/C206755178","wikidata":"https://www.wikidata.org/wiki/Q1131271","display_name":"Capacitive sensing","level":2,"score":0.5640279054641724},{"id":"https://openalex.org/C8590192","wikidata":"https://www.wikidata.org/wiki/Q1054694","display_name":"Frequency response","level":2,"score":0.5567792057991028},{"id":"https://openalex.org/C7070889","wikidata":"https://www.wikidata.org/wiki/Q902488","display_name":"Monolayer","level":2,"score":0.5273593068122864},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.527326762676239},{"id":"https://openalex.org/C56318395","wikidata":"https://www.wikidata.org/wiki/Q215928","display_name":"Transducer","level":2,"score":0.5083834528923035},{"id":"https://openalex.org/C21575042","wikidata":"https://www.wikidata.org/wiki/Q905132","display_name":"Ritz method","level":3,"score":0.4769686162471771},{"id":"https://openalex.org/C81288441","wikidata":"https://www.wikidata.org/wiki/Q20736125","display_name":"Ultrasonic sensor","level":2,"score":0.4602346420288086},{"id":"https://openalex.org/C37292000","wikidata":"https://www.wikidata.org/wiki/Q1257918","display_name":"Residual stress","level":2,"score":0.41222232580184937},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.33431476354599},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3341129422187805},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.24542149901390076},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1512804627418518},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13902857899665833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12028300762176514},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.09336388111114502},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.08246681094169617},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.08234202861785889},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/mi7040055","is_oa":true,"landing_page_url":"https://doi.org/10.3390/mi7040055","pdf_url":"https://www.mdpi.com/2072-666X/7/4/55/pdf?version=1459247500","source":{"id":"https://openalex.org/S96702057","display_name":"Micromachines","issn_l":"2072-666X","issn":["2072-666X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Micromachines","raw_type":"journal-article"},{"id":"pmid:30407428","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30407428","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Micromachines","raw_type":null},{"id":"pmh:oai:doaj.org/article:4fd94e514c5948558c2a795fab497b66","is_oa":true,"landing_page_url":"https://doaj.org/article/4fd94e514c5948558c2a795fab497b66","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Micromachines, Vol 7, Iss 4, p 55 (2016)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:5158171","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC6189930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6189930","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6189930","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Micromachines (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/mi7040055","is_oa":true,"landing_page_url":"https://doi.org/10.3390/mi7040055","pdf_url":"https://www.mdpi.com/2072-666X/7/4/55/pdf?version=1459247500","source":{"id":"https://openalex.org/S96702057","display_name":"Micromachines","issn_l":"2072-666X","issn":["2072-666X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Micromachines","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.5,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2802911279","display_name":null,"funder_award_id":"Young","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3085993365","display_name":null,"funder_award_id":"(Grant No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6249303001","display_name":null,"funder_award_id":"61201039","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7726157001","display_name":null,"funder_award_id":"Grant No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320331088","display_name":"Natural Science Foundation for Young Scientists of Shanxi Province","ror":null},{"id":"https://openalex.org/F4320335581","display_name":"Young Scientists Fund","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2329099558.pdf","grobid_xml":"https://content.openalex.org/works/W2329099558.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1982482817","https://openalex.org/W1993632429","https://openalex.org/W1994392420","https://openalex.org/W2009953819","https://openalex.org/W2015906754","https://openalex.org/W2094258590","https://openalex.org/W2097191972","https://openalex.org/W2105394554","https://openalex.org/W2121617973","https://openalex.org/W2123628918","https://openalex.org/W2128975336","https://openalex.org/W2129138429","https://openalex.org/W2130352026","https://openalex.org/W2147573776","https://openalex.org/W2150266890","https://openalex.org/W2150637132","https://openalex.org/W2155973730","https://openalex.org/W2156690225","https://openalex.org/W2170013480","https://openalex.org/W2205508142","https://openalex.org/W2982387198","https://openalex.org/W4388250519","https://openalex.org/W6685005859"],"related_works":["https://openalex.org/W4319718051","https://openalex.org/W2137987953","https://openalex.org/W3202163833","https://openalex.org/W2808928575","https://openalex.org/W4281663564","https://openalex.org/W2330836581","https://openalex.org/W3008955959","https://openalex.org/W2890862950","https://openalex.org/W2163011994","https://openalex.org/W2165649385"],"abstract_inverted_index":{"Capacitive":[0],"micromachined":[1],"ultrasonic":[2],"transducer":[3],"(CMUT)":[4],"multilayer":[5,30,37,55,70],"membrane":[6,38,71],"plays":[7],"an":[8,199],"important":[9],"role":[10],"in":[11,43],"the":[12,16,20,29,36,69,80,90,144,152,159,164,168,178,184],"performance":[13],"metrics":[14],"including":[15],"transmitting":[17],"efficiency":[18],"and":[19,60,65,83,95,114,130,156,181,198,205],"receiving":[21],"sensitivity.":[22],"However,":[23],"there":[24],"are":[25,98,147],"few":[26],"studies":[27],"of":[28,68],"membranes.":[31],"Some":[32],"analytical":[33,50,190],"models":[34,133],"simplify":[35],"as":[39,137,194],"monolayer,":[40],"which":[41,57],"results":[42,121],"inaccuracies.":[44],"This":[45,188],"paper":[46],"presents":[47],"a":[48,195],"new":[49],"model":[51,108,191],"for":[52,112,151,158,177,183,202],"CMUTs":[53,136],"with":[54,122,171],"membranes,":[56,143],"can":[58,192],"rapidly":[59],"accurately":[61],"predict":[62],"static":[63,93,153],"deflection":[64,154],"response":[66,96,160,185],"frequency":[67,97],"under":[72],"external":[73,91],"pressures.":[74],"The":[75,86,107],"derivation":[76],"is":[77,105,175],"based":[78],"on":[79],"Ritz":[81],"method":[82,104,125],"Hamilton's":[84],"principle.":[85],"mathematical":[87],"relationships":[88],"between":[89],"pressure,":[92],"deflection,":[94,180],"obtained.":[99],"Relevant":[100],"residual":[101,172],"stress":[102,173],"compensation":[103,174],"derived.":[106],"has":[109],"been":[110],"verified":[111],"three-layer":[113,141],"double-layer":[115,165],"CMUT":[116,142,166,203],"membranes":[117],"by":[118],"comparing":[119],"its":[120],"finite":[123],"element":[124],"(FEM)":[126],"simulations,":[127],"experimental":[128],"data,":[129],"other":[131],"monolayer":[132,138],"that":[134],"treat":[135],"plates/membranes.":[139],"For":[140,163],"relative":[145,169],"errors":[146],"ranging":[148],"from":[149],"0.71%\u207b3.51%":[150],"profiles,":[155],"0.35%\u207b4.96%":[157],"frequencies,":[161,186],"respectively.":[162,187],"membrane,":[167],"error":[170],"4.14%":[176],"central":[179],"-1.17%":[182],"proposed":[189],"serve":[193],"reliable":[196],"reference":[197],"accurate":[200],"tool":[201],"design":[204],"optimization.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}