{"id":"https://openalex.org/W4220658611","doi":"https://doi.org/10.1109/tvcg.2022.3158869","title":"Visualizing Higher-Order 3D Tensors by Multipole Lines","display_name":"Visualizing Higher-Order 3D Tensors by Multipole Lines","publication_year":2022,"publication_date":"2022-03-17","ids":{"openalex":"https://openalex.org/W4220658611","doi":"https://doi.org/10.1109/tvcg.2022.3158869","pmid":"https://pubmed.ncbi.nlm.nih.gov/35298379"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2022.3158869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2022.3158869","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5090357379","display_name":"Chiara Hergl","orcid":"https://orcid.org/0000-0002-4016-9113"},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Chiara Hergl","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Institute of Computer Science, Image and Signal Processing Group, Leipzig University, Leipzig, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4016-9113","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Institute of Computer Science, Image and Signal Processing Group, Leipzig University, Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079275693","display_name":"Thomas Nagel","orcid":"https://orcid.org/0000-0001-8459-4616"},"institutions":[{"id":"https://openalex.org/I61893789","display_name":"TU Bergakademie Freiberg","ror":"https://ror.org/031vc2293","country_code":"DE","type":"education","lineage":["https://openalex.org/I61893789"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Nagel","raw_affiliation_strings":["Chair of Soil Mechanics and Foundation Engineering, Geotechnical Institute, Technische Universit&#x00E4;t Bergakademie Freiberg, Freiberg, Germany"],"raw_orcid":"https://orcid.org/0000-0001-8459-4616","affiliations":[{"raw_affiliation_string":"Chair of Soil Mechanics and Foundation Engineering, Geotechnical Institute, Technische Universit&#x00E4;t Bergakademie Freiberg, Freiberg, Germany","institution_ids":["https://openalex.org/I61893789"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029336209","display_name":"Gerik Scheuermann","orcid":"https://orcid.org/0000-0001-5200-8870"},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerik Scheuermann","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Institute of Computer Science, Image and Signal Processing Group, Leipzig University, Leipzig, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5200-8870","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Institute of Computer Science, Image and Signal Processing Group, Leipzig University, Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1312,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.30827068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"7","first_page":"3405","last_page":"3418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.979200005531311,"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/T13650","display_name":"Computational Physics and Python Applications","score":0.9556999802589417,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multipole-expansion","display_name":"Multipole expansion","score":0.8143308162689209},{"id":"https://openalex.org/keywords/cartesian-tensor","display_name":"Cartesian tensor","score":0.78316330909729},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7231974005699158},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"Tensor contraction","score":0.5516076683998108},{"id":"https://openalex.org/keywords/tensor-density","display_name":"Tensor density","score":0.47690677642822266},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.45902949571609497},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.45234787464141846},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4497305750846863},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.4446500241756439},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.41871872544288635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3323186933994293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3059324026107788},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22231605648994446},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.15602290630340576},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15356206893920898}],"concepts":[{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.8143308162689209},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.78316330909729},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7231974005699158},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.5516076683998108},{"id":"https://openalex.org/C148125525","wikidata":"https://www.wikidata.org/wiki/Q904927","display_name":"Tensor density","level":4,"score":0.47690677642822266},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.45902949571609497},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.45234787464141846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4497305750846863},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.4446500241756439},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.41871872544288635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3323186933994293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3059324026107788},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22231605648994446},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.15602290630340576},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15356206893920898}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tvcg.2022.3158869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2022.3158869","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:35298379","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35298379","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":"IEEE transactions on visualization and computer graphics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1536847603","https://openalex.org/W1976381195","https://openalex.org/W1989704465","https://openalex.org/W1996559312","https://openalex.org/W2008440833","https://openalex.org/W2017950984","https://openalex.org/W2036621764","https://openalex.org/W2041405437","https://openalex.org/W2054866032","https://openalex.org/W2064592144","https://openalex.org/W2073672168","https://openalex.org/W2085585105","https://openalex.org/W2125105302","https://openalex.org/W2139079167","https://openalex.org/W2158810451","https://openalex.org/W2159936057","https://openalex.org/W2267977464","https://openalex.org/W2763619067","https://openalex.org/W2794501375","https://openalex.org/W2951014192","https://openalex.org/W2996519518","https://openalex.org/W3088854094","https://openalex.org/W3140358950","https://openalex.org/W3176602199","https://openalex.org/W3181590728","https://openalex.org/W4206744653","https://openalex.org/W4234438714","https://openalex.org/W4235074964","https://openalex.org/W4252903253","https://openalex.org/W6649300704","https://openalex.org/W6681356334","https://openalex.org/W6681619293","https://openalex.org/W6749467582","https://openalex.org/W6783678645","https://openalex.org/W6797690158"],"related_works":["https://openalex.org/W2981910625","https://openalex.org/W2765690628","https://openalex.org/W1965338607","https://openalex.org/W2607194831","https://openalex.org/W2058505222","https://openalex.org/W2403348579","https://openalex.org/W4360921185","https://openalex.org/W1993813870","https://openalex.org/W1887380982","https://openalex.org/W2166062232"],"abstract_inverted_index":{"Physics,":[0],"medicine,":[1],"earth":[2],"sciences,":[3],"mechanical":[4],"engineering,":[5],"geo-engineering,":[6],"bio-engineering":[7],"and":[8,145,166,209,226],"many":[9],"more":[10],"application":[11],"areas":[12],"use":[13,90],"tensorial":[14],"data.":[15],"For":[16,216],"example,":[17],"tensors":[18,44,98,173],"are":[19,52,60],"used":[20,80],"in":[21,102,159,212],"formulating":[22],"the":[23,35,76,91,150,181,199,204,207,210,213,217,237,240],"balance":[24],"equations":[25],"of":[26,42,53,78,99,112,118,137,152,171,174,183,198,239],"charge,":[27],"mass,":[28],"momentum,":[29],"or":[30],"energy":[31],"as":[32,34,188,190,231,234,236],"well":[33,189,235],"constitutive":[36],"relations":[37,223],"that":[38],"complement":[39],"them.":[40],"Some":[41],"these":[43],"(i.e.,":[45],"stiffness":[46,219],"tensor,":[47,220],"strain":[48],"gradient,":[49],"photo-elastic":[50],"tensor)":[51],"order":[54,101,114],"higher":[55],"than":[56],"two.":[57],"Currently,":[58],"there":[59],"nearly":[61],"no":[62],"visualization":[63,170,182],"techniques":[64],"for":[65,73,180],"such":[66,230],"data":[67],"beyond":[68],"glyphs.":[69],"An":[70],"important":[71,227],"reason":[72],"this":[74,85],"is":[75],"limit":[77],"currently":[79],"tensor":[81,111,164,186,192],"decomposition":[82,93,107],"techniques.":[83],"In":[84],"article,":[86],"we":[87,202,221],"propose":[88],"to":[89,94,163],"deviatoric":[92,106],"draw":[95],"lines":[96,154,165],"describing":[97],"arbitrary":[100],"three":[103],"dimensions.":[104],"The":[105],"splits":[108],"a":[109,134,160,168],"three-dimensional":[110,172],"any":[113,116,175],"with":[115],"type":[117],"index":[119],"symmetry":[120],"into":[121],"totally":[122],"symmetric,":[123,184],"traceless":[124],"tensors.":[125],"These":[126,147],"tensors,":[127],"called":[128],"deviators,":[129],"can":[130,156],"be":[131,157],"described":[132],"by":[133,141],"unique":[135],"set":[136],"directions":[138],"(called":[139],"multipoles":[140,148,208,225],"J.":[142],"C.":[143],"Maxwell)":[144],"scalars.":[146],"allow":[149,167,195],"definition":[151],"multipole":[153,200],"which":[155],"computed":[158],"similar":[161],"fashion":[162],"line-based":[169],"order.":[176],"We":[177],"give":[178],"examples":[179],"second-order":[185,214,241],"fields":[187],"fourth-order":[191,218],"fields.":[193],"To":[194],"an":[196],"interpretation":[197],"lines,":[201],"analyze":[203],"connection":[205],"between":[206,224],"eigenvectors/eigenvalues":[211],"case.":[215],"prove":[222],"physical":[228],"quantities":[229],"shear":[232],"moduli":[233],"eigenvectors":[238],"right":[242],"Cauchy-Green":[243],"tensor.":[244]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
