{"id":"https://openalex.org/W2963546043","doi":"https://doi.org/10.1137/16m107414x","title":"Generating Point Configurations via Hypersingular Riesz Energy with an External Field","display_name":"Generating Point Configurations via Hypersingular Riesz Energy with an External Field","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2963546043","doi":"https://doi.org/10.1137/16m107414x","mag":"2963546043"},"language":"en","primary_location":{"id":"doi:10.1137/16m107414x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m107414x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5066655505","display_name":"Douglas P. Hardin","orcid":"https://orcid.org/0000-0003-0867-2146"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. P. Hardin","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN, 37240"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN, 37240","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064321469","display_name":"E. B. Saff","orcid":null},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. B. Saff","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN, 37240"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN, 37240","institution_ids":["https://openalex.org/I200719446"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091293720","display_name":"Oleksandr Vlasiuk","orcid":null},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"O. V. Vlasiuk","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, Nashville, TN, 37240"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, Nashville, TN, 37240","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066655505"],"corresponding_institution_ids":["https://openalex.org/I200719446"],"apc_list":null,"apc_paid":null,"fwci":0.6918,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71403856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"49","issue":"1","first_page":"646","last_page":"673"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9984999895095825,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9116390943527222},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6543381810188293},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.6105865836143494},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6023688316345215},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5611234307289124},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5604401230812073},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5577356815338135},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46553435921669006},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37995675206184387},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29943299293518066},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2722023129463196},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09222280979156494}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9116390943527222},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6543381810188293},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.6105865836143494},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6023688316345215},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5611234307289124},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5604401230812073},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5577356815338135},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46553435921669006},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37995675206184387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29943299293518066},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2722023129463196},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09222280979156494},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m107414x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m107414x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.8399999737739563,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2630816297","display_name":"Applications and analysis of discrete energy and polarization","funder_award_id":"1516400","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4492641333","display_name":null,"funder_award_id":"DMS-1521749","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4942118900","display_name":null,"funder_award_id":"DMS-1516400","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7150043320","display_name":"Discrete Energy and Polarization Problems on Manifolds with Applications","funder_award_id":"1412428","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G893668492","display_name":null,"funder_award_id":"DMS-1412428","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1525000343","https://openalex.org/W1596978602","https://openalex.org/W1798492768","https://openalex.org/W1916127968","https://openalex.org/W1965592845","https://openalex.org/W1967649517","https://openalex.org/W1990400021","https://openalex.org/W2000049380","https://openalex.org/W2002345383","https://openalex.org/W2005284650","https://openalex.org/W2017770944","https://openalex.org/W2052885820","https://openalex.org/W2061819463","https://openalex.org/W2063360699","https://openalex.org/W2066981905","https://openalex.org/W2130853073","https://openalex.org/W2132731146","https://openalex.org/W2272220540","https://openalex.org/W2964031427","https://openalex.org/W2964314435","https://openalex.org/W3105377852","https://openalex.org/W3106212841"],"related_works":["https://openalex.org/W2384485326","https://openalex.org/W3102638686","https://openalex.org/W630101442","https://openalex.org/W2732277901","https://openalex.org/W2509014348","https://openalex.org/W2060523575","https://openalex.org/W3103351379","https://openalex.org/W2802747196","https://openalex.org/W2963712696","https://openalex.org/W2792001083","https://openalex.org/W2951021410","https://openalex.org/W2092988373","https://openalex.org/W3102098187","https://openalex.org/W3001332551","https://openalex.org/W2994816647","https://openalex.org/W2975491722","https://openalex.org/W3106236473","https://openalex.org/W2952568890","https://openalex.org/W2750967068","https://openalex.org/W2952058189"],"abstract_inverted_index":{"For":[0],"a":[1,23,66,77,84],"compact":[2],"$d$-dimensional":[3],"rectifiable":[4,85],"subset":[5,86],"of":[6,15,42,46,56,87,96],"${\\mathbb":[7,88],"R}^{p}$":[8],"we":[9,64],"study":[10],"asymptotic":[11,54],"properties":[12,95],"as":[13],"$N\\to\\infty$":[14],"$N$-point":[16],"configurations":[17,70],"minimizing":[18],"the":[19,32,39,52],"energy":[20,58],"arising":[21],"from":[22],"Riesz":[24],"$s$-potential":[25],"$1/r^s$":[26],"and":[27,51,93],"an":[28,62],"external":[29],"field":[30],"in":[31],"hypersingular":[33],"case":[34],"$s\\geq":[35],"d$.":[36],"Formulas":[37],"for":[38,68],"weak$^*$":[40],"limit":[41],"normalized":[43,72],"counting":[44,73],"measures":[45,74],"such":[47],"optimal":[48],"point":[49],"sets":[50],"first-order":[53],"values":[55],"minimal":[57],"are":[59,99,103],"obtained.":[60],"As":[61],"application,":[63],"derive":[65],"method":[67],"generating":[69],"whose":[71],"converge":[75],"to":[76],"given":[78],"absolutely":[79],"continuous":[80],"measure":[81],"supported":[82],"on":[83,91],"R}^{p}$.":[89],"Results":[90],"separation":[92],"covering":[94],"discrete":[97],"minimizers":[98],"given.":[100],"Our":[101],"theorems":[102],"illustrated":[104],"with":[105],"several":[106],"numerical":[107],"examples.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}