{"id":"https://openalex.org/W2046646196","doi":"https://doi.org/10.1137/040621636","title":"Renormalized Energy and Forces on Dislocations","display_name":"Renormalized Energy and Forces on Dislocations","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2046646196","doi":"https://doi.org/10.1137/040621636","mag":"2046646196"},"language":"en","primary_location":{"id":"doi:10.1137/040621636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040621636","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/A5081908028","display_name":"Paolo Cermelli","orcid":"https://orcid.org/0000-0002-2181-8800"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paolo Cermelli","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061082633","display_name":"Giovanni Leoni","orcid":"https://orcid.org/0000-0002-1228-8561"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giovanni Leoni","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081908028"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4057,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.61219886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"4","first_page":"1131","last_page":"1160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10204","display_name":"Microstructure and mechanical properties","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5920878648757935},{"id":"https://openalex.org/keywords/dislocation","display_name":"Dislocation","score":0.5397400259971619},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.49329227209091187},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.48886317014694214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48260772228240967},{"id":"https://openalex.org/keywords/elastic-energy","display_name":"Elastic energy","score":0.47698360681533813},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.46381089091300964},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.34489238262176514},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31563812494277954},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.1545308232307434},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13487458229064941}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5920878648757935},{"id":"https://openalex.org/C159122135","wikidata":"https://www.wikidata.org/wiki/Q737571","display_name":"Dislocation","level":2,"score":0.5397400259971619},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.49329227209091187},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.48886317014694214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48260772228240967},{"id":"https://openalex.org/C14041564","wikidata":"https://www.wikidata.org/wiki/Q891408","display_name":"Elastic energy","level":2,"score":0.47698360681533813},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.46381089091300964},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34489238262176514},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31563812494277954},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.1545308232307434},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13487458229064941},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040621636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040621636","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.207.7108","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.7108","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/CNA/Publications/publications2005/002abs/05-CNA-002.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8600000143051147,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W47436197","https://openalex.org/W135694094","https://openalex.org/W1483014895","https://openalex.org/W1499787021","https://openalex.org/W1519262584","https://openalex.org/W1543511296","https://openalex.org/W1565451952","https://openalex.org/W1572130436","https://openalex.org/W1590932878","https://openalex.org/W1596584641","https://openalex.org/W1866311589","https://openalex.org/W1967688238","https://openalex.org/W1969834664","https://openalex.org/W1979992765","https://openalex.org/W1989545882","https://openalex.org/W1990165462","https://openalex.org/W1995342349","https://openalex.org/W1997360736","https://openalex.org/W1998962009","https://openalex.org/W2041324809","https://openalex.org/W2042833347","https://openalex.org/W2051584669","https://openalex.org/W2051912022","https://openalex.org/W2052149891","https://openalex.org/W2054434559","https://openalex.org/W2054662694","https://openalex.org/W2058043530","https://openalex.org/W2060410734","https://openalex.org/W2061232593","https://openalex.org/W2068876583","https://openalex.org/W2129224265","https://openalex.org/W2148262800","https://openalex.org/W2148565139","https://openalex.org/W2165243201","https://openalex.org/W2190309998","https://openalex.org/W2323745889","https://openalex.org/W2488016630","https://openalex.org/W2626670328","https://openalex.org/W3042562017","https://openalex.org/W4285037076"],"related_works":["https://openalex.org/W4245687327","https://openalex.org/W2112549839","https://openalex.org/W4254637135","https://openalex.org/W2905483137","https://openalex.org/W3034896902","https://openalex.org/W1995867010","https://openalex.org/W2041203508","https://openalex.org/W752953485","https://openalex.org/W2328194834","https://openalex.org/W2013258421"],"abstract_inverted_index":{"In":[0],"this":[1,78],"work":[2],"we":[3,32,189],"discuss,":[4],"from":[5,82,166],"a":[6,13,20,24,43,50,59,89,182,200],"variational":[7],"viewpoint,":[8],"the":[9,37,40,54,63,67,83,97,101,104,118,127,132,145,149,153,156,164,185,197,204,207,220],"equilibrium":[10,35],"problem":[11],"for":[12,129,140,152],"finite":[14],"number":[15],"of":[16,27,39,42,45,53,62,88,91,100,131,135,155,161,168,173,176,184,199,206],"Volterra":[17],"dislocations":[18,92,130],"in":[19,159,217],"plane":[21],"domain.":[22],"For":[23],"given":[25,201],"set":[26,90],"singularities":[28],"at":[29],"fixed":[30],"locations,":[31],"characterize":[33],"elastic":[34],"as":[36,66,126,148],"limit":[38,158],"minimizers":[41],"family":[44],"energy":[46,65,86,147,180],"functionals,":[47],"obtained":[48],"by":[49,96],"finite-core":[51],"regularization":[52],"elastic-energy":[55],"functional.":[56],"We":[57,143],"give":[58],"sharpasymptotic":[60],"estimate":[61],"minimum":[64],"core":[68],"radius":[69],"tends":[70],"to":[71,76,171,196],"zero,":[72],"which":[73,108,213],"allows":[74],"one":[75],"eliminate":[77],"internal":[79],"length":[80],"scale":[81],"problem.":[84],"The":[85,178],"content":[87],"is":[93,181,203],"fully":[94],"characterized":[95],"regular":[98],"part":[99],"asymptotic":[102],"expansion,":[103],"so-called":[105],"renormalized":[106,146,179],"energy,":[107],"contains":[109],"all":[110],"information":[111],"regarding":[112],"self-":[113],"and":[114,138],"mutual":[115],"interactions":[116],"between":[117],"defects.":[119],"Thus":[120],"our":[121],"result":[122,134],"may":[123],"be":[124,215],"considered":[125],"analogue":[128],"classical":[133,221],"Bethuel,":[136],"Brezis":[137],"H\u00e9lein":[139],"Ginzburg--Landau":[141],"vortices.":[142],"view":[144],"basic":[150],"tool":[151],"study":[154],"discrete-to-continuum":[157],"plasticity":[160],"crystals,":[162],"i.e.,":[163],"passage":[165],"models":[167],"isolated":[169],"defects":[170],"theories":[172],"continuous":[174],"distributions":[175],"dislocations.":[177],"function":[183],"defect":[186],"positions":[187],"only:":[188],"prove":[190],"that":[191,211],"its":[192],"derivative":[193],"with":[194,219],"respect":[195],"position":[198],"dislocation":[202],"resultant":[205],"Eshelby":[208],"stress":[209],"on":[210],"dislocation,":[212],"can":[214],"identified":[216],"turn":[218],"Peach--K\u00f6hler":[222],"force.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":10},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}