{"id":"https://openalex.org/W2586591321","doi":"https://doi.org/10.1137/16m1069420","title":"The Steepest Descent Algorithm in Wasserstein Metric for the Sandpile Model of Self-Organized Criticality","display_name":"The Steepest Descent Algorithm in Wasserstein Metric for the Sandpile Model of Self-Organized Criticality","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2586591321","doi":"https://doi.org/10.1137/16m1069420","mag":"2586591321"},"language":"en","primary_location":{"id":"doi:10.1137/16m1069420","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1069420","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5102862771","display_name":"Viorel Barbu","orcid":"https://orcid.org/0000-0002-4715-9778"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Viorel Barbu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102862771"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.375,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.51388402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"55","issue":"1","first_page":"413","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6554770469665527},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5653594136238098},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.562846302986145},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5336008667945862},{"id":"https://openalex.org/keywords/abelian-sandpile-model","display_name":"Abelian sandpile model","score":0.4409765303134918},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34207361936569214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29657524824142456},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.09866243600845337}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6554770469665527},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5653594136238098},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.562846302986145},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5336008667945862},{"id":"https://openalex.org/C52359947","wikidata":"https://www.wikidata.org/wiki/Q4666685","display_name":"Abelian sandpile model","level":2,"score":0.4409765303134918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34207361936569214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29657524824142456},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.09866243600845337}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1069420","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1069420","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2008879046","https://openalex.org/W2050773281","https://openalex.org/W2054723044","https://openalex.org/W2071048859","https://openalex.org/W2073862024","https://openalex.org/W2076578223","https://openalex.org/W2105137465"],"related_works":["https://openalex.org/W2090824337","https://openalex.org/W2921498481","https://openalex.org/W2963371116","https://openalex.org/W2011310062","https://openalex.org/W2022920970","https://openalex.org/W2112911989","https://openalex.org/W2165425090","https://openalex.org/W2120101606","https://openalex.org/W2537850624","https://openalex.org/W2463625816"],"abstract_inverted_index":{"The":[0],"nonlinear":[1,103],"diffusion":[2,104],"equation":[3],"$\\rho_t-\\Delta(\\rho":[4],"H(\\rho-\\rho_c))=0$":[5],"in":[6],"$(0,\\infty)\\times":[7],"\\mathbb{R}^n$,":[8],"$\\rho(0,x)=\\rho_0(x)$,":[9],"where":[10,87],"$H$":[11],"is":[12,89,95,108],"the":[13,17,72,75,81,90,96,101,110,117],"Heaviside":[14],"function,":[15],"describes":[16],"sandpile":[18],"model":[19],"[P.":[20],"Bak,":[21],"C.":[22],"Tang,":[23],"and":[24,35,93,120,127,137],"K.":[25],"Wiesenfeld,":[26],"Phys.":[27,39],"Rev.":[28],"A":[29],"(3),":[30],"pp.":[31,43,53,135,145,153],"364--374;":[32],"P.":[33],"Bantay":[34],"I.":[36],"M.":[37],"Janosi,":[38],"A,":[40],"185":[41],"(1992),":[42],"11--18;":[44],"R.":[45],"Cafiero":[46],"et":[47],"al.,":[48],"Europhys.":[49],"Lett.,":[50],"29":[51,133],"(1995),":[52],"111--116]":[54],"with":[55,80],"critical":[56],"state":[57],"$\\rho_c\\in":[58],"L^\\infty(\\mathbb{R}^n)\\cap":[59],"L^1(\\mathbb{R}^n)$.":[60],"Here,":[61],"one":[62],"proves":[63],"that":[64,113],"a":[65],"solution":[66],"$\\rho=\\rho(t,x)$":[67],"can":[68],"be":[69],"obtained":[70,115],"as":[71],"limit":[73],"of":[74,112],"time-stepping":[76],"approximation":[77],"scheme":[78],"associated":[79],"variational":[82],"problem":[83],"$\\rho_k={\\rm":[84],"arg}\\,\\min_{\\rho\\in\\mathcal{P}}\\{\\frac1h\\":[85],"d^2(\\rho_{k-1},\\rho)+\\mathbb{E}(\\rho)\\}$,":[86],"$d$":[88],"$2$-Wasserstein":[91],"distance":[92],"$\\mathbb{E}$":[94],"energy":[97],"functional":[98],"corresponding":[99],"to":[100],"above":[102],"process.":[105],"This":[106],"result":[107],"on":[109],"line":[111],"previously":[114],"for":[116],"linear":[118],"Fokker--Planck":[119],"porous":[121],"media":[122],"equations":[123],"by":[124],"Jordan,":[125],"Kinderlehrer,":[126],"Otto":[128,138],"[SIAM":[129],"J.":[130],"Math.":[131],"Anal.,":[132,142],"(1998),":[134,144],"1--17]":[136],"[Arch.":[139],"Ration.":[140],"Mech.":[141],"141":[143],"63--103;":[146],"Comm.":[147],"Partial":[148],"Differential":[149],"Equations,":[150],"26":[151],"(2001),":[152],"101--174].":[154]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"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"}
