{"id":"https://openalex.org/W2883189343","doi":"https://doi.org/10.1137/18m1201032","title":"Stability and Convergence of the String Method for Computing Minimum Energy Paths","display_name":"Stability and Convergence of the String Method for Computing Minimum Energy Paths","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2883189343","doi":"https://doi.org/10.1137/18m1201032","mag":"2883189343"},"language":"en","primary_location":{"id":"doi:10.1137/18m1201032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1201032","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1807.06094","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057688610","display_name":"Brian Van Koten","orcid":"https://orcid.org/0000-0002-0225-7550"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brian Van Koten","raw_affiliation_strings":["University of Massachusetts"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Massachusetts","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036018970","display_name":"Mitchell Luskin","orcid":"https://orcid.org/0000-0003-1981-199X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mitchell Luskin","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1981-199X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0533273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"2","first_page":"873","last_page":"898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9975000023841858,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.993399977684021,"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/convergence","display_name":"Convergence (economics)","score":0.7758475542068481},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.7750557661056519},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6805627346038818},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5910772681236267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.570419430732727},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.48965007066726685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2222583293914795},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.05623385310173035}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7758475542068481},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.7750557661056519},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6805627346038818},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5910772681236267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.570419430732727},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48965007066726685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2222583293914795},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.05623385310173035},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1201032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1201032","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.06094","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1807.06094","pdf_url":"https://arxiv.org/pdf/1807.06094","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2883189343","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1807.06094.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1807.06094","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1807.06094","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.06094","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1807.06094","pdf_url":"https://arxiv.org/pdf/1807.06094","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G3170874447","display_name":null,"funder_award_id":"1547396","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4126563218","display_name":null,"funder_award_id":"DE-SC0012733","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7141758789","display_name":null,"funder_award_id":"SC0012733","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2883189343.pdf","grobid_xml":"https://content.openalex.org/works/W2883189343.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W582868771","https://openalex.org/W1518854728","https://openalex.org/W1550918041","https://openalex.org/W1557324374","https://openalex.org/W1972323103","https://openalex.org/W1979569363","https://openalex.org/W1983132551","https://openalex.org/W1986614779","https://openalex.org/W1998141434","https://openalex.org/W1998299443","https://openalex.org/W2006812353","https://openalex.org/W2023868145","https://openalex.org/W2031430816","https://openalex.org/W2049738344","https://openalex.org/W2065251521","https://openalex.org/W2083544350","https://openalex.org/W2088615896","https://openalex.org/W2092144432","https://openalex.org/W2110043143","https://openalex.org/W2122427541","https://openalex.org/W2141445032","https://openalex.org/W2205647194"],"related_works":["https://openalex.org/W2164555637","https://openalex.org/W2084151718","https://openalex.org/W2757244282","https://openalex.org/W1748748370","https://openalex.org/W3023160755","https://openalex.org/W2949314434","https://openalex.org/W2727477347","https://openalex.org/W3176625326","https://openalex.org/W2952866880","https://openalex.org/W3026399503","https://openalex.org/W180695596","https://openalex.org/W3192102061","https://openalex.org/W2358770766","https://openalex.org/W1973974006","https://openalex.org/W1511263746","https://openalex.org/W96441109","https://openalex.org/W2035797903","https://openalex.org/W3025815144","https://openalex.org/W2905758916","https://openalex.org/W3214118236"],"abstract_inverted_index":{"We":[0],"analyze":[1],"the":[2,5,29,33,40,48,59,64],"convergence":[3],"of":[4,8,47,58,66],"string":[6,41],"method":[7,42],"E,":[9],"Ren,":[10],"and":[11],"Vanden-Eijnden":[12],"[J.":[13],"Chem.":[14],"Phys.,":[15],"126":[16],"(2007),":[17],"164103]":[18],"to":[19,28,53],"a":[20,45],"minimum":[21,34,49,60],"energy":[22,35,50,61],"path.":[23],"Under":[24],"some":[25],"assumptions":[26],"relating":[27],"critical":[30],"points":[31],"on":[32],"path,":[36],"we":[37],"show":[38],"that":[39],"initialized":[43],"in":[44],"neighborhood":[46,57],"path":[51,62],"converges":[52],"an":[54],"arbitrarily":[55],"small":[56],"as":[63],"number":[65],"images":[67],"is":[68],"increased.":[69]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2022-08-04T00:00:00"}
