{"id":"https://openalex.org/W7214508231","doi":"https://doi.org/10.48550/arxiv.2609.29842","title":"The Two-Component Becker-D\u00f6ring System: Basic Properties","display_name":"The Two-Component Becker-D\u00f6ring System: Basic Properties","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214508231","doi":"https://doi.org/10.48550/arxiv.2609.29842"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29842","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29842","pdf_url":"https://arxiv.org/pdf/2609.29842","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29842","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025223961","display_name":"Jens Scholten","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Scholten, Jens","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5025223961"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.8910999894142151,"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":0.8910999894142151,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.011599999852478504,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.008999999612569809,"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/becker-doring-model","display_name":"Becker-D\u00f6ring model","score":0.9309999942779541},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.8130000233650208},{"id":"https://openalex.org/keywords/mass-conservation","display_name":"mass conservation","score":0.996999979019165},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.9340000152587891},{"id":"https://openalex.org/keywords/detailed-balance","display_name":"detailed balance","score":0.9879999756813049},{"id":"https://openalex.org/keywords/entropy-equation","display_name":"entropy equation","score":0.9169999957084656},{"id":"https://openalex.org/keywords/kullback-leibler-divergence","display_name":"Kullback-Leibler divergence","score":0.7770000100135803},{"id":"https://openalex.org/keywords/equilibrium-states","display_name":"equilibrium states","score":0.9610000252723694},{"id":"https://openalex.org/keywords/weak-topology","display_name":"weak topology","score":0.871999979019165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.612500011920929},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4327000081539154},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.421999990940094},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.37299999594688416},{"id":"https://openalex.org/C135694725","wikidata":"https://www.wikidata.org/wiki/Q1201087","display_name":"Detailed balance","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.31700000166893005},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2847999930381775},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27149999141693115},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29842","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29842","pdf_url":"https://arxiv.org/pdf/2609.29842","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.29842","doi":"https://doi.org/10.48550/arxiv.2609.29842","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29842","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29842","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29842","pdf_url":"https://arxiv.org/pdf/2609.29842","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1521016025","display_name":"EXC 2047: Hausdorff Center for Mathematics (HCM)","funder_award_id":"390685813","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4274133347","display_name":null,"funder_award_id":"390685813","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G5310617150","display_name":null,"funder_award_id":"EXC 2047","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G5686947098","display_name":null,"funder_award_id":"539309657","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G591746060","display_name":null,"funder_award_id":"EXC-2047","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8265043617","display_name":null,"funder_award_id":"CRC 1720","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214508231.pdf","grobid_xml":"https://content.openalex.org/works/W7214508231.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214333099","https://openalex.org/W7095162454","https://openalex.org/W2052276710","https://openalex.org/W2099609006","https://openalex.org/W4308281206","https://openalex.org/W3101512772","https://openalex.org/W1987715662","https://openalex.org/W2128137720","https://openalex.org/W7026868994","https://openalex.org/W7100708183"],"abstract_inverted_index":{"The":[0],"two-component":[1],"Becker-D\u00f6ring":[2],"model":[3],"is":[4],"a":[5,39,58],"two-dimensional":[6],"coagulation-fragmentation":[7],"equation":[8],"that":[9],"describes":[10],"the":[11,30,48,53,62,71,90,94],"dynamics":[12],"of":[13,20,35,50,61,73,79],"clusters":[14],"built":[15],"from":[16],"two":[17],"different":[18],"types":[19],"monomers":[21],"growing":[22],"and":[23,32,37,65,83,87],"shrinking":[24],"through":[25],"monomer":[26],"interaction.":[27],"We":[28,68],"show":[29],"existence":[31],"mass":[33],"conservation":[34],"solutions":[36],"give":[38],"partial":[40],"result":[41],"regarding":[42],"uniqueness.":[43],"Furthermore,":[44],"we":[45],"prove":[46],"under":[47,77],"assumption":[49],"detailed":[51,59],"balance":[52],"entropy":[54],"equation,":[55],"followed":[56],"by":[57],"study":[60],"equilibrium":[63],"states":[64],"relative":[66,75],"entropies.":[67],"can":[69],"determine":[70],"minimum":[72],"all":[74],"entropies":[76],"sequences":[78,92],"fixed":[80],"Type":[81,84],"I":[82],"II":[85],"masses":[86],"fully":[88],"describe":[89],"minimising":[91],"in":[93],"weak*":[95],"topology.":[96]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-27T00:00:00"}