{"id":"https://openalex.org/W2071053043","doi":"https://doi.org/10.1137/120904056","title":"Poisson--Nernst--Planck Systems for Ion Flow with a Local Hard-Sphere Potential for Ion Size Effects","display_name":"Poisson--Nernst--Planck Systems for Ion Flow with a Local Hard-Sphere Potential for Ion Size Effects","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2071053043","doi":"https://doi.org/10.1137/120904056","mag":"2071053043"},"language":"en","primary_location":{"id":"doi:10.1137/120904056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120904056","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","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/A5050604885","display_name":"Guojian Lin","orcid":"https://orcid.org/0000-0001-8650-0345"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guojian Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077033119","display_name":"Weishi Liu","orcid":"https://orcid.org/0000-0002-0543-6917"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weishi Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022440583","display_name":"Yingfei Yi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yingfei Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040653613","display_name":"Mingji Zhang","orcid":"https://orcid.org/0000-0002-8249-4758"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mingji Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1138,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.88463966,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"12","issue":"3","first_page":"1613","last_page":"1648"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10409","display_name":"Fuel Cells and Related Materials","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10409","display_name":"Fuel Cells and Related Materials","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11582","display_name":"Nanopore and Nanochannel Transport Studies","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12074","display_name":"Membrane-based Ion Separation Techniques","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/ion","display_name":"Ion","score":0.6229928135871887},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6084593534469604},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4888455271720886},{"id":"https://openalex.org/keywords/nernst-equation","display_name":"Nernst equation","score":0.4251166582107544},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.38547834753990173},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16660919785499573}],"concepts":[{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.6229928135871887},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6084593534469604},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4888455271720886},{"id":"https://openalex.org/C184501600","wikidata":"https://www.wikidata.org/wiki/Q751124","display_name":"Nernst equation","level":3,"score":0.4251166582107544},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.38547834753990173},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16660919785499573},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120904056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120904056","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W2127434","https://openalex.org/W1521219187","https://openalex.org/W1608239333","https://openalex.org/W1964582727","https://openalex.org/W1965195104","https://openalex.org/W1967135521","https://openalex.org/W1967543024","https://openalex.org/W1972270832","https://openalex.org/W1972760372","https://openalex.org/W1975219250","https://openalex.org/W1977899103","https://openalex.org/W1980001934","https://openalex.org/W1988689739","https://openalex.org/W1989521488","https://openalex.org/W1989987286","https://openalex.org/W1990265247","https://openalex.org/W1991033228","https://openalex.org/W1992465972","https://openalex.org/W1992971218","https://openalex.org/W1997029800","https://openalex.org/W1997596874","https://openalex.org/W2006062983","https://openalex.org/W2010931500","https://openalex.org/W2011372139","https://openalex.org/W2013351998","https://openalex.org/W2014241231","https://openalex.org/W2014943644","https://openalex.org/W2020292773","https://openalex.org/W2021411499","https://openalex.org/W2026480149","https://openalex.org/W2030155227","https://openalex.org/W2033681908","https://openalex.org/W2041496883","https://openalex.org/W2043340535","https://openalex.org/W2047841961","https://openalex.org/W2049498585","https://openalex.org/W2052476501","https://openalex.org/W2053748143","https://openalex.org/W2057876304","https://openalex.org/W2060304556","https://openalex.org/W2062726261","https://openalex.org/W2069020163","https://openalex.org/W2069831837","https://openalex.org/W2071267996","https://openalex.org/W2084236951","https://openalex.org/W2087201524","https://openalex.org/W2087496251","https://openalex.org/W2098494477","https://openalex.org/W2099887317","https://openalex.org/W2101833686","https://openalex.org/W2105344624","https://openalex.org/W2106989936","https://openalex.org/W2107145871","https://openalex.org/W2112769274","https://openalex.org/W2114889015","https://openalex.org/W2125407321","https://openalex.org/W2125758832","https://openalex.org/W2126264088","https://openalex.org/W2131194825","https://openalex.org/W2131852035","https://openalex.org/W2144992168","https://openalex.org/W2154030203","https://openalex.org/W2154711615","https://openalex.org/W2157649093","https://openalex.org/W2167085548","https://openalex.org/W2167152334","https://openalex.org/W2168869782","https://openalex.org/W2169530852","https://openalex.org/W2333337922","https://openalex.org/W3104973902","https://openalex.org/W4246164144","https://openalex.org/W4249698154"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"In":[0],"this":[1,101],"work,":[2],"we":[3,127],"analyze":[4],"a":[5,14,74,79,259],"one-dimensional":[6],"steady-state":[7],"Poisson--Nernst--Planck-type":[8],"model":[9,57,69],"for":[10,60,113,144],"ionic":[11,66],"flow":[12,228],"through":[13],"membrane":[15],"channel":[16],"with":[17,256,258],"fixed":[18],"boundary":[19,75,110,153,185,204,216,236],"ion":[20,29,51,61,115,122,145,170,191,223,246],"concentrations":[21,52,217],"(charges)":[22],"and":[23,34,38,137,212,252,266],"electric":[24],"potentials.":[25],"We":[26],"consider":[27],"two":[28,139,158,165],"species,":[30],"one":[31,35],"positively":[32],"charged":[33],"negatively":[36],"charged,":[37],"assume":[39],"zero":[40],"permanent":[41],"charge.":[42],"A":[43],"local":[44],"hard-sphere":[45,261],"potential":[46,163,262],"that":[47],"depends":[48],"pointwise":[49],"on":[50,64,88,97,197,203,226,240],"is":[53,71,86,117],"included":[54],"in":[55,215,245],"the":[56,65,89,109,121,133,162,169,180,187,198,227,238,241],"to":[58,108,176],"account":[59],"size":[62,146,171,224],"effects":[63,172,189,225],"flow.":[67],"The":[68,104],"problem":[70,77,112],"treated":[72],"as":[73,124],"value":[76,111],"of":[78,100,106,132,156,190,209,229,248],"singularly":[80],"perturbed":[81],"differential":[82],"system.":[83],"Our":[84],"analysis":[85],"based":[87],"geometric":[90],"singular":[91],"perturbation":[92],"theory":[93],"but,":[94],"most":[95],"importantly,":[96],"specific":[98],"structures":[99],"concrete":[102],"model.":[103],"existence":[105],"solutions":[107],"small":[114,125],"sizes":[116,123,192],"established":[118],"and,":[119],"treating":[120],"parameters,":[126],"also":[128,202,232],"derive":[129],"an":[130],"approximation":[131,244],"I-V":[134,210,250],"(current-voltage)":[135],"relation":[136],"identify":[138],"critical":[140,159,199,213,253],"potentials":[141,160,200,214,254],"or":[142],"voltages":[143],"effects.":[147],"Under":[148,234],"electroneutrality":[149,184,235],"(zero":[150],"net":[151],"charge)":[152],"conditions,":[154,186,237],"each":[155,177],"these":[157],"separates":[161],"into":[164],"regions":[166],"over":[167],"which":[168],"are":[173,218,231],"qualitatively":[174],"opposite":[175],"other.":[178],"On":[179],"other":[181],"hand,":[182],"without":[183],"qualitative":[188],"will":[193],"depend":[194],"not":[195],"only":[196],"but":[201],"concentrations.":[205],"Important":[206],"scaling":[207],"laws":[208],"relations":[211],"obtained.":[219],"Similar":[220],"results":[221,239],"about":[222],"matter":[230],"discussed.":[233],"first":[242],"order":[243],"diameters":[247],"solutions,":[249],"relations,":[251],"agree":[255],"those":[257],"nonlocal":[260],"examined":[263],"by":[264],"Ji":[265],"Liu":[267],"[J.":[268],"Dynam.":[269],"Differential":[270],"Equations,":[271],"24":[272],"(2012),":[273],"pp.":[274],"955--983].":[275]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
