{"id":"https://openalex.org/W1955809987","doi":"https://doi.org/10.1137/151003751","title":"Steadily Translating Parabolic Dissolution Fingers","display_name":"Steadily Translating Parabolic Dissolution Fingers","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1955809987","doi":"https://doi.org/10.1137/151003751","mag":"1955809987"},"language":"en","primary_location":{"id":"doi:10.1137/151003751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151003751","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","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/1507.04056","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064054118","display_name":"Pawe\u0142 Kondratiuk","orcid":"https://orcid.org/0000-0001-9467-2331"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Kondratiuk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056567736","display_name":"Piotr Szymczak","orcid":"https://orcid.org/0000-0001-8940-7891"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piotr Szymczak","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02939421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"75","issue":"5","first_page":"2193","last_page":"2213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"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/T11302","display_name":"CO2 Sequestration and Geologic Interactions","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dissolution","display_name":"Dissolution","score":0.7310236692428589},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6619717478752136},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.6073049902915955},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5770015120506287},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5631294846534729},{"id":"https://openalex.org/keywords/front","display_name":"Front (military)","score":0.5300495624542236},{"id":"https://openalex.org/keywords/radius-of-curvature","display_name":"Radius of curvature","score":0.4842948317527771},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.48063603043556213},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.4796450734138489},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.4448871910572052},{"id":"https://openalex.org/keywords/pressure-gradient","display_name":"Pressure gradient","score":0.43485477566719055},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.43308377265930176},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42596128582954407},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3345333933830261},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3324672281742096},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3277796506881714},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.30866605043411255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2691464126110077},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.24492871761322021},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"Mean curvature flow","score":0.14783117175102234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09064194560050964},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.07999271154403687}],"concepts":[{"id":"https://openalex.org/C88380143","wikidata":"https://www.wikidata.org/wiki/Q416674","display_name":"Dissolution","level":2,"score":0.7310236692428589},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6619717478752136},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6073049902915955},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5770015120506287},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5631294846534729},{"id":"https://openalex.org/C2777551076","wikidata":"https://www.wikidata.org/wiki/Q842332","display_name":"Front (military)","level":2,"score":0.5300495624542236},{"id":"https://openalex.org/C11665553","wikidata":"https://www.wikidata.org/wiki/Q1136069","display_name":"Radius of curvature","level":5,"score":0.4842948317527771},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.48063603043556213},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4796450734138489},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.4448871910572052},{"id":"https://openalex.org/C98156149","wikidata":"https://www.wikidata.org/wiki/Q2414143","display_name":"Pressure gradient","level":2,"score":0.43485477566719055},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.43308377265930176},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42596128582954407},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3345333933830261},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3324672281742096},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3277796506881714},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.30866605043411255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2691464126110077},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.24492871761322021},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.14783117175102234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09064194560050964},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.07999271154403687},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/151003751","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151003751","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1507.04056","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.04056","pdf_url":"https://arxiv.org/pdf/1507.04056","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":"","raw_type":"text"},{"id":"mag:1955809987","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1507.04056","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.1507.04056","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.04056","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.04056","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.04056","pdf_url":"https://arxiv.org/pdf/1507.04056","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1955809987.pdf"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1491152682","https://openalex.org/W1626888739","https://openalex.org/W1838832658","https://openalex.org/W1968802449","https://openalex.org/W1970934067","https://openalex.org/W1971055245","https://openalex.org/W1979004504","https://openalex.org/W1984986804","https://openalex.org/W1985662002","https://openalex.org/W1987955754","https://openalex.org/W1988538033","https://openalex.org/W1990663199","https://openalex.org/W1993728319","https://openalex.org/W1994500683","https://openalex.org/W1996969213","https://openalex.org/W1999238469","https://openalex.org/W2000329342","https://openalex.org/W2004716724","https://openalex.org/W2015482812","https://openalex.org/W2021074196","https://openalex.org/W2021121177","https://openalex.org/W2024125858","https://openalex.org/W2024665312","https://openalex.org/W2028070501","https://openalex.org/W2029772134","https://openalex.org/W2041868860","https://openalex.org/W2042667637","https://openalex.org/W2047351548","https://openalex.org/W2063332268","https://openalex.org/W2064849586","https://openalex.org/W2065384567","https://openalex.org/W2068362857","https://openalex.org/W2076978869","https://openalex.org/W2081520649","https://openalex.org/W2083814675","https://openalex.org/W2087147430","https://openalex.org/W2090197454","https://openalex.org/W2090456264","https://openalex.org/W2112847461","https://openalex.org/W2136492986","https://openalex.org/W2142690842","https://openalex.org/W2155219995","https://openalex.org/W2163471181","https://openalex.org/W2169798625","https://openalex.org/W2170432712","https://openalex.org/W2314637540","https://openalex.org/W2335285317","https://openalex.org/W3100147603"],"related_works":["https://openalex.org/W1694945543","https://openalex.org/W2109043305","https://openalex.org/W1969977859","https://openalex.org/W264452308","https://openalex.org/W2992474449","https://openalex.org/W1993113888","https://openalex.org/W2909230924","https://openalex.org/W97987241","https://openalex.org/W1983297774","https://openalex.org/W203125263","https://openalex.org/W2054235460","https://openalex.org/W3146702576","https://openalex.org/W1961366200","https://openalex.org/W2244881662","https://openalex.org/W2063329728","https://openalex.org/W3185551324","https://openalex.org/W2341805838","https://openalex.org/W2096511635","https://openalex.org/W2003735608","https://openalex.org/W3033603883"],"abstract_inverted_index":{"Dissolution":[0],"fingers":[1,38,110,131],"(or":[2],"wormholes)":[3],"are":[4],"formed":[5],"during":[6],"the":[7,20,31,40,45,54,59,65,68,74,80,83,87,90,93,105,118,123,130,135,145,159],"dissolution":[8,60],"of":[9,16,36,92,107,129,144,156],"a":[10,14,113],"porous":[11],"rock":[12],"as":[13],"result":[15],"nonlinear":[17],"feedbacks":[18],"between":[19,86],"flow,":[21],"transport":[22],"and":[23,33,82,89,100,122,127,132,164],"chemical":[24],"reactions":[25],"at":[26,58],"pore":[27],"surfaces.":[28],"We":[29,62,116],"analyze":[30],"shapes":[32],"growth":[34],"velocities":[35],"such":[37],"within":[39,137],"thin-front":[41],"approximation,":[42],"in":[43,158],"which":[44],"reaction":[46],"is":[47,71,95,139,147],"assumed":[48],"to":[49,149,153],"take":[50],"place":[51],"instantaneously":[52],"with":[53],"reactants":[55],"fully":[56],"consumed":[57],"front.":[61],"concentrate":[63],"on":[64],"case":[66],"when":[67],"main":[69],"flow":[70,136],"driven":[72],"by":[73,112],"constant":[75,165],"pressure":[76,124],"gradient":[77],"far":[78],"from":[79],"finger,":[81],"permeability":[84],"contrast":[85],"inside":[88,126],"outside":[91,128],"finger":[94,146],"finite.":[96],"Using":[97],"Ivantsov":[98],"ansatz":[99],"conformal":[101],"transformations":[102],"we":[103],"find":[104],"family":[106],"steadily":[108],"translating":[109],"characterized":[111],"parabolic":[114],"shape.":[115],"derive":[117],"reactant":[119],"concentration":[120],"field":[121,125],"show":[133],"that":[134],"them":[138],"uniform.":[140],"The":[141],"advancement":[142],"velocity":[143],"shown":[148],"be":[150],"inversely":[151],"proportional":[152],"its":[154],"radius":[155],"curvature":[157],"small":[160],"P\u00e9clet":[161,168],"number":[162],"limit":[163],"for":[166],"large":[167],"numbers.":[169]},"counts_by_year":[],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}