{"id":"https://openalex.org/W2004234558","doi":"https://doi.org/10.1137/s0036139999358180","title":"Dynamics of Free Surfaces in Random Porous Media","display_name":"Dynamics of Free Surfaces in Random Porous Media","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2004234558","doi":"https://doi.org/10.1137/s0036139999358180","mag":"2004234558"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139999358180","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139999358180","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":"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/A5049066010","display_name":"Daniel M. Tartakovsky","orcid":"https://orcid.org/0000-0001-9019-8935"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel M. Tartakovsky","raw_affiliation_strings":["Los Alamos National Laboratory,Theoretical Division"],"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory,Theoretical Division","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101747508","display_name":"C. L. Winter","orcid":"https://orcid.org/0000-0003-0230-9215"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. L. Winter","raw_affiliation_strings":["Los Alamos National Laboratory,Theoretical Division"],"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory,Theoretical Division","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049066010"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":11.5205,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.98116197,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"6","first_page":"1857","last_page":"1876"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10716","display_name":"Soil and Unsaturated Flow","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10716","display_name":"Soil and Unsaturated Flow","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10894","display_name":"Groundwater flow and contamination studies","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T10535","display_name":"Landslides and related hazards","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"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/mathematics","display_name":"Mathematics","score":0.6312919855117798},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5806843638420105},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.5480199456214905},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5248448848724365},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.46746495366096497},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4488902986049652},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.43537092208862305},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.41815224289894104},{"id":"https://openalex.org/keywords/hydraulic-conductivity","display_name":"Hydraulic conductivity","score":0.4149456322193146},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37764960527420044},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.18281373381614685},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17999064922332764},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17065128684043884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6312919855117798},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5806843638420105},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.5480199456214905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5248448848724365},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.46746495366096497},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4488902986049652},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.43537092208862305},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.41815224289894104},{"id":"https://openalex.org/C63184880","wikidata":"https://www.wikidata.org/wiki/Q2783041","display_name":"Hydraulic conductivity","level":3,"score":0.4149456322193146},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37764960527420044},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.18281373381614685},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17999064922332764},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17065128684043884},{"id":"https://openalex.org/C159390177","wikidata":"https://www.wikidata.org/wiki/Q9161265","display_name":"Soil science","level":1,"score":0.0},{"id":"https://openalex.org/C159750122","wikidata":"https://www.wikidata.org/wiki/Q96621023","display_name":"Soil water","level":2,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139999358180","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139999358180","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:CiteSeerX.psu:10.1.1.104.7247","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.7247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.lanl.gov/~dmt/papers/freesurfSIAM.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W614869411","https://openalex.org/W656701252","https://openalex.org/W1499509637","https://openalex.org/W1592093959","https://openalex.org/W1968190461","https://openalex.org/W1972293301","https://openalex.org/W1977191733","https://openalex.org/W1979757129","https://openalex.org/W1984556393","https://openalex.org/W1990193429","https://openalex.org/W2004716724","https://openalex.org/W2008201229","https://openalex.org/W2010006404","https://openalex.org/W2013736290","https://openalex.org/W2023169772","https://openalex.org/W2038694860","https://openalex.org/W2061693681","https://openalex.org/W2061941426","https://openalex.org/W2064681424","https://openalex.org/W2072509160","https://openalex.org/W2077422114","https://openalex.org/W2083603833","https://openalex.org/W2088842272","https://openalex.org/W2091659473","https://openalex.org/W2107773546","https://openalex.org/W2125825720","https://openalex.org/W2131698423","https://openalex.org/W2148651930","https://openalex.org/W2171429069","https://openalex.org/W2218684725","https://openalex.org/W2416983119","https://openalex.org/W2610642149","https://openalex.org/W2992474449","https://openalex.org/W4256082184"],"related_works":["https://openalex.org/W1597743604","https://openalex.org/W3149489606","https://openalex.org/W2038723108","https://openalex.org/W2084197631","https://openalex.org/W2115858945","https://openalex.org/W2050605513","https://openalex.org/W2099724751","https://openalex.org/W4205608118","https://openalex.org/W2373461954","https://openalex.org/W3016963406"],"abstract_inverted_index":{"We":[0,23,106],"consider":[1],"free":[2,66],"surface":[3],"flow":[4],"in":[5,30,57,115],"random":[6,18,55],"porous":[7,135],"media":[8],"by":[9,25,90,110],"treating":[10],"hydraulic":[11,124,162],"conductivity":[12],"of":[13,33,42,48,52,64,86,112,117,120,123,155,158,161],"a":[14,17,84],"medium":[15],"as":[16],"field":[19],"with":[20,78],"known":[21],"statistics.":[22],"start":[24],"recasting":[26],"the":[27,31,38,54,61,65,70,75,91,118,121,156,159],"boundary-value":[28],"problem":[29],"form":[32],"an":[34],"integral":[35],"equation":[36,50],"where":[37],"parameters":[39],"and":[40,68],"domain":[41],"integration":[43],"are":[44],"random.":[45],"Our":[46],"analysis":[47],"this":[49,127],"consists":[51],"expanding":[53],"integrals":[56],"Taylor's":[58],"series":[59],"about":[60],"mean":[62],"position":[63],"boundary":[67],"taking":[69],"ensemble":[71,94],"mean.":[72],"To":[73],"quantify":[74],"uncertainty":[76],"associated":[77],"such":[79,108,145],"predictions,":[80],"we":[81],"also":[82],"develop":[83],"set":[85],"integro-differential":[87],"equations":[88,99],"satisfied":[89],"corresponding":[92],"second":[93],"moments.":[95],"The":[96],"resulting":[97],"moment":[98],"require":[100],"closure":[101],"approximations":[102],"to":[103,132],"be":[104],"workable.":[105],"derive":[107],"closures":[109],"means":[111],"perturbation":[113,146],"expansions":[114,147],"powers":[116],"variance":[119,157],"logarithm":[122,160],"conductivity.":[125,163],"Though":[126],"formally":[128],"limits":[129],"our":[130,137],"solutions":[131,139],"mildly":[133],"heterogeneous":[134],"media,":[136],"analytical":[138],"for":[140,151],"one-dimensional":[141],"flows":[142],"demonstrate":[143],"that":[144],"may":[148],"remain":[149],"robust":[150],"relatively":[152],"large":[153],"values":[154]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}