{"id":"https://openalex.org/W2015242641","doi":"https://doi.org/10.1137/s0036144599364296","title":"Front Propagation in Heterogeneous Media","display_name":"Front Propagation in Heterogeneous Media","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2015242641","doi":"https://doi.org/10.1137/s0036144599364296","mag":"2015242641"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144599364296","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599364296","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5059708262","display_name":"Jack Xin","orcid":"https://orcid.org/0000-0002-6438-8476"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jack Xin","raw_affiliation_strings":["University of Texas at Austin#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin#TAB#","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5059708262"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":19.5493,"has_fulltext":false,"cited_by_count":560,"citation_normalized_percentile":{"value":0.99611766,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"42","issue":"2","first_page":"161","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9929999709129333,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9929999709129333,"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6791356801986694},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.6611646413803101},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5252865552902222},{"id":"https://openalex.org/keywords/front","display_name":"Front (military)","score":0.5181037783622742},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.49590668082237244},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.4839482605457306},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4737699329853058},{"id":"https://openalex.org/keywords/combustion","display_name":"Combustion","score":0.43407705426216125},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4279947876930237},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.42686840891838074},{"id":"https://openalex.org/keywords/deposition","display_name":"Deposition (geology)","score":0.4108573794364929},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40529772639274597},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.40109342336654663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32571911811828613},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3128403425216675},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.2542291581630707},{"id":"https://openalex.org/keywords/meteorology","display_name":"Meteorology","score":0.20684272050857544},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1927412450313568},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1742115020751953},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.15338969230651855},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.14886590838432312},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.14593049883842468},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.13807430863380432},{"id":"https://openalex.org/keywords/physical-chemistry","display_name":"Physical chemistry","score":0.11170139908790588}],"concepts":[{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6791356801986694},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.6611646413803101},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5252865552902222},{"id":"https://openalex.org/C2777551076","wikidata":"https://www.wikidata.org/wiki/Q842332","display_name":"Front (military)","level":2,"score":0.5181037783622742},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.49590668082237244},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.4839482605457306},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4737699329853058},{"id":"https://openalex.org/C105923489","wikidata":"https://www.wikidata.org/wiki/Q133235","display_name":"Combustion","level":2,"score":0.43407705426216125},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4279947876930237},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.42686840891838074},{"id":"https://openalex.org/C64297162","wikidata":"https://www.wikidata.org/wiki/Q1987070","display_name":"Deposition (geology)","level":3,"score":0.4108573794364929},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40529772639274597},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.40109342336654663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32571911811828613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3128403425216675},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.2542291581630707},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.20684272050857544},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1927412450313568},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1742115020751953},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.15338969230651855},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.14886590838432312},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.14593049883842468},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.13807430863380432},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.11170139908790588},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2816523","wikidata":"https://www.wikidata.org/wiki/Q180184","display_name":"Sediment","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036144599364296","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599364296","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":174,"referenced_works":["https://openalex.org/W7856492","https://openalex.org/W47357201","https://openalex.org/W90288657","https://openalex.org/W110991913","https://openalex.org/W236702750","https://openalex.org/W591468295","https://openalex.org/W1479813641","https://openalex.org/W1494276175","https://openalex.org/W1547249381","https://openalex.org/W1550382162","https://openalex.org/W1550828720","https://openalex.org/W1558902221","https://openalex.org/W1560060148","https://openalex.org/W1572551827","https://openalex.org/W1575147392","https://openalex.org/W1576267150","https://openalex.org/W1583602735","https://openalex.org/W1611389358","https://openalex.org/W1620963072","https://openalex.org/W1633669915","https://openalex.org/W1866311589","https://openalex.org/W1965218710","https://openalex.org/W1966964800","https://openalex.org/W1967814127","https://openalex.org/W1968190461","https://openalex.org/W1969182281","https://openalex.org/W1969336024","https://openalex.org/W1971208374","https://openalex.org/W1971411567","https://openalex.org/W1971469087","https://openalex.org/W1972194505","https://openalex.org/W1972224529","https://openalex.org/W1973143252","https://openalex.org/W1973159727","https://openalex.org/W1973771388","https://openalex.org/W1975110976","https://openalex.org/W1975642142","https://openalex.org/W1976529930","https://openalex.org/W1977082840","https://openalex.org/W1978023674","https://openalex.org/W1978239096","https://openalex.org/W1979893394","https://openalex.org/W1987139950","https://openalex.org/W1987432157","https://openalex.org/W1988606805","https://openalex.org/W1990257625","https://openalex.org/W1991474034","https://openalex.org/W1993206373","https://openalex.org/W1996255856","https://openalex.org/W1996495082","https://openalex.org/W1999648599","https://openalex.org/W2003166268","https://openalex.org/W2004914597","https://openalex.org/W2005722356","https://openalex.org/W2006870938","https://openalex.org/W2007823673","https://openalex.org/W2011698236","https://openalex.org/W2014653737","https://openalex.org/W2014863630","https://openalex.org/W2018793673","https://openalex.org/W2020718248","https://openalex.org/W2021474405","https://openalex.org/W2021573185","https://openalex.org/W2021611402","https://openalex.org/W2021669684","https://openalex.org/W2022072223","https://openalex.org/W2024226399","https://openalex.org/W2025935606","https://openalex.org/W2027703695","https://openalex.org/W2029076769","https://openalex.org/W2029291300","https://openalex.org/W2031385169","https://openalex.org/W2032316144","https://openalex.org/W2032348603","https://openalex.org/W2032469836","https://openalex.org/W2032874363","https://openalex.org/W2034790369","https://openalex.org/W2037760602","https://openalex.org/W2038991247","https://openalex.org/W2044102473","https://openalex.org/W2044879434","https://openalex.org/W2046904024","https://openalex.org/W2047075403","https://openalex.org/W2049045642","https://openalex.org/W2049286744","https://openalex.org/W2049565304","https://openalex.org/W2049805527","https://openalex.org/W2051002428","https://openalex.org/W2052151933","https://openalex.org/W2052172730","https://openalex.org/W2052827802","https://openalex.org/W2055826414","https://openalex.org/W2057131829","https://openalex.org/W2057462050","https://openalex.org/W2060024519","https://openalex.org/W2061121403","https://openalex.org/W2061330175","https://openalex.org/W2062877399","https://openalex.org/W2063152565","https://openalex.org/W2063225484","https://openalex.org/W2064651716","https://openalex.org/W2065580955","https://openalex.org/W2065906013","https://openalex.org/W2066212902","https://openalex.org/W2070823330","https://openalex.org/W2072211008","https://openalex.org/W2072345257","https://openalex.org/W2073289536","https://openalex.org/W2074505548","https://openalex.org/W2078460839","https://openalex.org/W2078535099","https://openalex.org/W2079949023","https://openalex.org/W2082241952","https://openalex.org/W2086126894","https://openalex.org/W2086593256","https://openalex.org/W2087269214","https://openalex.org/W2087496472","https://openalex.org/W2089452414","https://openalex.org/W2090519619","https://openalex.org/W2091636379","https://openalex.org/W2092459682","https://openalex.org/W2092572226","https://openalex.org/W2092574869","https://openalex.org/W2094910098","https://openalex.org/W2095365013","https://openalex.org/W2102032362","https://openalex.org/W2103045072","https://openalex.org/W2103426427","https://openalex.org/W2104631845","https://openalex.org/W2110049458","https://openalex.org/W2112543799","https://openalex.org/W2112906818","https://openalex.org/W2116942052","https://openalex.org/W2134675363","https://openalex.org/W2141645179","https://openalex.org/W2147035016","https://openalex.org/W2147564453","https://openalex.org/W2147982833","https://openalex.org/W2149563580","https://openalex.org/W2150449764","https://openalex.org/W2153188531","https://openalex.org/W2153631377","https://openalex.org/W2154461847","https://openalex.org/W2156205553","https://openalex.org/W2156610674","https://openalex.org/W2157408380","https://openalex.org/W2162778770","https://openalex.org/W2163195696","https://openalex.org/W2167500235","https://openalex.org/W2169071224","https://openalex.org/W2207223089","https://openalex.org/W2314750725","https://openalex.org/W2316336629","https://openalex.org/W2334560608","https://openalex.org/W2468303538","https://openalex.org/W2576544140","https://openalex.org/W2605312625","https://openalex.org/W2802739963","https://openalex.org/W2964197947","https://openalex.org/W2977474616","https://openalex.org/W3021722416","https://openalex.org/W3098409059","https://openalex.org/W3101556735","https://openalex.org/W3103907372","https://openalex.org/W3104092944","https://openalex.org/W4205832538","https://openalex.org/W4238101061","https://openalex.org/W4244726376","https://openalex.org/W4248513464","https://openalex.org/W4251046712","https://openalex.org/W4252414949","https://openalex.org/W4253109276","https://openalex.org/W4285719527","https://openalex.org/W4292081050"],"related_works":["https://openalex.org/W3036101264","https://openalex.org/W2163151373","https://openalex.org/W1523233633","https://openalex.org/W4238257821","https://openalex.org/W2165001118","https://openalex.org/W2022713607","https://openalex.org/W2161748076","https://openalex.org/W2794551621","https://openalex.org/W4246396821","https://openalex.org/W2726409237"],"abstract_inverted_index":{"A":[0],"review":[1],"is":[2],"presented":[3],"of":[4,64],"recent":[5],"results":[6,29],"on":[7],"front":[8],"propagation":[9],"in":[10,13,39,46,54,60,73],"reaction-diffusion-advection":[11],"equations":[12],"homogeneous":[14,40],"and":[15,21,49,51,76],"heterogeneous":[16],"media.":[17,56],"Formal":[18],"asymptotic":[19],"expansions":[20],"heuristic":[22],"ideas":[23],"are":[24,82],"used":[25],"to":[26],"motivate":[27],"the":[28,86],"wherever":[30],"possible.":[31],"The":[32],"fronts":[33,38,45,53,58],"include":[34],"constant-speed":[35],"monotone":[36],"traveling":[37,44],"media,":[41,48,75],"periodically":[42],"varying":[43],"periodic":[47],"fluctuating":[50],"fractal":[52],"random":[55],"These":[57],"arise":[59],"a":[61],"wide":[62],"range":[63],"applications":[65],"such":[66],"as":[67],"chemical":[68],"kinetics,":[69],"combustion,":[70],"biology,":[71],"transport":[72],"porous":[74],"industrial":[77],"deposition":[78],"processes.":[79],"Open":[80],"problems":[81],"briefly":[83],"discussed":[84],"along":[85],"way.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":24},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":33},{"year":2019,"cited_by_count":26},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":25},{"year":2015,"cited_by_count":31},{"year":2014,"cited_by_count":32},{"year":2013,"cited_by_count":29},{"year":2012,"cited_by_count":23}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}