{"id":"https://openalex.org/W2012050842","doi":"https://doi.org/10.1137/0915078","title":"A Gradient Random Walk Method for Two-Dimensional Reaction-Diffusion Equations","display_name":"A Gradient Random Walk Method for Two-Dimensional Reaction-Diffusion Equations","publication_year":1994,"publication_date":"1994-11-01","ids":{"openalex":"https://openalex.org/W2012050842","doi":"https://doi.org/10.1137/0915078","mag":"2012050842"},"language":"en","primary_location":{"id":"doi:10.1137/0915078","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915078","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5013857769","display_name":"Arthur Sherman","orcid":"https://orcid.org/0000-0002-8372-5941"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arthur Sherman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071387306","display_name":"Michael Mascagni","orcid":"https://orcid.org/0000-0003-3058-4580"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Mascagni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0985,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.75340867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"6","first_page":"1280","last_page":"1293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11048","display_name":"Bacteriophages and microbial interactions","score":0.9627000093460083,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"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/discretization","display_name":"Discretization","score":0.732959508895874},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6799178123474121},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.6430541276931763},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47545191645622253},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4694392681121826},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.46760550141334534},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.45912373065948486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45177122950553894},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43806812167167664},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.331274151802063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19689828157424927}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.732959508895874},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6799178123474121},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6430541276931763},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47545191645622253},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4694392681121826},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.46760550141334534},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.45912373065948486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45177122950553894},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43806812167167664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.331274151802063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19689828157424927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0915078","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915078","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.55.861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sushi.st.usm.edu/~mascagni/ftp/rgmtr.ps","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":24,"referenced_works":["https://openalex.org/W187557541","https://openalex.org/W1972194505","https://openalex.org/W1992906507","https://openalex.org/W1992957154","https://openalex.org/W1995623318","https://openalex.org/W2012189899","https://openalex.org/W2019045762","https://openalex.org/W2021950678","https://openalex.org/W2022214434","https://openalex.org/W2030738345","https://openalex.org/W2030752818","https://openalex.org/W2040193065","https://openalex.org/W2046899724","https://openalex.org/W2052582477","https://openalex.org/W2054557822","https://openalex.org/W2061191702","https://openalex.org/W2068306188","https://openalex.org/W2074106179","https://openalex.org/W2083206954","https://openalex.org/W2090698455","https://openalex.org/W2093943787","https://openalex.org/W2181588160","https://openalex.org/W3111685920","https://openalex.org/W4244396353"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W1507702947","https://openalex.org/W2370926798"],"abstract_inverted_index":{"An":[0],"extension":[1],"to":[2,24,53,72,112],"two":[3,75],"space":[4,76],"dimensions":[5],"of":[6,19,29,45,50,81,88],"the":[7,25,34,39,42,54,60,66,82,89],"gradient":[8,61],"random":[9,26],"walk":[10],"algorithm":[11],"for":[12],"reaction-diffusion":[13,115],"equations":[14],"is":[15,21,37,62,84,106,119],"presented.":[16],"This":[17],"family":[18],"algorithms":[20],"related":[22],"closely":[23],"vortex":[27],"method":[28,40,67,83,105],"computational":[30,35],"fluid":[31],"dynamics.":[32],"Although":[33],"cost":[36],"high,":[38],"has":[41],"desirable":[43],"features":[44,97],"being":[46],"grid":[47],"free":[48],"and":[49,109],"automatically":[51],"adapting":[52],"solution":[55],"by":[56],"concentrating":[57],"elements":[58],"where":[59],"large.":[63],"In":[64],"addition,":[65],"can":[68],"be":[69],"extended":[70],"easily":[71],"more":[73],"than":[74,92],"dimensions.":[77],"A":[78],"key":[79],"feature":[80],"discretization":[85],"in":[86,98],"terms":[87],"dependent,":[90],"rather":[91],"independent,":[93],"variable,":[94],"giving":[95],"it":[96],"common":[99],"with":[100],"Lagrangian":[101],"particle":[102],"methods.":[103],"The":[104],"derived":[107],"here":[108],"its":[110],"application":[111],"some":[113],"simple":[114],"wave":[116],"propagation":[117],"problems":[118],"illustrated.":[120]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}