{"id":"https://openalex.org/W7224831606","doi":"https://doi.org/10.21203/rs.3.rs-11309754/v1","title":"Memory-Driven Pattern Selection in Fractional Reaction--Diffusion Models of Metamorphic Rocks","display_name":"Memory-Driven Pattern Selection in Fractional Reaction--Diffusion Models of Metamorphic Rocks","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7224831606","doi":"https://doi.org/10.21203/rs.3.rs-11309754/v1"},"language":"en","primary_location":{"id":"doi:10.21203/rs.3.rs-11309754/v1","doi":"https://doi.org/10.21203/rs.3.rs-11309754/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11309754/v1","pdf_url":"https://www.researchsquare.com/article/rs-11309754/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.researchsquare.com/article/rs-11309754/latest.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124346721","display_name":"Biswajit Saha","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405275311","display_name":"Gobardanga Hindu College","ror":"https://ror.org/03bqs6m63","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405275311"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Biswajit Saha","raw_affiliation_strings":["Gobardanaga Hindu College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gobardanaga Hindu College","institution_ids":["https://openalex.org/I4405275311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033671814","display_name":"Manas Kumar Roy","orcid":"https://orcid.org/0009-0006-7061-6961","observed_orcids":["https://orcid.org/0009-0006-7061-6961"]},"institutions":[{"id":"https://openalex.org/I4405277791","display_name":"Brahmananda Keshab Chandra College","ror":"https://ror.org/03xd28271","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405277791"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Manas Kumar Roy","raw_affiliation_strings":["Brahmananda Keshab Chandra College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brahmananda Keshab Chandra College","institution_ids":["https://openalex.org/I4405277791"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.6342999935150146,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.6342999935150146,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.2572999894618988,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.013000000268220901,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/caputo-fractional-derivative","display_name":"Caputo fractional derivative","score":0.8080000281333923},{"id":"https://openalex.org/keywords/gray-scott-model","display_name":"Gray-Scott model","score":0.9279999732971191},{"id":"https://openalex.org/keywords/metamorphic-rock","display_name":"metamorphic rock","score":0.8519999980926514},{"id":"https://openalex.org/keywords/stripe-patterns","display_name":"stripe patterns","score":0.6600000262260437},{"id":"https://openalex.org/keywords/turing-instability","display_name":"Turing instability","score":0.8289999961853027},{"id":"https://openalex.org/keywords/memory-effects","display_name":"memory effects","score":0.3490000069141388},{"id":"https://openalex.org/keywords/lyapunov-functional","display_name":"Lyapunov functional","score":0.8169999718666077},{"id":"https://openalex.org/keywords/dissipativity","display_name":"dissipativity","score":0.8379999995231628},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"pattern formation","score":0.6729999780654907}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C26687426","wikidata":"https://www.wikidata.org/wiki/Q47069","display_name":"Metamorphic rock","level":2,"score":0.5059000253677368},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.49410000443458557},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.49140000343322754},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4803999960422516},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.4041000008583069},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3763999938964844},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C167284885","wikidata":"https://www.wikidata.org/wiki/Q764372","display_name":"Mafic","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3255000114440918},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31470000743865967},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.302700012922287},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.2935999929904938},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.21203/rs.3.rs-11309754/v1","doi":"https://doi.org/10.21203/rs.3.rs-11309754/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11309754/v1","pdf_url":"https://www.researchsquare.com/article/rs-11309754/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.21203/rs.3.rs-11309754/v1","doi":"https://doi.org/10.21203/rs.3.rs-11309754/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-11309754/v1","pdf_url":"https://www.researchsquare.com/article/rs-11309754/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224831606.pdf","grobid_xml":"https://content.openalex.org/works/W7224831606.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7128404886","https://openalex.org/W7095718598","https://openalex.org/W4410575931","https://openalex.org/W2946734931","https://openalex.org/W4281990829","https://openalex.org/W2809514780","https://openalex.org/W7213986077","https://openalex.org/W1982132835","https://openalex.org/W2177431737","https://openalex.org/W4220902766"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"study":[2],"models":[3,156],"striped":[4],"and":[5,21,54,75,107,109,118,125,145],"orbicular":[6],"patterns":[7],"in":[8,160],"metamorphic":[9,161],"rocks":[10],"using":[11],"a":[12,27,42,149],"Caputo":[13],"time-fractional":[14],"Gray--Scott":[15],"reaction--diffusion":[16],"system.":[17],"Simulations":[18],"for":[19,49,157],"\\(\\alpha\\in\\{0.99,0.95,0.90,0.85\\}\\)":[20],"six":[22],"mafic":[23],"diffusivities":[24],"(\\(D_{u0}\\in\\{1\\times10^{-4},4\\times10^{-4},5\\times10^{-4},6\\times10^{-4},8\\times10^{-4},1\\times10^{-3}\\}\\))":[25],"reveal":[26],"spot-to-stripe":[28],"transition,":[29],"with":[30,101,113],"lower":[31],"\\(\\alpha\\)":[32],"producing":[33],"more":[34],"diffuse":[35],"patterns.":[36],"Stability":[37],"analysis":[38],"at":[39,95],"\\(\\alpha=0.85\\)":[40],"gives":[41],"Matignon":[43],"angle":[44],"of":[45,64,69],"\\(76.5^\\circ\\),":[46],"Turing":[47,80],"instability":[48],"\\(\\mu\\in[0.0597,0.1003]\\),":[50],"critical":[51],"wavenumber":[52],"\\(k_c=17.77\\),":[53],"dimensionless":[55],"wavelength":[56],"\\(\\lambda=0.3535\\).":[57],"A":[58],"parameter":[59],"scan":[60],"over":[61],"800":[62],"values":[63],"\\(\\mu\\)":[65],"identifies":[66],"456":[67],"equilibria,":[68],"which":[70],"160":[71],"are":[72],"linearly":[73],"stable":[74],"66":[76],"satisfy":[77],"the":[78,83,87,133,139],"fractional":[79],"condition.":[81],"At":[82],"representative":[84],"value":[85],"\\(\\mu=0.05971\\),":[86],"homogeneous":[88],"steady":[89],"state":[90],"is":[91,146],"\\((u^*,v^*)=(0.546024,29.814209)\\).":[92],"Convergence":[93],"tests":[94],"\\(\\alpha=0.95\\)":[96],"confirm":[97],"second-order":[98],"spatial":[99],"accuracy,":[100],"grid-refinement":[102],"\\(L^2\\)":[103],"errors":[104,115],"\\(5.85\\times10^{-5}\\),":[105],"\\(1.42\\times10^{-5}\\),":[106],"\\(6.26\\times10^{-6}\\),":[108],"L1":[110],"temporal":[111],"accuracy":[112],"time-step":[114],"\\(7.18\\times10^{-6}\\),":[116],"\\(4.74\\times10^{-6}\\),":[117],"\\(2.39\\times10^{-6}\\).":[119],"The":[120,129],"Lyapunov":[121],"functional":[122],"decays":[123],"monotonically":[124],"\\(\\Lambda=0.032603>0\\),":[126],"confirming":[127],"dissipativity.":[128],"model":[130],"qualitatively":[131],"reproduces":[132],"four":[134],"interface":[135],"morphologies":[136],"reported":[137],"from":[138],"Chotanagpur":[140],"Granite":[141],"Gneissic":[142],"Complex,":[143],"India,":[144],"presented":[147],"as":[148],"complementary":[150],"framework":[151],"to":[152],"thermodynamically":[153],"based":[154],"geophysical":[155],"memory-driven":[158],"transport":[159],"rocks.":[162]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-31T00:00:00"}
