{"id":"https://openalex.org/W7225396607","doi":"https://doi.org/10.56578/jcmes020103","title":"Generalized Integral Transform Modeling of Complex Coupled-Field Transport in Two-Dimensional Keller\u2013Segel Chemotaxis: Verification, Spectral Convergence, and Self-Similar Localization","display_name":"Generalized Integral Transform Modeling of Complex Coupled-Field Transport in Two-Dimensional Keller\u2013Segel Chemotaxis: Verification, Spectral Convergence, and Self-Similar Localization","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225396607","doi":"https://doi.org/10.56578/jcmes020103"},"language":"en","primary_location":{"id":"doi:10.56578/jcmes020103","doi":"https://doi.org/10.56578/jcmes020103","is_oa":true,"landing_page_url":"https://doi.org/10.56578/jcmes020103","pdf_url":"https://library.acadlore.com/JCMES/2027/2/1/JCMES_02.01_03.pdf","source":{"id":"https://openalex.org/S7407057028","display_name":"Journal of Complex and Multiphysics Engineering Systems","issn_l":"3134-7932","issn":["3134-7932","3134-7940"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex and Multiphysics Engineering Systems","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://library.acadlore.com/JCMES/2027/2/1/JCMES_02.01_03.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161065828","display_name":"Alberto M.G. Tolentino","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alberto M.G. Tolentino","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5161126289","display_name":"Kalysta O.R. Borges","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I211891151","display_name":"Universidade do Estado do Par\u00e1","ror":"https://ror.org/042r36z33","country_code":"BR","type":"education","lineage":["https://openalex.org/I211891151"]},{"id":"https://openalex.org/I59606676","display_name":"Universidade Federal do Par\u00e1","ror":"https://ror.org/03q9sr818","country_code":"BR","type":"education","lineage":["https://openalex.org/I59606676"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Kalysta O.R. Borges","raw_affiliation_strings":["Center for Biological and Health Sciences (CCBS) , Campus XII Santar\u00e9m , State University of Par\u00e1 , 68040-090 Santar\u00e9m , Brazil","Graduate Program in Amazon Natural Resources Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Biological and Health Sciences (CCBS) , Campus XII Santar\u00e9m , State University of Par\u00e1 , 68040-090 Santar\u00e9m , Brazil","institution_ids":["https://openalex.org/I211891151"]},{"raw_affiliation_string":"Graduate Program in Amazon Natural Resources Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","institution_ids":["https://openalex.org/I59606676"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5161017248","display_name":"Carlos H.R. Moura","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos H.R. Moura","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038230194","display_name":"Bruno Marques Viegas","orcid":"https://orcid.org/0000-0002-2768-652X","observed_orcids":["https://orcid.org/0000-0002-2768-652X"]},"institutions":[{"id":"https://openalex.org/I59606676","display_name":"Universidade Federal do Par\u00e1","ror":"https://ror.org/03q9sr818","country_code":"BR","type":"education","lineage":["https://openalex.org/I59606676"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Bruno M. Viegas","raw_affiliation_strings":["Faculty of Biotechnology and Graduate Program in Biotechnology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Biotechnology and Graduate Program in Biotechnology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","institution_ids":["https://openalex.org/I59606676"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075573548","display_name":"Emanuel Negr\u00e3o Mac\u00eado","orcid":"https://orcid.org/0000-0002-4652-8316","observed_orcids":["https://orcid.org/0000-0002-4652-8316"]},"institutions":[{"id":"https://openalex.org/I59606676","display_name":"Universidade Federal do Par\u00e1","ror":"https://ror.org/03q9sr818","country_code":"BR","type":"education","lineage":["https://openalex.org/I59606676"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Emanuel N. Mac\u00eado","raw_affiliation_strings":["Graduate Program in Amazon Natural Resources Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","School of Chemical Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate Program in Amazon Natural Resources Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","institution_ids":["https://openalex.org/I59606676"]},{"raw_affiliation_string":"School of Chemical Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","institution_ids":["https://openalex.org/I59606676"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033683245","display_name":"Jo\u00e3o Nazareno Nonato Quaresma","orcid":"https://orcid.org/0000-0001-9365-7498","observed_orcids":["https://orcid.org/0000-0001-9365-7498"]},"institutions":[{"id":"https://openalex.org/I59606676","display_name":"Universidade Federal do Par\u00e1","ror":"https://ror.org/03q9sr818","country_code":"BR","type":"education","lineage":["https://openalex.org/I59606676"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jo\u00e3o N.N. Quaresma","raw_affiliation_strings":["Graduate Program in Amazon Natural Resources Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","School of Chemical Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate Program in Amazon Natural Resources Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","institution_ids":["https://openalex.org/I59606676"]},{"raw_affiliation_string":"School of Chemical Engineering , Institute of Technology , Federal University of Par\u00e1 , 66075-110 Bel\u00e9m , Brazil","institution_ids":["https://openalex.org/I59606676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5161058332","display_name":"Eenato M. Cotta","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eenato M. Cotta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"1","first_page":"32","last_page":"58"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.6904000043869019,"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"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.6904000043869019,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.10490000247955322,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.05469999834895134,"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/keller-segel-model","display_name":"Keller-Segel model","score":0.9779999852180481},{"id":"https://openalex.org/keywords/chemotaxis","display_name":"chemotaxis","score":0.9559999704360962},{"id":"https://openalex.org/keywords/generalized-integral-transform-technique","display_name":"generalized integral transform technique","score":0.8949999809265137},{"id":"https://openalex.org/keywords/spectral-convergence","display_name":"spectral convergence","score":0.7369999885559082},{"id":"https://openalex.org/keywords/aggregation","display_name":"aggregation","score":0.5429999828338623},{"id":"https://openalex.org/keywords/blow-up","display_name":"blow-up","score":0.7440000176429749},{"id":"https://openalex.org/keywords/two-dimensional-aggregation","display_name":"two-dimensional aggregation","score":0.3059999942779541},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"finite volume method","score":0.4059999883174896}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.661300003528595},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6348999738693237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6100999712944031},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5735999941825867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5128999948501587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4424000084400177},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4099999964237213},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.3400999903678894},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.30149999260902405},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.27889999747276306},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.27399998903274536},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.26429998874664307},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C46435376","wikidata":"https://www.wikidata.org/wiki/Q1829750","display_name":"Multiphysics","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.56578/jcmes020103","doi":"https://doi.org/10.56578/jcmes020103","is_oa":true,"landing_page_url":"https://doi.org/10.56578/jcmes020103","pdf_url":"https://library.acadlore.com/JCMES/2027/2/1/JCMES_02.01_03.pdf","source":{"id":"https://openalex.org/S7407057028","display_name":"Journal of Complex and Multiphysics Engineering Systems","issn_l":"3134-7932","issn":["3134-7932","3134-7940"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex and Multiphysics Engineering Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.56578/jcmes020103","doi":"https://doi.org/10.56578/jcmes020103","is_oa":true,"landing_page_url":"https://doi.org/10.56578/jcmes020103","pdf_url":"https://library.acadlore.com/JCMES/2027/2/1/JCMES_02.01_03.pdf","source":{"id":"https://openalex.org/S7407057028","display_name":"Journal of Complex and Multiphysics Engineering Systems","issn_l":"3134-7932","issn":["3134-7932","3134-7940"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Complex and Multiphysics Engineering Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225396607.pdf","grobid_xml":"https://content.openalex.org/works/W7225396607.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W592315147","https://openalex.org/W1987347396","https://openalex.org/W2021117151","https://openalex.org/W2026979923","https://openalex.org/W2042892258","https://openalex.org/W2047345239","https://openalex.org/W2126617016","https://openalex.org/W2737417353","https://openalex.org/W2754924973","https://openalex.org/W2766785595","https://openalex.org/W2962829881","https://openalex.org/W4298000032","https://openalex.org/W4323519760","https://openalex.org/W4413682176","https://openalex.org/W7166040514"],"related_works":["https://openalex.org/W2099307971","https://openalex.org/W7100931502","https://openalex.org/W3025553720","https://openalex.org/W7223896713","https://openalex.org/W2056670018","https://openalex.org/W7098182637","https://openalex.org/W7098482637","https://openalex.org/W2810788019","https://openalex.org/W2264161341","https://openalex.org/W2178664654"],"abstract_inverted_index":{"Complex":[0],"engineering":[1],"systems":[2,258],"often":[3],"involve":[4],"interacting":[5],"transport":[6,36,54],"fields":[7,85],"in":[8,26,88,145,168],"which":[9],"diffusion,":[10],"field-driven":[11],"fluxes,":[12],"production":[13],"or":[14],"decay,":[15],"and":[16,23,41,52,92,123,160,176,194,220,264],"nonlinear":[17,100,252],"feedback":[18],"jointly":[19],"control":[20],"stability,":[21],"transport,":[22,261],"localization.Although":[24],"originating":[25],"mathematical":[27,280],"biology,":[28],"the":[29,62,118,179,186,195],"Keller-Segel":[30,73],"system":[31,74],"is":[32,68],"a":[33,43,71,98,109,136,216,247,279],"canonical":[34],"coupled-field":[35,253],"model":[37],"with":[38,75,128,135,259,273],"this":[39],"structure":[40],"provides":[42],"stringent":[44],"benchmark":[45],"for":[46,70,154,251],"computational":[47],"methodologies":[48],"aimed":[49],"at":[50],"complex":[51],"multiphysics":[53],"problems.A":[55],"multidimensional":[56],"hybrid":[57,249],"numerical-analytical":[58],"formulation":[59],"based":[60],"on":[61],"Generalized":[63],"Integral":[64],"Transform":[65],"Technique":[66],"(GITT)":[67],"developed":[69],"parabolic-parabolic":[72],"homogeneous":[76],"Neumann":[77,90],"boundary":[78],"conditions.Spatial":[79],"averages":[80],"are":[81,86,105,152,161],"treated":[82],"analytically,":[83],"zero-mean":[84],"expanded":[87],"normalized":[89,227],"eigenfunctions,":[91],"exact":[93],"cosine-product":[94],"selection":[95],"rules":[96],"generate":[97],"sparse":[99],"modal":[101],"system.The":[102],"transformed":[103],"equations":[104],"advanced":[106],"using":[107],"CVODE,":[108],"variable-step,":[110],"variable-order":[111,129],"ordinary":[112],"differential":[113,255],"equation":[114,256],"(ODE)":[115],"solver":[116,144],"from":[117,188],"SUNDIALS":[119],"(Suite":[120],"of":[121,197,282],"Nonlinear":[122],"Differential/Algebraic":[124],"Equation":[125],"Solvers)":[126],"package,":[127],"backward":[130],"differentiation":[131],"formulas":[132],"(BDF),":[133],"together":[134],"matrix-free":[137],"scaled":[138],"preconditioned":[139],"generalized":[140],"minimal":[141],"residual":[142],"(SPGMR)":[143],"two":[146],"dimensions.Systematic":[147],"one-and":[148],"two-dimensional":[149,199],"convergence":[150],"studies":[151],"performed":[153],"chemotactic":[155],"sensitivities":[156],"\u03c7":[157,202],"=":[158,203],"1-5":[159],"complemented":[162],"by":[163],"independent":[164],"conservative":[165],"finite-volume/method-of-lines":[166],"solutions":[167],"physical":[169],"space.The":[170],"finite-volume":[171],"discretizations":[172],"exhibit":[173],"second-order":[174],"self-convergence":[175],"closely":[177],"reproduce":[178],"converged":[180],"GITT":[181],"fields.The":[182],"parametric":[183],"study":[184],"quantifies":[185],"transition":[187],"weak":[189],"relaxation":[190],"to":[191,208],"strong":[192],"aggregation":[193],"growth":[196],"genuinely":[198],"mixed":[200],"modes.For":[201],"5,":[204],"successive":[205],"truncations":[206],"up":[207],"7,920":[209],"spatial":[210],"modes":[211],"(15,840":[212],"coupled":[213],"ODEs)":[214],"resolve":[215],"strongly":[217],"localized":[218],"regime.Physical":[219],"spectral":[221],"localization":[222],"scales":[223],"contract":[224],"consistently,":[225],"while":[226,268],"profiles":[228],"collapse":[229],"onto":[230],"an":[231],"approximately":[232],"invariant":[233],"shape.Independent":[234],"late-time":[235],"extrapolations":[236],"yield":[237],"characteristic":[238],"times":[239],"clustered":[240],"near":[241],"t":[242],"\u2248":[243],"2.184.The":[244],"results":[245],"demonstrate":[246],"high-resolution":[248],"framework":[250],"partial":[254],"(PDE)":[257],"cross-field":[260],"evolving":[262],"localization,":[263],"demanding":[265],"multiscale":[266],"resolution,":[267],"providing":[269],"numerical":[270],"evidence":[271],"compatible":[272],"possible":[274],"finite-time":[275],"singularization":[276],"without":[277],"constituting":[278],"proof":[281],"blow-up.":[283]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}