Pesquisa

Minha área são as equações diferenciais parciais, em particular as leis de conservação, uma subárea das hiperbólicas não lineares. A aplicação em que mais trabalhei é o escoamento de fluidos em meios porosos: recuperação de petróleo, injeção de espumas, sequestro de CO₂ e sedimentação de partículas. Mas o interesse é amplo e gosto do contato com sistemas dinâmicos, teoria dos números e análise numérica.

“Meu cérebro está aberto.”
— Pál Erdős

No que ando agora

Universalidade no sequestro de CO₂

Com Frederico Furtado, da Universidade de Wyoming. Buscamos um análogo da U-Structure para a injeção de CO₂ em reservatórios maduros, com o objetivo de mitigar emissões.

Recuperação de parâmetros na injeção de espumas

Com Antonio Capella, do Instituto de Matemática da UNAM. A ideia é inverter o processo: reconstruir a função de fluxo a partir de perfis de saturação.

Artigos arbitrados

J. Tang, Castañeda, D. Marchesin e W. R. Rossen (2025) New insights from three-phase fractional-flow modeling of foam-oil displacements in porous media Geoenergy Science and Engineering 255: 214091

DOI · acesso aberto

@article{tang2025newinsights,
  author  = {Tang, Jinyu and Castañeda, Pablo and Marchesin, Dan and Rossen, William R.},
  title   = {New insights from three-phase fractional-flow modeling of foam-oil displacements in porous media},
  journal = {Geoenergy Science and Engineering},
  volume  = {255},
  pages   = {214091},
  year    = {2025},
  doi     = {10.1016/j.geoen.2025.214091},
}

S. Berres e Castañeda (2023) Bifurcation of solutions through a contact manifold in bidisperse models Frontiers in Applied Mathematics and Statistics 9

DOI · acesso aberto

@article{berres2023bifurcation,
  author  = {Berres, Stefan and Castañeda, Pablo},
  title   = {Bifurcation of solutions through a contact manifold in bidisperse models},
  journal = {Frontiers in Applied Mathematics and Statistics},
  volume  = {9},
  year    = {2023},
  doi     = {10.3389/fams.2023.1199011},
}

Castañeda, D. Marchesin e F. Furtado (2022) Universality of Riemann solutions in porous media Boletín de la Sociedad Matemática Mexicana 28: 6

DOI · acesso aberto

@article{castaneda2022universality,
  author  = {Castañeda, Pablo and Marchesin, Dan and Furtado, Frederico},
  title   = {Universality of Riemann solutions in porous media},
  journal = {Boletín de la Sociedad Matemática Mexicana},
  volume  = {28},
  number  = {1},
  pages   = {6},
  year    = {2022},
  doi     = {10.1007/s40590-021-00398-0},
}

J. Tang, Castañeda, D. Marchesin e W. R. Rossen (2022) Foam-oil displacements in porous media: insights from three-phase fractional-flow theory Abu Dhabi International Petroleum Exhibition and Conference (ADIPEC)

DOI

@inproceedings{tang2022adipec,
  author    = {Tang, Jinyu and Castañeda, Pablo and Marchesin, Dan and Rossen, William R.},
  title     = {Foam-oil displacements in porous media: insights from three-phase fractional-flow theory},
  booktitle = {Abu Dhabi International Petroleum Exhibition and Conference (ADIPEC)},
  publisher = {Society of Petroleum Engineers},
  year      = {2022},
  doi       = {10.2118/211467-MS},
}

Castañeda (2020) Embedded delta shocks Heliyon 6: e04152

DOI · acesso aberto

@article{castaneda2020embedded,
  author  = {Castañeda, Pablo},
  title   = {Embedded delta shocks},
  journal = {Heliyon},
  volume  = {6},
  number  = {6},
  pages   = {e04152},
  year    = {2020},
  doi     = {10.1016/j.heliyon.2020.e04152},
}

J. Tang, Castañeda, D. Marchesin e W. R. Rossen (2019) Three-phase fractional-flow theory of foam-oil displacement in porous media with multiple steady states Water Resources Research 55: 10319--10339

DOI · acesso aberto

@article{tang2019threephase,
  author  = {Tang, Jinyu and Castañeda, Pablo and Marchesin, Dan and Rossen, William R.},
  title   = {Three-phase fractional-flow theory of foam-oil displacement in porous media with multiple steady states},
  journal = {Water Resources Research},
  volume  = {55},
  number  = {12},
  pages   = {10319--10339},
  year    = {2019},
  doi     = {10.1029/2019WR025264},
}

Castañeda, E. Abreu, F. Furtado e D. Marchesin (2016) On a universal structure for immiscible three-phase flow in virgin reservoirs Computational Geosciences 20: 171--185

DOI ResearchGate

@article{castaneda2016universal,
  author  = {Castañeda, Pablo and Abreu, Eduardo and Furtado, Frederico and Marchesin, Dan},
  title   = {On a universal structure for immiscible three-phase flow in virgin reservoirs},
  journal = {Computational Geosciences},
  volume  = {20},
  pages   = {171--185},
  year    = {2016},
  doi     = {10.1007/s10596-016-9556-5},
}

Castañeda e F. Furtado (2016) The role of sonic shocks between two- and three-phase states in porous media Bulletin of the Brazilian Mathematical Society, New Series 47: 227--240

DOI ResearchGate

@article{castaneda2016sonic,
  author  = {Castañeda, Pablo and Furtado, Frederico},
  title   = {The role of sonic shocks between two- and three-phase states in porous media},
  journal = {Bulletin of the Brazilian Mathematical Society, New Series},
  volume  = {47},
  pages   = {227--240},
  year    = {2016},
  doi     = {10.1007/s00574-016-0134-1},
}

S. Berres e Castañeda (2016) Identification of shock profile solutions for bidisperse suspensions Bulletin of the Brazilian Mathematical Society, New Series 47: 105--115

DOI ResearchGate

@article{berres2016identification,
  author  = {Berres, Stefan and Castañeda, Pablo},
  title   = {Identification of shock profile solutions for bidisperse suspensions},
  journal = {Bulletin of the Brazilian Mathematical Society, New Series},
  volume  = {47},
  pages   = {105--115},
  year    = {2016},
  doi     = {10.1007/s00574-016-0125-2},
}

B. Fiedler e Castañeda (2012) Rainbow meanders and Cartesian billiards São Paulo Journal of Mathematical Sciences 6: 247--275

DOI · acesso aberto

@article{fiedler2012rainbow,
  author  = {Fiedler, Bernold and Castañeda, Pablo},
  title   = {Rainbow meanders and Cartesian billiards},
  journal = {São Paulo Journal of Mathematical Sciences},
  volume  = {6},
  number  = {2},
  pages   = {247--275},
  year    = {2012},
  doi     = {10.11606/issn.2316-9028.v6i2p247-275},
}

Castañeda, D. Marchesin e J. Bruining (2012) The dynamics of chemical reactors in porous media Advances in Differential Equations 17: 725--746

DOI · acesso aberto

@article{castaneda2012dynamics,
  author  = {Castañeda, Pablo and Marchesin, Dan and Bruining, Johannes},
  title   = {The dynamics of chemical reactors in porous media},
  journal = {Advances in Differential Equations},
  volume  = {17},
  pages   = {725--746},
  year    = {2012},
  doi     = {10.57262/ade/1355702974},
}

Capítulos de livro e anais

M. Núñez López, R. Zepeda-Tello, Castañeda, S. Skolnick, R. Meza e M. Hernández-Ávila (2023) Implementation of mitigation measures and modeling of in-hospital dynamics depending on the COVID-19 infection status Mathematical Modelling, Simulations, and AI for Emergent Pandemic Diseases: 175--198

DOI ResearchGate

@incollection{nunez2023covid,
  author    = {Núñez López, Mayra and Zepeda-Tello, Rodrigo and Castañeda, Pablo and Skolnick, Sarah and Meza, Rafael and Hernández-Ávila, Mauricio},
  title     = {Implementation of mitigation measures and modeling of in-hospital dynamics depending on the COVID-19 infection status},
  booktitle = {Mathematical Modelling, Simulations, and AI for Emergent Pandemic Diseases},
  pages     = {175--198},
  year      = {2023},
  doi       = {10.1016/B978-0-323-95064-0.00003-8},
}

Castañeda (2018) Explicit construction of effective flux functions for Riemann solutions Theory, Numerics and Applications of Hyperbolic Problems I, Springer Proceedings in Mathematics and Statistics 236: 273--284

DOI ResearchGate

@incollection{castaneda2018explicit,
  author    = {Castañeda, Pablo},
  editor    = {Klingenberg, Christian and Westdickenberg, Michael},
  title     = {Explicit construction of effective flux functions for Riemann solutions},
  booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I},
  series    = {Springer Proceedings in Mathematics and Statistics},
  publisher = {Springer},
  volume    = {236},
  pages     = {273--284},
  year      = {2018},
  doi       = {10.1007/978-3-319-91545-6_22},
}

Castañeda, D. Marchesin e F. Furtado (2014) On singular points for convex permeability models Hyperbolic Problems: Theory, Numerics, Applications (HYP2012), AIMS on Applied Mathematics 8: 415--422

@incollection{castaneda2014singular,
  author    = {Castañeda, Pablo and Marchesin, Dan and Furtado, Frederico},
  title     = {On singular points for convex permeability models},
  booktitle = {Hyperbolic Problems: Theory, Numerics, Applications (HYP2012)},
  series    = {AIMS on Applied Mathematics},
  volume    = {8},
  pages     = {415--422},
  year      = {2014},
}

V. Matos, Castañeda e D. Marchesin (2014) Classification of the umbilic point in immiscible three-phase flow in porous media Hyperbolic Problems: Theory, Numerics, Applications (HYP2012), AIMS on Applied Mathematics 8: 791--799

@incollection{matos2014umbilic,
  author    = {Matos, Vítor and Castañeda, Pablo and Marchesin, Dan},
  title     = {Classification of the umbilic point in immiscible three-phase flow in porous media},
  booktitle = {Hyperbolic Problems: Theory, Numerics, Applications (HYP2012)},
  series    = {AIMS on Applied Mathematics},
  volume    = {8},
  pages     = {791--799},
  year      = {2014},
}

Castañeda, D. Marchesin e J. Bruining (2009) Simulation of spontaneous ignition in porous media 30º Congresso Ibero-Latino-Americano de Métodos Computacionais em Engenharia (CILAMCE)

DOI

@inproceedings{castaneda2009cilamce,
  author    = {Castañeda, Pablo and Marchesin, Dan and Bruining, Johannes},
  title     = {Simulation of spontaneous ignition in porous media},
  booktitle = {30º Congresso Ibero-Latino-Americano de Métodos Computacionais em Engenharia (CILAMCE)},
  address   = {Armação de Búzios, Brasil},
  year      = {2009},
  doi       = {10.13140/2.1.2717.1522},
}

Preprints

Castañeda (2019) A dynamical approach towards Collatz conjecture arXiv:1910.08497

arXiv

@misc{castaneda2019collatz,
  author       = {Castañeda, Pablo},
  title        = {A dynamical approach towards Collatz conjecture},
  pages        = {10},
  year         = {2019},
  url          = {https://arxiv.org/abs/1910.08497},
  howpublished = {arXiv:1910.08497},
}

S. Berres e Castañeda (2015) Contact manifolds in a hyperbolic system of two nonlinear conservation laws arXiv:1501.06019

arXiv

@misc{berres2015contact,
  author       = {Berres, Stefan and Castañeda, Pablo},
  title        = {Contact manifolds in a hyperbolic system of two nonlinear conservation laws},
  pages        = {35},
  year         = {2015},
  url          = {https://arxiv.org/abs/1501.06019},
  howpublished = {arXiv:1501.06019},
}

Castañeda, F. Furtado e D. Marchesin (2015) Characteristic shocks for flow in porous media IMPA Preprint Série E 41

enlace

@techreport{castaneda2015characteristic,
  author      = {Castañeda, Pablo and Furtado, Frederico and Marchesin, Dan},
  title       = {Characteristic shocks for flow in porous media},
  institution = {IMPA},
  type        = {IMPA Preprint Série E},
  number      = {41},
  pages       = {9},
  year        = {2015},
  url         = {http://preprint.impa.br/visualizar?id=6382},
}

Castañeda, F. Furtado e D. Marchesin (2013) The convex permeability three-phase flow in reservoirs IMPA Preprint Série E 34

enlace

@techreport{castaneda2013convex,
  author      = {Castañeda, Pablo and Furtado, Frederico and Marchesin, Dan},
  title       = {The convex permeability three-phase flow in reservoirs},
  institution = {IMPA},
  type        = {IMPA Preprint Série E},
  number      = {34},
  pages       = {34},
  year        = {2013},
  url         = {https://preprint.impa.br/visualizar?id=2258},
}

Software e desenvolvimento de código

RPn e ELI são desenvolvidos em colaboração com o Laboratório de Fluidos do IMPA; o ELI está em eli.fluid.impa.br. O bpc foi feito exclusivamente para a Fundação de Antropologia Forense da Guatemala.

RPn n Riemann ProblemsSistema de análise assistida por computador para caracterizar soluções de problemas de Riemann em dimensão arbitrária. Dan Marchesin e colaboradores o iniciaram em 2004, no Laboratório de Fluidos do IMPA. Desenvolvi várias rotinas, entre elas o cálculo da bifurcação secundária e a classificação do locus de Hugoniot com o critério de Lax para n equações.
ELI 2 × 2 RPVersão otimizada do RPn para sistemas de duas equações, com rotinas mais eficientes para esse caso. Permite a análise dinâmica da estabilidade de ondas de choque, algo que os simuladores tradicionais não detectam de forma direta. Leva esse nome em homenagem póstuma a Eli L. Isaacson. Está em eli.fluid.impa.br.
bpc Binomial Probability, 2011A pedido da Fundação de Antropologia Forense da Guatemala, em colaboração com Rodrigo Morante. Os casos guatemaltecos são de uma escala muito superior à relatada na literatura, e em aritmética de ponto flutuante comum os cálculos binomiais transbordavam ao infinito numérico. O bpc os resolve com precisão estendida, duas ordens de magnitude acima do necessário, e com representação gráfica.

Coautores

Tive o prazer de trabalhar com grandes colegas.

Os nomes com marca levam ao seu registro público.

E. Abreu^Scopus
S. Berres^ORCID
C. Bosch Giral^ficha
V. F. Breña Medina^ORCID
J. Bruining^Scopus
L. Fernández Román^ficha
B. Fiedler^Scopus
F. Furtado^ORCID
M. Hernández-Ávila^Scopus
R. Kaufman^ficha
M. Madriz Mendoza^ficha
D. Marchesin^ORCID
J. Martínez Villarroya^ficha
V. Matos^ORCID
R. Meza^Scopus
M. Núñez López^Scopus
P. Padilla Longoria^ORCID
J. Rodríguez Lebrija
W. R. Rossen^Scopus
S. Skolnick^Scopus
J. Tang^ORCID
R. Zepeda Tello^ORCID

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