Investigación

Mi área son las ecuaciones diferenciales parciales, en particular las leyes de conservación, que son una subárea de las hiperbólicas no lineales. La aplicación que más he trabajado es el flujo de fluidos en medios porosos: extracción de petróleo, inyección de espumas, secuestro de CO₂ y sedimentación de partículas. Pero el interés es amplio y disfruto el contacto con los sistemas dinámicos, la teoría de números y el análisis numérico.

«Mi cerebro está abierto.»
— Pál Erdős

En qué ando ahora

Universalidad en el secuestro de CO₂

Con Frederico Furtado, de la Universidad de Wyoming. Buscamos un análogo de la U-Structure para la inyección de CO₂ en yacimientos maduros, con el objetivo de mitigar emisiones.

Recuperación de parámetros en inyección de espumas

Con Antonio Capella, del Instituto de Matemáticas de la UNAM. Se trata de invertir el proceso: reconstruir la función de flujo a partir de perfiles de saturación.

Artículos arbitrados

J. Tang, Castañeda, D. Marchesin y 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 · acceso abierto

@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 y Castañeda (2023) Bifurcation of solutions through a contact manifold in bidisperse models Frontiers in Applied Mathematics and Statistics 9

DOI · acceso abierto

@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 y F. Furtado (2022) Universality of Riemann solutions in porous media Boletín de la Sociedad Matemática Mexicana 28: 6

DOI · acceso abierto

@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 y 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 · acceso abierto

@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 y 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 · acceso abierto

@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 y 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 y 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 y 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 y Castañeda (2012) Rainbow meanders and Cartesian billiards São Paulo Journal of Mathematical Sciences 6: 247--275

DOI · acceso abierto

@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 y J. Bruining (2012) The dynamics of chemical reactors in porous media Advances in Differential Equations 17: 725--746

DOI · acceso abierto

@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 libro y actas

M. Núñez López, R. Zepeda-Tello, Castañeda, S. Skolnick, R. Meza y 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 y 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 y 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 y 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 y 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 y 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 y 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 y desarrollo de código

RPn y ELI se desarrollan en colaboración con el Laboratório de Fluidos del IMPA; ELI está en eli.fluid.impa.br. bpc se hizo en exclusiva para la Fundación de Antropología Forense de Guatemala.

RPn n Riemann ProblemsSistema de análisis asistido por computadora para caracterizar soluciones de problemas de Riemann en dimensión arbitraria. Lo inició Dan Marchesin con sus colaboradores en 2004, en el Laboratório de Fluidos del IMPA. Desarrollé varias rutinas, entre ellas el cálculo de la bifurcación secundaria y la clasificación del locus de Hugoniot con el criterio de Lax para n ecuaciones.
ELI 2 × 2 RPVersión optimizada de RPn para sistemas de dos ecuaciones, con rutinas más eficientes para ese caso. Permite el análisis dinámico de la estabilidad de ondas de choque, cosa que los simuladores tradicionales no detectan de forma directa. Lleva ese nombre en homenaje póstumo a Eli L. Isaacson.
bpc Binomial Probability, 2011A pedido de la Fundación de Antropología Forense de Guatemala, y en colaboración con Rodrigo Morante. Los casos guatemaltecos son de una escala muy superior a la reportada en la literatura, y en aritmética de punto flotante ordinaria los cálculos binomiales se desbordaban al infinito numérico. bpc los resuelve con precisión extendida, dos órdenes de magnitud por encima de lo necesario, y con representación gráfica.

Coautores

He tenido el gusto de trabajar con grandes colegas.

Los nombres con marca llevan a su 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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