Research

My area is partial differential equations, and in particular conservation laws, a subfield of the nonlinear hyperbolic equations. The application I have worked on most is fluid flow in porous media: oil recovery, foam injection, CO₂ sequestration and particle sedimentation. But the interest is broad, and I enjoy the contact with dynamical systems, number theory and numerical analysis.

“My brain is open.”
— Pál Erdős

What I am working on now

Universality in CO₂ sequestration

With Frederico Furtado, University of Wyoming. We are looking for an analogue of the U-Structure for CO₂ injection into mature reservoirs, aimed at mitigating emissions.

Parameter recovery in foam injection

With Antonio Capella, Institute of Mathematics, UNAM. The idea is to invert the process: to reconstruct the flux function from saturation profiles.

Peer-reviewed articles

J. Tang, Castañeda, D. Marchesin and 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 · open access

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

DOI · open access

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

DOI · open access

@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 and 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 · open access

@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 and 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 · open access

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

DOI · open access

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

DOI · open access

@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},
}

Book chapters and proceedings

M. Núñez López, R. Zepeda-Tello, Castañeda, S. Skolnick, R. Meza and 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 and 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 and 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 and 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 and 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 and 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 and 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 and code

RPn and ELI are developed in collaboration with IMPA's Laboratório de Fluidos; ELI lives at eli.fluid.impa.br. bpc was made exclusively for the Guatemalan Forensic Anthropology Foundation.

RPn n Riemann ProblemsA computer-aided analysis system for characterising solutions of Riemann problems in arbitrary dimension. Dan Marchesin and collaborators started it in 2004 at IMPA's Fluid Dynamics Laboratory. I developed several routines, among them the computation of the secondary bifurcation and the classification of the Hugoniot locus with the Lax criterion for n equations.
ELI 2 × 2 RPAn optimised version of RPn for two-equation systems, with more efficient routines for that case. It allows dynamic analysis of shock wave stability, something traditional simulators do not detect directly. It is named in posthumous tribute to Eli L. Isaacson. It lives at eli.fluid.impa.br.
bpc Binomial Probability, 2011At the request of the Guatemalan Forensic Anthropology Foundation, in collaboration with Rodrigo Morante. The Guatemalan cases are on a scale far above what the literature reports, and in ordinary floating-point arithmetic the binomial computations overflowed to numerical infinity. bpc solves them with extended precision, two orders of magnitude beyond what is needed, and with graphical output.

Co-authors

I have had the pleasure of working with fine colleagues.

Names with a marker link to their public record.

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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