I'm an assistant professor of mathematics in the Centre for Analysis, Scientific Computing and Applications at TU/e (Eindhoven University of Technology), in the group of Olga Mula. My work deals with the numerical analysis of kinetic equations and other partial differential equations (PDEs). I'm also interested in collective dynamics, self-organisation, and the control of agent-based models.

Prior to my current post, I was a research associate at the University of Oxford, affiliated with the Oxford Centre for Nonlinear Partial Differential Equations at the Mathematical Institute. I also worked as a postdoctoral researcher at the Université de Lille with the ANEDP and Inria RAPSODI groups, under the supervision of Thomas Rey. I earned my doctorate at Imperial College London, where my advisors were José Antonio Carrillo and Pierre Degond.

Recent Publications

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The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations

Rafael Bailo · José Antonio Carrillo · Jingwei Hu

Journal of Plasma Physics, 2024 (to appear).

Journal of Plasma Physics, 2024 (to appear).

@Article{BCH2024,
	title={The collisional particle-in-cell method for the {V}lasov-{M}axwell-{L}andau equations},
	author={Bailo, Rafael and Carrillo, José Antonio and Hu, Jingwei},
	journal={J. Plasma Phys. (to appear)},
	year={2024},
	doi={10.48550/arXiv.2401.01689},
	archivePrefix={arXiv},
	arXivId={2401.01689},
	eprint={2401.01689},
}

We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum, and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum, and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

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CBX: Python and Julia packages for consensus-based interacting particle methods

Journal of Open Source Software, 9 (98), 2024.

Journal of Open Source Software, 9 (98), 2024.

@Article{BBG2024,
	title={{CBX}: {P}ython and {J}ulia packages for
    consensus-based interacting particle methods},
	author={Bailo, Rafael and Barbaro, Alethea and Gomes, Susana N. and Riedl, Konstantin and Roith, Tim and Totzeck, Claudia and Vaes, Urbain},
	journal={Journal of Open Source Software},
	year={2024},
	doi={10.21105/joss.06611},
	volume={9},
	number={98},
	archivePrefix={arXiv},
	arXivId={2403.14470},
	eprint={2403.14470},
}

We introduce CBXPy and ConsensusBasedX.jl, Python and Julia implementations of consensus-based interacting particle systems (CBX), which generalise consensus-based optimisation methods (CBO) for global, derivative-free optimisation. The raison d'être of our libraries is twofold: on the one hand, to offer high-performance implementations of CBX methods that the community can use directly, while on the other, providing a general interface that can accommodate and be extended to further variations of the CBX family. Python and Julia were selected as the leading high-level languages in terms of usage and performance, as well as their popularity among the scientific computing community. Both libraries have been developed with a common ethos, ensuring a similar API and core functionality, while leveraging the strengths of each language and writing idiomatic code.

We introduce CBXPy and ConsensusBasedX.jl, Python and Julia implementations of consensus-based interacting particle systems (CBX), which generalise consensus-based optimisation methods (CBO) for global, derivative-free optimisation. The raison d'être of our libraries is twofold: on the one hand, to offer high-performance implementations of CBX methods that the community can use directly, while on the other, providing a general interface that can accommodate and be extended to further variations of the CBX family. Python and Julia were selected as the leading high-level languages in terms of usage and performance, as well as their popularity among the scientific computing community. Both libraries have been developed with a common ethos, ensuring a similar API and core functionality, while leveraging the strengths of each language and writing idiomatic code.

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Aggregation-diffusion equations for collective behaviour in the sciences

arXiv: 2405.16679, 2024.

arXiv: 2405.16679, 2024.

@Article{BCG2024,
	title={Aggregation-diffusion equations for collective behaviour in the sciences},
	author={Bailo, Rafael and Carrillo, José Antonio and Gómez-Castro, David},
	journal={Preprint arXiv: 2405.16679},
	year={2024},
	doi={10.48550/arXiv.2405.16679},
	archivePrefix={arXiv},
	arXivId={2405.16679},
	eprint={2405.16679},
}

This is a survey article based on the content of the plenary lecture given by José A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis, simulation, and applications of the vast area of aggregation-diffusion equations. We also discuss the implications in mathematical biology explaining cell sorting in tissue growth as an example of this modelling framework. This modelling strategy is quite successful in other timely applications such as global optimisation, parameter estimation and machine learning.

This is a survey article based on the content of the plenary lecture given by José A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis, simulation, and applications of the vast area of aggregation-diffusion equations. We also discuss the implications in mathematical biology explaining cell sorting in tissue growth as an example of this modelling framework. This modelling strategy is quite successful in other timely applications such as global optimisation, parameter estimation and machine learning.