I'm a research associate at the University of Oxford, affiliated with the Oxford Centre for Nonlinear Partial Differential Equations at the Mathematical Institute. In addition, I have served as a non-stipendiary lecturer at the Queen's College and as a tutor at Magdalen College.

Prior to this, I 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.

In June 2024 I will be moving to the Centre for Analysis, Scientific Computing and Applications at TU/e as an assistant professor.

My primary area of interest lies in the numerical analysis of kinetic equations and other partial differential equations (PDEs). I'm also fascinated by collective dynamics, self-organisation, and the control of agent-based models.

Recent Publications

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Pedestrian models with congestion effects

Mathematical Models and Methods in Applied Sciences, 2024 (to appear).

Mathematical Models and Methods in Applied Sciences, 2024 (to appear).

@Article{ABD2024
	title={Pedestrian models with congestion effects},
	author={Aceves-Sánchez, Pedro and Bailo, Rafael and Degond, Pierre and Mercier, Zoé},
	journal={Math Models Methods Appl Sci (to appear)},
	year={2024},
	doi={10.1142/S0218202524400050},
	archivePrefix={arXiv},
	arXivId={2401.08630},
	halId={hal-04334055},
	eprint={2401.08630},
}

We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behaviour. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution of the model efficiently. We perform the first numerical simulations of the dissipative Aw-Rascle system in one and two dimensions. We demonstrate the efficiency of the scheme in solving an array of numerical experiments, and we validate the model, ultimately showing that it correctly captures the fundamental diagram of pedestrian flow.

We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behaviour. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution of the model efficiently. We perform the first numerical simulations of the dissipative Aw-Rascle system in one and two dimensions. We demonstrate the efficiency of the scheme in solving an array of numerical experiments, and we validate the model, ultimately showing that it correctly captures the fundamental diagram of pedestrian flow.

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

Rafael Bailo · José Antonio Carrillo · Jingwei Hu

arXiv: 2401.01689, 2024.

arXiv: 2401.01689, 2024.

@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={Preprint arXiv: 2401.01689},
	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 operator that conserves mass, charge, momentum, and energy, while dissipating 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 operator that conserves mass, charge, momentum, and energy, while dissipating 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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Uncertainty quantification for the homogeneous Landau-Fokker-Planck equation via deterministic particle Galerkin methods

arXiv: 2312.07218, 2023.

arXiv: 2312.07218, 2023.

@Article{BCM2023
	title={Uncertainty quantification for the homogeneous {L}andau-{F}okker-{P}lanck equation via deterministic particle {G}alerkin methods},
	author={Bailo, Rafael and Carrillo, José Antonio and Medaglia, Andrea and Zanella, Mattia},
	journal={Preprint arXiv: 2312.07218},
	year={2023},
	doi={10.48550/arXiv.2312.07218},
	archivePrefix={arXiv},
	arXivId={2312.07218},
	eprint={2312.07218},
}

We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient flow on the set of probability measures, whereas the propagation of uncertain quantities is computed by means of a sg representation of each particle. This approach guarantees spectral accuracy in uncertainty space while preserving the fundamental structural properties of the model: the positivity of the solution, the conservation of invariant quantities, and the entropy production. We provide a regularity results for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.

We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the reformulation of the Landau equation as a formal gradient flow on the set of probability measures, whereas the propagation of uncertain quantities is computed by means of a sg representation of each particle. This approach guarantees spectral accuracy in uncertainty space while preserving the fundamental structural properties of the model: the positivity of the solution, the conservation of invariant quantities, and the entropy production. We provide a regularity results for the particle method in the random space. We perform the numerical validation of the particle method in a wealth of test cases.