Rafael Bailo
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View article: The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations
The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations Open
We introduce an extension of the particle-in-cell 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, le…
View article: Aggregation-Diffusion Equations for Collective Behaviour in the Sciences
Aggregation-Diffusion Equations for Collective Behaviour in the Sciences Open
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,…
View article: A finite-volume scheme for fractional diffusion on bounded domains
A finite-volume scheme for fractional diffusion on bounded domains Open
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show th…
View article: Pedestrian models with congestion effects
Pedestrian models with congestion effects Open
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 st…
View article: The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau Equations
The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau Equations Open
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 equati…
View article: Uncertainty Quantification for the Homogeneous Landau-Fokker-Planck Equation via Deterministic Particle Galerkin methods
Uncertainty Quantification for the Homogeneous Landau-Fokker-Planck Equation via Deterministic Particle Galerkin methods Open
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 fl…
View article: Pedestrian models with congestion effects
Pedestrian models with congestion effects Open
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 st…
View article: A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains
A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains Open
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show th…
View article: Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation
Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation Open
We propose finite-volume schemes for general continuity equations which\npreserve positivity and global bounds that arise from saturation effects in the\nmobility function. In the case of gradient flows, the schemes dissipate the\nfree ene…
View article: Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation
Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation Open
We propose finite-volume schemes for the Cahn-Hilliard equation which\nunconditionally and discretely preserve the boundedness of the phase field and\nthe dissipation of the free energy. Our numerical framework is applicable to a\nvariety …
View article: Projective and Telescopic Projective Integration for Non-Linear Kinetic Mixtures
Projective and Telescopic Projective Integration for Non-Linear Kinetic Mixtures Open
We propose fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and Bhatnagar-Gross-Krook (BGK) equations. The methods employ a sequence of small forward-Euler steps, intercalat…
View article: Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation
Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation Open
We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of …
View article: 02 — Large Crowd — Repulsion Effects
02 — Large Crowd — Repulsion Effects Open
Simulations for the article https://arxiv.org/abs/1808.07426
View article: Optimal consensus control of the Cucker-Smale model
Optimal consensus control of the Cucker-Smale model Open
We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive first-ord…
View article: 03 — Large Crowd — Slow Walker
03 — Large Crowd — Slow Walker Open
Simulations for the article https://arxiv.org/abs/1808.07426
View article: 05 — Corridor — High Density Setting
05 — Corridor — High Density Setting Open
Simulations for the article https://arxiv.org/abs/1808.07426
View article: 04 — Bottleneck — Frictional Effects
04 — Bottleneck — Frictional Effects Open
Simulations for the article https://arxiv.org/abs/1808.07426
View article: 01 — Frontal Collision — C Decision Potential
01 — Frontal Collision — C Decision Potential Open
Simulations for the article https://arxiv.org/abs/1808.07426