44 citations · 170 across the 12 of their papers we have counts for
12 papers
Aggregation-Diffusion Equations for Collective Behaviour in the Sciences
Rafael Bailo, José A. Carrillo, David Gómez-Castro
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…
CBX: Python and Julia packages for consensus-based interacting particle methods
Rafael Bailo, Alethea Barbaro, Susana N. Gomes +4
We introduce CBXPy and ConsensusBasedX.jl, Python and Julia implementations of consensus-based interacting particle systems (CBX), which generalise consensus-based optimization met…
The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau Equations
Rafael Bailo, José A. Carrillo, Jingwei Hu
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 regular…
Uncertainty Quantification for the Homogeneous Landau-Fokker-Planck Equation via Deterministic Particle Galerkin methods
Rafael Bailo, José Antonio Carrillo, Andrea Medaglia +1
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 r…
A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains
Rafael Bailo, José A. Carrillo, Stefano Fronzoni +1
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 pr…
Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation
Rafael Bailo, José A. Carrillo, Jingwei Hu
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the ca…
Projective and Telescopic Projective Integration for Non-Linear Kinetic Mixtures
Rafael Bailo, Thomas Rey
We propose fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and Bhatnagar-Gross-Krook (BGK) equations. The methods…
Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation
Rafael Bailo, José A. Carrillo, Serafim Kalliadasis +1
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 ene…
Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations
Rafael Bailo, Jose A. Carrillo, Hideki Murakawa +1
We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo,…
Fully Discrete Positivity-Preserving and Energy-Dissipating Schemes for Aggregation-Diffusion Equations with a Gradient Flow Structure
Rafael Bailo, Jose A. Carrillo, Jingwei Hu
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually k…
General relativity as a biconformal gauge theory
James T Wheeler
We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim…
Optimal consensus control of the Cucker-Smale model
Rafael Bailo, Mattia Bongini, José A. Carrillo +1
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…