40 citations · 90 across the 10 of their papers we have counts for
10 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…
Positivity-preserving and energy-dissipating discontinuous Galerkin methods for nonlinear nonlocal Fokker-Planck equations
José A. Carrillo, Hailiang Liu, Hui Yu
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find…
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 particle method for the multispecies Landau equation
José A. Carrillo, Jingwei Hu, Samuel Q. Van Fleet
The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as el…
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…
Global Minimizers of a Large Class of Anisotropic Attractive-Repulsive Interaction Energies in 2D
José A. Carrillo, Ruiwen Shu
We study a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas wh…
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…
Particle based gPC methods for mean-field models of swarming with uncertainty
J. A. Carrillo, L. Pareschi, M. Zanella
In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The metho…
Numerical Study of a Particle Method for Gradient Flows
J. A. Carrillo, Y. Huang, F. S. Patacchini +1
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-ov…