Imperial College London

ProfessorJose AntonioCarrillo de la Plata

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied and Numerical Analysis
 
 
 
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Contact

 

+44 (0)20 7594 8530carrillo Website CV

 
 
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Location

 

6M26Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

207 results found

Barre J, Carrillo JA, Degond P, Peurichard D, Zatorska Eet al., 2018, Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions, JOURNAL OF NONLINEAR SCIENCE, Vol: 28, Pages: 235-268, ISSN: 0938-8974

JOURNAL ARTICLE

CARRILLO JA, J√úNGEL A, SANTOS MC, 2018, Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations†, European Journal of Applied Mathematics, Pages: 1-20, ISSN: 0956-7925

Copyright © Cambridge University Press 2018 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. The displacement λ-convexity of a non-standard entropy with respect to a non-local transportation metric in finite state spaces is shown using a gradient flow approach. The constant λ is computed explicitly in terms of a priori estimates of the solution to a finite-difference approximation of a non-linear Fokker–Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.

JOURNAL ARTICLE

Carrillo J-A, Santambrogio F, 2018, L-infinity ESTIMATES FOR THE JKO SCHEME IN PARABOLIC-ELLIPTIC KELLER-SEGEL SYSTEMS, QUARTERLY OF APPLIED MATHEMATICS, Vol: 76, Pages: 515-530, ISSN: 0033-569X

JOURNAL ARTICLE

Carrillo JA, Choi Y-P, Totzeck C, Tse Oet al., 2018, An analytical framework for consensus-based global optimization method, MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, Vol: 28, Pages: 1037-1066, ISSN: 0218-2025

JOURNAL ARTICLE

Carrillo JA, Colombi A, Scianna M, 2018, Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles, JOURNAL OF THEORETICAL BIOLOGY, Vol: 445, Pages: 75-91, ISSN: 0022-5193

JOURNAL ARTICLE

Carrillo JA, During B, Matthes D, McCormick DSet al., 2018, A Lagrangian Scheme for the Solution of Nonlinear Diffusion Equations Using Moving Simplex Meshes, JOURNAL OF SCIENTIFIC COMPUTING, Vol: 75, Pages: 1463-1499, ISSN: 0885-7474

JOURNAL ARTICLE

Carrillo JA, Huang Y, Schmidtchen M, 2018, ZOOLOGY OF A NONLOCAL CROSS-DIFFUSION MODEL FOR TWO SPECIES, SIAM JOURNAL ON APPLIED MATHEMATICS, Vol: 78, Pages: 1078-1104, ISSN: 0036-1399

JOURNAL ARTICLE

Sun Z, Carrillo JA, Shu C-W, 2018, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 352, Pages: 76-104, ISSN: 0021-9991

JOURNAL ARTICLE

Calvez V, Carrillo JA, Hoffmann F, 2017, Equilibria of homogeneous functionals in the fair-competition regime, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, Vol: 159, Pages: 85-128, ISSN: 0362-546X

JOURNAL ARTICLE

Calvez V, Carrillo JA, Hoffmann F, 2017, The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime, Pages: 1-71, ISSN: 0075-8434

© Springer International Publishing AG 2017. We consider an aggregation-diffusion equation modelling particle interaction with non-linear diffusion and non-local attractive interaction using a homogeneous kernel (singular and non-singular) leading to variants of the Keller-Segel model of chemotaxis. We analyse the fair-competition regime in which both homogeneities scale the same with respect to dilations. Our analysis here deals with the one-dimensional case, building on the work in Calvez et al. (Equilibria of homogeneous functionals in the fair-competition regime), and provides an almost complete classification. In the singular kernel case and for critical interaction strength, we prove uniqueness of stationary states via a variant of the Hardy-Littlewood-Sobolev inequality. Using the same methods, we show uniqueness of self-similar profiles in the sub-critical case by proving a new type of functional inequality. Surprisingly, the same results hold true for any interaction strength in the non-singular kernel case. Further, we investigate the asymptotic behaviour of solutions, proving convergence to equilibrium in Wasserstein distance in the critical singular kernel case, and convergence to self-similarity for sub-critical interaction strength, both under a uniform stability condition. Moreover, solutions converge to a unique self-similar profile in the non-singular kernel case. Finally, we provide a numerical overview for the asymptotic behaviour of solutions in the full parameter space demonstrating the above results. We also discuss a number of phenomena appearing in the numerical explorations for the diffusion-dominated and attraction-dominated regimes.

CONFERENCE PAPER

Carrillo JA, Choi Y-P, Mucha PB, Peszek Jet al., 2017, Sharp conditions to avoid collisions in singular Cucker-Smale interactions, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, Vol: 37, Pages: 317-328, ISSN: 1468-1218

JOURNAL ARTICLE

Carrillo JA, Choi YP, Perez SP, 2017, A review on attractive–repulsive hydrodynamics for consensus in collective behavior, Modeling and Simulation in Science, Engineering and Technology, Pages: 259-298

© Springer International Publishing AG 2017. This survey summarizes and illustrates the main qualitative properties of hydrodynamics models for collective behavior. These models include a velocity consensus term together with attractive–repulsive potentials leading to non-trivial flock profiles. The connection between the underlying particle systems and the swarming hydrodynamic equations is performed through kinetic theory modeling arguments. We focus on Lagrangian schemes for the hydrodynamic systems showing the different qualitative behaviors of the systems and its capability of keeping properties of the original particle models. We illustrate the known results concerning large-time profiles and blowup in finite time of the hydrodynamic systems to validate the numerical scheme. We finally explore the unknown situations making use of the numerical scheme showcasing a number of conjectures based on the numerical results.

BOOK CHAPTER

Carrillo JA, Feireisl E, Gwiazda P, Swierczewska-Gwiazda Aet al., 2017, Weak solutions for Euler systems with non-local interactions, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, Vol: 95, Pages: 705-724, ISSN: 0024-6107

JOURNAL ARTICLE

Carrillo JA, Figalli A, Patacchini FS, 2017, Geometry of minimizers for the interaction energy with mildly repulsive potentials, ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, Vol: 34, Pages: 1299-1308, ISSN: 0294-1449

JOURNAL ARTICLE

Carrillo JA, Huang Y, 2017, EXPLICIT EQUILIBRIUM SOLUTIONS FOR THE AGGREGATION EQUATION WITH POWER-LAW POTENTIALS, KINETIC AND RELATED MODELS, Vol: 10, Pages: 171-192, ISSN: 1937-5093

JOURNAL ARTICLE

Carrillo JA, Huang Y, Patacchini FS, Wolansky Get al., 2017, NUMERICAL STUDY OF A PARTICLE METHOD FOR GRADIENT FLOWS, KINETIC AND RELATED MODELS, Vol: 10, Pages: 613-641, ISSN: 1937-5093

JOURNAL ARTICLE

Barbaro ABT, Canizo JA, Carrillo JA, Degond Pet al., 2016, PHASE TRANSITIONS IN A KINETIC FLOCKING MODEL OF CUCKER-SMALE TYPE, MULTISCALE MODELING & SIMULATION, Vol: 14, Pages: 1063-1088, ISSN: 1540-3459

JOURNAL ARTICLE

Bonnaillie-Noel V, Carrillo JA, Goudon T, Pavliotis GAet al., 2016, Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations, IMA JOURNAL OF NUMERICAL ANALYSIS, Vol: 36, Pages: 1536-1569, ISSN: 0272-4979

JOURNAL ARTICLE

Canizo JA, Carrillo JA, Laurencot P, Rosado Jet al., 2016, The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, Vol: 137, Pages: 291-305, ISSN: 0362-546X

JOURNAL ARTICLE

Carrillo JA, Choi Y-P, Karper TK, 2016, On the analysis of a coupled kinetic-fluid model with local alignment forces, ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, Vol: 33, Pages: 273-307, ISSN: 0294-1449

JOURNAL ARTICLE

Carrillo JA, Choi Y-P, Tadmor E, Tan Cet al., 2016, Critical thresholds in 1D Euler equations with non-local forces, MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, Vol: 26, ISSN: 0218-2025

JOURNAL ARTICLE

Carrillo JA, Choi Y-P, Zatorska E, 2016, On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior, Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

WORKING PAPER

Carrillo JA, Delgadino MG, Mellet A, 2016, Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems, COMMUNICATIONS IN MATHEMATICAL PHYSICS, Vol: 343, Pages: 747-781, ISSN: 0010-3616

JOURNAL ARTICLE

Carrillo JA, Di Francesco M, Toscani G, 2016, Condensation phenomena in nonlinear drift equations, ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, Vol: 15, Pages: 145-171, ISSN: 0391-173X

JOURNAL ARTICLE

Carrillo JA, James F, Lagoutiere F, Vauchelet Net al., 2016, The Filippov characteristic flow for the aggregation equation with mildly singular potentials, JOURNAL OF DIFFERENTIAL EQUATIONS, Vol: 260, Pages: 304-338, ISSN: 0022-0396

JOURNAL ARTICLE

Carrillo JA, Klar A, Roth A, 2016, SINGLE TO DOUBLE MILL SMALL NOISE TRANSITION VIA SEMI-LAGRANGIAN FINITE VOLUME METHODS, COMMUNICATIONS IN MATHEMATICAL SCIENCES, Vol: 14, Pages: 1111-1136, ISSN: 1539-6746

JOURNAL ARTICLE

Carrillo JA, Martin S, Wolfram M-T, 2016, An improved version of the Hughes model for pedestrian flow, MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, Vol: 26, Pages: 671-697, ISSN: 0218-2025

JOURNAL ARTICLE

Carrillo JA, Patacchini FS, Sternberg P, Wolansky Get al., 2016, CONVERGENCE OF A PARTICLE METHOD FOR DIFFUSIVE GRADIENT FLOWS IN ONE DIMENSION, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, Vol: 48, Pages: 3708-3741, ISSN: 0036-1410

JOURNAL ARTICLE

Carrillo JA, Ranetbauer H, Wolfram M-T, 2016, Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 327, Pages: 186-202, ISSN: 0021-9991

JOURNAL ARTICLE

Carrillo JA, Slepcev D, Wu L, 2016, NONLOCAL-INTERACTION EQUATIONS ON UNIFORMLY PROX-REGULAR SETS, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, Vol: 36, Pages: 1209-1247, ISSN: 1078-0947

JOURNAL ARTICLE

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