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

186 results found

Barré J, Carrillo JA, Degond P, Peurichard D, Zatorska Eet al., 2017, Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions, Journal of Nonlinear Science, Pages: 1-34, ISSN: 0938-8974

© 2017 The Author(s) We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation–diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.

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

Carrillo JA, Choi Y-P, Mucha PB, Peszele 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, 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

Sun Z, Carrillo de la Plata J, Shu CW, 2017, 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

We consider a class of time-dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of problems covers important cases such as Fokker–Planck type equations and aggregation models, which have been studied intensively in the past decades. In this paper, we design a high order discontinuous Galerkin method for such problems. If the interaction potential is not involved, or the interaction is defined by a smooth kernel, our semi-discrete scheme admits an entropy inequality on the discrete level. Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint. Our method also applies to two dimensional problems on Cartesian meshes. Numerical examples are given to confirm the high order accuracy for smooth test cases and to demonstrate the effectiveness for preserving long time asymptotics.

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

Pajaro M, Alonso AA, Carrillo JA, Vazquez Cet al., 2016, Stability of stochastic gene regulatory networks using entropy methods, 2nd IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory (TFMST), Publisher: ELSEVIER SCIENCE BV, Pages: 1-5, ISSN: 2405-8963

CONFERENCE PAPER

Blanchet A, Carrillo JA, Kinderlehrer D, Kowalczyk M, Laurencot P, Lisini Set al., 2015, A HYBRID VARIATIONAL PRINCIPLE FOR THE KELLER-SEGEL SYSTEM IN R-2, ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, Vol: 49, Pages: 1553-1576, ISSN: 0764-583X

JOURNAL ARTICLE

Bonaschi GA, Carrillo JA, Di Francesco M, Peletier MAet al., 2015, EQUIVALENCE OF GRADIENT FLOWS AND ENTROPY SOLUTIONS FOR SINGULAR NONLOCAL INTERACTION EQUATIONS IN 1D, ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, Vol: 21, Pages: 414-441, ISSN: 1292-8119

JOURNAL ARTICLE

Canizo JA, Carrillo JA, Patacchini FS, 2015, Existence of Compactly Supported Global Minimisers for the Interaction Energy, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Vol: 217, Pages: 1197-1217, ISSN: 0003-9527

JOURNAL ARTICLE

Carrillo JA, Castorina D, Volzone B, 2015, GROUND STATES FOR DIFFUSION DOMINATED FREE ENERGIES WITH LOGARITHMIC INTERACTION, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, Vol: 47, Pages: 1-25, ISSN: 0036-1410

JOURNAL ARTICLE

Carrillo JA, Chertock A, Huang Y, 2015, A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure, Communications in Computational Physics, Vol: 17, Pages: 233-258, ISSN: 1991-7120

JOURNAL ARTICLE

Carrillo JA, Eftimie R, Hoffmann F, 2015, NON-LOCAL KINETIC AND MACROSCOPIC MODELS FOR SELF-ORGANISED ANIMAL AGGREGATIONS, KINETIC AND RELATED MODELS, Vol: 8, Pages: 413-441, ISSN: 1937-5093

JOURNAL ARTICLE

Carrillo JA, Huang Y, Santos MC, Vazquez JLet al., 2015, Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure, JOURNAL OF DIFFERENTIAL EQUATIONS, Vol: 258, Pages: 736-763, ISSN: 0022-0396

JOURNAL ARTICLE

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