183 results found
Bostan M, Carrillo de la Plata J, Reduced fluid models for self-propelled particles interacting through alignment, Mathematical Models and Methods in Applied Sciences, ISSN: 0218-2025
The asymptotic analysis of kinetic models describing the behavior of particles interacting throughalignment is performed. We will analyze the asymptotic regime corresponding to large alignmentfrequency where the alignment effects are dominated by the self propulsion and friction forces. Theformer hypothesis leads to a macroscopic fluid model due to the fast averaging in velocity, while thesecond one imposes a fixed speed in the limit, and thus a reduction of the dynamics to a spherein the velocity space. The analysis relies on averaging techniques successfully used in the magneticconfinement of charged particles. The limiting particle distribution is supported on a sphere, andtherefore we are forced to work with measures in velocity. As for the Euler-type equations, the fluidmodel comes by integrating the kinetic equation against the collision invariants and its generalizationsin the velocity space. The main difficulty is their identification for the averaged alignment kernel inour functional setting of measures in velocity.
Carrillo JA, Colombi A, Scianna M, Adhesion and volume constraints via nonlocal interactions lead to cell sorting
We demonstrate how concepts of statistical mechanics of interacting particlescan have important implications in the choice of interaction potentials tomodel qualitative properties of cell aggregates in theoretical biology. Weillustrate this by showing cell sorting phenomena for cell groups withdifferent adhesiveness parameters: ranging from well-mixed cells aggregates tofull segregation of cell type passing through engulfment via adhesivenesstuning.
Carrillo de la Plata J, choi YP, Hauray M, et al., Mean-field limit for collective behavior models with sharp sensitivity regions, Journal of the European Mathematical Society, ISSN: 1435-9855
We rigorously show the mean-field limit for a large class of swarming individual based modelswith local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractiveforces locally averaged over sharp vision cones and Cucker-Smale interactions with discontinuous communicationweights. We construct global-in-time defined notion of solutions through a differential inclusionsystem corresponding to the particle descriptions. We estimate the error between the solutions to thedifferential inclusion system and weak solutions to the expected limiting kinetic equation by employingtools from optimal transport theory. Quantitative bounds on the expansion of the 1-Wasserstein distancealong flows based on a weak-strong stability estimate are obtained. We also provide different examplesof realistic sensitivity sets satisfying the assumptions of our main results.
Barré J, Carrillo JA, Degond P, et 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.
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
Carrillo JA, Choi Y-P, Mucha PB, et 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
Carrillo JA, Feireisl E, Gwiazda P, et 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
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
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
Carrillo JA, Huang Y, Patacchini FS, et al., 2017, NUMERICAL STUDY OF A PARTICLE METHOD FOR GRADIENT FLOWS, KINETIC AND RELATED MODELS, Vol: 10, Pages: 613-641, ISSN: 1937-5093
Barbaro ABT, Canizo JA, Carrillo JA, et al., 2016, PHASE TRANSITIONS IN A KINETIC FLOCKING MODEL OF CUCKER-SMALE TYPE, MULTISCALE MODELING & SIMULATION, Vol: 14, Pages: 1063-1088, ISSN: 1540-3459
Bonnaillie-Noel V, Carrillo JA, Goudon T, et 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
Canizo JA, Carrillo JA, Laurencot P, et 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
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
Carrillo JA, Choi Y-P, Tadmor E, et al., 2016, Critical thresholds in 1D Euler equations with non-local forces, MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, Vol: 26, ISSN: 0218-2025
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
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
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
Carrillo JA, James F, Lagoutiere F, et 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
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
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
Carrillo JA, Patacchini FS, Sternberg P, et 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
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
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
Pajaro M, Alonso AA, Carrillo JA, et 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
Blanchet A, Carrillo JA, Kinderlehrer D, et 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
Bonaschi GA, Carrillo JA, Di Francesco M, et 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
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
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
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
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.