Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems

On minimizers of interaction functionals with competing attractive and repulsive potentials

(2015) Rustum Choksi et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

Existence of Compactly Supported Global Minimisers for the Interaction Energy

(2015) José A. Cañizo et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Existence of Ground States of Nonlocal-Interaction Energies

(2015) Robert Simione et al.   JOURNAL OF STATISTICAL PHYSICS

First-order global asymptotics for confined particles with singular pair repulsion

(2014) Djalil Chafaï et al.   ANNALS OF APPLIED PROBABILITY

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

(2014) José A. Carrillo et al.   Communications in Computational Physics

Confinement for repulsive-attractive kernels

(2014) Daniel Balagué et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Nonlinear stability of flock solutions in second-order swarming models

(2014) J.A. Carrillo et al.   NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

On global minimizers of repulsive-attractive power-law interaction energies

(2014) J. A. Carrillo et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Stability Analysis of Flock and Mill Rings for Second Order Models in Swarming

(2014) G. Albi et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

Dimensionality of Local Minimizers of the Interaction Energy

(2013) D. Balagué et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Emergent behaviour in multi-particle systems with non-local interactions

(2013) Theodore Kolokolnikov et al.   PHYSICA D-NONLINEAR PHENOMENA

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

(2012) José A. Carrillo et al.   ADVANCES IN MATHEMATICS

On Soccer Balls and Linearized Inverse Statistical Mechanics

(2012) James H. von Brecht et al.   JOURNAL OF NONLINEAR SCIENCE

Equilibria of biological aggregations with nonlocal repulsive–attractive interactions

(2012) R.C. Fetecau et al.   PHYSICA D-NONLINEAR PHENOMENA

Nonlocal interactions by repulsive–attractive potentials: Radial ins/stability

(2012) D. Balagué et al.   PHYSICA D-NONLINEAR PHENOMENA

Nonlinear Porous Medium Flow with Fractional Potential Pressure

(2011) Luis Caffarelli et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

(2011) J. A. Carrillo et al.   DUKE MATHEMATICAL JOURNAL

AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS

(2011) ANDREA L. BERTOZZI et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Confinement in nonlocal interaction equations

(2011) J.A. Carrillo et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Swarm dynamics and equilibria for a nonlocal aggregation model

(2011) R C Fetecau et al.   NONLINEARITY

A Primer of Swarm Equilibria

(2011) Andrew J. Bernoff et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Energy Landscapes of Clusters Bound by Short-Ranged Potentials

(2010) David J. Wales   CHEMPHYSCHEM

Stability of stationary states of non-local equations with singular interaction potentials

(2010) Klemens Fellner et al.   MATHEMATICAL AND COMPUTER MODELLING

STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS

(2010) KLEMENS FELLNER et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

(2009) Andrea L Bertozzi et al.   NONLINEARITY