Classifying Minimum Energy States for Interacting Particles: Spherical Shells
DOI10.1137/21M1455309zbMath1495.49024arXiv2107.11718WikidataQ114073955 ScholiaQ114073955MaRDI QIDQ5097470
Tongseok Lim, Robert J. McCann, Cameron Davies
Publication date: 24 August 2022
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.11718
Lyapunov stabilityasymptotic stabilityconvexspherical shellaggregation equationinfinite-dimensional quadratic programming\(d_\infty\)-local minimumattractive-repulsive power-law interactionKantorovich-Rubinstein-Wasserstein distanceunique energy minimizer
Quadratic programming (90C20) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Optimization of shapes other than minimal surfaces (49Q10) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) The dynamics of infinite particle systems (70F45) PDEs in connection with mechanics of particles and systems of particles (35Q70)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A nonlocal continuum model for biological aggregation
- Dimensionality of local minimizers of the interaction energy
- The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions
- Stability of stationary states of non-local equations with singular interaction potentials
- Explicit equilibrium solutions for the aggregation equation with power-law potentials
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- Initiation of slime mold aggregation viewed as an instability
- On minimizers of interaction functionals with competing attractive and repulsive potentials
- A non-local model for a swarm
- Geometry of minimizers for the interaction energy with mildly repulsive potentials
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Isodiametry, variance, and regular simplices from particle interactions
- Minimizers for a one-dimensional interaction energy
- Uniqueness and radial symmetry of minimizers for a nonlocal variational problem
- On the strong attraction limit for a class of nonlocal interaction energies
- Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials
- Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
- Reverse Hardy-Littlewood-Sobolev inequalities
- Ring patterns and their bifurcations in a nonlocal model of biological swarms
- Nonlocal interactions by repulsive-attractive potentials: radial ins/stability
- Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
- Formation of clumps and patches in self-aggregation of finite-size particles
- One-dimensional kinetic models of granular flows
- A blob method for the aggregation equation
- Stability and clustering of self-similar solutions of aggregation equations
- PREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONS
- Random walk with persistence and external bias
- From Nash to Cournot–Nash equilibria via the Monge–Kantorovich problem
- Swarm dynamics and equilibria for a nonlocal aggregation model
- Stability Analysis of Flock and Mill Rings for Second Order Models in Swarming
- A kinetic equation for granular media
- The Variational Formulation of the Fokker--Planck Equation
- Nonlocal Shape Optimization via Interactions of Attractive and Repulsive Potentials
- A "liquid-solid" phase transition in a simple model for swarming, based on the "no flat-spots" theorem for subharmonic functions
- Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation
- Uniqueness and Nonuniqueness of Steady States of <scp>Aggregation‐Diffusion</scp> Equations
- Proof of spherical flocking based on quantitative rearrangement inequalities
- Nonlinear Stability through Algebraically Decaying Point Spectrum: Applications to Nonlocal Interaction Equations
This page was built for publication: Classifying Minimum Energy States for Interacting Particles: Spherical Shells
