A Primer of Swarm Equilibria

From MaRDI portal
Publication:2996502

DOI10.1137/100804504zbMath1255.35012arXiv1008.0881OpenAlexW2126564632WikidataQ58933900 ScholiaQ58933900MaRDI QIDQ2996502

Chad M. Topaz, Andrew J. Bernoff

Publication date: 2 May 2011

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0881




Related Items (62)

First-order aggregation models with alignmentSwarm Equilibria in Domains with BoundariesData-driven discovery of emergent behaviors in collective dynamicsRegularity of local minimizers of the interaction energy via obstacle problemsPREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONSNonlocal Interaction Equations in Environments with Heterogeneities and BoundariesWell-posedness theory for aggregation sheetsSwarming in domains with boundaries: approximation and regularization by nonlinear diffusionConvergence of Regularized Nonlocal Interaction EnergiesMulti-vortex crystal lattices in Bose–Einstein condensates with a rotating trapConsistent Dynamics of Stripes Formed by Cell-Type InterfacesExplicit flock solutions for Quasi-Morse potentialsConvergence of a linearly transformed particle method for aggregation equationsZero-diffusion limit for aggregation equations over bounded domainsAsymptotic behavior of a nonlocal advection system with two populationsAnticipation breeds alignmentNumerical simulation of nonlinear continuity equations by evolving diffeomorphismsDimensionality of local minimizers of the interaction energyLocalization and vector spherical harmonicsAn anisotropic interaction model for simulating fingerprintsOn soccer balls and linearized inverse statistical mechanicsQuantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish PatternsSome free boundary problems involving non-local diffusion and aggregationOn minimizers of interaction functionals with competing attractive and repulsive potentialsFlocking of the Cucker-Smale and Motsch-Tadmor models on general weighted digraphs via a probabilistic methodEmergent behaviors of two attractively coupled swarm sphere models with frustrationEquilibria and energy minimizers for an interaction model on the hyperbolic spaceEquilibria for an Aggregation Model with Two SpeciesA one-dimensional logistic like equation with nonlinear and nonlocal diffusion: strong convergence to equilibriumFrom the Lohe Tensor Model to the Lohe Hermitian Sphere Model and Emergent DynamicsPattern formation of a nonlocal, anisotropic interaction modelInterplay of inertia and adaptive couplings in the emergent dynamics of Kuramoto ensembleStationary Ring and Concentric-Ring Solutions of the Keller--Segel Model with Quadratic DiffusionNonlocal interactions by repulsive-attractive potentials: radial ins/stabilityEquilibria of biological aggregations with nonlocal repulsive-attractive interactionsSingular patterns for an aggregation model with a confining potentialEquilibria of an aggregation model with linear diffusion in domains with boundariesExponential convergence towards stationary states for the 1D porous medium equation with fractional pressureTwo-species particle aggregation and stability of co-dimension one solutionsDynamics of one-fold symmetric patches for the aggregation equation and collapse to singular measureOptimal lattice configurations for interacting spatially extended particlesUniversality of the weak pushed-to-pulled transition in systems with repulsive interactionsExplicit equilibrium solutions for the aggregation equation with power-law potentialsEmergent behaviors of the generalized Lohe matrix modelStability Analysis of Line Patterns of an Anisotropic Interaction ModelNonlocal Shape Optimization via Interactions of Attractive and Repulsive PotentialsA "liquid-solid" phase transition in a simple model for swarming, based on the "no flat-spots" theorem for subharmonic functionsAn intrinsic aggregation model on the special orthogonal group \(SO(3)\): well-posedness and collective behavioursGeometric Self-Assembly of Rigid Shapes: A Simple Voronoi ApproachHeterogeneity and Oscillations in Small SwarmsBiological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn--Hilliard ApproximationMean-Field Limit of a Microscopic Individual-Based Model Describing Collective MotionsThird-order phase transition: random matrices and screened Coulomb gas with hard wallsMechanical torque promotes bipolarity of the mitotic spindle through multi-centrosomal clusteringEmergent dynamics of the Lohe Hermitian sphere model with frustrationStable Steady-State Solutions of Some Biological Aggregation ModelsMinimal soft lattice theta functionsExistence of ground states of nonlocal-interaction energiesCollective Dynamics of Interacting Particles in Unsteady FlowsStationary States and Asymptotic Behavior of Aggregation Models with Nonlinear Local RepulsionNonlocal-interaction equations on uniformly prox-regular setsExistence of compactly supported global minimisers for the interaction energy




This page was built for publication: A Primer of Swarm Equilibria