Some aspects of the inertial spin model for flocks and related kinetic equations

DOI10.1142/S0218202520400151zbMath1462.82055arXiv1911.02447OpenAlexW3045786697MaRDI QIDQ3386866

Paolo Buttà, Dario Benedetto, Emanuele Caglioti

Publication date: 7 January 2021

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.02447

zbMATH Keywords

flockingkinetic limitinertial spin model

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Developmental biology, pattern formation (92C15) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Animal behavior (92D50) Fokker-Planck equations (35Q84)

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Cites Work

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• A nonlocal continuum model for biological aggregation
• Mean-field limit for the stochastic Vicsek model
• A new model for self-organized dynamics and its flocking behavior
• A conceptual model for milling formations in biological aggregates
• On the complete phase synchronization for the Kuramoto model in the mean-field limit
• From particle to kinetic and hydrodynamic descriptions of flocking
• Double milling in self-propelled swarms from kinetic theory
• On the mathematics of emergence
• Vlasov equations
• A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment
• Eulerian dynamics with a commutator forcing. III: Fractional diffusion of order \(0 < \alpha < 1\)
• A non-linear kinetic model of self-propelled particles with multiple equilibria
• Flocking dynamics of the inertial spin model with a multiplicative communication weight
• Propagation of chaos for topological interactions
• Flocking and turning: a new model for self-organized collective motion
• First-order aggregation models with alignment
• Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions
• STOCHASTIC MEAN-FIELD LIMIT: NON-LIPSCHITZ FORCES AND SWARMING
• Dynamics in a Kinetic Model of Oriented Particles with Phase Transition
• A WELL-POSEDNESS THEORY IN MEASURES FOR SOME KINETIC MODELS OF COLLECTIVE MOTION
• COOPERATIVE STRATEGIES IN FORMATION OF COMPLEX BACTERIAL PATTERNS
• FROM EMPIRICAL DATA TO INTER-INDIVIDUAL INTERACTIONS: UNVEILING THE RULES OF COLLECTIVE ANIMAL BEHAVIOR
• Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
• A new flocking model through body attitude coordination
• Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker–Smale models
• Emergent Behavior in Flocks
• Complex spatial group patterns result from different animal communication mechanisms
• Critical points of the Onsager functional on a sphere