A macroscopic model for a system of swarming agents using curvature control

Abstract

In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination of the Vicsek alignment model and the Persistent Turning Walker (PTW) model of motion by curvature control. The PTW model was designed to fit measured trajectories of individual fish. The PTWA model (Persistent Turning Walker with Alignment) describes the displacements of agents which modify their curvature in order to align with their neighbors. The derivation of its macroscopic limit uses the non-classical notion of generalized collisional invariant. The macroscopic limit of the PTWA model involves two physical quantities, the density and the mean velocity of individuals. It is a system of hyperbolic type but is non-conservative due to a geometric constraint on the velocity. This system has the same form as the macroscopic limit of the Vicsek model (the 'Vicsek hydrodynamics') but for the expression of the model coefficients. The numerical computations show that the numerical values of the coefficients are very close. The 'Vicsek Hydrodynamic model' appears in this way as a more generic macroscopic model of swarming behavior as originally anticipated.

References in corpus (10)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Boltzmann and hydrodynamic description for self-propelled particles
• Collective behavior of interacting self-propelled particles
• State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
• Continuum limit of self-driven particles with orientation interaction
• Large scale dynamics of the Persistent Turning Walker model of fish behavior
• New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
• Congestion in a macroscopic model of self-driven particles modeling gregariousness
• Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model

Cited by in corpus (13)

• Swarming, Schooling, Milling: Phase diagram of a data-driven fish school model
• Macroscopic limits and phase transition in a system of self-propelled particles
• Hydrodynamic models of self-organized dynamics: derivation and existence theory
• Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
• Kinetic limits for pair-interaction driven master equations and biological swarm models
• Self-Organized Hydrodynamics with congestion and path formation in crowds
• A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters
• Kinetic hierarchy and propagation of chaos in biological swarm models
• Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation
• Local stability of perfect alignment for a spatially homogeneous kinetic model
• Phase transitions and macroscopic limits in a BGK model of body-attitude coordination
• Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies
• Bulk topological states in a new collective dynamics model