A multi-layer model for self-propelled disks interacting through alignment and volume exclusion

Abstract

We present an individual-based model describing disk-like self-propelled particles moving inside parallel planes. The disk directions of motion follow alignment rules inside each layer. Additionally, the disks are subject to interactions with those of the neighboring layers arising from volume exclusion constraints. These interactions affect the disk inclinations with respect to the plane of motion. We formally de-rive a macroscopic model composed of planar Self-Organized Hydrodynamic (SOH) models describing the transport of mass and evolution of mean direction of motion of the disks in each plane, supplemented with transport equations for the mean disk inclination. These planar models are coupled due to the interactions with the neighboring planes. Numerical comparisons between the individual-based and macroscopic models are carried out. These models could be applicable, for instance, to describe sperm-cell collective dynamics.

References in corpus (13)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• Collective motion of self-propelled particles interacting without cohesion
• Phase transition in the collective migration of tissue cells: experiment and model
• Non-equilibrium clustering of self-propelled rods
• Active Jamming: Self-propelled soft particles at high density
• A new model for self-organized dynamics and its flocking behavior
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
• Mean-field limit for the stochastic Vicsek model
• Nonequilibrium Statistical Mechanics of Self-propelled Hard Rods
• Self-Organized Hydrodynamics with congestion and path formation in crowds
• Collective Behavior of Self Propelling Particles with Kinematic Constraints; The relation between the discrete and the continuous description

Cited by in corpus (7)

• Phase transitions and macroscopic limits in a BGK model of body-attitude coordination
• Propagation of chaos and moderate interaction for a piecewise deterministic system of geometrically enriched particles
• A continuum model for nematic alignment of self-propelled particles
• Quaternions in collective dynamics
• Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles
• Cauchy theory for general Vicsek models in collective dynamics and mean-field limit approximations
• An age-structured continuum model for myxobacteria