A multi-layer model for self-propelled disks interacting through alignment and volume exclusion
Authored by Pierre Degond, Laurent Navoret
Date Published: 2015
DOI: 10.1142/s021820251540014x
Sponsors:
French National Research Agency (ANR)
United Kingdom Engineering and Physical Sciences Research Council (EPSRC)
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
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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 derive 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.
Tags
collective behavior
hydrodynamics
System
Constraints
Driven particles
Continuum-limit
Flocks