Scale-Free Chaos in the 2D Harmonically Confined Vicsek Model

Area of Science:

• Physics
• Statistical Mechanics
• Active Matter

Background:

• Animal flocking and motion are key nonequilibrium phenomena studied in active matter.
• The Vicsek model with periodic boundaries shows phase transitions, but these differ from natural swarms.
• Confining particles with a harmonic potential in the Vicsek model leads to complex attractors, including scale-free chaos.

Purpose of the Study:

• Investigate the scale-free chaos phase transition in two-dimensional active matter systems.
• Compare simulation results to observations of natural insect swarms, like midges.
• Analyze critical exponents and dynamic correlations in this chaotic regime.

Main Methods:

• Numerical simulations of the Vicsek model with harmonic confinement.
• Calculation of largest Lyapunov exponents to identify chaos.
• Analysis of static and dynamic critical exponents.

Main Results:

• The chaotic swarm shape on the critical curve mirrors the core-and-vapor structure of midge swarms.
• Dynamic correlation functions exhibit collapse only over a limited range of scaled times.
• Scale-free chaos and power laws are observed on critical curves.

Conclusions:

• The harmonic potential Vicsek model provides a more realistic framework for studying natural swarms than periodic boundary conditions.
• Scale-free chaos in this model explains observed swarm structures and dynamics.
• Further comparison with three-dimensional models is warranted.