Density-independent model of self-propelled particles

Area of Science:

• Statistical physics
• Complex systems
• Computational modeling

Background:

• The Vicsek model is a standard for studying self-propelled particles and emergent order.
• Simulating dynamic particle interactions often requires efficient mesh updating algorithms.

Purpose of the Study:

• To investigate a modified Vicsek model using Delaunay triangulation for neighbor definition.
• To develop and validate a dynamic triangulation repair algorithm for simulations.
• To analyze the phase transition and critical behavior of this modified model.

Main Methods:

• Implemented a density-independent Vicsek model with neighbor interactions based on Delaunay triangulation.
• Developed a novel algorithm for dynamically updating the 2D Delaunay triangulation during simulations.
• Measured critical exponents and analyzed scaling relationships under varying noise and velocity regimes.

Main Results:

• The modified Vicsek model exhibits a continuous phase transition influenced by noise.
• A distinct set of critical exponents were measured, satisfying a hyperscaling relationship.
• Critical exponents varied between low and high velocity regimes but remained robust with repulsive interactions.

Conclusions:

• The developed dynamic triangulation algorithm is efficient for time-varying meshes.
• The model demonstrates robust collective behavior and scaling properties, even with repulsive forces.
• Evidence suggests correlation length scales with system size in the ordered phase, providing insights into emergent order.