Density-Independent Model of Self-Propelled Particles

TL;DR

This paper introduces a density-independent self-propelled particle model using Delaunay triangulation, revealing a continuous phase transition with variable critical exponents and a novel triangulation repair algorithm.

Contribution

It presents a new density-independent model with a triangulation-based interaction scheme and an efficient algorithm for dynamic triangulation repair.

Findings

The model exhibits a continuous phase transition with measurable critical exponents.

Critical exponents vary with velocity regimes but are robust to repulsive interactions.

Correlation length scales with system size even in the ordered phase.

Abstract

We examine a density-independent modification of the Vicsek model in which a particle interacts with neighbors defined by Delaunay triangulation. To feasibly simulate the model, an algorithm for repairing the triangulation over time was developed. This algorithm may also be applied to any time-varying two-dimensional Delaunay triangulation. This model exhibits a continuous phase transition with noise, and a distinct set of critical exponents were measured which satisfy a hyperscaling relationship. The critical exponents are found to vary between a low and high velocity regime, but they are robust under the inclusion of a repulsive interaction. We present evidence that the correlation length approximately scales with the size of the system even in the ordered phase.