Mixing, Enhanced Dissipation and Phase Transition in the Kinetic Vicsek Model

TL;DR

This paper analyzes the kinetic Vicsek model to understand how mixing and dissipation phenomena lead to phase transitions and stabilization of dynamics, mirroring behaviors seen in experiments with fibroblasts.

Contribution

It provides a rigorous analysis of the long-time behavior of the kinetic Vicsek model, confirming phase transitions at the kinetic level and elucidating the role of mixing and dissipation.

Findings

Mixing and enhanced dissipation stabilize the system dynamics.

The model exhibits a phase transition consistent with agent-based simulations.

Solutions behave similarly to spatially-homogeneous systems under certain conditions.

Abstract

In this paper, we study the kinetic Vicsek model, which serves as a starting point for describing the polarization phenomena observed in the experiments of fibroblasts moving on liquid crystalline substrates. The long-time behavior of the kinetic equation is analyzed, revealing that, within specific parameter regimes, the mixing and enhanced dissipation phenomena stabilize the dynamics and ensure effective information communication among agents. Consequently, the solution exhibits features similar to those of a spatially-homogeneous system. As a result, we confirm the phase transition observed in the agent-based Vicsek model at the kinetic level.