Modulation of the Monokinetic Limit for Models of Collective Dynamics

TL;DR

This paper analyzes how the monokinetic limit in collective dynamics models transitions under different regimes, revealing convergence behaviors to Gaussian and transport profiles.

Contribution

It introduces a modulation analysis connecting kinetic Cucker-Smale models to pressureless Euler systems under varying noise and Knudsen regimes.

Findings

Convergence to Gaussian distribution under strong Fokker-Planck force.

Distribution converges to a transport profile in noiseless Vlasov scheme.

Provides rigorous analysis of monokinetic limit modulation.

Abstract

In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a strong Fokker- Planck force with vanishing noise and Knudsen number, and a pure noiseless Vlasov scheme. In the former case, we demonstrate convergence of the modulated profile to the standard Gaussian distribution, while in the latter case, the distribution converges to a profile satisfying an explicit transport equation along limiting characteristics.