Alignment of self-propelled rigid bodies: from particle systems to macroscopic equations

TL;DR

This paper reviews models for the collective alignment of self-propelled rigid bodies across scales, introduces a new model, and demonstrates the derivation of a universal macroscopic equation from microscopic models.

Contribution

It introduces a new microscopic model for self-propelled rigid bodies and highlights the adaptability of existing methods in deriving macroscopic equations.

Findings

Different microscopic models lead to the same macroscopic equations.

The new model offers additional insights into alignment dynamics.

Methods are unified and simplified for broader applicability.

Abstract

The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in addition, we introduce a new model and apply on it the same methods. While the new model has its own interest, our aim is also to emphasize the methods by demonstrating their adaptability and by presenting them in a unified and simplified way. Furthermore, from the various microscopic models we derive the same macroscopic model, which is a good indicator of its universality.