Eur. Phys. J. E (2014) 37: 55
https://doi.org/10.1140/epje/i2014-14055-8

Regular Article

Tailoring the interactions between self-propelled bodies

Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, 69007, Lyon, France

^* e-mail: jeanbaptiste.caussin@ens-lyon.fr

Received: 18 April 2014
Revised: 4 June 2014
Accepted: 5 June 2014
Published online: 27 June 2014

Abstract

We classify the interactions between self-propelled particles moving at a constant speed from symmetry considerations. We establish a systematic expansion for the two-body forces in the spirit of a multipolar expansion. This formulation makes it possible to rationalize most of the models introduced so far within a common framework. We distinguish between three classes of physical interactions: i) potential forces, ii) inelastic collisions and iii) non-reciprocal interactions involving polar or nematic alignment with an induced field. This framework provides simple design rules for the modeling and the fabrication of self-propelled bodies interacting via physical interactions. A class of possible interactions that should yield new phases of active matter is highlighted.