Non-metric interaction rules in models of active matter

TL;DR

This paper explores the use of non-metric interaction rules in active matter models, challenging traditional pairwise distance-based interactions and proposing new paradigms for simulating complex, living systems.

Contribution

It introduces the concept of non-metric interactions in active matter models and discusses their implications for physical understanding and computational simulation.

Findings

Non-metric interactions can model non-reciprocal behaviors.

Traditional algorithms may need adaptation for non-metric rules.

Non-metric interactions are relevant for biological systems.

Abstract

It is common in the study of a dizzying array of soft matter systems to perform agent-based simulations of particles interacting via conservative and often short-ranged forces. In this context, well-established algorithms for efficiently computing the set of pairs of interacting particles have established excellent open-source packages to efficiently simulate large systems over long time scales -- a crucial consideration given the separation in time- and length-scales often observed in soft matter. What happens, though, when we think more broadly about what it means to construct a neighbor list? What if interactions are non-reciprocal, or if the "range" of an interaction is determined not by a distance scale but according to some other consideration? As the field of soft and active matter increasingly considers the properties of living matter -- from the cellular to the super-organismal scale -- these questions become increasingly relevant, and encourage us to think about new physical and computational paradigms in the modeling of active matter. In this chapter we examine case studies in the use of non-metric interactions.