Non-metric interaction rules in soft and living matter

The effect of what might be called “non-metric” interactions – for instance Voronoi-like interaction graphs that determine forces in models of dense cellular matter or k-nearest-neighbor rules dictating alignment interactions in models of flocking – arise naturally when studying active and living material systems. Do these novel forms of interaction support new material properties and dynamical behavior, and if so, how? In this talk, I will describe two vignettes from my group’s recent work that highlight how these types of interactions give rise to new phenomena in amorphous matter. In the context of cellular matter, I will discuss both the unusual mechanics and dynamics that arise when modeling disordered epithelial monolayers in this way, and I will comment on a puzzlingly robust data-driven approach for predicting local cellular rearrangements. I will then discuss models of flocking animals, describing how non-metric interaction rules are a natural source of microscopic non-reciprocity. This in turn has dramatic implications for the disordered flocking phases that can be observed.