Signatures of odd dynamics in viscoelastic systems: from spatiotemporal pattern formation to odd rheology

Non-reciprocal interactions fueled by local energy consumption are found in biological and synthetic active matter, where both viscosity and elasticity are often important. Such systems can be described by "odd" viscoelasticity, which assumes fewer material symmetries than traditional theories. In odd viscoelastic systems there is an interplay between the energy-consuming odd elastic elements and the traditional stabilizing elements. This leads to rich dynamical behavior which, due to a lack of appropriate numerical methods, has remained relatively unexplored. Furthermore, the implications associated with the presence of such odd terms in actomyosin and other similar anisotropic systems has not been addressed. Here, we study odd viscoelasticity analytically and using hydrodynamic simulations based on the lattice Boltzmann algorithm. We first outline how odd effects may naturally emerge from a theory of polymeric elasticity which can describe anisotropic systems like actomyosin. Next, we report on two striking features of odd viscoelastic dynamics: a pattern-forming instability which produces an oscillating array of fluid vortices, and strong transverse and rotational forces during a simulated rheological experiment. These findings can guide efforts to detect or engineer odd dynamics in soft active matter systems.