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.Comment: 29 pages, 14 figure