Phenomenological dynamics: From Navier–Stokes to chiral granular gases

This paper reviews the derivation of equations for slow dynamical processes in a variety of systems, including rotating rigid rotors, crystalline solids, isotropic and nematic elastomers, gels in an isotropic fluid background, and nematic liquid crystals. It presents a recent derivation of the Leslie-Ericksen equations for the dynamics of nematic liquid crystals that clarifies the nature of the nonhydrodynamic modes in these equations. As a final example of the phenomenological approach to slow dynamical processes, it discusses the dynamics of a driven nonequilibrium system: a two-dimensional gas of chiral ‘rattlebacks’ on a vibrating substrate.