We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new crosscoupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called ˆl vector in superfluid 3He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.
F.02 Pridobitev novih znanstvenih spoznanj