Eur. Phys. J. E (2011) 34: 128
https://doi.org/10.1140/epje/i2011-11128-2

Macroscopic behavior of systems with an axial dynamic preferred direction

¹ Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany
² Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany
³ Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1111, Ljubljana, Slovenia

^* e-mail: brand@uni-bayreuth.de
^** e-mail: pleiner@mpip-mainz.mpg.de
^*** e-mail: daniel.svensek@fmf.uni-lj.si

Received: 4 August 2011
Revised: 19 October 2011
Accepted: 3 November 2011
Published online: 28 November 2011

Abstract

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 cross-coupling 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 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.