Biological Physics & Soft Condensed Matter

Simon Fraser University







MACROSCOPIC BEHAVIOR OF ACTIVE SYSTEMS WITH A DYNAMIC PREFERRED DIRECTION

Helmut R. Brand

Theoretical Physics III, University Bayreuth, 95440 Bayreuth, Germany

We present the derivation of macroscopic equations for active systems with a dynamic preferred direction, which can be either axial or polar. Such an approach is expected to be applicable and important for biological systems, which have preferred directions only dynamically, but not permanently or in a static configuration. For an axial preferred direction we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. We investigate the coupling to a gel for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables. For the case of a dynamic polar preferred direction the additional macroscopic variables transforms like a velocity under parity and time reversal. This approach is expected to be useful for a number of biological systems including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such as Proteus mirabilis.