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Date: Sept. 19, 2014
Place: room #414, Faculty of Science Building (Hongo Campus), The University of Tokyo
Speaker: Helmut Brand (Universität Bayreuth)
Macroscopic behavior of active systems
with a dynamic preferred direction
We present the derivation of the macroscopic equations for active
systems with a dynamic preferred direction, which can be axial or
polar in nature.
In addition to the usual hydrodynamic variables
we introduce the mean angular velocity [1]
or the macroscopic velocity [2] associated with the motion of
the active units as a new variable and discuss their macroscopic
consequences [1,2]. Such an 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,
shoals of fish, flocks of birds and migrating insects.
As a concrete application we set up a macroscopic model of
bacterial growth and transport based on a polar dynamic
preferred direction -- the collective velocity of the
bacteria [3]. This collective velocity is subject to an
isotropic-nematic like transition modeling the density-controlled
transformation between immotile and motile bacterial states.
The approach can be applied also to other systems spontaneously
switching between individual (disordered) and collective (ordered)
behavior, and/or collectively responding to density variations,
e.g., bird flocks, fish schools etc. We observe a characteristic
and robust stop-and-go behavior of the type also observed for
the growth of bacteria experimentally [4].
[1] H.R. Brand, H. Pleiner and D. Svensek, Eur. Phys. J. E34, 128 (2011).
[2] H. Pleiner, D. Svensek and H.R. Brand, Eur. Phys. J. E36, 135 (2013).
[3] D. Svensek, H. Pleiner and H.R. Brand, Phys. Rev. Lett. 111,
228101 (2013).
[4] Y. Yamazaki et al., Physica D - Nonlinear Phenomena, 205 D, 236
(2005).