Shradha Mishra et al J. Stat. Mech. (2010) P02003 doi:10.1088/1742-5468/2010/02/P02003
Shradha Mishra1, R Aditi Simha2 and Sriram Ramaswamy3
Show affiliationsWe carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally irrelevant. We discover a special limit of parameters in which the equation of motion for the angle field bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of a hidden fluctuation–dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts.
61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order
61.30.Cz Molecular and microscopic models and theories of liquid crystal structure
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
82C28 Dynamic renormalization group methods (See also 81T17)
Issue 02 (February 2010)
Received 11 December 2009, accepted for publication 12 January 2010
Published 5 February 2010
Shradha Mishra et al J. Stat. Mech. (2010) P02003
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