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Reduction theory for symmetry breaking with applications to nematic systems

Gay-Balmaz, F and Tronci, C (2010) Reduction theory for symmetry breaking with applications to nematic systems Physica D: Nonlinear Phenomena, 239 (20-22). pp. 1929-1947.

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Abstract

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. The geometric construction applies to order parameter spaces consisting of either unsigned unit vectors (directors) or symmetric matrices (alignment tensors). On the Hamiltonian side, we provide the corresponding Poisson brackets in both Lie–Poisson and Hamilton–Poincaré formulations. The explicit form of the helicity invariant for uniaxial nematics is also presented, together with a whole class of invariant quantities (Casimirs) for two-dimensional incompressible flows.

Item Type: Article
Authors :
NameEmailORCID
Gay-Balmaz, FUNSPECIFIEDUNSPECIFIED
Tronci, Cc.tronci@surrey.ac.ukUNSPECIFIED
Date : 2010
Identification Number : https://doi.org/10.1016/j.physd.2010.07.002
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:21
Last Modified : 17 May 2017 15:03
URI: http://epubs.surrey.ac.uk/id/eprint/834961

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