The geometric structure of complex fluids
This paper develops the theory of affine Euler-Poincare and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microfluids, and liquid crystals. As a consequence of the Lagrangian approach, the variational formulation of the equations is determined. On the Hamiltonian side, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin-Noether circulation theorem is presented and is applied to these examples. (C) 2008 Elsevier Inc. All rights reserved.
Keywords: Affine Euler-Poincare equations ; Affine Lie-Poisson equations ; Diffeomorphism group ; Poisson brackets ; Complex fluids ; Yang-Mills magnetohydrodynamics ; Hall magnetohydrodynamics ; Superfluid dynamics ; Spin glasses ; Microfluids ; Liquid crystals ; Euler-Poincare Equations ; Yang-Mills Fluids ; Semidirect Products
Record created on 2010-11-30, modified on 2016-08-09