Gay-Balmaz, FrancoisRatiu, Tudor S.2010-11-302010-11-302010-11-30200910.1016/j.aam.2008.06.002https://infoscience.epfl.ch/handle/20.500.14299/60476WOS:000263610300004This 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.Affine Euler-Poincare equationsAffine Lie-Poisson equationsDiffeomorphism groupPoisson bracketsComplex fluidsYang-Mills magnetohydrodynamicsHall magnetohydrodynamicsSuperfluid dynamicsSpin glassesMicrofluidsLiquid crystalsEuler-Poincare EquationsYang-Mills FluidsSemidirect Productstext::journal::journal article::research article