The Geometric Structure of Complex Fluids

Details The Geometric Structure of Complex Fluids The Geometric Structure of Complex Fluids

2009-03-25

arxiv.org/abs/0903.4294v1

Adv. Appl. Math., 42 (2) (2008) 176-275

Physics

Mathematical Physics

Scientific paper

This paper develops the theory of affine Euler-Poincar\'e 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.

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