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.


Published in:
Advances In Applied Mathematics, 42, 176-275
Year:
2009
Publisher:
Elsevier
ISSN:
0196-8858
Keywords:
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 Record created 2010-11-30, last modified 2018-09-13

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