The Geometric Structure of Complex Fluids
Mathematical Physics
2009-03-26 v1 math.MP
Chaotic Dynamics
Abstract
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.
Cite
@article{arxiv.0903.4294,
title = {The Geometric Structure of Complex Fluids},
author = {François Gay-Balmaz and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:0903.4294},
year = {2009}
}