Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-03-23
Nonlinear Sciences
Chaotic Dynamics
50 pages, no figures. To appear in the Festschrift for Jerry Marsden on the occasion of his sixtieth birthday
Scientific paper
Lagrangian reduction by stages is used to derive the Euler-Poincar\'e equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous material variables. These order parameters may be regarded geometrically either as objects in a vector space, or as coset spaces of Lie symmetry groups with respect to subgroups that leave these objects invariant. Examples include liquid crystals, superfluids, Yang-Mills magnetofluids and spin-glasses. A Lie-Poisson Hamiltonian formulation of the dynamics for perfect complex fluids is obtained by Legendre transforming the Euler-Poincare formulation. These dynamics are also derived by using the Clebsch approach. In the Hamiltonian and Lagrangian formulations of perfect complex fluid dynamics Lie algebras containing two-cocycles arise as a characteristic feature. After discussing these geometrical formulations of the dynamics of perfect complex fluids, we give an example of how to introduce defects into the order parameter as imperfections (e.g., vortices) that carry their own momentum. The defects may move relative to the Lagrangian fluid material and thereby produce additional reactive forces and stresses.
No associations
LandOfFree
Euler-Poincaré Dynamics of Perfect Complex Fluids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Euler-Poincaré Dynamics of Perfect Complex Fluids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Euler-Poincaré Dynamics of Perfect Complex Fluids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-192971