87 citations · 877 across the 97 of their papers we have counts for
10 papers · 1 filter
The momentum map representation of images
M. Bruveris, F. Gay-Balmaz, D. D. Holm +1
This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geome…
Geometric dynamics of optimization
F. Gay-Balmaz, D. D. Holm, T. S. Ratiu
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on…
Lagrange-Poincare field equations
David C. P. Ellis, Francois Gay-Balmaz, Darryl D. Holm +1
The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/re…
Invariant generators for generalized distributions
Madeleine Jotz, Tudor S. Ratiu
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
Variational principles for spin systems and the Kirchhoff rod
F. Gay-Balmaz, D. D. Holm, T. S. Ratiu
We obtain the affine Euler-Poincaré equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in…
The Geometric Structure of Complex Fluids
François Gay-Balmaz, Tudor S. Ratiu
This paper develops the theory of affine Euler-Poincaré and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills an…
Affine Lie-Poisson Reduction, Yang-Mills magnetohydrodynamics, and superfluids
François Gay-Balmaz, Tudor S. Ratiu
This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of…
Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids
François Gay-Balmaz, Tudor S. Ratiu
The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian an…
Dynamics of charged molecular strands
David C. P. Ellis, Francois Gay-Balmaz, Darryl D. Holm +2
Euler-Poincare equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting ri…
Singular reduction of Dirac structures
Madeleine Jotz, Tudor S. Ratiu, Jedrzej Sniatycki
The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about -invariant vector field…