Geometric aspects of nonholonomic field theories

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.Comment: 29 pages; typos remove

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Influence of Distal Residue B10 on CO Dynamics in Myoglobin and Neuroglobin

For many years, myoglobin has served as a paradigm for structure–function studies in proteins. Ligand binding and migration within myoglobin has been studied in great detail by crystallography and spectroscopy, showing that gaseous ligands such as O2, CO, and NO not only bind to the heme iron but may also reside transiently in three internal ligand docking sites, the primary docking site B and secondary sites C and D. These sites affect ligand association and dissociation in specific ways. Neuroglobin is another vertebrate heme protein that also binds small ligands. Ligand migration pathways in neuroglobin have not yet been elucidated. Here, we have used Fourier transform infrared temperature derivative spectroscopy at cryogenic temperatures to compare the influence of the side chain volume of amino acid residue B10 on ligand migration to and rebinding from docking sites in myoglobin and neuroglobin