Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

Unraveling Dynamical Heterogeneity in the Ionic Liquid 1-Butyl-3-methylimidazolium Chloride

Heterogeneous dynamics within a time range of nanoseconds was investigated by molecular dynamics (MD) simulations of 1 -butyl-3-methylimidazolium chloride ([bmim]Cl). After identifying groups of fast and slow ions, it was shown that the separation between the location of the center of mass and the center of charge of cations, d(CMCC), is a signature of such difference in ionic mobility. The distance d(CMCC) can be used as a signature because it relaxes in the time window of the dynamical heterogeneity. The relationship between the parameter dcmcc and conformations of the side alkyl chain in [bmim] is discussed. Since the relatively slow relaxation of dcmcc is a consequence of coexisting polar and nonpolar domains in the bulk, the MD simulations reveal a subtle interplay between structural and dynamical heterogeneity in ionic liquids.