Geodesic Flow on the Diffeomorphism Group of the circle

We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.Comment: 15 page

A Comparative Analysis of the American and Romanian Business Education Programs

The purpose of this paper is to present a comparative analysis of the business education programs offered by Auburn University's College of Business, Alabama, U.S.A. and Faculty of Business Administration, Academy of Economic Studies, Bucharest Romania. This comparative analysis is conceived in a larger perspective of the two different cultures and traditions in developing business education programs. The analysis is performed taking into consideration several dimensions, from the curriculum structure to the academic work with honesty and integrity.business education, higher education, university programs.

Hydrodynamic study of fine metallic powders in an original spouted bed contactor in view of chemical vapor deposition treatments

An original gas–solid contactor was developed so as to treat by chemical vapor deposition, fine (mean diameter 23 μm) and dense (bulk density 7700 kg/m3) NiCoCrAlYTa powders with large size distribution. In order to avoid the presence of a distributor in the reactive zone, a spouted bed configuration was selected, consisting in a glass cylindrical column associated through a 60° cone to an inlet tube, connected at its bottom to a grid so as to support the powders at rest. A hydrodynamic study was conducted at ambient temperature and pressure, combining pressure drop measurements and visual observations as a function of gas velocity and of the ratio H/D of the height of the bed at rest over the bed diameter. Using conventional alumina particles belonging to Geldart's group B, it was shown that this equipment is able to ensure conventional spouted bed behavior, especially for H/D ratio equal to 1. From numerous experiments conducted with the fine metallic powders of interest, it was shown that (i) conventional pressure drop curves for spouted beds are obtained for H/D ratios between 1 and 1.8, (ii) due to the large grain size distribution of particles, minimum spouted bed velocities occur in a range rather than at precise values. Visual observations reveal the presence of the spout and fountain at the minimum spouted bed velocity and for H/D equal to 1

Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress

We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial diffusion of the polymeric stresses

Particle trajectories in linearized irrotational shallow water flows

We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the water particles beneath the irrotational shallow water waves. Depending on the strength of underlying uniform current, we obtain that some particle trajectories are undulating path to the right or to the left, some are looping curves with a drift to the right and others are parabolic curves or curves which have only one loop

On the particle paths and the stagnation points in small-amplitude deep-water waves

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.382

Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.Comment: 11 pages, 7 figure