Vortex motion around a circular cylinder above a plane

The study of vortex flows around solid obstacles is of considerable interest from both a theoretical and practical perspective. One geometry that has attracted renewed attention recently is that of vortex flows past a circular cylinder placed above a plane wall, where a stationary recirculating eddy can form in front of the cylinder, in contradistinction to the usual case (without the plane boundary) for which a vortex pair appears behind the cylinder. Here we analyze the problem of vortex flows past a cylinder near a wall through the lenses of the point-vortex model. By conformally mapping the fluid domain onto an annular region in an auxiliary complex plane, we compute the vortex Hamiltonian analytically in terms of certain special functions related to elliptic theta functions. A detailed analysis of the equilibria of the model is then presented. The location of the equilibrium in front of the cylinder is shown to be in qualitative agreement with the experimental findings. We also show that a topological transition occurs in phase space as the parameters of the systems are variedComment: 17 pages, 8 figure

Magnetization reversals in a disk-shaped small magnet with an interface

We consider a nanodisk possessing two coupled materials with different ferromagnetic exchange constant. The common border line of the two media passes at the disk center dividing the system exactly in two similar half-disks. The vortex core motion crossing the interface is investigated with a simple description based on a two-dimensional model which mimics a very thin real material with such a line defect. The main result of this study is that, depending on the magnetic coupling which connects the media, the vortex core can be dramatically and repeatedly flipped from up to down and vice versa by the interface. This phenomenon produces burst-like emission of spin waves each time the switching process takes place.Comment: 11 pages, 10 figure

The effects of tax incentives for small firms on employment levels

This paper will examine the effects of tax incentives for small businesseson employment level evaluating a program with this purpose implemented in Brazil in the 1990s. We first develop a theoretical framework which guides both the de nition of the parameters of interest and their identi cation. Selection problems both into the treatment group and into the data sampleare tackled by combining fi xed effects methods and regression discontinuity design on alternative sub-samples of a longitudinal database of manufacturing fi rms. The results show that on the one hand the size composition of thetreated fi rms may be changed due to the survival of some smaller fi rms that would have exited had it not been eligible to the program. On the other hand, the treated fi rms who do not depend on the program to survive do employ more workers.