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

Four-vortex motion around a circular cylinder

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized experimentally by placing a splitter plate in the center plane---, it is found that there is a family of linearly stable equilibria for same-signed vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated and several types of orbits are presented. The analysis reported here provides new insights and reveals novel features of this four-vortex system, such as the fact that there is no equilibrium for two pairs of vortices of opposite signs on the opposite sides of the cylinder. (It is argued that such equilibria might exist for vortex flows past a cylinder confined in a channel.) In addition, a new family of opposite-signed equilibria on the normal line is reported. The stability analysis for antisymmetric perturbations is also carried out and it shows that all equilibria are unstable in this case.Comment: 27 pages, 13 figures, to be published in Physics of Fluid

Hydrogen evolution and consumption in AOT–isooctane reverse micelles by Desulfovibrio gigas hydrogenase

The enzyme hydrogenase isolated from the sulphate reducing anaerobic bacterium Desulfovibrio gigas was encapsulated in reverse micelles of AOT–water–isooctane. The enzyme ability to consume molecular hydrogen was studied as a function of the micelle size (given by Wo = [H2O]/[organic solvent]). A peak of catalytic activity was obtained for Wo = 18, a micelle size theoretically fitting the heterodimeric hydrogenase molecule. At this Wo value, the recorded catalytic activity was slightly higher than in a buffer system(Kcat = 169.43 s−1 against the buffer value of 151 s−1). The optimal buffer used to encapsulate the enzyme was found to be imidazole 50 mM, pH 9.0. The molecular hydrogen production activity was also tested in this reverse micelle medium

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency