The one-round Voronoi game replayed

We consider the one-round Voronoi game, where player one (``White'', called ``Wilma'') places a set of n points in a rectangular area of aspect ratio r <=1, followed by the second player (``Black'', called ``Barney''), who places the same number of points. Each player wins the fraction of the board closest to one of his points, and the goal is to win more than half of the total area. This problem has been studied by Cheong et al., who showed that for large enough $n$ and r=1, Barney has a strategy that guarantees a fraction of 1/2+a, for some small fixed a. We resolve a number of open problems raised by that paper. In particular, we give a precise characterization of the outcome of the game for optimal play: We show that Barney has a winning strategy for n>2 and r>sqrt{2}/n, and for n=2 and r>sqrt{3}/2. Wilma wins in all remaining cases, i.e., for n>=3 and r<=sqrt{2}/n, for n=2 and r<=sqrt{3}/2, and for n=1. We also discuss complexity aspects of the game on more general boards, by proving that for a polygon with holes, it is NP-hard to maximize the area Barney can win against a given set of points by Wilma.Comment: 14 pages, 6 figures, Latex; revised for journal version, to appear in Computational Geometry: Theory and Applications. Extended abstract version appeared in Workshop on Algorithms and Data Structures, Springer Lecture Notes in Computer Science, vol.2748, 2003, pp. 150-16

Decoupling method for dynamical mean field theory calculations

In this paper we explore the use of an equation of motion decoupling method as an impurity solver to be used in conjunction with the dynamical mean field self-consistency condition for the solution of lattice models. We benchmark the impurity solver against exact diagonalization, and apply the method to study the infinite $U$ Hubbard model, the periodic Anderson model and the $pd$ model. This simple and numerically efficient approach yields the spectra expected for strongly correlated materials, with a quasiparticle peak and a Hubbard band. It works in a large range of parameters, and therefore can be used for the exploration of real materials using LDA+DMFT.Comment: 30 pages, 7 figure

Local impurity effects in superconducting graphene

We study the effect of impurities in superconducting graphene and discuss their influence on the local electronic properties. In particular, we consider the case of magnetic and non-magnetic impurities being either strongly localized or acting as a potential averaged over one unit cell. The spin dependent local density of states is calculated and possibilities for visualizing impurities by means of scanning tunneling experiments is pointed out. A possibility of identifying magnetic scatters even by non spin-polarized scanning tunneling spectroscopy is explained.Comment: 4 pages, 4 figure

Comparison of wing-span averaging effects on lift, rolling moment, and bending moment for two span load distributions and for two turbulence representations

An analytical method of computing the averaging effect of wing-span size on the loading of a wing induced by random turbulence was adapted for use on a digital electronic computer. The turbulence input was assumed to have a Dryden power spectral density. The computations were made for lift, rolling moment, and bending moment for two span load distributions, rectangular and elliptic. Data are presented to show the wing-span averaging effect for wing-span ratios encompassing current airplane sizes. The rectangular wing-span loading showed a slightly greater averaging effect than did the elliptic loading. In the frequency range most bothersome to airplane passengers, the wing-span averaging effect can reduce the normal lift load, and thus the acceleration, by about 7 percent for a typical medium-sized transport. Some calculations were made to evaluate the effect of using a Von Karman turbulence representation. These results showed that using the Von Karman representation generally resulted in a span averaging effect about 3 percent larger

Computed lateral power spectral density response of conventional and STOL airplanes to random atmospheric turbulence

A method of computing the power spectral densities of the lateral response of airplanes to random atmospheric turbulence was adapted to an electronic digital computer. By use of this program, the power spectral densities of the lateral roll, yaw, and sideslip angular displacement of several conventional and STOL airplanes were computed. The results show that for the conventional airplanes, the roll response is more prominent than that for yaw or sideslip response. For the STOL airplanes, on the other hand, the yaw and sideslip responses were larger than the roll response. The response frequency of the STOL airplanes generally is higher than that for the conventional airplanes. This combination of greater sensitivity of the STOL airplanes in yaw and sideslip and the frequency at which they occur could be a factor causing the poor riding qualities of this class of airplanes

Effect of High-lift Devices on the Low-speed Static Lateral and Yawing Stability Characteristics of an Untapered 45 Degrees Sweptback Wing

Results of a low-speed wind-tunnel investigation to determine the effect of high-lift devices on the static lateral stability derivatives and the yawing derivatives of an untapered 45 degrees sweptback wing are presented. The tests were made in the curved-flow test section of the Langley stability tunnel at a Reynolds number of 1.1 X 10 to the sixth power

Analytical Investigation of the Dynamic Behavior of a Nonlifting Manned Reentry Vehicle

An analytic investigation was made of the dynamic behavior of a nonlifting manned reentry vehicle as it descended through the atmosphere. The investigation included the effects of variations in the aerodynamic stability derivatives, the spin rate, reentry angle, and velocity. The effect of geostrophic winds and of employing a drogue parachute for stability purposes were also investigated. It was found that for the portion of the flight above a Mach number of 1 a moderate amount of negative damping could be tolerated but below a Mach number of 1 good damping is necessary. The low-speed stability could be improved by employing a drogue parachute. The effectiveness of the drogue parachute was increased when attached around the periphery of the rear of the vehicle rather than at the center. Neither moderate amounts of spin or the geostrophic winds had appreciable effects on the stability of the vehicle. The geostrophic winds and the reentry angle or velocity all showed important effects on the range covered by the reentry flight path