5d/4d U-dualities and N=8 black holes

We use the connection between the U-duality groups in d=5 and d=4 to derive properties of the N=8 black hole potential and its critical points (attractors). This approach allows to study and compare the supersymmetry features of different solutions.Comment: 23 pages, LaTeX; some notations cleared up; final version on Phys. Rev.

Robustness and Randomness

Robustness problems of computational geometry algorithms is a topic that has been subject to intensive research efforts from both computer science and mathematics communities. Robustness problems are caused by the lack of precision in computations involving floating-point instead of real numbers. This paper reviews methods dealing with robustness and inaccuracy problems. It discussed approaches based on exact arithmetic, interval arithmetic and probabilistic methods. The paper investigates the possibility to use randomness at certain levels of reasoning to make geometric constructions more robust

Day-Degree Methods for Pest Management

Recommendations are made for reporting day-degree methods which may have practical applications. Standardized thresholds (40, 50, and 60°F, or 5, 10, and 15°C) should be used. Day-degrees may be either sine wave approximations or exact units determined by instrumentation. Methods are proposed for converting current day-degree models to standardized thresholds and, ultimately, to actual day-degrees

Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings

We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider rather large systems numerically. We show that the wave functions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wave packets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wave packet with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wave packet and propose a modified lower bound for the absolute continuous regime.Comment: 25 pages, 13 figure