Modeling the effects of wind tunnel wall absorption on the acoustic radiation characteristics of propellers

Finite element theory is used to calculate the acoustic field of a propeller in a soft walled circular wind tunnel and to compare the radiation patterns to the same propeller in free space. Parametric solutions are present for a "Gutin" propeller for a variety of flow Mach numbers, admittance values at the wall, microphone position locations, and propeller to duct radius ratios. Wind tunnel boundary layer is not included in this analysis. For wall admittance nearly equal to the characteristic value of free space, the free field and ducted propeller models agree in pressure level and directionality. In addition, the need for experimentally mapping the acoustic field is discussed

Regression Depth and Center Points

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

The CKM matrix and CP Violation

The status of CP violation and the CKM matrix is reviewed. Direct CP violation in B decay has been established and the measurement of sin(2beta) in \psi K modes reached 5% accuracy. I discuss the implications of these, and of the possible deviations of the CP asymmetries in b->s modes from that in \psi K. The first meaningful measurements of alpha and gamma are explained, together with their significance for constraining both the SM and new physics in B-Bbar mixing. I also discuss implications of recent developments in the theory of nonleptonic decays for B->pi K rates and CP asymmetries, and for the polarization in charmless B decays to two vector mesons.Comment: Plenary talk at 32nd International Conference on High Energy Physics (ICHEP'04), August 16-22, 2004, Beijing, China. v2: Table 5 corrected, minor changes in some averages (updated to hfag, that include correlations between S and C). v3: Figure 8 fixed, minor final change