Complex Multiplication of Exactly Solvable Calabi-Yau Varieties

We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi-Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi-Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and the conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.Comment: 44 page

Angular momentum of the physical electron

The angular momentum of the physical electron, modelled as a Dirac fermion coupled to the electromagnetic field, is found to be hbar/2, the same as that of a bare Dirac fermion and independent of the size of the electric charge.Comment: revision, 3 pages pd

Layering Transitions and Solvation Forces in an Asymmetrically Confined Fluid

We consider a simple fluid confined between two parallel walls (substrates), separated by a distance L. The walls exert competing surface fields so that one wall is attractive and may be completely wet by liquid (it is solvophilic) while the other is solvophobic. Such asymmetric confinement is sometimes termed a `Janus Interface'. The second wall is: (i) purely repulsive and therefore completely dry (contact angle 180 degrees) or (ii) weakly attractive and partially dry (the contact angle is typically in the range 160-170 degrees). At low temperatures, but above the bulk triple point, we find using classical density functional theory (DFT) that the fluid is highly structured in the liquid part of the density profile. In case (i) a sequence of layering transitions occurs: as L is increased at fixed chemical potential (mu) close to bulk gas--liquid coexistence, new layers of liquid-like density develop discontinuously. In contrast to confinement between identical walls, the solvation force is repulsive for all wall separations and jumps discontinuously at each layering transition and the excess grand potential exhibits many metastable minima as a function of the adsorption. For a fixed temperature T=0.56Tc, where Tc is the bulk critical temperature, we determine the transition lines in the L, mu plane. In case (ii) we do not find layering transitions and the solvation force oscillates about zero. We discuss how our mean-field DFT results might be altered by including effects of fluctuations and comment on how the phenomenology we have revealed might be relevant for experimental and simulation studies of water confined between hydrophilic and hydrophobic substrates, emphasizing it is important to distinguish between cases (i) and (ii).Comment: 16 pages, 13 figure

Computational fluid dynamics challenges for hybrid air vehicle applications

This paper begins by comparing turbulence models for the prediction of hybrid air vehicle (HAV) flows. A 6 : 1 prolate spheroid is employed for validation of the computational fluid dynamics (CFD) method. An analysis of turbulent quantities is presented and the Shear Stress Transport (SST) k-ω model is compared against a k-ω Explicit Algebraic Stress model (EASM) within the unsteady Reynolds-Averaged Navier-Stokes (RANS) framework. Further comparisons involve Scale Adaptative Simulation models and a local transition transport model. The results show that the flow around the vehicle at low pitch angles is sensitive to transition effects. At high pitch angles, the vortices generated on the suction side provide substantial lift augmentation and are better resolved by EASMs. The validated CFD method is employed for the flow around a shape similar to the Airlander aircraft of Hybrid Air Vehicles Ltd. The sensitivity of the transition location to the Reynolds number is demonstrated and the role of each vehicle£s component is analyzed. It was found that the ¦ns contributed the most to increase the lift and drag

Science opportunities from the Topex/Poseidon mission

The U.S. National Aeronautics and Space Administration (NASA) and the French Centre National d'Etudes Spatiales (CNES) propose to conduct a Topex/Poseidon Mission for studying the global ocean circulation from space. The mission will use the techniques of satellite altimetry to make precise and accurate measurements of sea level for several years. The measurements will then be used by Principal Investigators (selected by NASA and CNES) and by the wider oceanographic community working closely with large international programs for observing the Earth, on studies leading to an improved understanding of global ocean dynamics and the interaction of the ocean with other processes influencing life on Earth. The major elements of the mission include a satellite carrrying an altimetric system for measuring the height of the satellite above the sea surface; a precision orbit determination system for referring the altimetric measurements to geodetic coordinates; a data analysis and distribution system for processing the satellite data, verifying their accuracy, and making them available to the scientific community; and a principal investigator program for scientific studies based on the satellite observations. This document describes the satellite, its sensors, its orbit, the data analysis system, and plans for verifying and distributing the data. It then discusses the expected accuracy of the satellite's measurements and their usefulness to oceanographic, geophysical, and other scientific studies. Finally, it outlines the relationship of the Topex/Poseidon mission to other large programs, including the World Climate Research Program, the U.S. Navy's Remote Ocean Sensing System satellite program and the European Space Agency's ERS-1 satellite program

A portable Ku-band front-end test package for beam-waveguide antenna performance evaluation

A 34-m beam-waveguide (BWG) antenna has been built a Deep Space Station 13 (DDS 13) in the Goldstone Deep Space Communications Complex. This antenna is designed to be efficient at X-, Ku-, and Ka-bands, and it is the first NASA tracking antenna to use a BWG design. The design of a Ku-band test package for the new BWG antenna at 11.7-12.2 GHz is presented. Results of linear polarization measurements with the test package on the ground are also presented. This report is the fifth in a series of articles concerned with test package design and performance

Baroclinic Vorticity Production in Protoplanetary Disks; Part I: Vortex Formation

The formation of vortices in protoplanetary disks is explored via pseudo-spectral numerical simulations of an anelastic-gas model. This model is a coupled set of equations for vorticity and temperature in two dimensions which includes baroclinic vorticity production and radiative cooling. Vortex formation is unambiguously shown to be caused by baroclinicity because (1) these simulations have zero initial perturbation vorticity and a nonzero initial temperature distribution; and (2) turning off the baroclinic term halts vortex formation, as shown by an immediate drop in kinetic energy and vorticity. Vortex strength increases with: larger background temperature gradients; warmer background temperatures; larger initial temperature perturbations; higher Reynolds number; and higher resolution. In the simulations presented here vortices form when the background temperatures are $\sim 200K$ and vary radially as $r^{-0.25}$, the initial vorticity perturbations are zero, the initial temperature perturbations are 5% of the background, and the Reynolds number is $10^9$. A sensitivity study consisting of 74 simulations showed that as resolution and Reynolds number increase, vortices can form with smaller initial temperature perturbations, lower background temperatures, and smaller background temperature gradients. For the parameter ranges of these simulations, the disk is shown to be convectively stable by the Solberg-H{\o}iland criteria.Comment: Originally submitted to The Astrophysical Journal April 3, 2006; resubmitted November 3, 2006; accepted Dec 5, 200

S190 interpretation techniques development and application to New York State water resources

The author has identified the following significant results. The program has demonstrated that Skylab imagery can be utilized to regularly monitor eutrophication indices of lakes, such as chlorophyll concentration and photic zone depth. The relationship between the blue to green reflectance ratio and chlorophyll concentration was shown, along with changes in lake properties caused by chlorophyll, lignin, and humic acid using reflectance ratios and changes. A data processing technique was developed for detecting atmospheric fluctuations occurring over a large lake

Helical Symmetry in Linear Systems

We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman--Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.Comment: 11 page