Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices

This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation frequency. The development of the solutions to this periodic differential equation can be described by a discrete map, where the matrix elements are given by the principal solutions for each cycle. Variations in the forcing strength and oscillation frequency lead to matrix elements that vary from cycle to cycle. This paper presents an analysis of the growth rates including cases where all of the cycles are highly unstable, where some cycles are near the stability border, and where the map would be stable in the absence of fluctuations. For all of these regimes, we provide expressions for the growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure

Designing Good Partial Coverage Satellite Constellations

Design of satellite constellations providing partial coverage of certain ground regions is becoming more important as small low-altitude satellites receive increased attention. The purpose of this study is to develop the procedures necessary for deriving the best constellations for partial coverage

A Field Range Bound for General Single-Field Inflation

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models. This shows that non-trivial dynamics can't evade the Lyth bound. We also present a weaker, but completely universal bound that holds whenever the Null Energy Condition (NEC) is satisfied at horizon crossing.Comment: 16 page

Universality and Lepton Flavor Violation in Upsilon Decays at CLEO

I present two analyses done with the CLEOIII detector at CESR. The first is a search for the Lepton Flavor Violating decay Upsilon to mu tau, with preliminary results, and the second constrains Lepton Universality in Upsilon to tau tau relative to Upsilon to mu mu. This second analysis, whose results are final, has dramatically improved uncertainties relative to other such measurements, and is also the first observation of the decay Upsilon(3S) to tau tau. A limit is also set on the involvement of a CP odd Higgs in the decay of the Upsilon(1S) to tau pairs.Comment: 8 pages, 5 figures, to appear in proceedings of The 9th International Workshop on Tau-Lepton Physics, Tau0

Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the Cylinder

Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for the quantization of these theories is formulated. Explicit examples are studied in some detail. In particular gravity and gauge theories with equivalent actions are compared. Big gauge transformations as well as the condition of metric nondegeneracy in gravity turn out to cause significant differences in the structure of the corresponding reduced phase spaces and the quantum spectra of Dirac observables. For $R^2$ gravity coupled to SU(2) Yang Mills the question of quantum dynamics (`problem of time') is addressed. [This article is a contribution to the proceedings (to appear in LNP) of the 3rd Baltic RIM Student Seminar (1993). Importance is attached to concrete examples. A more abstract presentation of the ideas underlying this article (including new developments) is found in hep-th/9405110.]Comment: 26, pages, TUW-94-

Inflationary cosmology in the central region of String/M-theory moduli space

The "central" region of moduli space of M- and string theories is where the string coupling is about unity and the volume of compact dimensions is about the string volume. Here we argue that in this region the non-perturbative potential which is suggested by membrane instanton effects has the correct scaling and shape to allow for enough slow-roll inflation, and to produce the correct amplitude of CMB anisotropies. Thus, the well known theoretical obstacles for achieving viable slow-roll inflation in the framework of perturbative string theory are overcome. Limited knowledge of some generic properties of the induced potential is sufficient to determine the simplest type of consistent inflationary model and its predictions about the spectrum of cosmic microwave background anisotropies: a red spectrum of scalar perturbations, and negligible amount of tensor perturbations.Comment: 9 pages, 1 figur