Multi-fuel rotary engine for general aviation aircraft

Design studies of advanced multifuel general aviation and commuter aircraft rotary stratified charge engines are summarized. Conceptual design studies were performed at two levels of technology, on advanced general aviation engines sized to provide 186/250 shaft kW/hp under cruise conditions at 7620 (25000 m/ft) altitude. A follow on study extended the results to larger (2500 hp max.) engine sizes suitable for applications such as commuter transports and helicopters. The study engine designs were derived from relevant engine development background including both prior and recent engine test results using direct injected unthrottled rotary engine technology. Aircraft studies, using these resultant growth engines, define anticipated system effects of the performance and power density improvements for both single engine and twin engine airplanes. The calculated results indicate superior system performance and 27 to 33 percent fuel economy improvement for the rotary engine airplanes as compared to equivalent airframe concept designs with current baseline engines. The research and technology activities required to attain the projected engine performance levels are also discussed

Oxide-apertured microcavity single-photon emitting diode

We have developed a microcavity single-photon source based on a single quantum dot within a planar cavity in which wet-oxidation of a high-aluminium content layer provides lateral confinement of both the photonic mode and the injection current. Lateral confinement of the optical mode in optically pumped structures produces a strong enhancement of the radiative decay rate. Using microcavity structures with doped contact layers, we demonstrate a single-photon emitting diode where current may be injected into a single dot

Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

Random Hamiltonian in thermal equilibrium

A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical distribution. The resulting equilibrium state is used to calculate quenched and annealed averages of quantum observables.Comment: 8 pages, 4 figures. To appear in DICE 2008 conference proceeding

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio

Differential Cross Sections for Higgs Boson Production at Tevatron Collider Energies

The transverse momentum $Q_T$ distribution is computed for inclusive Higgs boson production at $\sqrt{S} = 1.96$ TeV. We include all-orders resummation of large logarithms associated with emission of soft gluons at small $Q_T$. We provide results for Higgs boson and $Z^*$ masses from $M_Z$ to 200 GeV. The relatively hard transverse momentum distribution for Higgs boson production suggests possibilities for improvement of the signal to background ratio.Comment: 12 pages, latex, 7 figure

A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology

We examine the string cosmology equations with a dilaton potential in the context of the Pre-Big Bang Scenario with the desired scale factor duality, and give a generic algorithm for obtaining solutions with appropriate evolutionary properties. This enables us to find pre-big bang type solutions with suitable dilaton behaviour that are regular at $t=0$, thereby solving the graceful exit problem. However to avoid fine tuning of initial data, an `exotic' equation of state is needed that relates the fluid properties to the dilaton field. We discuss why such an equation of state should be required for reliable dilaton behaviour at late times.Comment: 16 pages LaTeX, 5 figures. To appear in Physical Review

Mod-Gaussian convergence and its applications for models of statistical mechanics

In this paper we complete our understanding of the role played by the limiting (or residue) function in the context of mod-Gaussian convergence. The question about the probabilistic interpretation of such functions was initially raised by Marc Yor. After recalling our recent result which interprets the limiting function as a measure of "breaking of symmetry" in the Gaussian approximation in the framework of general central limit theorems type results, we introduce the framework of $L^1$-mod-Gaussian convergence in which the residue function is obtained as (up to a normalizing factor) the probability density of some sequences of random variables converging in law after a change of probability measure. In particular we recover some celebrated results due to Ellis and Newman on the convergence in law of dependent random variables arising in statistical mechanics. We complete our results by giving an alternative approach to the Stein method to obtain the rate of convergence in the Ellis-Newman convergence theorem and by proving a new local limit theorem. More generally we illustrate our results with simple models from statistical mechanics.Comment: 49 pages, 21 figure