Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model

In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a first-order, discontinuous phase transition for appropriate values of the thermodynamic parameters that define the model. These phase transitions are analyzed both in terms of the empirical measure and the spin per site by studying bifurcation phenomena of the corresponding sets of canonical equilibrium macrostates, which are defined via large deviation principles. Analogous phase transitions with respect to the microcanonical ensemble are also studied via a combination of rigorous analysis and numerical calculations. Finally, probabilistic limit theorems for appropriately scaled values of the total spin are proved with respect to the canonical ensemble. These limit theorems include both central-limit-type theorems when the thermodynamic parameters are not equal to critical values and non-central-limit-type theorems when these parameters equal critical values.Comment: 33 pages, revtex

Consistency of dust solutions with div H=0

One of the necessary covariant conditions for gravitational radiation is the vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab} itself is nonzero. We complete a recent analysis by showing that in irrotational dust spacetimes, the condition div H=0 evolves consistently in the exact nonlinear theory.Comment: 3 pages Revte

Integrability of irrotational silent cosmological models

We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearised silent models, but not in the general exact non-linear case. Thus there is a linearisation instability, and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class. Quantum Grav.; 16 pages Ioplpp

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

Dynamics of Inflationary Universes with Positive Spatial Curvature

If the spatial curvature of the universe is positive, then the curvature term will always dominate at early enough times in a slow-rolling inflationary epoch. This enhances inflationary effects and hence puts limits on the possible number of e-foldings that can have occurred, independently of what happened before inflation began and in particular without regard for what may have happened in the Planck era. We use a simple multi-stage model to examine this limit as a function of the present density parameter $\Omega_0$ and the epoch when inflation ends.Comment: 9 Pages RevTex4. Revised and update

Materials and methods for large-area solar cells Final report, 17 Dec. 1964 - 16 Dec. 1965

Growth and evaluation of gallium arsenide-indium arsenide-aluminum foil structures in construction of thin film large area solar cells for satellite

Exact non-equilibrium solutions of the Einstein-Boltzmann equations. II

We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the bulk viscous pressure of an FRW distribution that relaxes towards collision-dominated equilibrium. If the relaxation is toward collision-free equilibrium, the bulk viscosity vanishes - but there is still entropy production. The Bianchi I solutions have zero heat flux and bulk viscosity, but nonzero shear viscosity. The solutions are used to construct a realisation of the Weyl Curvature Hypothesis.Comment: 16 pages LaTex, CQG documentstyle (ioplppt