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

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

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

The Mass Assembly Histories of Galaxies of Various Morphologies in the GOODS Fields

We present an analysis of the growth of stellar mass with cosmic time partitioned according to galaxy morphology. Using a well-defined catalog of 2150 galaxies based, in part, on archival data in the GOODS fields, we assign morphological types in three broad classes (Ellipticals, Spirals, Peculiar/Irregulars) to a limit of z_AB=22.5 and make the resulting catalog publicly available. We combine redshift information, optical photometry from the GOODS catalog and deep K-band imaging to assign stellar masses. We find little evolution in the form of the galaxy stellar mass function from z~1 to z=0, especially at the high mass end where our results are most robust. Although the population of massive galaxies is relatively well established at z~1, its morphological mix continues to change, with an increasing proportion of early-type galaxies at later times. By constructing type-dependent stellar mass functions, we show that in each of three redshift intervals, E/S0's dominate the higher mass population, while spirals are favored at lower masses. This transition occurs at a stellar mass of 2--3 times 10^{10} Msun at z~0.3 (similar to local studies) but there is evidence that the relevant mass scale moves to higher mass at earlier epochs. Such evolution may represent the morphological extension of the ``downsizing'' phenomenon, in which the most massive galaxies stop forming stars first, with lower mass galaxies becoming quiescent later. We infer that more massive galaxies evolve into spheroidal systems at earlier times, and that this morphological transformation may only be completed 1--2 Gyr after the galaxies emerge from their active star forming phase. We discuss several lines of evidence suggesting that merging may play a key role in generating this pattern of evolution.Comment: 24 pages, 1 table, 8 figures, accepted for publication in Ap

Characterization of Jets in Relativistic Heavy Ion Collisions

Jet quenching is considered to be one of the signatures of the formation of quark gluon plasma. In order to investigate the jet quenching, it is necessary to detect jets produced in relativistic heavy ion collisions, determine their properties and compare those with the jets one obtains in hadron-hadron or $e^+-e^-$ collisions. In this work, we propose that calculation of flow parameters may be used to detect and characterize jets in relativistic heavy ion collisions.Comment: 18 pages, 4 figures, more discussions are added, to be published in Phys. Rev.

Is simultaneous yy and ξ\xi--scaling in the quasi-elastic region accidental?

We study the $y$ and $\xi$--scaling of the nuclear response at large momentum transfer in order to understand how scaling based on very different descriptions of the elementary interaction can occur simultaneously. We find that the approximate validity of $\xi$-scaling at low energy loss arises from the coincidental behavior of the quasielastic and deep inelastic cross sections.Comment: 4 pages, 3 Postscript figure

The exterior degree of a pair of finite groups

The exterior degree of a pair of finite groups $(G,N)$, which is a generalization of the exterior degree of finite groups, is the probability for two elements $(g,n)$ in $(G,N)$ such that $g\wedge n=1$. In the present paper, we state some relations between this concept and the relative commutatively degree, capability and the Schur multiplier of a pair of groups.Comment: To appear in Mediterr. J. Mat