Breaking and restoring of diffeomorphism symmetry in discrete gravity

We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so--called perfect actions, with exact symmetries and we will review first steps towards this end.Comment: to appear in the Proceedings of the XXV Max Born Symposium "The Planck Scale", Wroclaw, 29 June - 3 July, 200

Past and Present Large Solid Rocket Motor Test Capabilities

A study was performed to identify the current and historical trends in the capability of solid rocket motor testing in the United States. The study focused on test positions capable of testing solid rocket motors of at least 10,000 lbf thrust. Top-level information was collected for two distinct data points plus/minus a few years: 2000 (Y2K) and 2010 (Present). Data was combined from many sources, but primarily focused on data from the Chemical Propulsion Information Analysis Center s Rocket Propulsion Test Facilities Database, and heritage Chemical Propulsion Information Agency/M8 Solid Rocket Motor Static Test Facilities Manual. Data for the Rocket Propulsion Test Facilities Database and heritage M8 Solid Rocket Motor Static Test Facilities Manual is provided to the Chemical Propulsion Information Analysis Center directly from the test facilities. Information for each test cell for each time period was compiled and plotted to produce a graphical display of the changes for the nation, NASA, Department of Defense, and commercial organizations during the past ten years. Major groups of plots include test facility by geographic location, test cells by status/utilization, and test cells by maximum thrust capability. The results are discussed

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

A note on drastic product logic

The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. This $t$-norm is not left-continuous, and hence it does not admit a residuum. So, there are no drastic product $t$-norm based many-valued logics, in the sense of [EG01]. However, if we renounce standard completeness, we can study the logic whose semantics is provided by those MTL chains whose monoidal operation is the drastic product. This logic is called ${\rm S}_{3}{\rm MTL}$ in [NOG06]. In this note we justify the study of this logic, which we rechristen DP (for drastic product), by means of some interesting properties relating DP and its algebraic semantics to a weakened law of excluded middle, to the $\Delta$ projection operator and to discriminator varieties. We shall show that the category of finite DP-algebras is dually equivalent to a category whose objects are multisets of finite chains. This duality allows us to classify all axiomatic extensions of DP, and to compute the free finitely generated DP-algebras.Comment: 11 pages, 3 figure

Homogeneity and plane-wave limits

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.Comment: In memory of Stanley Hobert, 33 pages. Minor corrections and some simplification of Section 4.3.

MnAs dots grown on GaN(0001)-(1x1) surface

MnAs has been grown by means of MBE on the GaN(0001)-(1x1) surface. Two options of initiating the crystal growth were applied: (a) a regular MBE procedure (manganese and arsenic were delivered simultaneously) and (b) subsequent deposition of manganese and arsenic layers. It was shown that spontaneous formation of MnAs dots with the surface density of 1$\cdot 10^{11}$ cm$^{-2}$ and $2.5\cdot 10^{11}$ cm$^{-2}$, respectively (as observed by AFM), occurred for the layer thickness higher than 5 ML. Electronic structure of the MnAs/GaN systems was studied by resonant photoemission spectroscopy. That led to determination of the Mn 3d - related contribution to the total density of states (DOS) distribution of MnAs. It has been proven that the electronic structures of the MnAs dots grown by the two procedures differ markedly. One corresponds to metallic, ferromagnetic NiAs-type MnAs, the other is similar to that reported for half-metallic zinc-blende MnAs. Both system behave superparamagnetically (as revealed by magnetization measurements), but with both the blocking temperatures and the intra-dot Curie temperatures substantially different. The intra-dot Curie temperature is about 260 K for the former system while markedly higher than room temperature for the latter one. Relations between growth process, electronic structure and other properties of the studied systems are discussed. Possible mechanisms of half-metallic MnAs formation on GaN are considered.Comment: 20+ pages, 8 figure