Energy localization in two chaotically coupled systems

We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled elastomechanical systems. Our random matrix model properly describes the main features of the findings by Weaver and Lobkis. Due to its general character, our model is also applicable to similar systems in other areas of physics -- for example, to chaotically coupled quantum dots.Comment: 20 pages, 15 figure

The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to $\exp( - c w_2^{3/2})$, where $w_2$ is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.Comment: 17 pages, 2 figure

The limit space of a Cauchy sequence of globally hyperbolic spacetimes

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I als show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case.Comment: 31 pages, 5 figures, submitted to Classical and Quantum gravity, seriously improved presentatio

The Ideal Intersection Property for Groupoid Graded Rings

We show that if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property

Hydrodynamics of confined colloidal fluids in two dimensions

We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to study the dynamics of two dimensional colloidal discs in confined geometries. We calculate the velocity autocorrelation functions, and observe the predicted $t^{-1}$ long time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the $t^{-1}$ tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge, but instead depends logarithmically on the overall size of the system.Comment: RevTex 13 pages, 9 figure

High- and low energy nonthermal X-ray emission from the cluster of galaxies A 2199

We report the detection of both soft and hard excess X-ray emission in the cluster of galaxies A 2199, based upon spatially resolved spectroscopy with data from the BeppoSAX, EUVE and ROSAT missions. The excess emission is visible at radii larger than 300 kpc and increases in strength relative to the isothermal component. The total 0.1-100 keV luminosity of this component is 15 % of the cluster luminosity, but it dominates the cluster luminosity at high and low energies. We argue that the most plausible interpretation of the excess emission is an inverse Compton interaction between the cosmic microwave background and relativistic electrons in the cluster. The observed spatial distribution of the non-thermal component implies that there is a large halo of cosmic ray electrons between 0.5-1.5 Mpc surrounding the cluster core. The prominent existence of this component has cosmological implications, as it is significantly changing our picture of a clusters's particle acceleration history, dynamics between the thermal and relativistic media, and total mass budgets.Comment: Accepted for publication in Astrophysical Journal, Letter

Manifestations of quantum holonomy in interferometry

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.Comment: Some changes, journal reference adde

Octet Baryon Magnetic Moments in the Chiral Quark Model with Configuration Mixing

The Coleman-Glashow sum-rule for magnetic moments is always fulfilled in the chiral quark model, independently of SU(3) symmetry breaking. This is due to the structure of the wave functions, coming from the non-relativistic quark model. Experimentally, the Coleman-Glashow sum-rule is violated by about ten standard deviations. To overcome this problem, two models of wave functions with configuration mixing are studied. One of these models violates the Coleman-Glashow sum-rule to the right degree and also reproduces the octet baryon magnetic moments rather accurately.Comment: 22 pages, RevTe

A Feasibility Study of Automated Support for Similarity Analysis of Natural Language Requirements in Market-Driven Development

In market-driven software development there is a strong need for support to handle congestion in the requirements engineering process, which may occur as the demand for short time-to-market is combined with a rapid arrival of new requirements from many different sources. Automated analysis of the continuous flow of incoming requirements provides an opportunity to increase the efficiency of the requirements engineering process. This paper presents empirical evaluations of the benefit of automated similarity analysis of textual requirements, where existing information retrieval techniques are used to statistically measure requirements similarity. The results show that automated analysis of similarity among textual requirements is a promising technique that may provide effective support in identifying relationships between requirements

The k-Point Random Matrix Kernels Obtained from One-Point Supermatrix Models

The k-point correlation functions of the Gaussian Random Matrix Ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials