Crossover and scaling in SU(3) lattice gauge theories with Susskind fermions

The phase diagram of SU(3) lattice gauge theories with Susskind fermions is investigated by Monte Carlo methods. For three flavors in the continuum a significant shift in the location of the peak in the specific heat is found, as compared to the pure gauge case. These results suggest that the crossover region moves to smaller β when fermion polarization effects are included.     

Progress in development of Nuclotron accelerator complex

The Nuclotron superconducting synchrotron was constructed in 1987–1992 [1]; it is the world’s first synchrotron based on fast cycling “window frame” electromagnets with a superconducting coil. For a design field of dipole magnets of 2 T, the magnetic rigidity is 45 T m, which corresponds to the energy of heavy nuclei (for example, gold) of 4.5 GeV/nucleon. The Nuclotron accelerator complex is currently being upgraded (the Nuclotron-M project); this upgrade is considered a key part of the first stage of fulfilling the new Joint Institute for Nuclear Research (JINR) project: the Nuclotron-based Ion Collider fAcility and Multi-Purpose Detector (NICA/MPD). The most important task of this new project is the preparation of basic Nuclotron systems for its reliable operation as part of the NICA accelerator complex. Basic results of activity on the project, which started in 2007, are presented and the results of the last Nuclotron runs are analyzed.     

Entropy enhancement and black hole microstates

We show that the entropy of fluctuating two-charge supertubes placed in three-charge scaling microstate solutions depends on their "effective" charges, which in strong magnetic fields can be much larger than their charges. This leads to a much larger entropy than one naively would expect. Since fluctuating supertubes source smooth geometries in certain duality frames, we propose that such an entropy enhancement mechanism might lead to a black-hole-like entropy coming entirely from configurations that are smooth and horizonless in the regime of parameters where the classical black hole exists.     

Measure extension by local approximation

Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned sense if and only if it is Carathéodory-measurable.     

Géométries Lorentziennes de dimension 3 : classification et complétude

We classify three-dimensional Lorentz homogeneous spaces G/I having a compact manifold locally modeled on them. We prove a completeness result: any compact locally homogeneous Lorentz threefold M is isometric to a quotient of a Lorentz homogeneous space G/I by a discrete subgroup Γ of G acting properly and freely on G/I. Moreover, if I is noncompact, G/I is isometric to a Lie group L endowed with a left invariant Lorentz metric, where L is isomorphic to one of the following Lie groups:

Hyperspectral Imaging in the Medical Field: Present and Future

Abstract

Hyperspectral imaging is an optical method that provides a large amount of information about the investigated object. Its medical applications are reviewed in this article, including tumor delimitation and identification, assessing tissue perfusion and its pathological conditions (including some complications like diabetic foot ulceration), making accurate surgical decisions, evaluating the health of dental structures, etc. Many of the articles show very promising results that required brief comments by the authors. It is clear that choosing the appropriate hyperspectral imaging system for each medical field, together with the most reliable hyperspectral image processing methods, are the main goals of future studies, before hyperspectral imaging becomes a widely applicable evaluation method in medicine. The authors try to answer some questions on this topic and set up some directions for future research.     

Integrable Scalar Cosmologies I. Foundations and links with String Theory

We build a number of integrable one-scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non-integrable ones. These include the impossibility for the scalar to emerge from the initial singularity descending along asymptotically exponential potentials with logarithmic slopes exceeding a critical value (“climbing phenomenon”) and the inevitable collapse in a Big Crunch whenever the scalar tries to settle at negative extrema of the potential. We also elaborate on the links between these types of potentials and “brane supersymmetry breaking”, a mechanism that ties together string scale and scale of supersymmetry breaking in a class of orientifold models.     

Approximation of periodic solutions for a dissipative hyperbolic equation

This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force $f$ . These approximations are obtained by combining a fixed point algorithm with the Galerkin method. It is known that the energy of the usual discrete models does not decay uniformly with respect to the mesh size. Our aim is to analyze this phenomenon’s consequences on the convergence of the approximation method and its error estimates. We prove that, under appropriate regularity assumptions on $f$ , the approximation method is always convergent. However, our error estimates show that the convergence’s properties are improved if a numerically vanishing viscosity is added to the system. The same is true if the nonhomogeneous term $f$ is monochromatic. To illustrate our theoretical results we present several numerical simulations with finite element approximations of the wave equation in one or two dimensional domains and with different forcing terms.     

CR immersions and Lorentzian geometry

We study the geometry of the second fundamental form of pseudohermitian immersions among nondegenerate CR manifolds. In particular we study existence and uniqueness of pseudohermitian immersions $\phi : M \rightarrow S^{2n+3}$ of a strictly pseudoconvex CR manifold $M$ into an odd dimensional sphere, as determined by the pseudohermitian Gauss and Weingarten equations.     

Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.