Inhomogeneous Fermi and quantum spin systems on lattices

We study the thermodynamic properties of a certain type of space-inhomogeneous Fermi and quantum spin systems on lattices. We are particularly interested in the case where the space scale of the inhomogeneities stays macroscopic, but very small as compared to the side-length of the box containing fermions or spins. The present study is however not restricted to "macroscopic inhomogeneities" and also includes the (periodic) microscopic and mesoscopic cases. We prove that - as in the homogeneous case - the pressure is, up to a minus sign, the conservative value of a two-person zero-sum game, named here thermodynamic game. Because of the absence of space symmetries in such inhomogeneous systems, it is not clear from the beginning what kind of object equilibrium states should be in the thermodynamic limit. However, we give rigorous statements on correlations functions for large boxes. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4763465]

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system. (C) 2012 Elsevier Ltd. All rights reserved.

Star formation in H I tails: HCG 92, HCG 100 and six interacting systems

We present new Gemini spectra of 14 new objects found within the H?i tails of Hickson Compact Groups (HCGs) 92 and 100. Nine of them are Galaxy Evolution Explorer (GALEX) far-ultraviolet (FUV) and near-ultraviolet (NUV) sources. The spectra confirm that these objects are members of the compact groups and have metallicities close to solar, with an average value of 12+log(O/H) similar to 8.5. They have average FUV luminosities 7 x 10(40)?erg?s-1 and very young ages (<100?Myr), and two of them resemble tidal dwarf galaxy (TDG) candidates. We suggest that they were created within gas clouds that were ejected during galaxygalaxy interactions into the intergalactic medium, which would explain the high metallicities of the objects, inherited from the parent galaxies from which the gas originated. We conduct a search for similar objects in six interacting systems with extended H?i tails: NGC 2623, NGC 3079, NGC 3359, NGC 3627, NGC 3718 and NGC 4656. We found 35 ultraviolet (UV) sources with ages < 100?Myr; however, most of them are on average less luminous/massive than the UV sources found around HCG 92 and HCG 100. We speculate that this might be an environmental effect and that compact groups of galaxies are more favourable to TDG formation than other interacting systems.

Color-space distortions following long-term occupational exposure to mercury vapor

Color vision was examined in subjects with long-term occupational exposure to mercury (Hg) vapor. The color vision impairment was assessed by employing a quantitative measure of distortion of individual and group perceptual color spaces. Hg subjects (n = 18; 42.1 +/- 6.5 years old; exposure time = 10.4 +/- 5.0 years; time away from the exposure source = 6.8 +/- 4.6 years) and controls (n = 18; 46.1 +/- 8.4 years old) were examined using two arrangement tests, D-15 and D-15d, in the traditional way, and also in a triadic procedure. From each subject`s `odd-one-out` choices, matrices of inter-cap subjective dissimilarities were derived and processed by non-metric multidimensional scaling (MDS). D-15d results differed significantly between the Hg-group and the control group (p < 0.05), with the impairment predominantly along the tritan axis. 2D perceptual color spaces, individual and group, were reconstructed, with the dimensions interpreted as the red-green (RG) and the blue-yellow (BY) systems. When color configurations from the Hg-group were compared to those of the controls, they presented more fluctuations along both chromatic dimensions, indicating a statistically significant difference along the BY axis. In conclusion, the present findings confirm that color vision impairments persist in subjects that have received long-term occupational exposure to Hg-vapor although, at the time of testing, they were presenting mean urinary concentration within the normal range for non-exposed individuals. Considering the advantages of the triadic procedure in clinical evaluation of acquired color vision deficiencies, further studies should attempt to verify and/or improve its efficacy.

Internal fit of two all-ceramic systems and metal-ceramic crowns

Objectives: The aim of this study was to investigate the internal fit (IF) of glass-infiltrated alumina (ICA - In-Ceram Alumina), yttria-stabilized tetragonal zirconia polycrystals (Y-TZP - IPS e.max ZirCAD), and metal-ceramic (MC - Ni-Cr alloy) crowns. Material and Methods: Sixty standardized resin-tooth replicas of a maxillary first molar were produced for crown placement and divided into 3 groups (n=20 each) according to the core material used (metal, ICA or Y-TZP). The IF of the crowns was measured using the replica technique, which employs a light body polyvinyl siloxane impression material to simulate the cement layer thickness. The data were analyzed according to the surfaces obtained for the occlusal space (OS), axial space (AS) and total mean (TM) using two-way ANOVA with Tukey's multiple comparison test (p<0.05). Results: No differences among the different areas were detected in the MC group. For the Y-TZP and ICA groups, AS was statistically lower than both OS and TM. No differences in AS were observed among the groups. However, OS and TM showed significantly higher values for ICA and Y-TZP groups than MC group. Comparisons of ICA and Y-TZP revealed that OS was significantly lower for Y-TZP group, whereas no differences were observed for TM. Conclusions: The total mean achieved by all groups was within the range of clinical acceptability. However, the metal-ceramic group demonstrated significantly lower values than the all-ceramic groups, especially in OS.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

Transiting exoplanets from the CoRoT space mission XXI. CoRoT-19b: a low density planet orbiting an old inactive F9V-star

Context. Observations of transiting extrasolar planets are of key importance to our understanding of planets because their mass, radius, and mass density can be determined. These measurements indicate that planets of similar mass can have very different radii. For low-density planets, it is generally assumed that they are inflated owing to their proximity to the host-star. To determine the causes of this inflation, it is necessary to obtain a statistically significant sample of planets with precisely measured masses and radii. Aims. The CoRoT space mission allows us to achieve a very high photometric accuracy. By combining CoRoT data with high-precision radial velocity measurements, we derive precise planetary radii and masses. We report the discovery of CoRoT-19b, a gas-giant planet transiting an old, inactive F9V-type star with a period of four days. Methods. After excluding alternative physical configurations mimicking a planetary transit signal, we determine the radius and mass of the planet by combining CoRoT photometry with high-resolution spectroscopy obtained with the echelle spectrographs SOPHIE, HARPS, FIES, and SANDIFORD. To improve the precision of its ephemeris and the epoch, we observed additional transits with the TRAPPIST and Euler telescopes. Using HARPS spectra obtained during the transit, we then determine the projected angle between the spin of the star and the orbit of the planet. Results. We find that the host star of CoRoT-19b is an inactive F9V-type star close to the end of its main-sequence life. The host star has a mass M-* = 1.21 +/- 0.05 M-circle dot and radius R-* = 1.65 +/- 0.04 R-circle dot. The planet has a mass of M-P = 1.11 +/- 0.06 M-Jup and radius of R-P = 1.29 +/- 0.03 R-Jup. The resulting bulk density is only rho = 0.71 +/- 0.06 g cm (3), which is much lower than that for Jupiter. Conclusions. The exoplanet CoRoT-19b is an example of a giant planet of almost the same mass as Jupiter but a approximate to 30% larger radius.

Transiting exoplanets from the CoRoT space mission XIX. CoRoT-23b: a dense hot Jupiter on an eccentric orbit

We report the detection of CoRoT-23b, a hot Jupiter transiting in front of its host star with a period of 3.6314 +/- 0.0001 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite, combined with spectroscopic radial velocity (RV) measurements. A photometric search for possible background eclipsing binaries conducted at CFHT and OGS concluded with a very low risk of false positives. The usual techniques of combining RV and transit data simultaneously were used to derive stellar and planetary parameters. The planet has a mass of M-p = 2.8 +/- 0.3 M-Jup, a radius of R-pl = 1.05 +/- 0.13 R-Jup, a density of approximate to 3 gcm(-3). RV data also clearly reveal a nonzero eccentricity of e = 0.16 +/- 0.02. The planet orbits a mature G0 main sequence star of V = 15.5 mag, with a mass M-star = 1.14 +/- 0.08 M-circle dot, a radius R-star = 1. 61 +/- 0.18 R-circle dot and quasi-solar abundances. The age of the system is evaluated to be 7 Gyr, not far from the transition to subgiant, in agreement with the rather large stellar radius. The two features of a significant eccentricity of the orbit and of a fairly high density are fairly uncommon for a hot Jupiter. The high density is, however, consistent with a model of contraction of a planet at this mass, given the age of the system. On the other hand, at such an age, circularization is expected to be completed. In fact, we show that for this planetary mass and orbital distance, any initial eccentricity should not totally vanish after 7 Gyr, as long as the tidal quality factor Q(p) is more than a few 10(5), a value that is the lower bound of the usually expected range. Even if CoRoT-23b features a density and an eccentricity that are atypical of a hot Jupiter, it is thus not an enigmatic object.

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Transiting exoplanets from the CoRoT space mission XXII. CoRoT-16b: a hot Jupiter with a hint of eccentricity around a faint solar-like star

Aims. We report the discovery of CoRoT-16b, a low density hot jupiter that orbits a faint G5V star (mV = 15.63) in 5.3523 +/- 0.0002 days with slight eccentricity. A fit of the data with no a priori assumptions on the orbit leads to an eccentricity of 0.33 +/- 0.1. We discuss this value and also derive the mass and radius of the planet. Methods. We analyse the photometric transit curve of CoRoT-16 given by the CoRoT satellite, and radial velocity data from the HARPS and HIRES spectrometers. A combined analysis using a Markov chain Monte Carlo algorithm is used to get the system parameters. Results. CoRoT-16b is a 0.535 -0.083/+0.085 M-J, 1.17 -0.14/+0.16 R-J hot Jupiter with a density of 0.44 -0.14/+0.21 g cm(-3). Despite its short orbital distance (0.0618 +/- 0.0015 AU) and the age of the parent star (6.73 +/- 2.8 Gyr), the planet orbit exhibits significantly non-zero eccentricity. This is very uncommon for this type of objects as tidal effects tend to circularise the orbit. This value is discussed taking into account the characteristics of the star and the observation accuracy.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Vortices in the extended Skyrme-Faddeev model

We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a (3 + 1) dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the kinetic term, and a potential which breaks the SO(3) symmetry down to SO(2). The construction makes use of an ansatz, invariant under the joint action of the internal SO(2) and three commuting U(1) subgroups of the Poincare group, and which reduces the equations of motion to an ordinary differential equation for a profile function depending on the distance to the x(3) axis. The vortices have finite energy per unit length, and have waves propagating along them with the speed of light. The analytical vortices are obtained for a special choice of potentials, and the numerical ones are constructed using the successive over relaxation method for more general potentials. The spectrum of solutions is analyzed in detail, especially its dependence upon special combinations of coupling constants.