Asymptotic boundary forms for tight Gabor frames and lattice localization domains

We consider Gabor localization operators $G_{\phi,\Omega}$ defined by two parameters, the generating function $\phi$ of a tight Gabor frame $\{\phi_\lambda\}_{\lambda \in \Lambda}$, parametrized by the elements of a given lattice $\Lambda \subset \Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\Bbb{R}^2$, and a lattice localization domain $\Omega \subset \Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\Lambda$. We find an explicit formula for the boundary form $BF(\phi,\Omega)=\text{A}_\Lambda \lim_{R\rightarrow \infty}\frac{PF(G_{\phi,R\Omega})}{R}$, the normalized limit of the projection functional $PF(G_{\phi,\Omega})=\sum_{i=0}^{\infty}\lambda_i(G_{\phi,\Omega})(1-\lambda_i(G_{\phi,\Omega}))$, where $\lambda_i(G_{\phi,\Omega})$ are the eigenvalues of the localization operators $G_{\phi,\Omega}$ applied to dilated domains $R\Omega$, $R$ is an integer and $\text{A}_\Lambda$ is the area of the fundamental domain of the lattice $\Lambda$.Comment: 35 page

The GTC exoplanet transit spectroscopy survey. VII. Detection of sodium in WASP-52b's cloudy atmosphere

We report the first detection of sodium absorption in the atmosphere of the hot Jupiter WASP-52b. We observed one transit of WASP-52b with the low-resolution Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at the 10.4 m Gran Telescopio Canarias (GTC). The resulting transmission spectrum, covering the wavelength range from 522 nm to 903 nm, is flat and featureless, except for the significant narrow absorption signature at the sodium doublet, which can be explained by an atmosphere in solar composition with clouds at 1 mbar. A cloud-free atmosphere is stringently ruled out. By assessing the absorption depths of sodium in various bin widths, we find that temperature increases towards lower atmospheric pressure levels, with a positive temperature gradient of 0.88 +/- 0.65 K/km, possibly indicative of upper atmospheric heating and a temperature inversion.Comment: 6 pages, 5 figures, accepted for publication in A&A Lette

Evolutionary prisoner's dilemma games with optional participation

Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This results in a rock-scissors-paper type cyclic dominance of the three strategies. The players are located either on square lattices or random regular graphs with the same connectivity. Occasionally, every player reassesses its strategy by sampling the payoffs in its neighborhood. The loner strategy efficiently prevents successful spreading of selfish, defective behavior and avoids deadlocks in states of mutual defection. On square lattices, Monte Carlo simulations reveal self-organizing patterns driven by the cyclic dominance, whereas on random regular graphs different types of oscillatory behavior are observed: the temptation to defect determines whether damped, periodic or increasing oscillations occur. These results are compared to predictions by pair approximation. Although pair approximation is incapable of distinguishing the two scenarios because of the equal connectivity, the average frequencies as well as the oscillations on random regular graphs are well reproduced.Comment: 6 pages, 7 figure

Relativistic Iron Lines in Galactic Black Holes: Recent Results and Lines in the ASCA Archive

Recent observations with Chandra and XMM-Newton, aided by broad-band spectral coverage from RXTE, have revealed skewed relativistic iron emission lines in stellar-mass Galactic black hole systems. Such systems are excellent laboratories for testing General Relativity, and relativistic iron lines provide an important tool for making such tests. In this contribution to the Proceedings of the 10th Annual Marcel Grossmann Meeting on General Relativity, we briefly review recent developments and present initial results from fits to archival ASCA observations of Galactic black holes. It stands to reason that relativistic effects, if real, should be revealed in many systems (rather than just one or two); the results of our archival work have borne-out this expectation. The ASCA spectra reveal skewed, relativistic lines in XTE J1550-564, GRO J1655-40, GRS 1915+105, and Cygnus X-1.Comment: to appear in the proc. of the 10th Annual Marcel Grossmann Meeting on General Relativity, 5 pages, 1 figure, uses specific .cls and .sty file

Study of 'ratio' automatically assembled structures final report, 15 jun. 1963 - 15 jun. 1964

Structural analysis of RATIO automatically assembled panel sections for application to spaceborne paraboloidal antenn

The GTC exoplanet transit spectroscopy survey. VII. An optical transmission spectrum of WASP-48b

We obtained long-slit optical spectroscopy of one transit of WASP-48b with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) spectrograph at the 10.4 m Gran Telescopio Canarias (GTC). We integrated the spectrum of WASP-48 and one reference star in several channels with different wavelength ranges, creating numerous color light curves of the transit. We fit analytic transit curves to the data taking into account the systematic effects present in the time series in an effort to measure the change of the planet-to-star radius ratio ($R_p/R_s$) across wavelength. After removing the transit model and systematic trends to the curves we reached precisions between 261 ppm and 455-755 ppm for the white and spectroscopic light curves, respectively. We obtained $R_p/R_s$ uncertainty values between $0.8 \times 10^{-3}$ and $1.5\times 10^{-3}$ for all the curves analyzed in this work. The measured transit depth for the curves made by integrating the wavelength range between 530 nm and 905 nm is in agreement with previous studies. We report a relatively flat transmission spectrum for WASP-48b with no statistical significant detection of atmospheric species, although the theoretical models that fit the data more closely include of TiO and VO.Comment: 8 pages, 8 figures. Accepted for publication in Astronomy and Astrophysic

The GTC exoplanet transit spectroscopy survey. VI. A spectrally-resolved Rayleigh scattering slope in GJ 3470b

Aims. As a sub-Uranus-mass low-density planet, GJ 3470b has been found to show a flat featureless transmission spectrum in the infrared and a tentative Rayleigh scattering slope in the optical. We conducted an optical transmission spectroscopy project to assess the impacts of stellar activity and to determine whether or not GJ 3470b hosts a hydrogen-rich gas envelop. Methods. We observed three transits with the low-resolution OSIRIS spectrograph at the 10.4 m Gran Telescopio Canarias, and one transit with the high-resolution UVES spectrograph at the 8.2 m Very Large Telescope. Results. From the high-resolution data, we find that the difference of the Ca II H+K lines in- and out-of-transit is only 0.67 +/- 0.22%, and determine a magnetic filling factor of about 10-15%. From the low-resolution data, we present the first optical transmission spectrum in the 435-755 nm band, which shows a slope consistent with Rayleigh scattering. Conclusions. After exploring the potential impacts of stellar activity in our observations, we confirm that Rayleigh scattering in an extended hydrogen/helium atmosphere is currently the best explanation. Further high-precision observations that simultaneously cover optical and infrared bands are required to answer whether or not clouds and hazes exist at high-altitude.Comment: 12 pages, 11 figures, accepted for publication in A&

Evolutionary prisoner's dilemma game on a square lattice

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing state when varying the value of temptation to defect. In the limits $c \to 0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.Comment: 6 pages including 6 figure

Influence of the temperature on the depinning transition of driven interfaces

We study the dynamics of a driven interface in a two-dimensional random-field Ising model close to the depinning transition at small but finite temperatures T using Glauber dynamics. A square lattice is considered with an interface initially in (11)-direction. The drift velocity v is analyzed for the first time using finite size scaling at T = 0 and additionally finite temperature scaling close to the depinning transition. In both cases a perfect data collapse is obtained from which we deduce beta = 1/3 for the exponent which determines the dependence of v on the driving field, nu = 1 for the exponent of the correlation length and delta = 5 for the exponent which determines the dependence of v on T.Comment: 5 pages, Latex, Figures included, to appear in Europhys. Let