Black hole entropy functions and attractor equations

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N=2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.Comment: 21 pages,LaTeX,minor change

Nambu monopoles interacting with lattice defects in two-dimensional artificial square spin ice

The interactions between an excitation (similar to a pair of Nambu monopoles) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the "imperfect" island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We have shown that the two extreme points of a malformed island behave like two opposite magnetic charges. Then, the effective interaction between a pair of Nambu monopoles with the deformed island is a problem involving four magnetic charges (two pairs of opposite poles) and a string. We also sketch the configuration of the field lines of these four charges to confirm this picture. The influence of the string on this interaction decays rapidly with the string distance from the defect.Comment: 7 pages, 13 figure

Non-Kaehler attracting manifolds

We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski "attractor points'' for 3-form fluxes are special-hermitian manifolds.Comment: 18 pages. v2: Minor polishing, reference added. v3: More cleanup, final version for JHE

On the canonical map of surfaces with q>=6

We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a curve of genus >1. We prove that for q>=6 the canonical map is birational. Combining this result with the analysis of the canonical system, we also prove the inequality: K^2>=7\chi+2. This improves an earlier result of the first and second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in Geom. 10 (3) (2010), 549-555].Comment: Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in the special issue of Science of China Ser.A: Mathematics dedicated to him. V2:some typos have been correcte

The WFCAM Multi-wavelength Variable Star Catalog

Stellar variability in the near-infrared (NIR) remains largely unexplored. The exploitation of public science archives with data-mining methods offers a perspective for the time-domain exploration of the NIR sky. We perform a comprehensive search for stellar variability using the optical-NIR multi-band photometric data in the public Calibration Database of the WFCAM Science Archive (WSA), with the aim of contributing to the general census of variable stars, and to extend the current scarce inventory of accurate NIR light curves for a number of variable star classes. We introduce new variability indices designed for multi-band data with correlated sampling, and apply them for pre-selecting variable star candidates, i.e., light curves that are dominated by correlated variations, from noise-dominated ones. Pre-selection criteria are established by robust numerical tests for evaluating the response of variability indices to colored noise characteristic to the data. We find 275 periodic variable stars and an additional 44 objects with suspected variability with uncertain periods or apparently aperiodic variation. Only 44 of these objects had been previously known, including 11 RR~Lyrae stars in the outskirts of the globular cluster M3 (NGC~5272). We provide a preliminary classification of the new variable stars that have well-measured light curves, but the variability types of a large number of objects remain ambiguous. We classify most of the new variables as contact binary stars, but we also find several pulsating stars, among which 34 are probably new field RR~Lyrae and 3 are likely Cepheids. We also identify 32 highly reddened variable objects close to previously known dark nebulae, suggesting that these are embedded young stellar objects. We publish our results and all light-curve data as the WFCAM Variable Star Catalog.Comment: 21 pages, 11 figure

The 20 February 2010 Madeira flash-floods: synoptic analysis and extreme rainfall assessment

This study aims to characterise the rainfall exceptionality and the meteorological context of the 20 February 2010 flash-floods in Madeira (Portugal). Daily and hourly precipitation records from the available rain-gauge station networks are evaluated in order to reconstitute the temporal evolution of the rainstorm, as its geographic incidence, contributing to understand the flash-flood dynamics and the type and spatial distribution of the associated impacts. The exceptionality of the rainstorm is further confirmed by the return period associated with the daily precipitation registered at the two long-term record stations, with 146.9 mm observed in the city of Funchal and 333.8 mm on the mountain top, corresponding to an estimated return period of approximately 290 yr and 90 yr, respectively. Furthermore, the synoptic associated situation responsible for the flash-floods is analysed using different sources of information, e.g., weather charts, reanalysis data, Meteosat images and radiosounding data, with the focus on two main issues: (1) the dynamical conditions that promoted such anomalous humidity availability over the Madeira region on 20 February 2010 and (2) the uplift mechanism that induced deep convection activity

Exact Solution of Ising Model on a Small-World Network

We present an exact solution of a one-dimensional Ising chain with both nearest neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.Comment: 9 pages, 7 figures, submitted to pr