Geometrical and spectral study of beta-skeleton graphs

We perform an extensive numerical analysis of beta-skeleton graphs, a particular type of proximity graphs. In beta-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter beta is an element of (0, infinity), is satisfied. Moreover, for beta > 1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of beta, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at beta = 1

Continuum discretized BCS approach for weakly bound nuclei

The Bardeen-Cooper-Schrieffer (BCS) formalism is extended by including the single-particle continuum in order to analyse the evolution of pairing in an isotopic chain from stability up to the drip line. We propose a continuum discretized generalized BCS based on single-particle pseudostates (PS). These PS are generated from the diagonalization of the single-particle Hamiltonian within a Transformed Harmonic Oscillator (THO) basis. The consistency of the results versus the size of the basis is studied. The method is applied to neutron rich Oxygen and Carbon isotopes and compared with similar previous works and available experimental data. We make use of the flexibility of the proposed model in order to study the evolution of the occupation of the low-energy continuum when the system becomes weakly bound. We find a larger influence of the non-resonant continuum as long as the Fermi level approaches zero.Comment: 20 pages, 16 figures, to be submitte

Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass

We study the Heisenberg spin glass by large-scale Monte Carlo simulations for sizes up to 32^3, down to temperatures below the transition temperature claimed in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes, indicating the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a quite similar manner.Comment: 8 pages, 8 figures. Replaced with published versio

TeV neutrinos from core collapse supernovae and hypernovae

A fraction of core collapse supernovae of type Ib/c are associated with Gamma-ray bursts, which are thought to produce highly relativistic jets. Recently, it has been hypothesized that a larger fraction of core collapse supernovae produce slower jets, which may contribute to the disruption and ejection of the supernova envelope, and explain the unusually energetic hypernovae. We explore the TeV neutrino signatures expected from such slower jets, and calculate the expected detection rates with upcoming Gigaton Cherenkov experiments. We conclude that individual jetted SNe may be detectable from nearby galaxies.Comment: 4 pages 2 figures. Modified from the published version. Errors in Eqs. 2, 3, 5 are corrected and predicted neutrino event rates are modified accordingly. The conclusions for the diffuse flux remain unchanged, and those for individual nearby sources are strengthene

Quicksort with unreliable comparisons: a probabilistic analysis

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.Comment: 29 pages, 3 figure

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

Geiger-Mode Avalanche Photodiodes in Particle Detection

It is well known that avalanche photodiodes operated in the Geiger mode above the breakdown voltage offer a virtually infinite sensitivity and time accuracy in the picosecond range that can be used for single photon detection. However, their performance in particle detection remains still unexplored. In this contribution, we are going to expose the different steps that we have taken in order to prove the efficiency of Geiger mode avalanche photodiodes in the aforementioned field. In particular, we will present an array of pixels of 1mmx1mm fabricated with a standard CMOS technology for characterization in a test beam.Comment: 7 pages, 2 figures, Proceedings of LCWS1