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

Shear localization as a mesoscopic stress-relaxation mechanism in fused silica glass at high strain rates

Molecular dynamics (MD) simulations of fused silica glass deforming in pressure-shear, while revealing useful insights into processes unfolding at the atomic level, fail spectacularly in that they grossly overestimate the magnitude of the stresses relative to those observed, e. g., in plate-impact experiments. We interpret this gap as evidence of relaxation mechanisms that operate at mesoscopic lengthscales and which, therefore, are not taken into account in atomic-level calculations. We specifically hypothesize that the dominant mesoscopic relaxation mechanism is shear banding. We evaluate this hypothesis by first generating MD data over the relevant range of temperature and strain rate and then carrying out continuum shear-banding calculations in a plate-impact configuration using a critical-state plasticity model fitted to the MD data. The main outcome of the analysis is a knock-down factor due to shear banding that effectively brings the predicted level of stress into alignment with experimental observation, thus resolving the predictive gap of MD calculations

Bar pattern speed evolution over the last 7 Gyr

The tumbling pattern of a bar is the main parameter characterising its dynamics. From numerical simulations, its evolution since bar formation is tightly linked to the dark halo in which the bar is formed through dynamical friction and angular momentum exchange. Observational measurements of the bar pattern speed with redshift can restrict models of galaxy formation and bar evolution. We aim to determine, for the first time, the bar pattern speed evolution with redshift based on morphological measurements. We have selected a sample of 44 low inclination ringed galaxies from the SDSS and COSMOS surveys covering the redshift range 0 <z< 0.8 to investigate the evolution of the bar pattern speed. We have derived morphological ratios between the deprojected outer ring radius (R_{ring}) and the bar size (R_{bar}). This quantity is related to the parameter {\cal R}=R_{CR}/R_{bar} used for classifiying bars in slow and fast rotators, and allow us to investigate possible differences with redshift. We obtain a similar distribution of $R$ at all redshifts. We do not find any systematic effect that could be forcing this result. The results obtained here are compatible with both, the bulk of the bar population (~70%) being fast-rotators and no evolution of the pattern speed with redshift. We argue that if bars are long-lasting structures, the results presented here imply that there has not been a substantial angular momentum exchange between the bar and halo, as predicted by numerical simulations. In consequence, this might imply that the discs of these high surface-brightness galaxies are maximal.Comment: Accepted for publication in A&

The structures underlying soliton solutions in integrable hierarchies

We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special ``vacuum solutions'' such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those ``vacuum solitons'' by the dressing transformation procedure.Comment: Talk given at the I Latin American Symposium on High Energy Physics, I SILAFAE, Merida, Mexico, November/96, 5 pages, LaTeX, needs aipproc.tex, aipproc.sty, aipproc.cls, available from ftp://ftp.aip.org/ems/tex/macros/proceedings/6x9