Fractal Structure of Random Matrices

A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the transition between the universality ensembles of random matrix theory and Poisson

Nonlinear Lattice Dynamics of Bose-Einstein Condensates

The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in non-metallic solids and develop ``experimental'' techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems--including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECS, in particular, due to their widely ranging and easily manipulated dynamical apparatuses--with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials--provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.Comment: 10 pages, revtex, two-columns, 3 figs, accepted fpr publication in Chaos's focus issue on the 50th anniversary of the publication of the Fermi-Pasta-Ulam problem; minor clarifications (and a couple corrected typos) from previous versio

Supernova Kicks and Misaligned Be Star Binaries

Be stars are rapidly spinning B stars surrounded by an outflowing disc of gas in Keplerian rotation. Be star/X-ray binary systems contain a Be star and a neutron star. They are found to have non-zero eccentricities and there is evidence that some systems have a misalignment between the spin axis of the star and the spin axis of the binary orbit. The eccentricities in these systems are thought to be caused by a kick to the neutron star during the supernova that formed it. Such kicks would also give rise to misalignments. In this paper we investigate the extent to which the same kick distribution can give rise to both the observed eccentricity distribution and the observed misalignments. We find that a Maxwellian distribution of velocity kicks with a low velocity dispersion, $\sigma_k \approx 15\rm km s^{-1}$, is consistent with the observed eccentricity distribution but is hard to reconcile with the observed misalignments, typically $i \ge 25^\circ$. Alternatively a higher velocity kick distribution, $\sigma_k = 265 \rm km s^{-1}$, is consistent with the observed misalignments but not with the observed eccentricities, unless post-supernova circularisation of the binary orbits has taken place. We discuss briefly how this might be achieved.Comment: Accepted for publication in MNRA

Morphology of Silicon Nitride Grown from a Liquid Phase

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66251/1/j.1151-2916.1998.tb02676.x.pd

Unfamiliar face matching with photographs of infants and children

Background Infants and children travel using passports that are typically valid for five years (e.g. Canada, United Kingdom, United States and Australia). These individuals may also need to be identified using images taken from videos and other sources in forensic situations including child exploitation cases. However, few researchers have examined how useful these images are as a means of identification. Methods We investigated the effectiveness of photo identification for infants and children using a face matching task, where participants were presented with two images simultaneously and asked whether the images depicted the same child or two different children. In Experiment 1, both images showed an infant (<1 year old), whereas in Experiment 2, one image again showed an infant but the second image of the child was taken at 4–5 years of age. In Experiments 3a and 3b, we asked participants to complete shortened versions of both these tasks (selecting the most difficult trials) as well as the short version Glasgow face matching test. Finally, in Experiment 4, we investigated whether information regarding the sex of the infants and children could be accurately perceived from the images. Results In Experiment 1, we found low levels of performance (72% accuracy) for matching two infant photos. For Experiment 2, performance was lower still (64% accuracy) when infant and child images were presented, given the significant changes in appearance that occur over the first five years of life. In Experiments 3a and 3b, when participants completed both these tasks, as well as a measure of adult face matching ability, we found lowest performance for the two infant tasks, along with mixed evidence of within-person correlations in sensitivities across all three tasks. The use of only same-sex pairings on mismatch trials, in comparison with random pairings, had little effect on performance measures. In Experiment 4, accuracy when judging the sex of infants was at chance levels for one image set and above chance (although still low) for the other set. As expected, participants were able to judge the sex of children (aged 4–5) from their faces. Discussion Identity matching with infant and child images resulted in low levels of performance, which were significantly worse than for an adult face matching task. Taken together, the results of the experiments presented here provide evidence that child facial photographs are ineffective for use in real-world identification

Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model

We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed distances from the localization center are well approximated by log-normal fits which become exact at large distances. These fits are consistent with the standard single parameter scaling theory for the Anderson model in 1d, but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in 2d. From the log-normal distributions we calculate analytically the decay of the mean wave functions. For short distances from the localization center we find stretched exponential localization ("sublocalization") in both, 1d and 2d. In 1d, for large distances, the mean wave functions depend on the number of configurations N used in the averaging procedure and decay faster that exponentially ("superlocalization") converging to simple exponential behavior only in the asymptotic limit. In 2d, in contrast, the localization length increases logarithmically with the distance from the localization center and sublocalization occurs also in the second regime. The N-dependence of the mean wave functions is weak. The analytical result agrees remarkably well with the numerical calculations.Comment: 12 pages with 9 figures and 1 tabl

Bostonia: The Boston University Alumni Magazine. Volume 12

Founded in 1900, Bostonia magazine is Boston University’s main alumni publication