On Equivalence of Critical Collapse of Non-Abelian Fields

We continue our study of the gravitational collapse of spherically symmetric skyrmions. For certain families of initial data, we find the discretely self-similar Type II critical transition characterized by the mass scaling exponent $\gamma \approx 0.20$ and the echoing period $\Delta \approx 0.74$. We argue that the coincidence of these critical exponents with those found previously in the Einstein-Yang-Mills model is not accidental but, in fact, the two models belong to the same universality class.Comment: 7 pages, REVTex, 2 figures included, accepted for publication in Physical Review

From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity Ns of the inherent structures generically has a lognormal distribution. In addition, the large volume limit of ln/ differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.Comment: 10 pages, 9 figs, slightly improved presentation, more references, accepted for publication in Phys Rev

Dispersion and collapse of wave maps

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte

Star Formation, Radio Sources, Cooling X-ray Gas, and Galaxy Interactions in the Brightest Cluster Galaxy in 2A0335+096

We present deep emission-line imaging taken with the SOAR Optical Imaging Camera of the brightest cluster galaxy (BCG) in the nearby (z=0.035) X-ray cluster 2A0335+096. We analyze long-slit optical spectroscopy, archival VLA, Chandra X-ray, and XMM UV data. 2A0335+096 is a bright, cool-core X-ray cluster, once known as a cooling flow. Within the highly disturbed core revealed by Chandra X-ray observations, 2A0335+096 hosts a highly structured optical emission-line system. The redshift of the companion is within 100 km/s of the BCG and has certainly interacted with the BCG, and is likely bound to it. The comparison of optical and radio images shows curved filaments in H-alpha emission surrounding the resolved radio source. The velocity structure of the emission-line bar between the BCG nucleus and the companion galaxy provides strong evidence for an interaction between the two in the last ~50 Myrs. The age of the radio source is similar to the interaction time, so this interaction may have provoked an episode of radio activity. We estimate a star formation rate of >7 solar mass/yr based on the Halpha and archival UV data, a rate similar to, but somewhat lower than, the revised X-ray cooling rate of 10-30 solar masses/year estimated from XMM spectra by Peterson & workers. The Halpha nebula is limited to a region of high X-ray surface brightness and cool X-ray temperature. The detailed structures of H-alpha and X-ray gas differ. The peak of the X-ray emission is not the peak of H-alpha emission, nor does it lie in the BCG. The estimated age of the radio lobes and their interaction with the optical emission-line gas, the estimated timescale for depletion and accumulation of cold gas, and the dynamical time in the system are all similar, suggesting a common trigger mechanism.Comment: Accepted AJ, July 2007 publication. Vol 134, p. 14-2

Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications

Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. A key question is whether beams can support chaotic orbits, and if so, under what conditions? We numerically investigate the parameter space of three-dimensional thermal-equilibrium beams with space charge, confined by linear external focusing forces, to determine whether the associated potentials support chaotic orbits. We find that a large subset of the parameter space does support chaos and, in turn, chaotic mixing. Details and implications are enumerated.Comment: 39 pages, including 14 figure

pp-sdsd shell gap reduction in neutron-rich systems and cross-shell excitations in 20^{20}O

Excited states in $^{20}$O were populated in the reaction $^{10}$Be($^{14}$C,$\alpha$) at Florida State University. Charged particles were detected with a particle telescope consisting of 4 annularly segmented Si surface barrier detectors and $\gamma$ radiation was detected with the FSU $\gamma$ detector array. Five new states were observed below 6 MeV from the $\alpha$-$\gamma$ and $\alpha$-$\gamma$-$\gamma$ coincidence data. Shell model calculations suggest that most of the newly observed states are core-excited 1p-1h excitations across the $N = Z = 8$ shell gap. Comparisons between experimental data and calculations for the neutron-rich O and F isotopes imply a steady reduction of the $p$-$sd$ shell gap as neutrons are added

Higher Order Correlations in Quantum Chaotic Spectra

The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the spectral fluctuatations of these systems is available only up to this order. For a complete understanding of spectral properties it is highly desirable to study the higher order spectral correlations. This will also inform us about the limitations of random matrix theory in modelling the properties of quantum chaotic systems. Our main purpose in this paper is to carry out this study by a semiclassical calculation for the quantum maps; however results are also valid for time-independent systems.Comment: Revtex, Four figures (Postscript files), Phys. Rev E (in press

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

A deep Chandra observation of the Perseus cluster: shocks and ripples

We present preliminary results from a deep observation lasting almost 200 ks, of the centre of the Perseus cluster of galaxies around NGC 1275. The X-ray surface brightness of the intracluster gas beyond the inner 20 kpc, which contains the inner radio bubbles, is very smooth apart from some low amplitude quasi-periodic ripples. A clear density jump at a radius of 24 kpc to the NE, about 10 kpc out from the bubble rim, appears to be due to a weak shock driven by the northern radio bubble. A similar front may exist round both inner bubbles but is masked elsewhere by rim emission from bright cooler gas. The continuous blowing of bubbles by the central radio source, leading to the propagation of weak shocks and viscously-dissipating sound waves seen as the observed fronts and ripples, gives a rate of working which balances the radiative cooling within the inner 50 kpc of the cluster core.Comment: Accepted for publication in MNRAS (minor changes) Higher picture quality available from http://www-xray.ast.cam.ac.uk/papers/per_200ks.pd