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

Accuracy of Trace Formulas

Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues.Comment: 20 pages, uuencoded and gzipped, 1 LaTex text file and 9 PS files for figure

On the integrability of stationary and restricted flows of the KdV hierarchy.

A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space.Comment: 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A: Math. Gen.

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Coefficient of restitution for elastic disks

We calculate the coefficient of restitution, $\epsilon$, starting from a microscopic model of elastic disks. The theory is shown to agree with the approach of Hertz in the quasistatic limit, but predicts inelastic collisions for finite relative velocities of two approaching disks. The velocity dependence of $\epsilon$ is calculated numerically for a wide range of velocities. The coefficient of restitution furthermore depends on the elastic constants of the material via Poisson's number. The elastic vibrations absorb kinetic energy more effectively for materials with low values of the shear modulus.Comment: 25 pages, 12 Postscript figures, LaTex2

Radiative Efficiency and Content of Extragalactic Radio Sources: Toward a Universal Scaling Relation Between Jet Power and Radio Power

We present an analysis of the energetics and particle content of the lobes of 24 radio galaxies at the cores of cooling clusters. The radio lobes in these systems have created visible cavities in the surrounding hot, X-ray-emitting gas, which allow direct measurement of the mechanical jet power of radio sources over six decades of radio luminosity, independently of the radio properties themselves. Using these measurements, we examine the ratio between radio power and total jet power (the radiative efficiency). We find that jet (cavity) power increases with radio synchrotron power approximately as P_jet ~ (L_radio)^beta, where 0.35 < beta < 0.70 depending on the bandpass of measurement and state of the source. However, the scatter about these relations caused by variations in radiative efficiency spans more than four orders of magnitude. After accounting for variations in synchrotron break frequency (age), the scatter is reduced by ~ 50%, yielding the most accurate scaling relation available between the lobe bolometric radio power and the jet (cavity) power. We place limits on the magnetic field strengths and particle content of the radio lobes using a variety of X-ray constraints. We find that the lobe magnetic field strengths vary between a few to several tens of microgauss depending on the age and dynamical state of the lobes. If the cavities are maintained in pressure balance with their surroundings and are supported by internal fields and particles in equipartition, the ratio of energy in electrons to heavy particles (k) must vary widely from approximately unity to 4000, consistent with heavy (hadronic) jets.Comment: 20 pages, 11 figures. Accepted for publication in Ap

Genomic analysis of Campylobacter fetus subspecies: identification of candidate virulence determinants and diagnostic assay targets

Background: Campylobacter fetus subspecies venerealis is the causative agent of bovine genital campylobacteriosis, asymptomatic in bulls the disease is spread to female cattle causing extensive reproductive loss. The microbiological and molecular differentiation of C. fetus subsp. venerealis from C. fetus subsp. fetus is extremely difficult. This study describes the analysis of the available C. fetus subsp. venerealis AZUL-94 strain genome (~75–80%) to identify elements exclusively found in C. fetus subsp. venerealis strains as potential diagnostic targets and the characterisation of subspecies virulence genes. Results: Eighty Kb of genomic sequence (22 contigs) was identified as unique to C. fetus subsp. venerealis AZUL-94 and consisted of type IV secretory pathway components, putative plasmid genes and hypothetical proteins. Of the 9 PCR assays developed to target C. fetus subsp. venerealis type IV secretion system genes, 4 of these were specific for C. fetus subsp. venerealis biovar venerealis and did not detect C. fetus subsp. venerealis biovar intermedius. Two assays were specific for C. fetus subsp. venerealis AZUL-94 strain, with a further single assay specific for the AZUL-94 strain and C. fetus subsp. venerealis biovar intermedius (and not the remaining C. fetus subsp. venerealis biovar venerealis strains tested). C. fetus subsp. fetus and C. fetus subsp. venerealis were found to share most common Campylobacter virulence factors such as SAP, chemotaxis, flagellar biosynthesis, 2-component systems and cytolethal distending toxin subunits (A, B, C). We did not however, identify in C. fetus the full complement of bacterial adherence candidates commonly found in other Campylobacter spp. Conclusion: The comparison of the available C. fetus subsp. venerealis genome sequence with the C. fetus subsp. fetus genome identified 80 kb of unique C. fetus subsp. venerealis AZUL94 sequence, with subsequent PCR confirmation demonstrating inconsistent amplification of these targets in all other C. fetus subsp. venerealis strains and biovars tested. The assays developed here highlight the complexity of targeting strain specific virulence genes for field studies for the molecular identification and epidemiology of C. fetus

From Regular to Chaotic States in Atomic Nuclei

An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order$\to$chaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).Comment: 65 pages, LaTex (the figures are not included), Preprint DFPD/94/TH/26, University of Padov

Generalization of the NpNnN_pN_n Scheme and the Structure of the Valence Space

The $N_pN_n$ scheme, which has been extensively applied to even-even nuclei, is found to be a very good benchmark for odd-even, even-odd, and doubly-odd nuclei as well. There are no apparent shifts in the correlations for these four classes of nuclei. The compact correlations highlight the deviant behavior of the Z=78 nuclei, are used to deduce effective valence proton numbers near Z=64, and to study the evolution of the Z=64 subshell gap.Comment: 10 pages, 4 figure