Amenability of Groupoids Arising from Partial Semigroup Actions and Topological Higher Rank Graphs

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable set $D\subset G$ such that $c(G^{u})D=Q$ for all $u\in G^{(0)}$. We show that our result is applicable to groupoids arising from partial semigroup actions. We explore these actions in detail and show that these groupoids include those arising from directed graphs, higher rank graphs and even topological higher rank graphs. We believe our methods yield a nice alternative groupoid approach to these important constructions.Comment: Revised as suggested by a very helpful referee. In particular, a gap in the proof of Theorem 5.13 has been repaired resulting in a much improved version (with fewer hypotheses

Fractional Boundaries for Fluid Spheres

A single Israel layer can be created when two metrics adjoin with no continuous metric derivative across the boundary. The properties of the layer depend only on the two metrics it separates. By using a fractional derivative match, a family of Israel layers can be created between the same two metrics. The family is indexed by the order of the fractional derivative. The method is applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The method creates new ranges of modeling parameters for fluid spheres. A thin shell analysis clarifies pressure/tension in the family of boundary layers.Comment: to appear in J. Math. Phy

Jensen-Feynman approach to the statistics of interacting electrons

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists in a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen's inequality to a more convenient convex function.Comment: submitted to Physical Review

Dynamics of the formation of a hydrogel by a pathogenic amyloid peptide: islet amyloid polypeptide

Many chronic degenerative diseases result from aggregation of misfolded polypeptides to form amyloids. Many amyloidogenic polypeptides are surfactants and their assembly can be catalysed by hydrophobic-hydrophilic interfaces (an air-water interface in-vitro or membranes in-vivo). We recently demonstrated the specificity of surface-induced amyloidogenesis but the mechanisms of amyloidogenesis and more specifically of adsorption at hydrophobic-hydrophilic interfaces remain poorly understood. Thus, it is critical to determine how amyloidogenic polypeptides behave at interfaces. Here we used surface tensiometry, rheology and electron microscopy to demonstrate the complex dynamics of gelation by full-length human islet amyloid polypeptide (involved in type II diabetes) both in the bulk solution and at hydrophobic-hydrophilic interfaces (air-water interface and phospholipids). We show that the hydrogel consists of a 3D supramolecular network of fibrils. We also assessed the role of solvation and dissected the evolution over time of the assembly processes. Amyloid gelation could have important pathological consequences for membrane integrity and cellular functions

Bose-Einstein transition temperature in a dilute repulsive gas

We discuss certain specific features of the calculation of the critical temperature of a dilute repulsive Bose gas. Interactions modify the critical temperature in two different ways. First, for gases in traps, temperature shifts are introduced by a change of the density profile, arising itself from a modification of the equation of state of the gas (reduced compressibility); these shifts can be calculated simply within mean field theory. Second, even in the absence of a trapping potential (homogeneous gas in a box), temperature shifts are introduced by the interactions; they arise from the correlations introduced in the gas, and thus lie inherently beyond mean field theory - in fact, their evaluation requires more elaborate, non-perturbative, calculations. One illustration of this non-perturbative character is provided by the solution of self-consistent equations, which relate together non-linearly the various energy shifts of the single particle levels k. These equations predict that repulsive interactions shift the critical temperature (at constant density) by an amount which is positive, and simply proportional to the scattering length a; nevertheless, the numerical coefficient is difficult to compute. Physically, the increase of the temperature can be interpreted in terms of the reduced density fluctuations introduced by the repulsive interactions, which facilitate the propagation of large exchange cycles across the sample.Comment: two minor corrections, two refs adde

Nuclear star formation on 100 parsec scales: 10" resolution radio continuum, HI and CO observations

A program of radio line and continuum studies of star formation in nearby spiral galaxies is reported. The objective is a search for hot gas and peculiar dynamics in spiral nuclei with 10" to 30" angular resolution. Vigorous star formation is found to be a common phenomenon in the inner kpc of spirals. Arcsecond resolution observations of radio continuum emission at 6 and 2 cm were used to separate the thermal and nonthermal radio components. It was found that thermal and nonthermal emission are well mixed even on sizescales of 10 pc. To understand the reason for the increased level of star formation activity in spiral nuclei, HI and CO emission in these galaxies is studied. The CO transition was detected in M51, M82, NGC 253, NGC 6946 and IC 342 with T sub a approx. 0.5 to 2.0 K, at 20" angular resolution. The dynamics and spatial distribution of nuclear gas are being studied using VLA HI maps with 30" synthesized beams. Evidence for noncircular motions in HI was found in the nucleus of IC 342

Two-photon decay of pseudoscalar quarkonia

We report on our recent evaluation of the two-photon width of the pseudoscalar quarkonia, eta_c(nS) and eta_b(nS) in an approach based on Heavy-Quark Spin Symmetry (HQSS). To what concerns the 1S state eta_c, our parameter-free computation agrees with experiments, as well as most of other theoretical works. On the other hand, our computation for the 2S-state looks 2S like a confirmation that there may exist an anomaly related to the decay of eta_c(2S), especially in the light of the new preliminary result of the Belle collaboration. We also point out that the essentially model-independent ratio of eta_b two-photon width to the Upsilon leptonic width and the eta_b two-photon width could be used to extract the strong coupling constant alpha_s.Comment: Presented by T.N. Pham at the Joint Meeting Heidelberg-Liege-Paris-Wroclaw (HLPW08), Spa, Belgium, 6-8 March 2008, 9 pages, 2 figures, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included

Site occupation constraints in mean-field approaches of quantum spin systems at finite temperature

We study the effect of site occupation on the description of quantum spin systems at finite temperature and mean-field level. We impose each lattice site to be occupied by a single electron. This is realized by means of a specific prescription. The outcome of the prescription is compared to the result obtained by means of a projection procedure which fixes the site occupation to one particle per site on an average. The comparison is performed for different representations of the Hamiltonian in Fock space leading to different types of mean-field solutions. The behaviour of order parameters is analyzed for each choice of the mean-field and constraint which fixes the occupation rate at each site. Sizable quantitative differences between the outcomes obtained with the two different constraints are observed.Comment: 18 pages, 2 figure

A System of Interaction and Structure II: The Need for Deep Inference

This paper studies properties of the logic BV, which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV is presented in the calculus of structures, a proof theoretic formalism that supports deep inference, in which inference rules can be applied anywhere inside logical expressions. The use of deep inference results in a simple logical system for MLL extended with the self-dual non-commutative operator, which has been to date not known to be expressible in sequent calculus. In this paper, deep inference is shown to be crucial for the logic BV, that is, any restriction on the ``depth'' of the inference rules of BV would result in a strictly less expressive logical system