Density of states "width parity" effect in d-wave superconducting quantum wires

We calculate the density of states (DOS) in a clean mesoscopic d-wave superconducting quantum wire, i.e. a sample of infinite length but finite width $N$. For open boundary conditions, the DOS at zero energy is found to be zero if $N$ is even, and nonzero if $N$ is odd. At finite chemical potential, all chains are gapped but the qualtitative differences between even and odd $N$ remain.Comment: 7 pages, 8 figures, new figures and extended discussio

Failure time and microcrack nucleation

The failure time of samples of heterogeneous materials (wood, fiberglass) is studied as a function of the applied stress. It is shown that in these materials the failure time is predicted with a good accuracy by a model of microcrack nucleation proposed by Pomeau. It is also shown that the crack growth process presents critical features when the failure time is approached.Comment: 13 pages, 4 figures, submitted to Europhysics Letter

Spontaneous Chiral-Symmetry Breaking in Three-Dimensional QED with a Chern--Simons Term

In three-dimensional QED with a Chern--Simons term we study the phase structure associated with chiral-symmetry breaking in the framework of the Schwinger--Dyson equation. We give detailed analyses on the analytical and numerical solutions for the Schwinger--Dyson equation of the fermion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function renormalization for the fermion. In the absence of the Chern--Simons term, there exists a finite critical number of four-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place and below which the chiral symmetry is spontaneously broken. In the presence of the Chern--Simons term, we find that the spontaneous chiral-symmetry-breaking transition continues to exist, but the type of phase transition turns into a discontinuous first-order transition. A simple stability argument is given based on the effective potential, whose stationary point gives the solution of the Schwinger-Dyson equation.Comment: 34 pages, revtex, with 9 postscriptfigures appended (uuencoded

Singularity subtraction for nonlinear weakly singular integral equations of the second kind

The singularity subtraction technique for computing an approximate solution of a linear weakly singular Fredholm integral equation of the second kind is generalized to the case of a nonlinear integral equation of the same kind. Convergence of the sequence of approximate solutions to the exact one is proved under mild standard hypotheses on the nonlinear factor, and on the sequence of quadrature rules used to build an approximate equation. A numerical example is provided with a Hammerstein operator to illustrate some practical aspects of effective computations.The third author was partially supported by CMat (UID/MAT/00013/2013), and the second and fourth authors were partially supported by CMUP (UID/ MAT/ 00144/2013), which are funded by FCT (Portugal) with national funds (MCTES) and European structural funds (FEDER) under the partnership agreement PT2020

Rota-Baxter algebras and new combinatorial identities

The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.Comment: 8 pages, improved versio

Zooplankton variability at four monitoring sites of the Northeast Atlantic shelves differing in latitude and trophic status

Zooplankton abundance series (1999–2013) from the coastal sites of Bilbao 35 (B35), Urdaibai 35 (U35), Plymouth L4 (L4) and Stonehaven (SH), in the Northeast Atlantic were compared to assess differences in the magnitude of seasonal, interannual and residual scales of variability, and in patterns of seasonal and interannual variation in relation to latitudinal location and trophic status. Results showed highest seasonal variability at SH consistent with its northernmost location, highest interannual variability at U35 associated to an atypical event identified in 2012 in the Bay of Biscay, and highest residual variability at U35 and B35 likely related to lower sampling frequency and higher natural and anthropogenic stress. Interannual zooplankton variations were not coherent across sites, suggesting the dominance of local influences over large scale environmental drivers. For most taxa the seasonal pattern showed coherent differences across sites, the northward delay of the annual peak being the most common feature. The between-site seasonal differences in spring–summer zooplankton taxa were related mainly to phytoplankton biomass, in turn, related to differences in latitude or anthropogenic nutrient enrichment. The northward delay in water cooling likely accounted for between-site seasonal differences in taxa that increase in the second half of the year

Coloured peak algebras and Hopf algebras

For $G$ a finite abelian group, we study the properties of general equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of $G$ with the symmetric group \SG_n, also known as the $G$-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of \k G_n as well as graded connected Hopf subalgebras of \bigoplus_{n\ge o} \k G_n. In particular we construct a $G$-coloured peak subalgebra of the Mantaci-Reutenauer algebra (or $G$-coloured descent algebra). We show that the direct sum of the $G$-coloured peak algebras is a Hopf algebra. We also have similar results for a $G$-colouring of the Loday-Ronco Hopf algebras of planar binary trees. For many of the equivalence relations under study, we obtain a functor from the category of finite abelian groups to the category of graded connected Hopf algebras. We end our investigation by describing a Hopf endomorphism of the $G$-coloured descent Hopf algebra whose image is the $G$-coloured peak Hopf algebra. We outline a theory of combinatorial $G$-coloured Hopf algebra for which the $G$-coloured quasi-symmetric Hopf algebra and the graded dual to the $G$-coloured peak Hopf algebra are central objects.Comment: 26 pages latex2

Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.Comment: 36 pages, 19 figure

A densitometric analysis of IIaO film flown aboard the space shuttle transportation system STS-3, STS-8, and STS-7

Three canisters of IIaO film were prepared along with packets of color film from the National Geographic Society, which were then placed on the Space Shuttle #3. The ultimate goal was to obtain reasonably accurate data concerning the background fogging effects on IIaO film as it relates to the film's total environmental experience. This includes: the ground based packing, and loading of the film from Goddard Space Flight Center to Cape Kennedy; the effects of the solar wind, humidity, and cosmic rays; the Van Allen Belt radiation exposure; various thermal effect; reentry and off-loading of the film during take off, and 8 day, 3 hour 15 minutes orbits. The total densitometric change caused by all of the above factors were examined. The results of these studies have implications for the utilization of IIaO spectroscopic film on the future shuttle and space lab missions. These responses to standard photonic energy sources will have immediate application for the uneven responses of the film photographing a star field in a terrestrial or extraterrestrial environment with associated digital imaging equipment

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures