Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR

Irreducible triangulations of surfaces with boundary

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary

A topological classification of convex bodies

The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity-preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also generalizes the known classification scheme in [36]. Our expansion algorithm is essentially the dual procedure to the algorithm presented by Edelsbrunner et al. in [21], producing a hierarchy of increasingly coarse Morse-Smale complexes. We point out applications to pebble shapes.Comment: 25 pages, 10 figure

Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor improvements. 44 pages, 14 figure

Advertising media strategies in the film industry

The primary aim of this article is to estimate the multiple determinants of film advertising expenditures in four important media, namely television, press, outdoor and radio, in the UK. First, television advertising, the leading film advertising medium, is examined as part of a system of equations, capturing the interdependences between advertising, the number of screens on which films are initially shown and box office revenues. Then a reduced form model is put forward to reveal the determinants of film advertising in the four media. While major distribution companies have different preferences for the use of the alternative advertising media, results highlight the importance of quality signals, such as critical reviews, in determining advertising expenditures in the film industry. Moreover, advertising expenditures can themselves be considered to offer potential cinema goers signals of film quality

Cuinse2 Homojunction Diode Fabricated by Phosphorus OP9

Homojunction diodes were fabricated by doping of phosphorus to n-type Cu-In-Se thin films. The junction prepared by P implantation at the energy of 50 keV with the dose of 1 x 10(15) ions/cm 2 showed a rectification ratio of more than 100. Conduction in Cu-In-Se thin films, whose crystal structure is of the chalcopyrite type, changes from n- to p-type in such a way that group V elements (N, P, Sb, or Bi) substitute for Se in the film

Cuinse2 Homojunction Diode Fabricated by Phosphorus OP9

Homojunction diodes were fabricated by doping of phosphorus to n-type Cu-In-Se thin films. The junction prepared by P implantation at the energy of 50 keV with the dose of 1 x 10(15) ions/cm 2 showed a rectification ratio of more than 100. Conduction in Cu-In-Se thin films, whose crystal structure is of the chalcopyrite type, changes from n- to p-type in such a way that group V elements (N, P, Sb, or Bi) substitute for Se in the film

Reconfiguring triangulations with edge flips and point moves

Abstract. We examine reconfigurations between triangulations and neartriangulations of point sets, and give new bounds on the number of point moves and edge flips sufficient for any reconfiguration. We show that with O(n log n) edge flips and point moves, we can transform any geometric near-triangulation on n points to any other geometric near-triangulation on n possibly different points. This improves the previously known bound of O(n 2) edge flips and point moves.