The distribution of the ratio of consecutive level spacings in random matrix ensembles

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.Comment: 5 pages, 4 figure

Pricing and hedging game options in currency models with proportional transaction costs

The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise strategies are presented, together with numerical examples, as well as probabilistic dual representations for the bid and ask price of a game option

Scattering by a toroidal coil

In this paper we consider the Schr\"odinger operator in ${\mathbb R}^3$ with a long-range magnetic potential associated to a magnetic field supported inside a torus ${\mathbb{T}}$. Using the scheme of smooth perturbations we construct stationary modified wave operators and the corresponding scattering matrix $S(\lambda)$. We prove that the essential spectrum of $S(\lambda)$ is an interval of the unit circle depending only on the magnetic flux $\phi$ across the section of $\mathbb{T}$. Additionally we show that, in contrast to the Aharonov-Bohm potential in ${\mathbb{R}}^2$, the total scattering cross-section is always finite. We also conjecture that the case treated here is a typical example in dimension 3.Comment: LaTeX2e 17 pages, 1 figur

Large scale numerical simulations of "ultrametric" long-range depinning

The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for a drastic reduction of the numerical complexity of the problem. Based on large scale simulations, two to three orders of magnitude larger than previously considered, we obtain a very precise determination of critical exponents which are shown to be indistinguishable from their Euclidean metric counterparts. Moreover the scaling functions are shown to be unchanged. The choice of an ultrametric distance thus does not affect the universality class of the depinning transition and opens the way to an analytic real space renormalization group approach.Comment: submitted to Phys. Rev.

Generalized solvent boundary potential for computer simulations

Copyright 2001 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at http://dx.doi.org/10.1063/1.1336570.A general approach has been developed to allow accurate simulations of a small region part of a large macromolecular system while incorporating the influence of the remaining distant atoms with an effective boundary potential. The method is called the Generalized Solvent Boundary Potential (GSBP). By representing the surrounding solvent as a continuum dielectric, both the solvent-shielded static field from the distant atoms of the macromolecule and the reaction field from the dielectricsolvent acting on the atoms in the region of interest are included. The static field is calculated once, using the finite-difference Poisson–Boltzmann (PB) equation, and the result is stored on a discrete grid for efficient simulations. The solventreaction field is developed using a basis-set expansion whose coefficients correspond to generalized electrostatic multipoles. A matrix representing the reaction field Green’s function between those generalized multipoles is calculated only once using the PB equation and stored for efficient simulations. In the present work, the formalism is applied to both spherical and orthorhombic simulation regions for which orthonormal basis-sets exist based on spherical harmonics or cartesian Legendre polynomials. The GSBP method is also tested and illustrated with simple model systems and two detailed atomic systems: the active site region of aspartyl-tRNA synthetase (spherical region) and the interior of the KcsA potassium channel (orthorhombic region). Comparison with numerical finite-difference PB calculations shows that GSBP can accurately describe all long-range electrostatic interactions and remain computationally inexpensive

Internal states of model isotropic granular packings. III. Elastic properties

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P, which determines the stiffness of contacts by Hertz's law, elastic moduli are chiefly sensitive to the coordination number, the possible values of which are not necessarily correlated with the density. Comparisons of numerical and experimental results for glass beads in the 10kPa-10MPa range reveal similar differences between dry samples compacted by vibrations and lubricated packings. The greater stiffness of the latter, in spite of their lower density, can hence be attributed to a larger coordination number. Voigt and Reuss bounds bracket bulk modulus B accurately, but simple estimation schemes fail for shear modulus G, especially in poorly coordinated configurations under low P. Tenuous, fragile networks respond differently to changes in load direction, as compared to load intensity. The shear modulus, in poorly coordinated packings, tends to vary proportionally to the degree of force indeterminacy per unit volume. The elastic range extends to small strain intervals, in agreement with experimental observations. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page

Material-independent crack arrest statistics: Application to indentation experiments

An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics can be described by a universal (i.e. material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters, namely, an asymptotic crack length (or macroscopic toughness) value and a power law size dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales

Design aspects of a hospital playroom to aid the well-being of hospitalised oncology children - a case study

Published ArticleThe aim of this research was to identify the design aspects necessary to create an aesthetically appealing playroom environment to aid the well-being of hospitalised oncology children at a public hospital in Bloemfontein, South Africa. The methodology design is overall qualitative within the interpretivist paradigm with a triangulation methodology design with explanatory components. These components consisted of a literature review which was further explored by means of a qualitative questionnaire. The playroom was created as part of a community project according to the literature review and questionnaire after which semi-structured individual interviews were conducted with the children themselves

Towards a guided atom interferometer based on a superconducting atom chip

We evaluate the realization of a novel geometry of a guided atom interferometer based on a high temperature superconducting microstructure. The interferometer type structure is obtained with a guiding potential realized by two current carrying superconducting wires in combination with a closed superconducting loop sustaining a persistent current. We present the layout and realization of our superconducting atom chip. By employing simulations we discuss the critical parameters of the interferometer guide in particular near the splitting regions of the matter waves. Based on measurements of the relevant chip properties we discuss the application of a compact and reliable on-chip atom interferometer.Comment: 14 pages, 7 figures, accepted for New Journal of Physic