Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp

Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This "FENE-PG" force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely-extensible bead-spring chains with hydrodynamic interactions. The closed set of ODE's governing the evolution of the second-moments of the configurational probability distribution in the approximate models are used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynamics simulations. In particular, predictions of coil-stretch hysteresis are in quantitative agreement with simulations' results. Additional simplifying diagonalization-of-normal-modes assumptions are found to lead to considerable savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200

Evidence from Rb–Sr mineral ages for multiple orogenic events in the Caledonides of Shetland, Scotland

Shetland occupies a unique central location within the North Atlantic Caledonides. Thirty-three new high-precision Rb–Sr mineral ages indicate a polyorogenic history. Ages of 723–702 Ma obtained from the vicinity of the Wester Keolka Shear Zone indicate a Neoproterozoic (Knoydartian) age and preclude its correlation with the Silurian Moine Thrust. Ordovician ages of c. 480–443 Ma obtained from the Yell Sound Group and the East Mainland Succession constrain deformation fabrics and metamorphic assemblages to have formed during Grampian accretionary orogenic events, broadly contemporaneously with orogenesis of the Dalradian Supergroup in Ireland and mainland Scotland. The relative paucity of Silurian ages is attributed to a likely location at a high structural level in the Scandian nappe pile relative to mainland Scotland. Ages of c. 416 and c. 411 Ma for the Uyea Shear Zone suggest a late orogenic evolution that has more in common with East Greenland and Norway than with northern mainland Scotland

Modeling the initiation of others into injection drug use, using data from 2,500 injectors surveyed in Scotland during 2008-2009

The prevalence of injection drug use has been of especial interest for assessment of the impact of blood-borne viruses. However, the incidence of injection drug use has been underresearched. Our 2-fold aim in this study was to estimate 1) how many other persons, per annum, an injection drug user (IDU) has the equivalent of full responsibility (EFR) for initiating into injection drug use and 2) the consequences for IDUs' replacement rate. EFR initiation rates are strongly associated with incarceration history, so that our analysis of IDUs' replacement rate must incorporate when, in their injecting career, IDUs were first incarcerated. To do so, we have first to estimate piecewise constant incarceration rates in conjunction with EFR initiation rates, which are then combined with rates of cessation from injecting to model IDUs' replacement rate over their injecting career, analogous to the reproduction number of an epidemic model. We apply our approach to Scotland's IDUs, using over 2,500 anonymous injector participants who were interviewed in Scotland's Needle Exchange Surveillance Initiative during 2008-2009. Our approach was made possible by the inclusion of key questions about initiations. Finally, we extend our model to include an immediate quit rate, as a reasoned compensation for higher-than-expected replacement rates, and we estimate how high initiates' quit rate should be for IDUs' replacement rate to be 1

Reactive self-heating model of aluminum spherical nanoparticles

Aluminum-oxygen reaction is important in many highly energetic, high pressure generating systems. Recent experiments with nanostructured thermites suggest that oxidation of aluminum nanoparticles occurs in a few microseconds. Such rapid reaction cannot be explained by a conventional diffusion-based mechanism. We present a rapid oxidation model of a spherical aluminum nanoparticle, using Cabrera-Mott moving boundary mechanism, and taking self-heating into account. In our model, electric potential solves the nonlinear Poisson equation. In contrast with the Coulomb potential, a "double-layer" type solution for the potential and self-heating leads to enhanced oxidation rates. At maximal reaction temperature of 2000 C, our model predicts overall oxidation time scale in microseconds range, in agreement with experimental evidence.Comment: submitte