Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

The Coefficient of Variance as an index of L2 lexical processing skill

The Coefficient of Variance (mean standard deviation/mean Response time) is a measure of response time variability that corrects for differences in mean Response time (RT) (Segalowitz & Segalowitz, 1993). A positive correlation between decreasing mean RTs and CVs (rCV-RT) has been proposed as an indicator of L2 automaticity and more generally as an index of processing efficiency. The current study evaluates this claim by examining lexical decision performance by individuals from three levels of English proficiency (Intermediate ESL, Advanced ESL and L1 controls) on stimuli from four levels of item familiarity, as defined by frequency of occurrence. A three-phase model of skill development defined by changing rCV-RT.values was tested. Results showed that RTs and CVs systematically decreased as a function of increasing proficiency and frequency levels, with the rCV-RT serving as a stable indicator of individual differences in lexical decision performance. The rCV-RT and automaticity/restructuring account is discussed in light of the findings. The CV is also evaluated as a more general quantitative index of processing efficiency in the L2.

On the validity of the shrinking core model in noncatalytic gas solid reaction

By using a matched asymptotic expansion technique, the shrinking core model (SCM) used in non-catalytic gas solid reactions with general kinetic expression is rigorously justified in this paper as a special case of the homogeneous model when the reaction rate is much faster than that of diffusion. The time-pendent velocity of the moving reacted-unreacted interface is found to be proportional to the gas flux at that interface for all geometries of solid particles, and the thickness order of the reaction zone and also the degree of chemical reaction at the interface is discussed in this paper.

Using the level set method to model endogenous lava dome growth

Modeling volcanic phenomena is complicated by free-surfaces often supporting large rheological gradients. Analytical solutions and analogue models provide explanations for fundamental characteristics of lava flows. But more sophisticated models are needed, incorporating improved physics and rheology to capture realistic events. To advance our understanding of the flow dynamics of highly viscous lava in Peléean lava dome formation, axi-symmetrical Finite Element Method (FEM) models of generic endogenous dome growth have been developed. We use a novel technique, the level-set method, which tracks a moving interface, leaving the mesh unaltered. The model equations are formulated in an Eulerian framework. In this paper we test the quality of this technique in our numerical scheme by considering existing analytical and experimental models of lava dome growth which assume a constant Newtonian viscosity. We then compare our model against analytical solutions for real lava domes extruded on Soufrière, St. Vincent, W.I. in 1979 and Mount St. Helens, USA in October 1980 using an effective viscosity. The level-set method is found to be computationally light and robust enough to model the free-surface of a growing lava dome. Also, by modeling the extruded lava with a constant pressure head this naturally results in a drop in extrusion rate with increasing dome height, which can explain lava dome growth observables more appropriately than when using a fixed extrusion rate. From the modeling point of view, the level-set method will ultimately provide an opportunity to capture more of the physics while benefiting from the numerical robustness of regular grids.

Combining GIS and Expert Opinion to Model Landscapes for a Smallholder Forest Extension Program in Leyte, the Philippines

A Geographic Information System (GIS) was used to model datasets of Leyte Island, the Philippines, to identify land which was suitable for a forest extension program on the island. The datasets were modelled to provide maps of the distance of land from cities and towns, land which was a suitable elevation and slope for smallholder forestry and land of various soil types. An expert group was used to assign numeric site suitabilities to the soil types and maps of site suitability were used to assist the selection of municipalities for the provision of extension assistance to smallholders. Modelling of the datasets was facilitated by recent developments of the ArcGIS® suite of computer programs and derivation of elevation and slope was assisted by the availability of digital elevation models (DEM) produced by the Shuttle Radar Topography (SRTM) mission. The usefulness of GIS software as a decision support tool for small-scale forestry extension programs is discussed.

Parliament House Competition Model, Canberra

View of model for competition entry.

An introduction to efficiency and productivity analysis

The second edition of An Introduction to Efficiency and Productivity Analysis is designed to be a general introduction for those who wish to study efficiency and productivity analysis. The book provides an accessible, well-written introduction to the four principal methods involved: econometric estimation of average response models; index numbers, data envelopment analysis (DEA); and stochastic frontier analysis (SFA). For each method, a detailed introduction to the basic concepts is presented, numerical examples are provided, and some of the more important extensions to the basic methods are discussed. Of special interest is the systematic use of detailed empirical applications using real-world data throughout the book. In recent years, there have been a number of excellent advance-level books published on performance measurement. This book, however, is the first systematic survey of performance measurement with the express purpose of introducing the field to a wide audience of students, researchers, and practitioners. Indeed, the 2nd Edition maintains its uniqueness: (1) It is a well-written introduction to the field. (2) It outlines, discusses and compares the four principal methods for efficiency and productivity analysis in a well-motivated presentation. (3) It provides detailed advice on computer programs that can be used to implement these performance measurement methods. The book contains computer instructions and output listings for the SHAZAM, LIMDEP, TFPIP, DEAP and FRONTIER computer programs. More extensive listings of data and computer instruction files are available on the book's website: (www.uq.edu.au/economics/cepa/crob2005).