A numerical model of twin disc test arrangement for the evaluation of railway wheel wear prediction methods

Twin disc tests are commonly used to study wear in railway materials. In this work the implementation of a numerical model of the twin disc arrangement is given, which reproduces the distribution of tangential forces over the contact patch between the two discs. Wear is subsequently calculated by relating the forces and creepage between the two discs using three different wear functions found in the literature. The resulting wear rates are compared with experimental data for discs made of common railway wheel and rail steels. This allows a comparison and assessment of the validity of the different wear algorithms considered

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition

Evolution of InAs branches in InAs/GaAs nanowire heterostructures

Branched nanowireheterostructures of InAs∕GaAs were observed during Au-assisted growth of InAs on GaAsnanowires. The evolution of these branches has been determined through detailed electron microscopy characterization with the following sequence: (1) in the initial stage of InAsgrowth, the Au droplet is observed to slide down the side of the GaAsnanowire, (2) the downward movement of Aunanoparticle later terminates when the nanoparticle encounters InAsgrowing radially on the GaAsnanowire sidewalls, and (3) with further supply of In and As vapor reactants, the Aunanoparticles assist the formation of InAs branches with a well-defined orientation relationship with GaAs∕InAs core/shell stems. We anticipate that these observations advance the understanding of the kink formation in axial nanowireheterostructures.The Australian Research Council is acknowledged for the financial support of this project. One of the authors M.P. acknowledges the support of an International Postgraduate Research Scholarship

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

Comorbidity and Quality of Life in Adults with Hair Pulling Disorder

Hair pulling disorder (HPD; trichotillomania) is thought to be associated with significant psychiatric comorbidity and functional impairment. However, few methodologically rigorous studies of HPD have been conducted, rendering such conclusions tenuous. The following study examined comorbidity and psychosocial functioning in a well-characterized sample of adults with HPD (N=85) who met DSM-IV criteria, had at least moderate hair pulling severity, and participated in a clinical trial. Results revealed that 38.8% of individuals with HPD had another current psychiatric diagnosis and 78.8% had another lifetime (present and/or past) psychiatric diagnosis. Specifically, HPD showed substantial overlap with depressive, anxiety, addictive, and other body-focused repetitive behavior disorders. The relationships between certain comorbidity patterns, hair pulling severity, current mood and anxiety symptoms, and quality of life were also examined. Results showed that current depressive symptoms were the only predictor of quality of life deficits. Implications of these findings for the conceptualization and treatment of HPD are discussed