The significance of work allocation in the professional apprenticeship of solicitors

It is a peculiarity of the solicitors’ profession that it has historically relied on methods of pre-qualification ‘training’ by way of apprenticeship and that an entirely respectable non-graduate route into the profession remains. In a political context, however, where the profession is called upon positively to demonstrate its standards of performance, the professional regulator seeks to attach a competence framework to the existing model; shifting the focus from how the trainee learns to what the trainee learns. This paper will explore the period of traineeship from the perspective of the trainees themselves, drawing on two small qualitative studies, focussing on the fundamental context factor of the allocation and structuring of their work. In the first study the context for this evaluation is the set of outcomes being tested by the professional regulator and in the second, the perceptions of qualified individuals looking back at their apprenticeship, The paper concludes that there remains work for the profession to do not only in fostering supportive and expansive apprenticeships, but in attending, however, supportive the surrounding environment, to the work being carried out by trainees and its relationship with the work carried out by newly qualified solicitors

Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio

Playing a quantum game with a corrupted source

The quantum advantage arising in a simplified multi-player quantum game, is found to be a disadvantage when the game's qubit-source is corrupted by a noisy "demon". Above a critical value of the corruption-rate, or noise-level, the coherent quantum effects impede the players to such an extent that the optimal choice of game changes from quantum to classical.Comment: This version will appear in PRA (Rapid Comm.

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

The Quark Propagator from the Dyson-Schwinger Equations: I. the Chiral Solution

Within the framework of the Dyson-Schwinger equations in the axial gauge, we study the effect that non-perturbative glue has on the quark propagator. We show that Ward-Takahashi identities, combined with the requirement of matching perturbative QCD at high momentum transfer, guarantee the multiplicative renormalisability of the answer. Technically, the matching with perturbation theory is accomplished by the introduction of a transverse part to the quark-gluon vertex. We show that this transverse vertex is crucial for chiral symmetry breaking, and that massless solutions exist below a critical value of the strong coupling constant. Using the gluon propagator that we previously calculated, we obtain small corrections to the quark propagator, which keeps a pole at the origin in the chiral phase.Comment: 21 pages, 6 figures; McGill/94-24, SHEP 93/94-26 We generalise our results by showing that they are not sensitive to the specific choice that we make for the transverse vertex. We illustrate that fact in two new figure

Comparative study of normal and branched alkane monolayer films adsorbed on a solid surface. II. Dynamics

doi:10.1063/1.2464092 (17 pages)The dynamics of monolayer films of the n-alkane tetracosane (n-C24H52) and the branched alkane squalane (C30H62) adsorbed on graphite have been studied by quasielastic and inelastic neutron scattering and molecular dynamics (MD) simulations. Both molecules have 24 carbon atoms along their carbon backbone, and squalane has an additional six methyl side groups symmetrically placed along its length. The authors' principal objective has been to determine the influence of the side groups on the dynamics of the squalane monolayer and thereby assess its potential as a nanoscale lubricant. To investigate the dynamics of these monolayers they used both the disk chopper spectrometer (DCS) and the high flux backscattering spectrometer (HFBS) at the National Institute of Standards and Technology. These instruments made it possible to study dynamical processes such as molecular diffusive motions and vibrations on very different time scales: 1-40--ps (DCS) and 0.1-4--ns (HFBS). The MD simulations were done on corresponding time scales and were used to interpret the neutron spectra. The authors found that the dynamics of the two monolayers are qualitatively similar on the respective time scales and that there are only small quantitative differences that can be understood in terms of the different masses and moments of inertia of the two molecules. In the course of this study, the authors developed a procedure to separate out the low-frequency vibrational modes in the spectra, thereby facilitating an analysis of the quasielastic scattering. They conclude that there are no major differences in the monolayer dynamics caused by intramolecular branching. It remains to be seen whether this similarity in monolayer dynamics also holds for the lubricating properties of these molecules in confined geometries.This work was supported by the U.S. National Science Foundation under Grant Nos. DMR-0109057 and DMR-0411748 and by the U.S. Department of Energy through Grant No. DE-FG02-01ER45912. The neutron scattering facilities in this work are supported in part by the National Science Foundation under Agreement No. DMR-0454672. One of the authors (A.D.E.) thanks the Oticon Foundation, Denmark for financial support

Towards T1-limited magnetic resonance imaging using Rabi beats

Two proof-of-principle experiments towards T1-limited magnetic resonance imaging with NV centers in diamond are demonstrated. First, a large number of Rabi oscillations is measured and it is demonstrated that the hyperfine interaction due to the NV's 14N can be extracted from the beating oscillations. Second, the Rabi beats under V-type microwave excitation of the three hyperfine manifolds is studied experimentally and described theoretically.Comment: 6 pages, 8 figure

Mining metrics for buried treasure

The same but different: That might describe two metrics. On the surface CLASSI may show two metrics are locally equivalent, but buried beneath one may be a wealth of further structure. This was beautifully described in a paper by M.A.H. MacCallum in 1998. Here I will illustrate the effect with two flat metrics -- one describing ordinary Minkowski spacetime and the other describing a three-parameter family of Gal'tsov-Letelier-Tod spacetimes. I will dig out the beautiful hidden classical singularity structure of the latter (a structure first noticed by Tod in 1994) and then show how quantum considerations can illuminate the riches. I will then discuss how quantum structure can help us understand classical singularities and metric parameters in a variety of exact solutions mined from the Exact Solutions book.Comment: 16 pages, no figures, minor grammatical changes, submitted to Proceedings of the Malcolm@60 Conference (London, July 2004

The templated growth of a chiral transition metal chalcogenide

We demonstrate that an intrinsically chiral, high Miller index surface of an achiral metal can be used to template the enantioselective growth of chiral transition metal chalcogenide films. Specifically, Cu(643)R can be used as a template for the enantioselective growth of a chiral copper telluride alloy surface. Beyond a critical alloy thickness the chiral influence of the Cu(643)R surface diminishes and an achiral surface forms. Our work demonstrates a new method of producing chiral transition metal chalcogenide surfaces, with potential applications in the study of structurally chiral topological insulators

Compaction of Rods: Relaxation and Ordering in Vibrated, Anisotropic Granular Material

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical vibrations evolve to a dense, highly ordered, nematic state in which the long particle axes align with the vertical tube walls. We find that the orientational ordering process is reflected in a characteristic, steep rise in the local packing fraction. At any given height inside the packing, the ordering is initiated at the container walls and proceeds inward. We explore the evolution of the local as well as the height-averaged packing fraction as a function of vibration parameters and compare our results to relaxation experiments conducted on spherically shaped granular materials.Comment: 9 pages incl. 7 figure