Generalised discrete torsion and mirror symmetry for G_2 manifolds

A generalisation of discrete torsion is introduced in which different discrete torsion phases are considered for the different fixed points or twist fields of a twisted sector. The constraints that arise from modular invariance are analysed carefully. As an application we show how all the different resolutions of the T^7/Z_2^3 orbifold of Joyce have an interpretation in terms of such generalised discrete torsion orbifolds. Furthermore, we show that these manifolds are pairwise identified under G_2 mirror symmetry. From a conformal field theory point of view, this mirror symmetry arises from an automorphism of the extended chiral algebra of the G_2 compactification.Comment: LaTeX, 25 pages, 1 figure; v2: one reference added and comment about higher loop modular invariance corrected, version to be publishe

The phase shift of an ultrasonic pulse at an oil layer and determination of film thickness

An ultrasonic pulse incident on a lubricating oil film in a machine element will be partially reflected and partially transmitted. The proportion of the wave amplitude reflected, termed the reflection coefficient, depends on the film thickness and the acoustic properties of the oil. When the appropriate ultrasonic frequency is used, the magnitude of the reflection coefficient can be used to determine the oil film thickness. However, the reflected wave has both a real component and an imaginary component, and both the amplitude and the phase are functions of the film thickness. The phase of the reflected wave will be shifted from that of the incident wave when it is reflected. In the present study, this phase shift is explored as the film changes and is evaluated as an alternative means to measure oil film thickness. A quas i-static theoretical model of the reflection response from an oil film has been, developed. This model relates the phase shift to the wave frequency and the film properties. Measurements of reflection coefficient from a static model oil film and also from a rotating journal bearing have been recorded. These have been used to determine the oil film thickness using both amplitude and phase shift methods. In both cases, the results agree closely with independent assessments of the oil film thickness. The model of ultrasonic reflection is further extended to incorporate mass and damping terms. Experiments show that both the mass and the internal damping of the oil films tested in this work have a negligible effect on ultrasonic reflection. A potentially v ery useful application for the simultaneous measurement of reflection coefficient amplitude and phase is that the data can be used to negate the need for a reference. The theoretical relationship between phase and amplitude is fitted to the data. An extrapolation is performed to determine the values of amplitude and phase for an infinitely thick layer. This is equivalent to the reference signal determined by measuring the reflection coefficient directly, but importantly does not require the materials to be separated. This provides a simple and effective means of continuously calibrating the film measurement approach

A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy

Starting from the superconformal algebras associated with $G_2$ manifolds, I extend the algebra to the manifolds with spin(7) holonomy. I show how the mirror symmetry in manifolds with spin(7) holonomy arises as the automorphism in the extended sperconformal algebra. The automorphism is realized as 14 kinds of T-dualities on the supersymmetric $T^4$ toroidal fibrations. One class of Joyce's orbifolds are pairwise identified under the symmetry.Comment: 12 pages, harvmac bi

On the geometry of closed G2-structure

We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kahler geometry. The result was generalized by R.L.Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main theorem is generalized to the assumption that the Weyl tensor is divergence-free, clarity improved, typos correcte

The application of ultrasonic NDT techniques in tribology

The use of ultrasonic reflection is emerging as a technique for studying tribological contacts. Ultrasonic waves can be transmitted non-destructively through machine components and their behaviour at an interface describes the characteristics of that contact. This paper is a review of the current state of understanding of the mechanisms of ultrasonic reflection at interfaces, and how this has been used to investigate the processes of dry rough surface contact and lubricated contact. The review extends to cover how ultrasound has been used to study the tribological function of certain engineering machine elements

Executive function in first-episode schizophrenia

BACKGROUND: We tested the hypothesis that schizophrenia is primarily a frontostriatal disorder by examining executive function in first-episode patients. Previous studies have shown either equal decrements in many cognitive domains or specific deficits in memory. Such studies have grouped test results or have used few executive measures, thus, possibly losing information. We, therefore, measured a range of executive ability with tests known to be sensitive to frontal lobe function. METHODS: Thirty first-episode schizophrenic patients and 30 normal volunteers, matched for age and NART IQ, were tested on computerized test of planning, spatial working memory and attentional set shifting from the Cambridge Automated Neuropsychological Test Battery. Computerized and traditional tests of memory were also administered for comparison. RESULTS: Patients were worse on all tests but the profile was non-uniform. A componential analysis indicated that the patients were characterized by a poor ability to think ahead and organize responses but an intact ability to switch attention and inhibit prepotent responses. Patients also demonstrated poor memory, especially for free recall of a story and associate learning of unrelated word pairs. CONCLUSIONS: In contradistinction to previous studies, schizophrenic patients do have profound executive impairments at the beginning of the illness. However, these concern planning and strategy use rather than attentional set shifting, which is generally unimpaired. Previous findings in more chronic patients, of severe attentional set shifting impairment, suggest that executive cognitive deficits are progressive during the course of schizophrenia. The finding of severe mnemonic impairment at first episode suggests that cognitive deficits are not restricted to one cognitive domain