Solitons and Vertex Operators in Twisted Affine Toda Field Theories

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields display interesting patterns in their masses and coupling and which have recently been shown to extend to the classical soliton solutions arising when the couplings are imaginary. Here these results are extended from the untwisted to the twisted algebras. The new soliton solutions and their masses are found by a folding procedure which can be applied to the affine Kac-Moody algebras themselves to provide new insights into their structures. The relevant foldings are related to inner automorphisms of the associated finite dimensional Lie group which are calculated explicitly and related to what is known as the twisted Coxeter element. The fact that the twisted affine Kac-Moody algebras possess vertex operator constructions emerges naturally and is relevant to the soliton solutions.Comment: 27 pages (harvmac) + 3 figures (LaTex) at the end of the file, Swansea SWAT/93-94/1

Perceived stress among dental students at the University of the Western Cape

Introduction: A high prevalence of stress among dental students has been reported. Aim: To determine perceived stress among dental students at the University of the Western Cape. Method: A self-administered questionnaire to students (n=411) was used to collect data. Variables measured included demographic characteristics of students and their perceived stress in the dental environment using the Dental Environment Stress (DES) survey and the Maslach Burnout Inventory (MBI). Results: The response rate was 78%. Respondents were in the 18 to 21 age category; mostly female (n=207); multilingual, with 63% having English as their home language. Huge problems identified from the DES were lack of time for relaxation, inadequate breaks during the day, fear of failing a year or module, work load, inconsistency between clinical supervisors and patients being late for appointments. The MBI found high EE (28.91), low DP (7.13) and high PA (30.06) scores. Fourth year students experienced the highest degree of stress on the DES and MBI. Conclusion: Stressors identified are consistent with international dental literature. Levels of stress increased over the academic years and peaked in the fourth year. Stressors experienced may impact student academic and future professional development, motivating a need for intervention at Faculty level.DHE

On the gravity-driven draining of a rivulet of a viscoplastic material down a slowly varying substrate

We use the lubrication approximation to investigate the steady locally unidirectional gravity-driven draining of a thin rivulet of viscoplastic material, modeled as a biviscosity fluid (or, as a special case, as a Bingham material), down a slowly varying substrate. In contrast to the earlier work on viscoplastic rivulets we consider small-scale flows, such as those found in many industrial coating and printing processes, in which surface-tension effects play a significant role. We interpret our results as describing a slowly varying rivulet draining in the azimuthal direction from the top to the bottom of a large horizontal circular cylinder. Provided that the yield stress is nonzero we find that the flow is always unyielded near the top of the cylinder (where the rivulet becomes infinitely wide in the transverse direction), and, except in the special case when the viscosity ratio is zero, near the bottom of the cylinder (where it becomes infinitely deep). For sufficiently small values of the prescribed volume flux the flow is unyielded everywhere, but for larger values of the flux the flow near the substrate in the center of the rivulet is yielded. We obtain numerically calculated values of the semiwidth of the rivulet and of the yielded region as well as of the maximum height of the rivulet and of the yielded region for a range of parameter values, and describe the asymptotic behavior of the solution in the limits of large and small yield stress, large and small flux, and small viscosity ratio. In the special case of a Bingham material the flow near the top of the cylinder consists of an infinitely wide rigid and stationary plug, while elsewhere it consists of two rigid and stationary 'levæ#169;es' at the edges of the rivulet and a central region in which the flow near the free surface is a 'pseudoplug' whose velocity does not vary normally to the substrate, separated from the 'fully plastic' flow near the substrate by a 'pseudoyield surface.' ¦#169;2002 American Institute of Physics

Thin-film flow of a viscoplastic material round a large horizontal stationary or rotating cylinder

We consider the steady two-dimensional thin-film flow of a viscoplastic material, modelled as a biviscosity fluid with a yield stress, round the outside of a large horizontal stationary or rotating cylinder. In both cases we determine the leading- order solution both when the ratio of the viscosities in the 'yielded' and 'unyielded' regions is of order unity and when this ratio approaches zero in the appropriate distinguished limit. When the viscosity ratio is of order unity the flow consists, in general, of a region of yielded fluid adjacent to the cylinder and a region of unyielded fluid adjacent to the free surface, separated by the yield surface. In the distinguished limit the flow consists, in general, of a region of yielded fluid adjacent to the cylinder whose stress is significantly above the yield stress and a pseudo-plug region adjacent to the free surface, in which the leading-order azimuthal component of velocity varies azimuthally but not radially, separated by the pseudo-yield surface; the pseudo-plug is itself, in general, divided by the yield surface into a region of yielded fluid whose stress is only just above the yield stress and a region of unyielded fluid adjacent to the free surface whose stress is significantly below the yield stress. The solution for a stationary cylinder represents a curtain of fluid with prescribed volume flux falling onto the top of and off at the bottom of the cylinder. If the flux is sufficiently small then the flow is unyielded everywhere, but when it exceeds a critical value there is a yielded region. In the distinguished limit the yielded region always extends all the way round the cylinder, but the unyielded region does so only when the flux is sufficiently small. For a rotating cylinder a film with finite thickness everywhere is possible only when the flux is sufficiently small. Depending on the value of the flux and the speed of rotation the flow may be unyielded everywhere, have a yielded region on the right of the cylinder only, or have yielded regions on both the right and left of the cylinder. At the critical maximum flux the maximum supportable weight of fluid on the cylinder is attained and the pseudo-yield, yield and free surfaces all have a corner. In the distinguished limit there are rigid plugs (absent in the stationary case) near the top and bottom of the cylinder

PT Invariant Complex E (8) Root Spaces

We provide a construction procedure for complex root spaces invariant under antilinear transformations, which may be applied to any Coxeter group. The procedure is based on the factorisation of a chosen element of the Coxeter group into two factors. Each of the factors constitutes an involution and may therefore be deformed in an antilinear fashion. Having the importance of the E(8)-Coxeter group in mind, such as underlying a particular perturbation of the Ising model and the fact that for it no solution could be found previously, we exemplify the procedure for this particular case. As a concrete application of this construction we propose new generalisations of Calogero-Moser Sutherland models and affine Toda field theories based on the invariant complex root spaces and deformed complex simple roots, respectively

Single and vertically coupled type II quantum dots in a perpendicular magnetic field: exciton groundstate properties

The properties of an exciton in a type II quantum dot are studied under the influence of a perpendicular applied magnetic field. The dot is modelled by a quantum disk with radius $R$, thickness $d$ and the electron is confined in the disk, whereas the hole is located in the barrier. The exciton energy and wavefunctions are calculated using a Hartree-Fock mesh method. We distinguish two different regimes, namely $d<<2R$ (the hole is located at the radial boundary of the disk) and $d>>2R$ (the hole is located above and below the disk), for which angular momentum $(l)$ transitions are predicted with increasing magnetic field. We also considered a system of two vertically coupled dots where now an extra parameter is introduced, namely the interdot distance $d_{z}$. For each $l_{h}$ and for a sufficient large magnetic field, the ground state becomes spontaneous symmetry broken in which the electron and the hole move towards one of the dots. This transition is induced by the Coulomb interaction and leads to a magnetic field induced dipole moment. No such symmetry broken ground states are found for a single dot (and for three vertically coupled symmetric quantum disks). For a system of two vertically coupled truncated cones, which is asymmetric from the start, we still find angular momentum transitions. For a symmetric system of three vertically coupled quantum disks, the system resembles for small $d_{z}$ the pillar-like regime of a single dot, where the hole tends to stay at the radial boundary, which induces angular momentum transitions with increasing magnetic field. For larger $d_{z}$ the hole can sit between the disks and the $l_{h}=0$ state remains the groundstate for the whole $B$-region.Comment: 11 pages, 16 figure

Geology of the Llanidloes district : British Geological Survey Sheet 164

This Sheet Explanation provides a summary of the geology of the district covered by Geological 1:50 000 Series Map Sheet 164 (Llanidloes), published in 2010 as a Bedrock and Superficial Deposits edition. The district mostly lies within the county of Powys, but includes small parts of Ceredigion in the extreme west and south-west. Much of the western part of the district is occupied by the deeply dissected uplands of the Cambrian Mountains, a designated Area of Outstanding Natural Beauty. In this area the land rises to 740 m on the flanks of Plynlimon (Pumlumon Fawr), the highest summit in the range. It falls away towards the eastern part of the district into rolling countryside that includes the important catchment of the River Severn (Afon Hafren) and its tributaries, the largest of which are the rivers Carno, Trannon, Cerist, Clywedog and Dulas. A major reservoir (Llyn Clywedog) occupies the upper reaches of the Clywedog valley, its purpose being to regulate river discharge and groundwater levels within the catchment. The south-western part of the district is drained by the River Wye (Afon Gwy) and its tributaries, that flow south-eastwards via Llangurig. The sources of both the Severn and Wye are situated on the eastern flanks of Plynlimon within the western part of the district. The town of Llanidloes is the main centre of population, with smaller settlements at Llangurig, Carno, Trefeglwys, Caersws and Staylittle; the Newtown conurbation impinges on the eastern part of the district. Much of the district is given over to beef and dairy farming, although sheep are reared in the remote upland areas in the west and extensive forestry plantations have been developed in places. The Ordovician and Silurian rocks of the district have been exploited locally, in the past, as a source of building material and, recently, commercial quantities of sandstone aggregate have been excavated at Penstrowed Quarry [SO 0680 9100]. The district includes part of the Central Wales Mining Field from which substantial volumes of lead and zinc ore were extracted during the 19th and early 20th centuries. A number of former mine sites are still visible, notably along the Van, Nant-y-ricket, Dylife, Dyfngwm and Llanerchyraur lodes (Jones, 1922[1]; IGS, 1974), and the historic Bryntail Mine, below the Clywedog Dam has been restored as a site of industrial archaeological interest. The district is underlain by a succession of Late Ordovician (Ashgill) to Silurian sedimentary rocks, over 5 km thick, deposited between 450 and 420 million years ago in the Early Palaeozoic Welsh Basin (Figure P930911). The basin developed on a fragment of the ancient supercontinent of Gondwana, known as Eastern Avalonia (e.g. Pickering et al., 1988[2]), that drifted northwards to collide with the continents of Baltica and Laurentia during the Late Ordovician and Silurian (Soper and Hutton, 1984[3]; Soper and Woodcock, 1990[4]; Woodcock and Strachan, 2000[5]). To the east and the south of the basin lay the Midland Platform, a relatively stable shallow marine shelf that was subject to periodic emergence. The basinal sediments are predominantly deep marine turbiditic facies that were introduced into the district by density currents from southerly, south-easterly and north-westerly quadrants. Coeval shallower-water ‘shelfal’ sediments were deposited north and east of the district, and locally impinge on its northern margins. Thickness variations within the major sedimentary units suggest that, at times, syndepositional fault movements were an important control on their distribution. During late Silurian (Ludlow) times, shallowing of the basin occurred, and sandstones, variably interpreted as a turbiditic (Cave and Hains, 2001[6]) or storm-generated facies (Tyler and Woodcock, 1987[7]), were laid down over the eastern part of the district and adjacent areas. The shallowing was a result of tectonic reconfiguration of the basin, a precursor to the late Caledonian (Acadian) Orogeny that affected the region during the late Early Devonian, around 400 million years ag

Quantifying distortions in two-photon remote focussing microscope images using a volumetric calibration specimen

This Document is Protected by copyright and was first published by Frontiers. All rights reserved. it is reproduced with permission.Remote focussing microscopy allows sharp, in-focus images to be acquired at high speed from outside of the focal plane of an objective lens without any agitation of the specimen. However, without careful optical alignment, the advantages of remote focussing microscopy could be compromised by the introduction of depth-dependent scaling artifacts. To achieve an ideal alignment in a point-scanning remote focussing microscope, the lateral (XY) scan mirror pair must be imaged onto the back focal plane of both the reference and imaging objectives, in a telecentric arrangement. However, for many commercial objective lenses, it can be difficult to accurately locate the position of the back focal plane. This paper investigates the impact of this limitation on the fidelity of three-dimensional data sets of living cardiac tissue, specifically the introduction of distortions. These distortions limit the accuracy of sarcomere measurements taken directly from raw volumetric data. The origin of the distortion is first identified through simulation of a remote focussing microscope. Using a novel three-dimensional calibration specimen it was then possible to quantify experimentally the size of the distortion as a function of objective misalignment. Finally, by first approximating and then compensating the distortion in imaging data from whole heart rodent studies, the variance of sarcomere length (SL) measurements was reduced by almost 50%.Medical Research Council (MRC)Engineering and Physical Sciences Research Council (EPSRC)Biotechnology and Biological Sciences Research Council (BBSRC)British Heart Foundation Centre of Research Excellence, Oxfor

The Anderson-Mott Transition as a Random-Field Problem

The Anderson-Mott transition of disordered interacting electrons is shown to share many physical and technical features with classical random-field systems. A renormalization group study of an order parameter field theory for the Anderson-Mott transition shows that random-field terms appear at one-loop order. They lead to an upper critical dimension $d_{c}^{+}=6$ for this model. For $d>6$ the critical behavior is mean-field like. For $d<6$ an $\epsilon$-expansion yields exponents that coincide with those for the random-field Ising model. Implications of these results are discussed.Comment: 8pp, REVTeX, db/94/