Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

Energy storage apparatus

A high efficiency, flywheel type energy storage device which comprises an electronically commutated d.c. motor/generator unit having a massive flywheel rotor magnetically suspended around a ring shaped stator is presented. During periods of low energy demand, the storage devices were operated as a motor, and the flywheel motor was brought up to operating speed. Energy was drawn from the device functioning as a generator as the flywheel rotor rotated during high energy demand periods

Lensing Properties of Cored Galaxy Models

A method is developed to evaluate the magnifications of the images of galaxies with lensing potentials stratified on similar concentric ellipses. A simple contour integral is provided which enables the sums of the magnifications of even parity or odd parity or the central image to be easily calculated. The sums for pairs of images vary considerably with source position, while the signed sums can be remarkably uniform inside the tangential caustic in the absence of naked cusps. For a family of models in which the potential is a power-law of the elliptic radius, the number of visible images is found as a function of flattening, external shear and core radius. The magnification of the central image depends on the core radius and the slope of the potential. For typical source and lens redshifts, the missing central image leads to strong constraints; the mass distribution in the lensing galaxy must be nearly cusped, and the cusp must be isothermal or stronger. This is in accord with the cuspy cores seen in high resolution photometry of nearby, massive, early-type galaxies, which typically have the surface density falling like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy cores by themselves can provide an explanation of the missing central images. Dark matter at large radii may alter the slope of the projected density; provided the slope remains isothermal or steeper and the break radius remains small, then the central image remains unobservable. The sensitivity of the radio maps must be increased fifty-fold to find the central images in abundance.Comment: 42 pages, 11 figures, ApJ in pres

A New Superintegrable Hamiltonian

We identify a new superintegrable Hamiltonian in 3 degrees of freedom, obtained as a reduction of pure Keplerian motion in 6 dimensions. The new Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r potential with three barrier terms preventing the particle crossing the principal planes. In 3 degrees of freedom, there are 5 functionally independent integrals of motion, and all bound, classical trajectories are closed and strictly periodic. The generalisation of the Laplace-Runge-Lenz vector is identified and shown to provide functionally independent isolating integrals. They are quartic in the momenta and do not arise from separability of the Hamilton-Jacobi equation. A formulation of the system in action-angle variables is presented.Comment: 11 pages, 4 figures, submitted to The Journal of Mathematical Physic

Secondary prevention of stroke: Using the experiences of patients and carers to inform the development of an educational resource

Copyright @ The Author 2008. This article is available open access through the publisher’s website at the link below.Background. Patients who have had one stroke are at increased risk of another. Secondary prevention strategies that address medical risk factors and promote healthy lifestyles can reduce the risk. However, concordance with secondary prevention strategies is poor and there has been little research into patient and carer views. Objectives. To explore the experiences of patients and carers of receiving secondary prevention advice and use these to inform the development of an educational resource. Methods. A total of 38 participants (25 patients and 13 carers) took part in the study which used an action research approach. Focus groups and interviews were undertaken with patients and carers who had been discharged from hospital after stroke (between 3 and 24 months previously). Framework analysis was used to examine the data and elicit action points to develop an educational resource. Results. Participants’ main concern was their desire for early access to information. They commented on their priorities for what information or support they needed, the difficulty of absorbing complex information whilst still an in-patient and how health professionals’ use of language was often a barrier to understanding. They discussed the facilitators and barriers to making lifestyle changes. The educational resource was developed to include specific advice for medical and lifestyle risk factors and an individual action plan. Conclusion. An educational resource for secondary prevention of stroke was developed using a participatory methodology. Our findings suggest that this resource is best delivered in a one-to-one manner, but further work is needed to identify its potential utility.Peninsula Primary Care Research Networ

Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids

The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical Density Functional Theory (DFT). We show that the general LMF equation for the effective reference potential phi_R follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (Fundamental Measures) DFT for the non-uniform hard-sphere reference fluid we determine phi_R for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density 'gas' layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one- dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.Comment: 35 pages, 10 Fig

HLA-B27 Positivity: associated health implications

HLA-B27 positivity makes the onset of autoimmune diseases such as uveitis, ankylosing spondylitis and Crohn's disease more likely to occur. Ankylosing spondylitis and Crohn's disease are two types of HLA-B27 positive diseases that demonstrate a direct association with uveitis. Although the possession of HLA-B27 positivity is not mandatory for autoimmune diseases such as uveitis to occur, HLA-B27 positivity not only makes it more likely but may modify the clinical picture in which a patient presents. In relation to assessment and diagnosis it is imperative that the medical history of patients is thoroughly examined to ensure pathological sequelae are appropriately treated. Nurses play an important role in assessing patients that have uveitis and should suspect ankylosing spondylitis or Crohn's disease may be present

Mechanical capacitor

A new energy storage system (the mechanical capacitor), using a spokeless magnetically levitated composite ring rotor, is described and design formulas for sizing the components are presented. This new system is configured around a permanent magnet (flux biased) suspension which has active servo control in the radial direction and passive control in the axial direction. The storage ring is used as a moving rotor and electronic commutation of the stationary armature coils is proposed. There is no mechanical contact with the rotating spokeless ring; therefore, long life and near zero rundown losses are projected. A 7-kW h system is sized to demonstrate feasibility. A literature review of flywheel energy storage systems is also presented and general formulas are developed for comparing rotor geometries

Prediction of microgeometrical influences on micropitting fatigue damage on 32CrMoV13 steel

Dr Fabre's sabbatical period at the Cardiff School of Engineering allowed the research to be conducted. Thanks are due to the M2P department of Arts et Métiers ParisTech, to Arts et Métiers ParisTech—Aix en Provence, and to the MécaSurf laboratory for supporting the visit financially, and to Cardiff University for provision of research facilities. Dr Sharif's contribution to the research was supported financially by UK Engineering & Physical Sciences Research Council (EPSRC) with Grant no. EP/G06024X/1.Micropitting is a form of surface fatigue damage that occurs in the gear teeth. It is due to the effect of variation in the mechanical loading in the contact zone between the two teeth, induced especially by flank roughness. In this study, generic roughness profiles were built with geometrical parameters to simulate the contact between two rough surfaces. Using elastohydrodynamic lubrication code and Crossland’s fatigue criteria, the influence on fatigue lifetime was analysed for changes in each parameter. The relevant parameters were determined that influence(i) the conventional pitting,(ii) the extent to which the von Mises equivalent stress exceeds the material yield stress in the zone where micropitting occurs, and(iii) the fatigue lifetime for steel teeth. With nitriding benefits, the same trends were shown with weaker effects