Fast and accurate con-eigenvalue algorithm for optimal rational approximations

The need to compute small con-eigenvalues and the associated con-eigenvectors of positive-definite Cauchy matrices naturally arises when constructing rational approximations with a (near) optimally small $L^{\infty}$ error. Specifically, given a rational function with $n$ poles in the unit disk, a rational approximation with $m\ll n$ poles in the unit disk may be obtained from the $m$th con-eigenvector of an $n\times n$ Cauchy matrix, where the associated con-eigenvalue $\lambda_{m}>0$ gives the approximation error in the $L^{\infty}$ norm. Unfortunately, standard algorithms do not accurately compute small con-eigenvalues (and the associated con-eigenvectors) and, in particular, yield few or no correct digits for con-eigenvalues smaller than the machine roundoff. We develop a fast and accurate algorithm for computing con-eigenvalues and con-eigenvectors of positive-definite Cauchy matrices, yielding even the tiniest con-eigenvalues with high relative accuracy. The algorithm computes the $m$th con-eigenvalue in $\mathcal{O}(m^{2}n)$ operations and, since the con-eigenvalues of positive-definite Cauchy matrices decay exponentially fast, we obtain (near) optimal rational approximations in $\mathcal{O}(n(\log\delta^{-1})^{2})$ operations, where $\delta$ is the approximation error in the $L^{\infty}$ norm. We derive error bounds demonstrating high relative accuracy of the computed con-eigenvalues and the high accuracy of the unit con-eigenvectors. We also provide examples of using the algorithm to compute (near) optimal rational approximations of functions with singularities and sharp transitions, where approximation errors close to machine precision are obtained. Finally, we present numerical tests on random (complex-valued) Cauchy matrices to show that the algorithm computes all the con-eigenvalues and con-eigenvectors with nearly full precision

Investigation of the electroplastic effect using nanoindentation

A promising approach to deform metallic-intermetallic composite materials is the application of electric current pulses during the deformation process to achieve a lower yield strength and enhanced elongation to fracture. This is known as the electroplastic effect. In this work, a novel setup to study the electroplastic effect during nanoindentation on individual phases and well-defined interfaces was developed. Using a eutectic Al-Al2Cu alloy as a model material, electroplastic nanoindentation results were directly compared with macroscopic electroplastic compression tests. The results of the micro- and macroscopic investigations reveal current induced displacement shifts and stress drops, respectively, with the first displacement shift/stress drop being higher than the subsequent ones. A higher current intensity, higher loading rate and larger pulsing interval all cause increased displacement shifts. This observation, in conjunction with the fact that the first displacement shift is highest, strongly indicates that de-pinning of dislocations from obstacles dominates the mechanical response, rather than solely thermal effects

Dislocation-mediated plasticity in the Al2_{2}Cu {\theta}-phase

The deformation behaviour of the intermetallic Al$_{2}$Cu-phase was investigated using atomistic simulations and micropillar compression, where slip on the unexpected {211} and {022} slip planes was revealed. Additionally, all possible slip systems for the intermetallic phases were further evaluated and a preference for the activation of slip systems based on their effective interplanar distances as well as the effective Burgers vector is proposed. The effective interplanar distance corresponds to the manually determined interplanar distance, whereas the effective Burgers vector takes a potential dislocation dissociation into account. This new order is: {211}1/2, {022}1/2 and {022}, {110}, {310}, {022}, {110}1/2, {112} and {112}1/2 from high to low ratio of deff/beff. Also, data on the critical resolved shear stresses of several of these slip systems were measured.Comment: 27 pages, 17 figure

Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone

The original publication is available at www.springerlink.comNon peer reviewedPostprin

Mindfulness-based interventions in epilepsy: a systematic review

Mindfulness based interventions (MBIs) are increasingly used to help patients cope with physical and mental long-term conditions (LTCs). Epilepsy is associated with a range of mental and physical comorbidities that have a detrimental effect on quality of life (QOL), but it is not clear whether MBIs can help. We systematically reviewed the literature to determine the effectiveness of MBIs in people with epilepsy. Medline, Cochrane Central Register of Controlled Trials, EMBASE, CINAHL, Allied and Complimentary Medicine Database, and PsychInfo were searched in March 2016. These databases were searched using a combination of subject headings where available and keywords in the title and abstracts. We also searched the reference lists of related reviews. Study quality was assessed using the Cochrane Collaboration risk of bias tool. Three randomised controlled trials (RCTs) with a total of 231 participants were included. The interventions were tested in the USA (n = 171) and China (Hong Kong) (n = 60). Significant improvements were reported in depression symptoms, quality of life, anxiety, and depression knowledge and skills. Two of the included studies were assessed as being at unclear/high risk of bias - with randomisation and allocation procedures, as well as adverse events and reasons for drop-outs poorly reported. There was no reporting on intervention costs/benefits or how they affected health service utilisation. This systematic review found limited evidence for the effectiveness of MBIs in epilepsy, however preliminary evidence suggests it may lead to some improvement in anxiety, depression and quality of life. Further trials with larger sample sizes, active control groups and longer follow-ups are needed before the evidence for MBIs in epilepsy can be conclusively determined

Custom-designed orthopedic implants evaluated using finite element analysis of patient-specific computed tomography data: femoral-component case study

<p>Abstract</p> <p>Background</p> <p>Conventional knee and hip implant systems have been in use for many years with good success. However, the custom design of implant components based on patient-specific anatomy has been attempted to overcome existing shortcomings of current designs. The longevity of cementless implant components is highly dependent on the initial fit between the bone surface and the implant. The bone-implant interface design has historically been limited by the surgical tools and cutting guides available; and the cost of fabricating custom-designed implant components has been prohibitive.</p> <p>Methods</p> <p>This paper describes an approach where the custom design is based on a Computed Tomography scan of the patient's joint. The proposed design will customize both the articulating surface and the bone-implant interface to address the most common problems found with conventional knee-implant components. Finite Element Analysis is used to evaluate and compare the proposed design of a custom femoral component with a conventional design.</p> <p>Results</p> <p>The proposed design shows a more even stress distribution on the bone-implant interface surface, which will reduce the uneven bone remodeling that can lead to premature loosening.</p> <p>Conclusion</p> <p>The proposed custom femoral component design has the following advantages compared with a conventional femoral component. (i) Since the articulating surface closely mimics the shape of the distal femur, there is no need for resurfacing of the patella or gait change. (ii) Owing to the resulting stress distribution, bone remodeling is even and the risk of premature loosening might be reduced. (iii) Because the bone-implant interface can accommodate anatomical abnormalities at the distal femur, the need for surgical interventions and fitting of filler components is reduced. (iv) Given that the bone-implant interface is customized, about 40% less bone must be removed. The primary disadvantages are the time and cost required for the design and the possible need for a surgical robot to perform the bone resection. Some of these disadvantages may be eliminated by the use of rapid prototyping technologies, especially the use of Electron Beam Melting technology for quick and economical fabrication of custom implant components.</p