Finite element schemes for elliptic boundary value problems with rough coefficients

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We consider the task of computing reliable numerical approximations of the solutions of elliptic equations and systems where the coefficients vary discontinuously, rapidly, and by large orders of magnitude. Such problems, which occur in diffusion and in linear elastic deformation of composite materials, have solutions with low regularity with the result that reliable numerical approximations can be found only in approximating spaces, invariably with high dimension, that can accurately represent the large and rapid changes occurring in the solution. The use of the Galerkin approach with such high dimensional approximating spaces often leads to very large scale discrete problems which at best can only be solved using efficient solvers. However, even then, their scale is sometimes so large that the Galerkin approach becomes impractical and alternative methods of approximation must be sought. In this thesis we adopt two approaches. We propose a new asymptotic method of approximation for problems of diffusion in materials with periodic structure. This approach uses Fourier series expansions and enables one to perform all computations on a periodic cell; this overcomes the difficulty caused by the rapid variation of the coefficients. In the one dimensional case we have constructed problems with discontinuous coefficients and computed the analytical expressions for their solutions and the proposed asymptotic approximations. The rates at which the given asymptotic approximations converge, as the period of the material decreases, are obtained through extensive computational tests which show that these rates are fundamentally dependent on the level of regularity of the right hand sides of the equations. In the two dimensional case we show how one can use the Galerkin method to approximate the solutions of the problems associated with the periodic cell. We construct problems with discontinuous coefficients and perform extensive computational tests which show that the asymptotic properties of the approximations are identical to those observed in the one dimensional case. However, the computational results show that the application of the Galerkin method of approximation introduces a discretization error which can obscure the precise asymptotic rate of convergence for low regularity right hand sides. For problems of two dimensional linear elasticity we are forced to consider an alternative approach. We use domain decomposition techniques that interface the subdomains with conjugate gradient methods and obtain algorithms which can be efficiently implemented on computers with parallel architectures. We construct the balancing preconditioner, M,, and show that it has the optimal conditioning property k(Mh(^-1)Sh) = 0 is a constant which is independent of the magnitude of the material discontinuities, H is the maximum subdomain diameter, and h is the maximum finite element diameter. These properties of the preconditioning operator Mh allow one to use the computational power of a parallel computer to overcome the difficulties caused by the changing form of the solution of the problem. We have implemented this approach for a variety of problems of planar linear elasticity and, using different domain decompositions, approximating spaces, and materials, find that the algorithm is robust and scales with the dimension of the approximating space and the number of subdomains according to the condition number bound above and is unaffected by material discontinuities. In this we have proposed and implemented new inner product expressions which we use to modify the bilinear forms associated with problems over subdomains that have pure traction boundary conditions.This work is funded by the Engineering and Physical Sciences Research Council

TETRA Observation of Gamma Rays at Ground Level Associated with Nearby Thunderstorms

Terrestrial Gamma ray Flashes (TGFs) -- very short, intense bursts of electrons, positrons, and energetic photons originating from terrestrial thunderstorms -- have been detected with satellite instruments. TETRA, an array of NaI(Tl) scintillators at Louisiana State University, has now been used to detect similar bursts of 50 keV to over 2 MeV gamma rays at ground level. After 2.6 years of observation, twenty-four events with durations 0.02- 4.2 msec have been detected associated with nearby lightning, three of them coincident events observed by detectors separated by ~1000 m. Nine of the events occurred within 6 msec and 3 miles of negative polarity cloud-to-ground lightning strokes with measured currents in excess of 20 kA. The events reported here constitute the first catalog of TGFs observed at ground level in close proximity to the acceleration site.Comment: To be published in Journal of Geophysical Research: Space Phys. 118,

Chronic traumatic encephalopathy — confusion and controversies

The term chronic traumatic encephalopathy (CTE) has recently entered public consciousness via media reports and even a Hollywood movie. However, in contrast to general impressions, the incidence of CTE is unknown, the clinical diagnostic criteria have not been agreed upon and the current neuropathological characterization of CTE is acknowledged as preliminary. Additionally, few studies have compared the pathologies of CTE with those of other neurodegenerative disorders or of age-matched controls. Consequently, disagreement continues about the neuropathological aspects that make CTE unique. Furthermore, CTE is widely considered to be a consequence of exposure to repeated head blows, but evidence suggests that a single moderate or severe traumatic brain injury can also induce progressive neuropathological changes. These unresolved aspects of CTE underlie disparate claims about its clinical and pathological features, leading to confusion among the public and health-care professionals alike

Mechanical design engineering. NASA/university advanced design program: Lunar Bulk Material Transport Vehicle

The design of a Lunar Bulk Material Transport Vehicle (LBMTV) is discussed. Goals set in the project include a payload of 50 cubic feet of lunar soil with a lunar of approximately 800 moon-pounds, a speed of 15 mph, and the ability to handle a grade of 20 percent. Thermal control, an articulated steering mechanism, a dump mechanism, a self-righting mechanism, viable power sources, and a probable control panel are analyzed. The thermal control system involves the use of small strip heaters to heat the housing of electronic equipment in the absence of sufficient solar radiation and multi-layer insulation during periods of intense solar radiation. The entire system uses only 10 W and weighs about 60 pounds, or 10 moon-pounds. The steering mechanism is an articulated steering joint at the center of the vehicle. It utilizes two actuators and yields a turning radius of 10.3 feet. The dump mechanism rotates the bulk material container through an angle of 100 degree using one actuator. The self-righting mechanism consists of two four bar linkages, each of which is powered by the same size actuator as the other linkages. The LBMTV is powered by rechargeable batteries. A running time of at least two hours is attained under a worst case analysis. The weight of the batteries is 100 pounds. A control panel consisting of feedback and control instruments is described. The panel includes all critical information necessary to control the vehicle remotely. The LBMTV is capable of handling many types of cargo. It is able to interface with many types of removable bulk material containers. These containers are made to interface with the three-legged walker, SKITTER. The overall vehicle is about 15 feet in length and has a weight of about 1000 pounds, or 170 lunar pounds

Chronic traumatic encephalopathy is a common co-morbidity, but less frequent primary dementia in former soccer and rugby players

Chronic traumatic encephalopathy (CTE) is reported at high prevalence in selected autopsy case series of former contact sports athletes. Nevertheless, the contribution of CTE pathology to clinical presentation and its interaction with co-morbid neurodegenerative pathologies remain unclear. To address these issues, we performed comprehensive neuropathology assessments on the brains of former athletes with dementia and considered these findings together with detailed clinical histories to derive an integrated clinicopathological diagnosis for each case. Consecutive, autopsy-acquired brains from former soccer and rugby players with dementia were assessed for neurodegenerative pathologies using established and preliminary consensus protocols. Thereafter, next of kin interviews were conducted to obtain detailed accounts of the patient’s clinical presentation and course of disease to inform a final, integrated clinicopathological diagnosis. Neuropathologic change consistent with CTE (CTE-NC) was confirmed in five of seven former soccer and three of four former rugby players’ brains, invariably in combination with mixed, often multiple neurodegenerative pathologies. However, in just three cases was the integrated dementia diagnosis consistent with CTE, the remainder having alternate diagnoses, with the most frequent integrated diagnosis Alzheimer’s disease (AD) (four cases; one as mixed AD and vascular dementia). This consecutive autopsy series identifies neuropathologic change consistent with preliminary diagnostic criteria for CTE (CTE-NC) in a high proportion of former soccer and rugby players dying with dementia. However, in the majority, CTE-NC appears as a co-morbidity rather than the primary, dementia causing pathology. As such, we suggest that while CTE-NC might be common in former athletes with dementia, in many cases its clinical significance remains uncertain

Violence after discharge from forensic units in the safe pilot study : a prospective study with matched pair design

Objective: This paper reports on a prospective naturalistic study of violent recidivism after discharge from forensic mental health. Main aims were to find predictors of violence and to test the feasibility of a matched pair design for this purpose. Methods: Patients from the Safe pilot project (n=18) and a group of controls (n=18) were matched on 10 variables, such as diagnosis, seriousness of violence, setting after discharge, and risk management plans. All the Safe pilot patients had been through repeated measurement of dynamic risk factors of violence the year before discharge to develop efficient risk management plans for use after discharge. We wanted to test whether violent recidivism during follow-up would be lower and less serious in the Safe pilot group. Results: We found no significant between-group difference concerning number of patients with violent recidivism. However, the Safe pilot patients had significantly lower rates of violence and fewer severe violent episodes. In the control group, there was a significant association between a high number of risk management plans and high rates of violence. There was a statistical trend for the opposite association in the Safe pilot group. Conclusion: We discuss this in terms of a possible gap between the development and implementation of plans. Keywords: forensic mental health, discharge, violence, matched pairpublishedVersio

In ovo exposure to o,p -DDE affects sexual development but not sexual differentiation in Japanese medaka (Oryzias latipes).

Despite being banned in many countries, dichlorodiphenyltrichloroethane (DDT) and its metabolites dichlorodiphenyldichloroethylene (DDE) and dichlorodiphenyldichloroethane (DDD) continue to be found in fish tissues at concentrations of concern. Like o,p -DDT, o,p -DDE is estrogenic and is believed to exert its effects through binding to the estrogen receptor. The limited toxicologic data for o,p -DDE suggest that it decreases fecundity and fertility of fishes. We conducted an egg injection study using the d-rR strain of medaka and environmentally relevant concentrations of o,p -DDE to examine its effects on sexual differentiation and development. The gonads of exposed fish showed no evidence of sex reversal or intersex. However, other gonad abnormalities occurred in exposed individuals. Females exhibited few vitellogenic oocytes and increased atresia. Male testes appeared morphologically normal but were very small. Gonadosomatic index values for both sexes were lower for exposed fish. Our observations of abnormal female and very small male gonads after in ovo o,p -DDE exposure may be indicative of effects on early endocrine processes important for normal ovarian and testicular development

Selection of ground motion prediction equations for the global earthquake model

Ground motion prediction equations (GMPEs) relate ground motion intensity measures to variables describing earthquake source, path, and site effects. From many available GMPEs, we select those models recommended for use in seismic hazard assessments in the Global Earthquake Model. We present a GMPE selection procedure that evaluates multidimensional ground motion trends (e.g., with respect to magnitude, distance, and structural period), examines functional forms, and evaluates published quantitative tests of GMPE performance against independent data. Our recommendations include: four models, based principally on simulations, for stable continental regions; three empirical models for interface and in-slab subduction zone events; and three empirical models for active shallow crustal regions. To approximately incorporate epistemic uncertainties, the selection process accounts for alternate representations of key GMPE attributes, such as the rate of distance attenuation, which are defensible from available data. Recommended models for each domain will change over time as additional GMPEs are developed

Competition of lattice and basis for alignment of nematic liquid crystals

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts