An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation

In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements

Punitive Damages and the Processing of Tort Claims

Punitive damages are one of the most controversial aspects of tort litigation and have been the subject of various theoretical, empirical, and experimental studies. One criticism of punitive damages refers to the effect that they have on civil litigation processes. In particular, Polinsky (1997) argues that the uncertainty and unpredictability that punitive damage claims inject into a case may increase both the rate and amount of settlements, thus implying that punitive damages carry systemic consequences for the general processing of tort claims. This paper represents the first, empirical examination of this implication. With one of the largest and most comprehensive data sets of tort litigation (over 25,000 cases filed from 1994 through 1997 in several counties in Georgia), we examine the effect of the decision to seek punitive damages on several major decision points in the tort litigation process in a series of logit regression models. With extensive control variables for type of case, the presence or absence of caps on damages, and other potentially important variables, we find that seeking punitive damages has no statistically significant effect on most phases of the tort litigation process.Torts, Litigation, Punitive Damages, Settlement Rates

Using rapid scan EPR to improve the detection limit of quantitative EPR by more than one order of magnitude

X band rapid scan EPR was implemented on a commercially available Bruker ELEXSYS E580 spectrometer. Room temperature rapid scan and continuous wave EPR spectra were recorded for amorphous silicon powder samples. By comparing the resulting signal intensities the feasibility of performing quantitative rapid scan EPR is demonstrated. For different hydrogenated amorphous silicon samples, rapid scan EPR results in signal to noise improvements by factors between 10 and 50. Rapid scan EPR is thus capable of improving the detection limit of quantitative EPR by at least one order of magnitude. In addition, we provide a recipe for setting up and calibrating a conventional pulsed and continuous wave EPR spectrometer for rapid scan EP

Testing Two Assumptions About Federalism and Tort Reform

In, 1996 both the United States House of Representatives and Senate passed legislation that, if enacted, would preempt state tort laws in significant ways. Why would a Congress otherwise apparently committed to vesting states with greater policymaking autonomy call for federal control of tort law? Tort policymaking has traditionally been done at the state level. One assumption underlying this distribution of power is that states are better able than the national government to fashion tort rules appropriate for local conditions and circumstances. In other words, states are thought to have a special competence in crafting tort rules responsive to local needs. Some advocates for tort reform at the federal level maintain, however, that states are incapable or unlikely to develop tort rules – especially in the realm of product liability – consistent with national economic policy. Federal tort reform is needed, so the argument goes, to counter pressures that exist at the state level to use tort law as a vehicle for redistributing wealth from nonresident defendants to resident plaintiffs. Our paper examines these two, contradictory assumptions about state competence in the realm of tort policymaking. First we explore the proposition that states are incompetent to formulate sensible tort law policy, especially in the area of product liability. Second, we employ social scientific research methodology to question whether states have special competence to formulate tort policy

Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature

Numerical simulations of mixed states quantum computation

We describe quantum-octave package of functions useful for simulations of quantum algorithms and protocols. Presented package allows to perform simulations with mixed states. We present numerical implementation of important quantum mechanical operations - partial trace and partial transpose. Those operations are used as building blocks of algorithms for analysis of entanglement and quantum error correction codes. Simulation of Shor's algorithm is presented as an example of package capabilities.Comment: 6 pages, 4 figures, presented at Foundations of Quantum Information, 16th-19th April 2004, Camerino, Ital

Key barriers to community cohesion: views from residents of 20 London deprived neighbourhoods

The notion of community has been central to the political project of renewal of New Labour in the UK. The paper explores how the discourses of community are framed within New Labour and discusses these in the light of the results from research which focuses on how people within urban deprived areas construct their community. It draws upon the results of one part of a larger research project (the ‘Well London’ programme) which aimed to capture the views of residents from 20 disadvantaged neighbourhoods throughout London using an innovative qualitative method known as the ‘World Café’. Our results show the centrality of young people to the development of cohesive communities, the importance of building informal relationships between residents alongside encouraging greater participation to policy making, and the need to see these places as fragile and temporary locations but with considerable social strengths. Government policies are only partially addressing these issues. They pay greater attention to formally encouraging citizens to become more involved in policy making, largely ignore the contribution young people could make to the community cohesion agenda, and weakly define the shared norms and values that are crucial in building cohesive communities. Thus, the conclusion is that whilst an emphasis of the government on ‘community’ is to be welcome, more needs to be done in terms of considering the ‘voices’ of the community as well as enabling communities to determine and act upon their priorities

Longitudinal measurement of the developing grey matter in preterm subjects using multi-modal MRI.

Preterm birth is a major public health concern, with the severity and occurrence of adverse outcome increasing with earlier delivery. Being born preterm disrupts a time of rapid brain development: in addition to volumetric growth, the cortex folds, myelination is occurring and there are changes on the cellular level. These neurological events have been imaged non-invasively using diffusion-weighted (DW) MRI. In this population, there has been a focus on examining diffusion in the white matter, but the grey matter is also critically important for neurological health. We acquired multi-shell high-resolution diffusion data on 12 infants born at ≤28weeks of gestational age at two time-points: once when stable after birth, and again at term-equivalent age. We used the Neurite Orientation Dispersion and Density Imaging model (NODDI) (Zhang et al., 2012) to analyse the changes in the cerebral cortex and the thalamus, both grey matter regions. We showed region-dependent changes in NODDI parameters over the preterm period, highlighting underlying changes specific to the microstructure. This work is the first time that NODDI parameters have been evaluated in both the cortical and the thalamic grey matter as a function of age in preterm infants, offering a unique insight into neuro-development in this at-risk population

Isogeometric analysis for the multigroup neutron diffusion equation with applications in reactor physics

Isogeometric Analysis (IGA) has been applied to heterogeneous reactor physics problems using the multigroup neutron dif- fusion equation. IGA uses a computer-aided design (CAD) description of the geometry commonly built from Non-Uniform Rational B-Splines (NURBS), which can exactly represent complicated curved shapes such as circles and cylinders, common features in reactor design. This work has focused on comparing IGA to nite element analysis (FEA) for heterogeneous reactor physics problems, including the OECD/NEA C5G7 LWR benchmark. The exact geometry and increased basis function continuity contribute to the accuracy of IGA and an improvement over comparable FEA calculations has been observed