Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Regulating Multi-National Corporations Through State-Based Laws : Problems with Enforcing Human Rights Under The Alien Tort Statute

Under the Alien Tort Statute United States of America (“America”) Federal Courts have the jurisdiction to hear claims for civil wrongs, committed against non-American citizens, which were perpetrated outside America’s national borders. The operation of this law has confronted American Federal Courts with difficulties on how to manage conflicts between American executive foreign policy and judicial interpretations of international law. Courts began to pass judgment over conduct which was approved by foreign governments. Then in 2005 the American Supreme Court wound back the scope of the Alien Tort Statute. This article will review the problems with the expansion of the Alien Tort Statute and the reasons for its subsequent narrowing.

Teachers’ attitudes toward reporting child sexual abuse : problems with existing research leading to new scale development

This paper details a systematic literature review identifying problems in extant research relating to teachers’ attitudes towards reporting child sexual abuse, and offers a model for new attitude scale development and testing. Scale development comprised a five-phase process grounded in contemporary attitude theories including: a) developing the initial item pool; b) conducting a panel review; c) refining the scale via an expert focus group; d) building content validity through cognitive interviews; e) assessing internal consistency via field testing. The resulting 21-item scale displayed construct validity in preliminary testing. The scale may prove useful as a research tool, given the theoretical supposition that attitudes may be changed with time, context, experience, and education. Further investigation with a larger sample is warranted.

Some problems with a behavioristic account of early group pretense

In normal child development, both individual and group pretense first emerges at approximately two years of age. The metarepresentational account of pretense holds that children already have the concept PRETEND when they first engage in early group pretense. A behavioristic account suggests that early group pretense is analogous to early beliefs or desires and thus require no mental state concepts. I argue that a behavioral account does not explain the actual behavior observed in children and it cannot explain how children come to understand that a specific action is one of pretense versus one of belief. I conclude that a mentalistic explanation of pretense best explains the behavior under consideration.

Problems with a great idea : referral by prehospital emergency services to a community-based falls-prevention service

Background and aim Falls are the leading cause of injury in older adults. Identifying people at risk before they experience a serious fall requiring hospitalisation allows an opportunity to intervene earlier and potentially reduce further falls and subsequent healthcare costs. The purpose of this project was to develop a referral pathway to a community falls-prevention team for older people who had experienced a fall attended by a paramedic service and who were not transported to hospital. It was also hypothesised that providing intervention to this group of clients would reduce future falls-related ambulance call-outs, emergency department presentations and hospital admissions. Methods An education package, referral pathway and follow-up procedures were developed. Both services had regular meetings, and work shadowing with the paramedics was also trialled to encourage more referrals. A range of demographic and other outcome measures were collected to compare people referred through the paramedic pathway and through traditional pathways. Results Internal data from the Queensland Ambulance Service indicated that there were approximately six falls per week by community-dwelling older persons in the eligible service catchment area (south west Brisbane metropolitan area) who were attended to by Queensland Ambulance Service paramedics, but not transported to hospital during the 2-year study period (2008–2009). Of the potential 638 eligible patients, only 17 (2.6%) were referred for a falls assessment. Conclusion Although this pilot programme had support from all levels of management as well as from the service providers, it did not translate into actual referrals. Several explanations are provided for these preliminary findings.

Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Problems with the coronial determination of ‘suicide’

After over 100 years of constant dissatisfaction with the accuracy of suicide data, this paper suggests that the problem may actually lie with the category of suicide itself. In almost all previous research, ‘suicide’ is taken to be a self-evidently valid category of death, not an object of study in its own right. Instead, the focus in this paper is upon the presupposition that how a social fact like suicide is counted depends upon norms for its governmental regulation, leading to a reciprocal relationship between social norms and statistical norms. Since this relationship is centred almost entirely in the coroner’s office, this paper examines governmental, definitional and categorisational issues relating to how coroners reach findings of suicide. The intention of this paper is to contribute to international debates over how suicide can best be conceptualised and adjudged.

Some major problems with existing models and terminology associated with kimberlite pipes from a volcanological perspective, and some suggestions

Five significant problems hinder advances in understanding of the volcanology of kimberlites: (1) kimberlite geology is very model driven; (2) a highly genetic terminology drives deposit or facies interpretation; (3) the effects of alteration on preserved depositional textures have been grossly underestimated; (4) the level of understanding of the physical process significance of preserved textures is limited; and, (5) some inferred processes and deposits are not based on actual, modern volcanological processes. These issues need to be addressed in order to advance understanding of kimberlite volcanological pipe forming processes and deposits. The traditional, steep-sided southern African pipe model (Class I) consists of a steep tapering pipe with a deep root zone, a middle diatreme zone and an upper crater zone (if preserved). Each zone is thought to be dominated by distinctive facies, respectively: hypabyssal kimberlite (HK, descriptively called here massive coherent porphyritic kimberlite), tuffisitic kimberlite breccia (TKB, descriptively here called massive, poorly sorted lapilli tuff) and crater zone facies, which include variably bedded pyroclastic kimberlite and resedimented and reworked volcaniclastic kimberlite (RVK). Porphyritic coherent kimberlite may, however, also be emplaced at different levels in the pipe, as later stage intrusions, as well as dykes in the surrounding country rock. The relationship between HK and TKB is not always clear. Sub-terranean fluidisation as an emplacement process is a largely unsubstantiated hypothesis; modern in-vent volcanological processes should initially be considered to explain observed deposits. Crater zone volcaniclastic deposits can occur within the diatreme zone of some pipes, indicating that the pipe was largely empty at the end of the eruption, and subsequently began to fill-in largely through resedimentation and sourcing of pyroclastic deposits from nearby vents. Classes II and III Canadian kimberlite models have a more factual, descriptive basis, but are still inadequately documented given the recency of their discovery. The diversity amongst kimberlite bodies suggests that a three-model classification is an over-simplification. Every kimberlite is altered to varying degrees, which is an intrinsic consequence of the ultrabasic composition of kimberlite and the in-vent context; few preserve original textures. The effects of syn- to post-emplacement alteration on original textures have not been adequately considered to date, and should be back-stripped to identify original textural elements and configurations. Applying sedimentological textural configurations as a guide to emplacement processes would be useful. The traditional terminology has many connotations about spatial position in pipe and of process. Perhaps the traditional terminology can be retained in the industrial situation as a general lithofacies-mining terminological scheme because it is so entrenched. However, for research purposes a more descriptive lithofacies terminology should be adopted to facilitate detailed understanding of deposit characteristics, important variations in these, and the process origins. For example every deposit of TKB is different in componentry, texture, or depositional structure. However, because so many deposits in many different pipes are called TKB, there is an implication that they are all similar and that similar processes were involved, which is far from clear.

Problems with geoengineering schemes to combat climate change

The accelerated rate of increase in atmospheric CO2 concentration in recent years has revived the idea of stabilizing the global climate through geoengineering schemes. Majority of the proposed geoengineering schemes will attempt to reduce the amount of solar radiation absorbed by our planet. Climate modelling studies of these so called 'sunshade geoengineering schemes' show that global warming from increasing concentrations of CO2 can be mitigated by intentionally manipulating the amount of sunlight absorbed by the climate system. These studies also suggest that the residual changes could be large on regional scales, so that climate change may not be mitigated on a local basis. More recent modelling studies have shown that these schemes could lead to a slow-down in the global hydrological cycle. Other problems such as changes in the terrestrial carbon cycle and ocean acidification remain unsolved by sunshade geoengineering schemes. In this article, I review the proposed geoengineering schemes, results from climate models and discuss why geoengineering is not the best option to deal with climate change.

Aircraft pursuit-evasion problems with variable speeds

Aircraft pursuit-evasion encounters in a plane with variable speeds are analysed as a differential game. An engagement-dependent coordinate system confers open-loop optimality on the game. Each aircraft's optimal motion can be represented by extremel trajectory maps which are independent of role, adversary and capture radius. These maps are used in two different ways to construct the feedback solution. Some examples are given to illustrate these features. The paper draws on earlier results and surveys several existing papers on the subject.