Efficient PML for the wave equation

In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, however, usually require wave equations stated in their standard second-order form to be reformulated as first-order systems, thereby introducing many additional unknowns. To circumvent this cumbersome and somewhat expensive step, we instead propose a simple PML formulation directly for the wave equation in its second-order form. Inside the absorbing layer, our formulation requires only two auxiliary variables in two space dimensions and four auxiliary variables in three space dimensions; hence it is cheap to implement. Since our formulation requires no higher derivatives, it is also easily coupled with standard finite difference or finite element methods. Strong stability is proved while numerical examples in two and three space dimensions illustrate the accuracy and long time stability of our PML formulation.Comment: 16 pages, 6 figure

WaND Briefing Note 28 Revised Options for UK Domestic Water Reduction - A Review

Demand pressure on UK water supplies is expected to increase in the next 20 years driven by increasing population, new housing development and reducing household size. Regionally and at town level migration will also affect demand particularly in the South-East which is forecast to have a larger than average growth in population and house building. The water demand moderating trends that are considered to have the greatest effect on UK consumption, in approximate order, are: 1. Metering 2. Low flush toilets 3. Normal showers 4. Efficient washing machines 5. Dishwashers 6. Cistern displacement devices (in existing homes with large cisterns) 7. Water efficient gardening measures can play an important role in reducing demand during critical drought period

The Options for UK Domestic Water Reduction: A Review

Demand pressure on UK water supplies is expected to increase in the next 20 years driven by increasing population, new housing development and reducing household size. Regionally and locally migration will also afect demand particularly in the South-East. The water reduction trends that will have the greatest reduction effect on UK consumption are: 1. For new homes; metering and new efficiencies in design and construction (e.g. low flush toilets, heating and plumbing efficiences) 2. For established housing; metering and modern washing machines

Adolescent Health Services: Missing Opportunities

Examines the status of adolescents' health and health services, including critical needs, promising models, and components for improving disease prevention and health promotion. Recommends better primary care, coordinated policy, and expanded coverage

Investigation in haemodynamic stability during intermittent haemodialysis in the critically ill

No abstract available

An investigation into the effects of commencing haemodialysis in the critically ill

<b>Introduction:</b> We have aimed to describe haemodynamic changes when haemodialysis is instituted in the critically ill. 3 hypotheses are tested: 1)The initial session is associated with cardiovascular instability, 2)The initial session is associated with more cardiovascular instability compared to subsequent sessions, and 3)Looking at unstable sessions alone, there will be a greater proportion of potentially harmful changes in the initial sessions compared to subsequent ones. <b>Methods:</b> Data was collected for 209 patients, identifying 1605 dialysis sessions. Analysis was performed on hourly records, classifying sessions as stable/unstable by a cutoff of >+/-20% change in baseline physiology (HR/MAP). Data from 3 hours prior, and 4 hours after dialysis was included, and average and minimum values derived. 3 time comparisons were made (pre-HD:during, during HD:post, pre-HD:post). Initial sessions were analysed separately from subsequent sessions to derive 2 groups. If a session was identified as being unstable, then the nature of instability was examined by recording whether changes crossed defined physiological ranges. The changes seen in unstable sessions could be described as to their effects: being harmful/potentially harmful, or beneficial/potentially beneficial. <b>Results:</b> Discarding incomplete data, 181 initial and 1382 subsequent sessions were analysed. A session was deemed to be stable if there was no significant change (>+/-20%) in the time-averaged or minimum MAP/HR across time comparisons. By this definition 85/181 initial sessions were unstable (47%, 95% CI SEM 39.8-54.2). Therefore Hypothesis 1 is accepted. This compares to 44% of subsequent sessions (95% CI 41.1-46.3). Comparing these proportions and their respective CI gives a 95% CI for the standard error of the difference of -4% to 10%. Therefore Hypothesis 2 is rejected. In initial sessions there were 92/1020 harmful changes. This gives a proportion of 9.0% (95% CI SEM 7.4-10.9). In the subsequent sessions there were 712/7248 harmful changes. This gives a proportion of 9.8% (95% CI SEM 9.1-10.5). Comparing the two unpaired proportions gives a difference of -0.08% with a 95% CI of the SE of the difference of -2.5 to +1.2. Hypothesis 3 is rejected. Fisher’s exact test gives a result of p=0.68, reinforcing the lack of significant variance. <b>Conclusions:</b> Our results reject the claims that using haemodialysis is an inherently unstable choice of therapy. Although proportionally more of the initial sessions are classed as unstable, the majority of MAP and HR changes are beneficial in nature