Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region

Maximising gain for minimal pain: Utilising natural game mechanics

This paper considers the application of natural games mechanics within higher education as a vehicle to encourage student engagement and achievement of desired learning outcomes. It concludes with desiderata of features for a learning environment when used for assessment and a reflection on the gap between current and aspired learning provision. The context considered is higher (tertiary) education, where the aims are both to improve students’ engagement with course content and also to bring about potential changes in the students’ learning behaviour. Whilst traditional approaches to teaching and learning may focus on dealing with large classes, where the onus is frequently on efficiency and on the effectiveness of feedback in improving understanding and future performance, intelligent systems can provide technology to enable alternative methods that can cope with large classes that preserve the cost-benefits. However, such intelligent systems may also offer improved learning outcomes via a personalised learning experience. This paper looks to exploit particular properties which emerge from the game playing process and seek to engage them in a wider educational context. In particular we aim to use game engagement and Flow as natural dynamics that can be exploited in the learning experience

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$

Constraining cometary ejection models from meteor storm observations

Modelling and observations of the Leonids have shown that maxima in the meteor storm activity can be identified as due to particles released from the comet during certain perihelion passages. If the particles originating from a certain perihelion passage can be identified, the next obvious question to ask is what information can be gained about the ejection process of particles from a cometary nucleus. We have developed a method to calculate the set of all possible dust trajectories that reach the Earth at some given time. The method involves numerical integration of a few dust particles only and is applied to the Leonid activity in the year 2000. We show that particles of different sizes entering the Earth's atmosphere at the same time were released from the comet at different heliocentric distances. Therefore one has to make assumptions about the activity of the comet with heliocentric distance in order to derive the cometary mass distribution from an observed meteor mass distribution. However, we outline how lower limits on the ejection velocity of the observed particles can be derived

American postmodernist fiction and the past by Theophilus Savvas

A review of American Postmodernist Fiction and the Past by Theophilus Savva

Boundary integral methods in high frequency scattering

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources

Do teachers matter? Measuring the variation in teacher effectiveness in England

Using a unique primary dataset for the UK, we estimate the effect of individual teachers on student outcomes, and the variability in teacher quality. This links over 7000 pupils to the individual teachers who taught them, in each of their compulsory subjects in the high-stakes exams at age 16. We use point-in-time fixed effects and prior attainment to control for pupil heterogeneity. We find considerable variability in teacher effectiveness, a little higher than the estimates found in the few US studies. We also corroborate recent findings that observed teachers’ characteristics explain very little of the differences in estimated effectiveness.education, test scores, teacher effectiveness