Global existence of near-affine solutions to the compressible Euler equations

We establish global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into vacuum. Vacuum states can occur with either smooth or singular sound speed, the latter corresponding to the so-called physical vacuum singularity when the enthalpy vanishes on the vacuum wave front like the distance function. In this instance, the Euler equations lose hyperbolicity and form a degenerate system of conservation laws, for which a local existence theory has only recently been developed. Sideris found a class of expanding finite degree-of-freedom global-in-time affine solutions, obtained by solving nonlinear ODEs. In three space dimensions, the stability of these affine solutions, and hence global existence of solutions, was established by Had\v{z}i\'{c} \& Jang with the pressure-density relation $p = \rho^\gamma$ with the constraint that $1< \gamma\le {\frac{5}{3}}$. They asked if a different approach could go beyond the $\gamma > {\frac{5}{3}}$ threshold. We provide an affirmative answer to their question, and prove stability of affine flows and global existence for all $\gamma >1$, thus also establishing global existence for the shallow water equations when $\gamma=2$.Comment: 51 pages, details added to Section 4.7, to appear in Arch. Rational Mech. Ana

What did the Romans ever do for us? ‘Next generation’ networks and hybrid learning resources

Networked learning is fundamentally concerned with the use of information and communication technologies (ICT) to link people to people and resources, to support the process of learning. This paper explores some current and forthcoming changes in ICT and some potential implications of these developments for networked learning. Whilst we aim to avoid taking a technologically determinist stance, we explore the potential for future practice and how some educational and pedagogic practices are evolving to exploit and shape the digital environment. We argue that we can change both the ways in which connections between people (learners and other learners; learners and tutors) are made and the nature of the resources that learning communities (particularly distributed communities) can engage with. In doing this we draw on two strands of work. Firstly, we draw on the ‘IBZL Education’ a UK Open University initiative to develop new scholarship in the context of STEM (Science, Technology, Engineering and Mathematics) through which educators are encouraged to think about technological change in the next five to ten years and ways in which we can intervene and shape these developments. We use problem-based learning as an example of a learning experience that can be difficult to implement in a networked learning environment. IBZL identified two broad strands of significant technological development. 'Superfast' broadband networks that are capable of supporting novel applications are being rolled in the UK (and elsewhere). Also, boundaries between the real and virtual worlds are becoming blurred as in the ‘internet of things’ where, for example, RFID tags enable information about the real world to be brought into the virtual one. We use the term ‘artefact’ to describe designed components, whether entirely digital, such as a computer forum, or material, such as a tablet PC. Networked ‘hybrid’ technologies of virtual and material components have may great potential for use in education. Secondly, we illustrate how these changes may be beginning to happen in distance education using the example of TU100 My Digital Life, a new introductory Open University. . TU100 Students use an electronics board in their own homes to work on a programming problem in collaboration other students through a tutor-led tutorial in a web conferencing system. We also note some of the evident complexity that establishing such resources as part of wider infrastructures of networked learning would be likely to involve

Affine motion of 2d incompressible fluids surrounded by vacuum and flows in SL(2,R){\rm SL}(2,{\mathbb R})

The affine motion of two-dimensional (2d) incompressible fluids surrounded by vacuum can be reduced to a completely integrable and globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in ${\rm SL}(2,{\mathbb R})$. In the case of perfect fluids, the motion is given by geodesic flow in ${\rm SL}(2,{\mathbb R})$ with the Euclidean metric, while for magnetically conducting fluids (MHD), the motion is governed by a harmonic oscillator in ${\rm SL}(2,{\mathbb R})$. A complete classification of the dynamics is given including rigid motions, rotating eddies with stable and unstable manifolds, and solutions with vanishing pressure. For perfect fluids, the displacement generically becomes unbounded, as $t\to\pm\infty$. For MHD, solutions are bounded and generically quasi-periodic and recurrent.Comment: 60 pages, 7 figure

CFRP truss for the CCAT 25 m diameter submillimeter-wave telescope

CCAT will be a 25 m diameter submillimeter-wave telescope that will operate inside a dome located on Cerro Chajnantor in the Atacama Desert. The telescope must have high aperture efficiency at a wavelength of 350 microns and good performance out to a wavelength of 200 microns. A conceptual design for a carbon fiber reinforced plastic (CFRP) truss and primary reflector support truss has been developed. This design yields a telescope with a net �½ wave front error of <10 microns using a lookup table to adjust the segment actuators to compensate for gravitational deflections. Minor corrections may be required to compensate for the expected 20 C temperature excursions. These can be handled using a coarse lookup table

An investigation into the effects of gender, prior academic achievement, place of residence, age and attendance on first year undergraduate attainment

The number of people engaging in higher education (HE) has increased considerably over the past decade. However, there is a need to achieve a balance between increasing access and bearing down on rates of non-completion. It has been argued that poor attainment and failure within the first year are significant contributors to the overall statistics for non-progression and that, although research has concentrated on factors causative of student withdrawal, less attention has focused on students who fail academically. This study investigated the effects of a number of a number of factors on the academic attainment of first-year undergraduates within the Faculty of Humanities and Social Sciences at the University of Glamorgan. Results showed that gender and age had only minor impacts upon educational achievement, while place of residence, prior educational attainment and attendance emerged as significant predictors of attainment. Further analysis showed these three factors to be interrelated , with attendance correlating strongly with both entry points and place or residence. In turn, prior attainment was strongly linked to place of residence. Findings may be used to identify and proactively target students at risk of poor academic performance and dropout in order in order to improve rates of performance and progression

Digital, material and networked: some emerging themes for SET education

Boundaries between the digital and material worlds are becoming blurred as the internet increasingly connects us to things as well as people and information. This is increasingly relevant to education as initiatives which significantly combine digital and material elements in networks are becoming a reality for Science, Engineering and Technology (SET) learning. Our paper reports on the initial findings of a project to carry out a ‘state of the art’ review of literature to establish the key themes, opportunities and obstacles that are emerging from the development and use of these ‘hybrid’ systems in learning. We wanted to explore the extent to which this new domain of study is being reported in the literature and to identify work representative of this area. Our aim was to investigate the depth of research in this area by going beyond the technologically descriptive to focus on pedagogical and organisational issues raised in the literature. To identify the state of current research in the area we carried out a systematic search of databases of Science, Engineering and Technology education literature. We found 808 papers relating to the hybrid learning initiatives we are interested in, of which the majority, 81%, involved the Engineering and Technology disciplines while 6.8% related to Science. The vast majority of papers referred to remote laboratories and most of these were concerned with describing the technologies involved. In order to explore issues emerging from the research, we carried out an in-depth text review of a particular subset of the papers found that focussed on pedagogical issues. The three main themes that emerged were: the importance of real data and authenticity in learning; the importance of a sense of presence (e.g. telepresence, social presence and/or immersion) and the locus of control in, and responsiveness of, a hybrid system. We conclude that these new digital ‘hybrid’ pedagogies offer a lens with which to view both the more traditional material pedagogies, e.g. laboratory-based learning, and purely digital pedagogies, e.g. virtual labs. Finally, issues of authenticity, presence and control/responsiveness will be of increasing pedagogical importance to other ‘hybrid’ systems, such as those involving ubiquitous computing

Visualization of toner ink adsorption at bubble surfaces

Flotation deinking involves interactions between inks particles and bubbles surfaces. These interactions are very difficult to observe directly or to quantify in bench-scale experiments or mill operations, making it difficult to evaluate effects of process conditions such as bubble size and solution chemistry on deinking efficiency. This paper presents images and measurements of toner ink interactions with bubble surfaces in laboratory-scale flotation processes. Stable adsorption of toner ink was observed at surfaces of stationary and suspended bubbles for several system chemistries. Interactions of toner particles and bubbles were quantified by high magnification and high temporal resolution digital videos obtained in bubble flow facilities creating both stationary and flowing bubbles. Large (>200 micron), flat toner particles adsorbed to bubble surfaces by single contact points. Smaller toner particles formed very stable complexes in fatty acid chemistries. Desorption of toner ink from bubble surfaces was not observed, even for vigorous flows. Bubbles were observed to be fully covered with toner after 4 minutes of residence time in the suspending bubble flow facility. Initial estimates indicate that bubbles with diameters of approximately 1 mm carry more than 1 mg of ink per bubble