Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Extraction efficiency of drifting electrons in a two-phase xenon time projection chamber

We present a measurement of the extraction efficiency of quasi-free electrons from the liquid into the gas phase in a two-phase xenon time-projection chamber. The measurements span a range of electric fields from 2.4 to 7.1 kV/cm in the liquid xenon, corresponding to 4.5 to 13.1 kV/cm in the gaseous xenon. Extraction efficiency continues to increase at the highest extraction fields, implying that additional charge signal may be attained in two-phase xenon detectors through careful high-voltage engineering of the gate-anode region

Calibration of a two-phase xenon time projection chamber with a 37^{37}Ar source

We calibrate a two-phase xenon detector at 0.27 keV in the charge channel and at 2.8 keV in both the light and charge channels using a $^{37}$Ar source that is directly released into the detector. We map the light and charge yields as a function of electric drift field. For the 2.8 keV peak, we calculate the Thomas-Imel box parameter for recombination and determine its dependence on drift field. For the same peak, we achieve an energy resolution, $E_{\sigma}/E_{mean}$, between 9.8% and 10.8% for 0.1 kV/cm to 2 kV/cm electric drift fields.Comment: 12 pages, 7 figure

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

Soft-bed experiments beneath Engabreen, Norway: regelation infiltration, basal slip and bed deformation

To avoid some of the limitations of studying soft-bed processes through boreholes, a prism of simulated till (1.8 m × 1.6 m × 0.45 m) with extensive instrumentation was constructed in a trough blasted in the rock bed of Engabreen, a temperate glacier in Norway. Tunnels there provide access to the bed beneath 213 m of ice. Pore-water pressure was regulated in the prism by pumping water to it. During experiments lasting 7–12 days, the glacier regelated downward into the prism to depths of 50– 80 mm, accreting ice-infiltrated till at rates predicted by theory. During periods of sustained high pore water pressure (70–100% of overburden), ice commonly slipped over the prism, due to a water layer at the prism surface. Deformation of the prism was activated when this layer thinned to a sub-millimeter thickness. Shear strain in the till was pervasive and decreased with depth. A model of slip by ploughing of ice-infiltrated till across the prism surface accounts for the slip that occurred when effective pressure was sufficiently low or high. Slip at low effective pressures resulted from water-layer thickening that increased non-linearly with decreasing effective pressure. If sufficiently widespread, such slip over soft glacier beds, which involves no viscous deformation resistance, may instigate abrupt increases in glacier velocity

On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure

Multi-modalities in classroom learning environments

This paper will present initial findings from the second phase of a Horizon 2020 funded project, Managing Affective-learning Through Intelligent Atoms and Smart Interactions (MaTHiSiS). The project focusses on the use of different multi-modalities used as part of the project in classrooms across Europe. The MaTHiSiS learning vision is to develop an integrated learning platform, with re-usable learning components which will respond to the needs of future education in primary, secondary, special education schools, vocational environments and learning beyond the classroom. The system comprises learning graphs which attach individual learning goals to the system. Each learning graph is developed from a set of smart learning atoms designed to support learners to achieve progression. Cutting edge technologies are being used to identify the affect state of learners and ultimately improve engagement of learners. Much research identifies how learners engage with learning platforms (c.f. [1], [2], [3]). Not only do e-learning platforms have the capability to engage learners, they provide a vehicle for authentic classroom and informal learning [4] enabling ubiquitous and seamless learning [5] within a non-linear environment. When experiencing more enjoyable interaction learners become more confident and motivated to learn and become less anxious, especially those with learning disabilities or at risk of social exclusion [6], [13]. [7] identified the importance of understanding the affect state of learners who may experience emotions such as 'confusion, frustration, irritation, anger, rage, or even despair' resulting in disengaging with learning. The MaTHiSiS system will use a range of platform agents such as NAO robots and Kinects to measure multi-modalities that support the affect state: facial expression analysis and gaze estimation [8], mobile device-based emotion recognition [9], skeleton motion using depth sensors and speech recognition. Data has been collected using multimodal learning analytics developed for the project, including annotated multimodal recordings of learners interacting with the system, facial expression data and position of the learner. In addition, interviews with teachers and learners, from mainstream education as well as learners with profound multiple learning difficulties and autism, have been carried out to measure engagement and achievement of learners. Findings from schools based in the United Kingdom, mainstream and special schools will be presented and challenges shared

Cascading the use of Web 2.0 technology in secondary schools in the United Kingdom: identifying the barriers beyond pre-service training

This paper reports on research that took place at Nottingham Trent University and Sheffield Hallam University, United Kingdom, over two years. The research focuses on the use of Web 2.0 technology, specifically web logs, with pre-service teachers, both during their university programme and the first year of teaching as full-time newly qualified teachers (NQTs). The purpose of this research was to add a developing body of knowledge by identifying whether technology used by pre-service teachers during their training course can be cascaded into their practice once qualified. Key findings identify a number of enablers and barriers to cascading technology in the classroom; these include curriculum time, pupil skills and support. The research concludes that early professional support and development should be on-going and assumptions about new teachers as champions of cascading innovative use of Web 2 technologies into their practice as NQTs may be over optimisti