Electronic marking of mathematics assignments using Microsoft Word 2007

This paper describes on-going work within the Department of Mathematics and Statistics at The Open University to enable distance learning students to electronically submit assignments rich in mathematical notation and diagrams, and for those assignments to be marked and returned electronically by their tutor. A trial is currently underway of a prototype system that enables students to submit assignments in a range of electronic formats, which are then converted to Microsoft Word 2007 format to enable tutors to take advantage of various features of this software for marking and providing mathematical comments. The systems developed for this trial are described and preliminary findings presented

A dynamic simulation of low-carbon policy influences on endogenous electricity demand in an isolated island system

This paper considers the dynamics of electricity demand in response to changes arising from low-carbon policies and socio-economic developments. As part of an investigation into the evolution of such systems on small economically-developed islands, endogenous electricity demand and associated policies are studied for the Azorean island of São Miguel. A comprehensive System Dynamics (SD) model covering the period 2005 − 2050 is presented which captures both historical behaviours and real-world influences on the endogenous demand dynamics of an island-based electricity system. The impact of tourism, energy efficiency and electric vehicles (EV) expansion allied with associated policy options, are critically evaluated by the SD model using a series of scenarios. The model shows that energy efficiency measures exhibit the most significant long-term impact on electricity demand, while in contrast, policies to increase tourism have a much less direct impact and EV expansion has thought-provoking impacts on the long-term demand, although this is not as influential as energy efficiency measures

Perceptions of online tutorials for distance learning in mathematics and computing

We report on student and staff perceptions of synchronous online teaching and learning sessions in mathematics and computing. The study is based on two surveys of students and tutors conducted 5 years apart, and focusses on the educational experience as well as societal and accessibility dimensions. Key conclusions are that both staff and students value online sessions, to supplement face-to-face sessions, mainly for their convenience, but interaction within the sessions is limited. Students find the recording of sessions particularly helpful in their studies

Developing STACK practice questions for the Mathematics Masters Programme at the OU

The design and implementation of Masters level e-assessment in STACK is described for the introductory module M820 Calculus of Variations and Advanced Calculus in the Open Universitys Masters Programme in Mathematics. Some basic design principles are described and illustrated for an online practice quiz on the use of the Jacobi equation to classify stationary paths

Renormalization of wave function fluctuations for a generalized Harper equation

A renormalization analysis is presented for a generalized Harper equation (1 + α cos(2π(ω(i + 1/2) + φ)))ψi+1 + (1 + α cos(2π(ω(i − 1/2) + φ)))ψi−1 +2λ cos(2π(iω + φ))ψi = Eψi. (0.1) For values of the parameter ω having periodic continued-fraction expansion, we construct the periodic orbits of the renormalization strange sets in function space that govern the wave function fluctuations of the solutions of the generalized Harper equation in the strong-coupling limit λ→∞. For values of ω with non-periodic continued fraction expansions, we make some conjectures based on work of Mestel and Osbaldestin on the likely structure of the renormalization strange set.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Electronic marking of mathematics assignments using Microsoft 2007

This paper describes on-going work within the Department of Mathematics and Statistics at The Open University to enable distance learning students to electronically submit assignments rich in mathematical notation and diagrams, and for those assignments to be marked and returned electronically by their tutor. A trial is currently underway of a prototype system that enables students to submit assignments in a range of electronic formats, which are then converted to Microsoft Word 2007 format to enable tutors to take advantage of various features of this software for marking and providing mathematical comments. The systems developed for this trial are described and preliminary findings presented

Insights into the Thermal Generation Futures of Isolated Island Electricity Systems Using System Dynamics

In future, long-term thermal generation investments will be greatly influenced by the best available mixes of legacy fossil fuels and renewable sources. Intuitively, a detailed first look at the dynamics which surrounds thermal investments will assist policy makers in shaping optimally required generation mixes. To achieve this, a system dynamics model of an isolated island electricity system was developed. This model gauges the long-term investment decisions that can exist within such systems. It addresses the thermal capacity additions and the extent to which financially influenced and demand growth influenced additions affects the long-term stability of the system. Reflecting a reality typical of island systems, this model does not have a supply and demand driven pricing mechanism and thus adopts exogenous electricity tariffs. It however accounts endogenously for changes in the thermal capacity margins and capacity costing. The case study used considers the Azorean island of Sao Miguel; which provides a background for the model and is used for testing its ability to capture various aspects of historical behaviors and real-world influences on the long-term thermal generation decisions. The paper concludes with a discussion of the investment decision insights gained and the possible future extensions, uses and modifications of the model

Hot Jupiter Magnetospheres

(Abridged) The upper atmospheres of close-in gas giant exoplanets are subjected to intense heating/tidal forces from their parent stars. Atomic/ionized hydrogen (H) layers are sufficiently rarefied that magnetic pressure may dominate gas pressure for expected planetary magnetic field strength. We examine the magnetospheric structure using a 3D isothermal magnetohydrodynamic model that includes: a static "dead zone" near the magnetic equator containing magnetically confined gas; a "wind zone" outside the magnetic equator in which thermal pressure gradients and the magneto-centrifugal-tidal effect give rise to transonic outflow; and a region near the poles where sufficiently strong tidal forces may suppress transonic outflow. Using dipole field geometry, we estimate the size of the dead zone to be ~1-10 planetary radii for a range of parameters. To understand appropriate base conditions for the 3D isothermal model, we compute a 1D thermal model in which photoelectric heating from the stellar Lyman continuum is balanced by collisionally-excited Lyman {\alpha} cooling. This 1D model exhibits a H layer with temperatures T=5000-10000K down to pressures of 10-100 nbar. Using the 3D isothermal model, we compute H column densities and Lyman {\alpha} transmission spectra for parameters appropriate to HD 209458b. Line-integrated transit depths of 5-10% can be achieved for the above base conditions. Strong magnetic fields increase the transit signal while decreasing the mass loss, due to higher covering fraction and density of the dead zone. In our model, most of the transit signal arises from magnetically confined gas, some of which may be outside the L1 equipotential. Hence the presence of gas outside the L1 equipotential does not directly imply mass loss. Lastly, we discuss the domain of applicability for the magnetic wind model described in this paper and in the Roche-lobe overflow model.Comment: 26 pages, 17 figures (5 color), 2 appendices; submitted to ApJ; higher resolution version available at http://www.astro.virginia.edu/~gbt8f/HotJupMag_fullres_astroph.pd

Escaping Particle fluxes in the atmospheres of close-in exoplanets: I. model of hydrogen

A multi-fluid model for an atomic hydrogen-proton mixture in the upper atmosphere of extrosolar planet is presented when the continuity and momentum equations of each component have been already solved with an energy equation. The particle number density, the temperature distribution and the structure of velocity can be found by means of the model. We chose two special objects, HD 209458b and HD 189733b, as discussion samples and the conclusion is that their mass loss rates predicted by the model are in accordance with those of observation. The most important physical process in coupling each component is charge exchange which tightly couples atomic hydrogen with protons. Most of the hydrogen escaping from hot Jupiters is protons, especially in young star-planet system. We found that the single-fluid model can describe the escape of particles when the mass loss rate is higher than a few times $10^{9}$ g/s while below $10^{9}$ g/s the multi-fluid model is more suitable for it due to the decoupling of particles. We found that the predicted mass loss rates of HD 189733b with the assumption of energy-limit are a factor of 10 larger than that calculated by our models due to the high ionization degree. For the ionized wind which is almost compose of protons, the assumption of energy-limit is no longer effective. We fitted the mass loss rates of the ionized wind as a function of $F_{UV}$ by calculating the variation of the mass loss rates with UV fluxes.Comment: 35 pages, 6 figures, submitted to Ap