Lattice Green Function (at 0) for the 4d Hypercubic Lattice

The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kampe-de-Feriet function. Various properties of the associated walks are enumerated.Comment: latex, 5 pages, Res. Report 1

Predictive thermodynamics for condensed phases

Thermodynamic information is central to assessment of the stability and reactivity of materials. However, because of both the demanding nature of experimental thermodynamics and the virtually unlimited number of conceivable compounds, experimental data is often unavailable or, for hypothetical materials, necessarily impossible to obtain. We describe simple procedures for thermodynamic prediction for condensed phases, both ionic and organic covalent, principally via formula unit volumes ( or density); our volume-based approach (VBT) provides a new thermodynamic tool for such assessment. These methods, being independent of detailed knowledge of crystal structures, are applicable to liquids and amorphous materials as well as to crystalline solids. Examples of their use are provided

Predictive Thermodynamics for Ionic Solids and Liquids

The application of thermodynamics is simple, even if the theory may appear intimidating. We describe tools, developed over recent years, which make it easy to estimate often elusive thermodynamic parameter values, generally (but not exclusively) for ionic materials, both solid and liquid, as well as for their solid hydrates and solvates. The tools are termed volume-based thermodynamics (VBT) and thermodynamic difference rules (TDR), supplemented by the simple salt approximation (SSA) and single-ion values for volume, Vm, heat capacity, Image ID:c6cp00235h-t1.gif, entropy, Image ID:c6cp00235h-t2.gif, formation enthalpy, ?fH°, and Gibbs formation energy, ?fG°. These tools can be applied to provide values of thermodynamic and thermomechanical properties such as standard enthalpy of formation, ?fH°, standard entropy, Image ID:c6cp00235h-t3.gif, heat capacity, Cp, Gibbs function of formation, ?fG°, lattice potential energy, UPOT, isothermal expansion coefficient, a, and isothermal compressibility, ß, and used to suggest the thermodynamic feasibility of reactions among condensed ionic phases. Because many of these methods yield results largely independent of crystal structure, they have been successfully extended to the important and developing class of ionic liquids as well as to new and hypothesised materials. Finally, these predictive methods are illustrated by application to K2SnCl6, for which known experimental results are available for comparison. A selection of applications of VBT and TDR is presented which have enabled input, usually in the form of thermodynamics, to be brought to bear on a range of topical problems. Perhaps the most significant advantage of VBT and TDR methods is their inherent simplicity in that they do not require a high level of computational expertise nor expensive high-performance computation tools – a spreadsheet will usually suffice – yet the techniques are extremely powerful and accessible to non-experts. The connection between formula unit volume, Vm, and standard thermodynamic parameters represents a major advance exploited by these techniques

Longitudinal surface structures (flowstripes) on Antarctic glaciers

Longitudinal surface structures (“flowstripes”) are common on many glaciers but their origin and significance are poorly understood. In this paper we present observations of the development of these longitudinal structures from four different Antarctic glacier systems; the Lambert Glacier/Amery Ice Shelf area, the Taylor and Ferrar Glaciers in the Ross Sea sector, Crane and Jorum Glaciers (ice-shelf tributary glaciers) on the Antarctic Peninsula, and the onset zone of a tributary to the Recovery Glacier Ice Stream in the Filchner Ice Shelf area. Mapping from optical satellite images demonstrates that longitudinal surface structures develop in two main situations: (1) as relatively wide flow stripes within glacier flow units and (2) as relatively narrow flow stripes where there is convergent flow around nunataks or at glacier confluence zones. Our observations indicate that the confluence features are narrower, sharper, and more clearly defined features. They are characterised by linear troughs or depressions on the ice surface and are much more common than the former type. Longitudinal surface structures within glacier flow units have previously been explained as the surface expression of localised bed perturbations but a universal explanation for those forming at glacier confluences is lacking. Here we propose that these features are formed at zones of ice acceleration and extensional flow at glacier confluences. We provide a schematic model for the development of longitudinal surface structures based on extensional flow that can explain their ridge and trough morphology as well as their down-ice persistence

The Cauchy-Schlomilch transformation

The Cauchy-Schl\"omilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given

Generating Diffusion MRI scalar maps from T1 weighted images using generative adversarial networks

Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive microstructure assessment technique. Scalar measures, such as FA (fractional anisotropy) and MD (mean diffusivity), quantifying micro-structural tissue properties can be obtained using diffusion models and data processing pipelines. However, it is costly and time consuming to collect high quality diffusion data. Here, we therefore demonstrate how Generative Adversarial Networks (GANs) can be used to generate synthetic diffusion scalar measures from structural T1-weighted images in a single optimized step. Specifically, we train the popular CycleGAN model to learn to map a T1 image to FA or MD, and vice versa. As an application, we show that synthetic FA images can be used as a target for non-linear registration, to correct for geometric distortions common in diffusion MRI

“More than scaling up”: a critical and practical inquiry into operationalizing sustainability competencies

This chapter starts from the UN Decade of Education for Sustainable Development (DESD) Final Report’s call that in Higher Education, ‘more than scaling up of good practice’ and ‘greater attention to systemic approaches to curriculum change and capacity building for leaders will be needed’ (UNESCO 2014a, p. 31). It recognises this need and the additional, rather profound reform and transformation of educational policy and practice that is required to meet the heightened expectations of education in an increasingly volatile, conflict laden, and challenging world. The emphasis is on clarification and framing of work to date and identification of relevant research gaps. In particular, it addresses the current status of the literature on competencies in ESD, which is characterised by a sea of labels, terminological confusion, and relative inattention to pedaogogic implications. The research outlined is both a critical inquiry into the status of work to date on sustainability competencies and a practical inquiry into the possibility of innovative and transformative institutional strategies and pedagogies around a suite of specific competencies. To this end, the early stages of an international and cross-institutional pilot project collaboration designed to help realize the UN’s ambitious Sustainable Development Goals (SDGs) and UNESCO’s Global Action Plan (GAP) (UNESCO 2014b), is described briefl

‘More than scaling-up’: Sustainability contexts, competencies, and consequences - a critical inquiry

To identify and problematise the key issues characterising the relationship between global sustainability contexts and the limited response of HE to date - with the purpose of unlocking the potential for innovative, replicable efforts to develop sustainability competencies through innovation in curriculum policy and practice, through addressing these sub-aims: How far does HE policy accommodate and reflect the need for sustainability competencies? How can capacity for teaching for competency be built and supported through new policies? How can curricula and pedagogy be better aligned to facilitate the building of sustainability competency in learners and teachers? What effect and influence does education for sustainability competency have in terms of facilitating transformative social learning, supporting systems structure change, and cultivating informed responsibility (in terms of policy and everyday decision making)?PedRI