Mathematical perspectives on waves and currents

The behaviour of waves on the surface of a fluid has fascinated scientists for centuries. Attempts to describe the problem mathematically have revealed a rich geometric structure, as well as a number of celebrated equations. When considering a stochastic theory of water waves, it is therefore sensible to begin with a structure preserving methodology of introducing a stochastic noise into a fluid model. Within this thesis, the mathematical framework of semi-martingale driven variational principles is introduced, which reveals a new methodology of formulating problems for which we have a stochastic action integral. The inclusion of stochastic advection by Lie transport into the underlying fluid momentum equation will allow us to achieve a novel stochastic perturbation of water wave theory which preserves its geometric properties. A number of phenomena observable on the free surface of a fluid are challenging to describe using existing modelling approaches. In particular, the classical modelling approach requires modification to permit the introduction of thermal gradients or rotational flows. Through a new variational perspective involving the composition of two maps, the interaction between waves and thermal fronts in the upper ocean is studied. This approach involves a natural separation of waves and currents on the free surface as vertical oscillations around a horizontal two dimensional flow, and allows the consideration of wave-current interactions. Separately, currents are responsible for the advection of material suspended within the fluid. We consider the procession of an inertial object through a fluid domain, which involves fluid equations with the structure of a fractional order differential equation. It is shown that the most commonly applied such equation, the Maxey-Riley equation, is globally well-posed, a fact which was absent from the literature prior to this thesis.Open Acces

Lagrangian reduction and wave mean flow interaction

How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid dynamical systems, whose motion can be expressed as the composition of two or more Lie-group actions. Hybrid systems abound in fluid dynamics. Examples include: the dynamics of complex fluids such as liquid crystals; wind-driven waves propagating with the currents moving on the sea surface; turbulence modelling in fluids and plasmas; and classical-quantum hydrodynamic models in molecular chemistry. From among these examples, the motivating question in this paper is: How do wind-driven waves produce ocean surface currents? The paper first summarises the geometric mechanics approach for deriving hybrid models of multiscale, multiphysics motions in ideal fluid dynamics. It then illustrates this approach for WMFI in the examples of 3D WKB waves and 2D wave amplitudes governed by the nonlinear Schr\"odinger (NLS) equation propagating in the frame of motion of an ideal incompressible inhomogeneous Euler fluid flow. The results for these examples tell us that the fluid flow in WMFI does not create waves. However, feedback in the opposite direction is possible, since 3D WKB and 2D NLS wave dynamics can indeed create circulatory fluid flow.Comment: 2nd version, 32 pages, 3 figures, comments welcome by emai

Geometric Mechanics of the Vertical Slice Model

The goals of the present work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Models (VSMs) of ocean dynamics; and (ii) illustrate the versatility and utility of deterministic and stochastic variational approaches by deriving several variants of wave-current interaction models which describe the effects of internal waves propagating within a vertical planar slice embedded in a 3D region of constant horizontal gradient of buoyancy in the direction transverse to the vertical pane.Comment: 32 pages, 3 figures, comments welcome by emai

Lea Valley Drift: Beyond the Olympic Park

This book accompanies the 'Lea Valley Drift' maps commissioned by the London Legacy Development Corporation for distribution at the opening of the Queen Elizabeth Olympic Park in 2013. It investigates the ways we interact with the city, observing the public realm and exploring our relationships with the unremarkable spaces we use and inhabit every day. The project is located in the neighbourhoods around the 2010 London Olympic site in the lower Lea Valley; a location at an important juncture in its geographic history, and a fascinating condenser of voices prioritising the past or the future

Lea Valley Drift: Maps

A pair of maps commissioned by the LLDC for distribution at the opening of the Queen Elizabeth Olympic Park, Stratford, London

Teachers as writers: a systematic review

This paper is a critical literature review of empirical work from 1990-2015 on teachers as writers. It interrogates the evidence on teachers’ attitudes to writing, their sense of themselves as writers and the potential impact of teacher writing on pedagogy or student outcomes in writing. The methodology was carried out in four stages. Firstly, educational databases keyword searches located 438 papers. Secondly, initial screening identified 159 for further scrutiny, 43 of which were found to specifically address teachers’ writing identities and practices. Thirdly, these sources were screened further using inclusion/exclusion criteria. Fourthly, the 22 papers judged to satisfy the criteria were subject to in-depth analysis and synthesis. The findings reveal that the evidence base in relation to teachers as writers is not strong, particularly with regard to the impact of teachers’ writing on student outcomes. The review indicates that teachers have narrow conceptions of what counts as writing and being a writer and that multiple tensions exist, relating to low self-confidence, negative writing histories, and the challenge of composing and enacting teacher and writer positions in school. However, initial training and professional development programmes do appear to afford opportunities for reformulation of attitudes and sense of self as writer

Using a machine learning model to risk stratify for the presence of significant liver disease in a primary care population

Background: Current strategies for detecting significant chronic liver disease (CLD) in the community are based on the extrapolation of diagnostic tests used in secondary care settings. Whilst this approach provides clinical utility, it has limitations related to diagnostic accuracy being predicated on disease prevalence and spectrum bias, which will differ in the community. Machine learning (ML) techniques provide a novel way of identifying significant variables without preconceived bias. As a proof-of-concept study, we wanted to examine the performance of nine different ML models based on both risk factors and abnormal liver enzyme tests in a large community cohort.Methods: Routine demographic and laboratory data was collected on 1,453 patients with risk factors for CLD, including high alcohol consumption, diabetes and obesity, in a community setting in Nottingham (UK) as part of the Scarred Liver project. A total of 87 variables were extracted. Transient elastography (TE) was used to define clinically significant liver fibrosis. The data was split into a training and hold out set. The median age of the cohort was 59, mean body mass index (BMI) 29.7 kg/m2, median TE 5.5 kPa, 49.2% had type 2 diabetes and 20.3% had a TE >8 kPa.Results: The nine different ML models, which included Random Forrest classifier, Support Vector classification and Gradient Boosting classifier, had a range of area under the curve (AUC) statistics of 0.5 to 0.75. Ensemble Stacker model showed the best performance, and this was replicated in the testing dataset (AUC 0.72). Recursive feature elimination found eight variables had a significant impact on model output. The model had superior sensitivity (74%) compared to specificity (60%).Conclusions: ML shows encouraging performance and highlights variables that may have bespoke value for diagnosing community liver disease. Optimising how ML algorithms are integrated into clinical pathways of care and exploring new biomarkers will further enhance diagnostic utility

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie