A finite-volume shallow layer method for the MHD instabilities in an aluminium production cell

An electrolytic cell for Aluminium production contains molten metal and molten electrolyte, which are subject to high dc-currents and magnetic fields. Lorentz forces arising from the cross product of current and magnetic field may amplify natural gravity waves at the interface between the two fluids, leading to short circuits in extreme cases. The external magnetic field and current distribution in the production cell is computed through a detailed finite element analysis at Torino Polytechnic. The results are then used to compute the magnetohydrodynamic and thermal effects in the aluminium/electrolyte bath. Each cell has lateral dimensions of 6m x 2m, whilst the bath depth is only 30cm. the electrically resistive electrolyte path, which is critical in the operation of the cell, has layer depth of only a few centimetres below each carbon anode. Because the shallow dimensions of the liquid layer a finite-volume shallow-layer technique has been used at Greenwich to compute the resulting flow-field and interface perturbations. The information obtained from this method, i.e. depth averaged velocities and aluminium/electrolyte interface position is then embedded in the three-dimensional finite volume code PHYSICA and will be used to compute the heat transfer and phase change in the cell.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These non-local models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

Forecasting exchange rates in the presence of instabilities

Many exchange rate papers articulate the view that instabilities constitute a major impediment to exchange rate predictability. In this thesis we implement Bayesian and other techniques to account for such instabilities, and examine some of the main obstacles to exchange rate models' predictive ability. We first consider in Chapter 2 a time-varying parameter model in which fluctuations in exchange rates are related to short-term nominal interest rates ensuing from monetary policy rules, such as Taylor rules. Unlike the existing exchange rate studies, the parameters of our Taylor rules are allowed to change over time, in light of the widespread evidence of shifts in fundamentals - for example in the aftermath of the Global Financial Crisis. Focusing on quarterly data frequency from the crisis, we detect forecast improvements upon a random walk (RW) benchmark for at least half, and for as many as seven out of 10, of the currencies considered. Results are stronger when we allow the time-varying parameters of the Taylor rules to differ between countries. In Chapter 3 we look closely at the role of time-variation in parameters and other sources of uncertainty in hindering exchange rate models' predictive power. We apply a Bayesian setup that incorporates the notion that the relevant set of exchange rate determinants and their corresponding coefficients, change over time. Using statistical and economic measures of performance, we first find that predictive models which allow for sudden, rather than smooth, changes in the coefficients yield significant forecast improvements and economic gains at horizons beyond 1-month. At shorter horizons, however, our methods fail to forecast better than the RW. And we identify uncertainty in coefficients' estimation and uncertainty about the precise degree of coefficients variability to incorporate in the models, as the main factors obstructing predictive ability. Chapter 4 focus on the problem of the time-varying predictive ability of economic fundamentals for exchange rates. It uses bootstrap-based methods to uncover the time-specific conditioning information for predicting fluctuations in exchange rates. Employing several metrics for statistical and economic evaluation of forecasting performance, we find that our approach based on pre-selecting and validating fundamentals across bootstrap replications generates more accurate forecasts than the RW. The approach, known as bumping, robustly reveals parsimonious models with out-of-sample predictive power at 1-month horizon; and outperforms alternative methods, including Bayesian, bagging, and standard forecast combinations. Chapter 5 exploits the predictive content of daily commodity prices for monthly commodity-currency exchange rates. It builds on the idea that the effect of daily commodity price fluctuations on commodity currencies is short-lived, and therefore harder to pin down at low frequencies. Using MIxed DAta Sampling (MIDAS) models, and Bayesian estimation methods to account for time-variation in predictive ability, the chapter demonstrates the usefulness of suitably exploiting such short-lived effects in improving exchange rate forecasts. It further shows that the usual low-frequency predictors, such as money supplies and interest rates differentials, typically receive little support from the data at monthly frequency, whereas MIDAS models featuring daily commodity prices are highly likely. The chapter also introduces the random walk Metropolis-Hastings technique as a new tool to estimate MIDAS regressions.

A kinetic energy budget and internal instabilities in the Fine Resolution Antarctic Model

An energy analysis of the Fine Resolution Antarctic Model (FRAM) reveals the instability processes in the model. The main source of time-mean kinetic energy is the wind stress and the main sink is transfer to mean potential energy. The wind forcing thus helps maintain the density structure. Transient motions result from internal instabilities of the Bow rather than seasonal variations of the forcing. Baroclinic instability is found to be an important mechanism in FRAM. The highest values of available potential energy are found in the western boundary regions as well as in the Antarctic Circumpolar Current (ACC) region. All subregions with predominantly zonal flow are found to be baroclinically unstable. The observed deficit of eddy kinetic energy in FRAM occurs as a result of the high lateral friction, which decreases the growth rates of the most unstable waves. This high friction is required for the numerical stability of the model and can only be made smaller by using a finer horizontal resolution. A grid spacing of at least 10-15 km would be required to resolve the most unstable waves in the southern part of the domain. Barotropic instability is also found to be important for the total domain balance. The inverse transfer (that is, transfer from eddy to mean kinetic energy) does not occur anywhere, except in very localized tight jets in the ACC. The open boundary condition at the northern edge of the model domain does not represent a significant source or sink of eddy variability. However, a large exchange between internal and external mode energies is found to occur. It is still unclear how these boundary conditions affect the dynamics of adjacent regions.

Fingering Instabilities in Dewetting Nanofluids

The growth of fingering patterns in dewetting nanofluids (colloidal solutions of thiol-passivated gold nanoparticles) has been followed in real time using contrast-enhanced video microscopy. The fingering instability on which we focus here arises from evaporatively-driven nucleation and growth a nanoscopically thin "precursor" solvent film behind the macroscopic contact line. We find that well-developed isotropic fingering structures only form for a narrow range of experimental parameters. Numerical simulations, based on a modification of the Monte Carlo approach introduced by Rabani et al. [Nature 426, 271 (2003)], reproduce the patterns we observe experimentally.

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Nonlinear development of matrix-converter instabilities

Matrix converters convert a three-phase alternating-current power supply to a power supply of a different peak voltage and frequency, and are an emerging technology in a wide variety of applications. However, they are susceptible to an instability, whose behaviour is examined herein. The desired “steady-state” mode of operation of the matrix converter becomes unstable in a Hopf bifurcation as the output/input voltage transfer ratio, q, is increased through some threshold value, qc. Through weakly nonlinear analysis and direct numerical simulation of an averaged model, we show that this bifurcation is subcritical for typical parameter values, leading to hysteresis in the transition to the oscillatory state: there may thus be undesirable large-amplitude oscillations in the output voltages even when q is below the linear stability threshold value qc.

Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Experimental tests on structural members fabricated from high strength steel materials

Typical high strength steels (HSS) have exceptional high strengths with improved weldability making the material attractive in modern steel constructions. However, due to lack of understanding, most of the current steel design standards are limited to conventional low strength steels (LSS, i.e. fy ≤ 450 MPa). This paper presents the details of full-scale experimental tests on short beams fabricated from BISPLATE80 HSS materials (nominal fy = 690 MPa). The various slenderness ratios of the plate elements in the test specimens were chosen in the range near the current yield limit (AS4100-1998, etc.). The experimental studies presented in this paper have produced a better understanding of the structural behaviour of HSS members subjected to local instabilities. Comparisons have also presented in the paper regarding to the design predictions from the current steel standards (AS4100-1998). This study has enabled to provide a series of proposals for proper assessment of plate slenderness limits for structural members made of representative HSS materials. This research work also enables the inclusion of further versions in the steel design specifications for typical HSS materials to be used in buildings and bridges. This paper also presents a distribution model of residual stresses in the longitudinal direction for typical HSS I-sections.

Struggles Over Difference: Curriculum, texts and pedagogy in the Asia-Pacific

Struggles over Difference addresses education, schools, textbooks, and pedagogies in various countries of the Asia-Pacific, offering critical curriculum studies and policy analyses of national and regional educational systems. These systems face challenges linked to new economic formations, cultural globalization, and emergent regional and international geopolitical instabilities and conflicts. Contributors offer insights on how official knowledge, text, discourse and discipline should be shaped; who should shape it; through which institutional agencies it should be administered: and social and cultural practices through which this should occur.

Stripping Sight Bare : Alison Jones’ ‘Portraits by Proxy’

In this paper I analyse UK artist Alison Jones’ sonic interventions Portrait of the Artist by Proxy (2008), Voyeurism by Proxy (2008) and Art, Lies and Audio Tapes (2009). In Portrait of the Artist by Proxy, Jones – who, due to deteriorating vision, has not seen her reflection in a mirror in years – asks and trusts participants to audio-describe her own image back to her. In Voyeurism by Proxy, Jones asks participants to audio-describe erotic drawings by Gustav Klimt. In Art, Lies and Audio Tapes, Jones asks participants to audio-describe other artworks, such as W.F. Yeames’ And When Did You Last see Your Father?. In these portraits by proxy, Jones opens her image, and other images, to interpretation. In doing so, Jones draws attention to the way sight is privileged as a mode of access to fixed, fundamental truths in Western culture – a mode assumed to be untainted by filters that skew perception of the object. “In a culture where vision is by far the dominant sense,” Jones says, “and as a visual artist with a visual impairment, I am reliant on audio-description …Inevitably, there are limitations imposed by language, time and the interpreter’s background knowledge of the subject viewed, as well as their personal bias of what is deemed important to impart in their description” . In these works, Jones strips these background knowledges, biases and assumptions bare. She reveals different perceptions, as well as tendencies or censor, edit or exaggerate descriptions. In this paper, I investigate how, by revealing unconscious biases, Jones’ works renders herself and her participants vulnerable to a change of perception. I also examine how Jones’ later editing of the audio-descriptions allows her to show the instabilities of sight, and, in Portrait of the Artist by Proxy, to reclaim authorship of her own image.

Driving Ge island ordering on nanostructured Si surfaces

Semiconductor epitaxial nanostructures have been recently proposed as the key building blocks of many innovative applications in materials science and technology. To bring their tremendous potential to fruition, a fine control of nanostructure size and placement is necessary. We present a detailed investigation of the self-ordering process in the prototype case of Ge/Si heteroepitaxy. Starting from a bottom-up strategy (step-bunching instabilities), our analysis moves to lithographic techniques (scanning tunneling lithography, nanomechanical stamping, focused ion beam patterning) with the aim of developing a hybrid approach in which the exogenous intervention is specifically designed to suit and harness the natural self-organization dynamics of the system.