Natural convection and the evolution of a reactive porous medium

We describe a mathematical model of buoyancy-driven flow and solute transport in a saturated porous medium, the porosity and permeability of which evolve through precipitation and dissolution as a mineral is lost or gained from the pore fluid. Imposing a vertically varying equilibrium solubility creates a density gradient which can drive convective circulation. We characterise the onset of convection using linear stability analysis, and explore the further development of the coupled reaction–convection system numerically. At low Rayleigh numbers, the effect of the reaction–permeability feedback is shown to be destabilising through a novel reaction–diffusion mechanism; at higher Rayleigh numbers, the precipitation and dissolution have a stabilising effect. Over longer time scales, reaction–permeability feedback triggers secondary instabilities in quasi-steady convective circulation, leading to rapid reversals in the direction of circulation. Over very long time scales, characteristic patterns of porosity emerge, including horizontal layering as well as the development of vertical chimneys of enhanced porosity. We discuss the implications of these findings for more comprehensive models of reactive convection in porous media

Free Decay of Turbulence and Breakdown of Self-Similarity

It has been generally assumed, since the work of von Karman and Howarth in 1938, that free decay of fully-developed turbulence is self-similar. We present here a simple phenomenological model of the decay of 3D incompressible turbulence, which predicts breakdown of self-similarity for low-wavenumber spectral exponents $n$ in the range $n_c<n<4$, where $n_c$ is some threshold wavenumber. Calculations with the eddy-damped quasi-normal Markovian approximation give the value as $n_c\approx 3.45$. The energy spectrum for this range of exponents develops two length-scales, separating three distinct wavenumber ranges.Comment: 8 pages, no figure

Silicon optical modulators

Optical technology is poised to revolutionise short reach interconnects. The leading candidate technology is silicon photonics, and the workhorse of such interconnect is the optical modulator. Modulators have been improved dramatically in recent years. Most notably the bandwidth has increased from the MHz to the multi GHz regime in little more than half a decade. However, the demands of optical interconnect are significant, and many questions remain unanswered as to whether silicon can meet the required performance metrics. Minimising metrics such as the energy per bit, and device footprint, whilst maximising bandwidth and modulation depth are non trivial demands. All of this must be achieved with acceptable thermal tolerance and optical spectral width, using CMOS compatible fabrication processes. Here we discuss the techniques that have, and will, be used to implement silicon optical modulators, as well as the outlook for these devices, and the candidate solutions of the future

Growth and volatility regime switching models for New Zealand GDP data

This paper fits hidden Markov switching models to New Zealand GDP data. A primary objective is to better understand the utility of these methods for modelling growth and volatility regimes present in the New Zealand data and their interaction. Properties of the models are developed together with a description of the estimation methods, including use of the Expectation Maximisation (EM) algorithm. The models are fitted to New Zealand GDP and production sector growth rates to analyse changes in their mean and volatility over time. The paper discusses applications of the methodology to identifying changes in growth performances, and examines the timing of growth and volatility regime switching between production sectors. Conclusions to emerge are that, in contrast to the 1980s, New Zealand GDP growth experienced an unusually long period of time in high growth and low volatility regimes during the 1990s. The paper evaluates sector contributions to this 1990s experience and discusses directions for further development.Hidden Markov models; regime switching; growth; business cycles; volatility; production sectors; GDP.

Calm after the Storm?: Supply-side contributions to New Zealand’s GDP volatility decline

The variance of New Zealand’s real GDP has declined since the mid-1980s. To investigate why, this paper decomposes the variance of chain-weighted estimates of production-based real GDP growth into sector shares, sector growth rate variances and co-variances. The principal explanation for the decline in GDP volatility is a fall in the sum of sector variances driven by a decline in the Services and Manufacturing sector production growth variances. Sector co-variances have had a dominant influence on the profile of GDP volatility and this influence has not diminished. Despite marked changes in sector shares, notably increases in Services and Primary sector shares and a decrease in the share of Manufacturing, this has not been a significant factor influencing the decline in GDP volatility. We postulate that policy interventions such as “Think Big”, regulatory interventions during the early 1980s, and the introduction of GST are key explanations for the higher volatility until the mid 1980s. Cessation of these interventions, deregulation and possibly changes in inventory management methods are important reasons why GDP volatility has fallen since then.Volatility, growth, production sector shares, manufacturing, services, primary, construction.

Network power flow analysis for a high penetration of distributed generation

Increasing numbers of very small generators are being connected to electricity distribution systems around the world. Examples include photovoltaics (PV) and gas-fired domestic-scale combined heat and power (micro-CHP) systems, with electrical outputs in the region of 1 to 2 kW. These generators are normally installed within consumers' premises and connected to the domestic electricity supply network (230 V single-phase in Europe, 120 V in North America). There is a growing need to understand and quantify the technical impact that high penetrations of such generators may have on the operation of distribution systems. This paper presents an approach to analyzing this impact together with results indicating that considerable penetrations of micro-generation can be accommodated in a typical distribution system

Sensitivity-analysis method for inverse simulation application

An important criticism of traditional methods of inverse simulation that are based on the Newton–Raphson algorithm is that they suffer from numerical problems. In this paper these problems are discussed and a new method based on sensitivity-analysis theory is developed and evaluated. The Jacobian matrix may be calculated by solving a sensitivity equation and this has advantages over the approximation methods that are usually applied when the derivatives of output variables with respect to inputs cannot be found analytically. The methodology also overcomes problems of input-output redundancy that arise in the traditional approaches to inverse simulation. The sensitivity- analysis approach makes full use of information within the time interval over which key quantities are compared, such as the difference between calculated values and the given ideal maneuver after each integration step. Applications to nonlinear HS125 aircraft and Lynx helicopter models show that, for this sensitivity-analysis method, more stable and accurate results are obtained than from use of the traditional Newton–Raphson approach