Division of Information Technology, Engineering and the Environment
School of Mathematics and Statistics
School of Mathematics and Statistics
Newcastle University, Newcastle upon Tyne, UK
Thermal excitations in helium 3: theory of turbulence measurements at ultralow temperatures
Experiments at very low temperatures, in both helium 3 and helium II, have produced intriguing results which raise challenging questions to both fluid mechanicists and physicists alike. The context of this presentation is quantum turbulence in superfluid helium 3-B at very low temperatures such that the viscous normal fluid component can be neglected, and quantum turbulence takes its purest form: a tangle of quantized vortex filaments which move in a fluid without viscosity. The experimental study of quantum turbulence would be greatly facilitated if better visualization techniques were available. A drawback of most of the existing techniques is that they only measure quantities averaged over a large region, while it is important to have local information about fluctuations. This problem has been recognized: in helium II, at temperature above 1 K, a major breakthrough has been the implementation of the PIV and particle tracking techniques. In the more difficult regime of very low temperature helium 3-B, the technique based on the so-called Andreev reflection of thermal quasiparticle excitations has been a major advance in providing a tool for studying turbulence. Aiming at the wider audience consisting of mathematicians, physicists, and engineers interested in turbulence and fluid mechanics in general, this talk will start with the general and accessible description of quantum turbulence, physical properties of helium 3, and mechanism of superfluidity. The further topics covered in this presentation will be as follows:
Bio-sketch:
Professor Sergeev’s research interests are mainly in quantum turbulence and superfluidity, although work is being done in the area of classical turbulence as well. In the past was active in a number of areas of physics and fluid dynamics, such as two-phase turbulence, fluid dynamics of dense suspensions and fluidization, kinetic theory, nonlinear waves, hydrodynamic instabilities, diffusion in liquids, and magnetohydrodynamics. Professor Sergeev is the author and co-author of more than 130 research papers. He recently co-authored and co-edited (jointly with C.F. Barenghi) a book “Vortices and Turbulence at Very Low Temperatures” (Springer, 2008).
Efficient designs for two-colour microarray experiments
Designs for two-colour microarray experiments can be viewed as block designs with two treatments per block. Explicit formulae for the A- and D- optimality criteria can be given when c, the number of blocks minus the number of treatments, is small. These show that the A- and D-optimality criteria conflict badly if there are ten or more treatments. This problem can be avoided by slightly increasing the number of blocks. However, for any given value of c there is a threshold such that when the number of treatments is bigger than the threshold the optimality criteria conflict. The two colours used in each block effectively turn the block design into a row-column design. There is no need to use a design in which every treatment has each colour equally often: rather, an efficient row-column design should be used. For odd replication, I recommend using the row-column design based on the bipartite graph corresponding to an optimal block design for half the number of treatments. I show how to adapt them for experiments in which some treatments have replication only two.
Bivariate Beta Binomial Distribution
This new distribution is applicable to discrete choice data where the alternatives have two attributes each of two levels. The distribution can be used to (i) evaluate correlations and interactions (ii) determines the impact of attributes on consumers' consistency in their repeated choices and on behavioural loyalty and (iii) separate the between and within subject variation. These are relatively standard outcomes for metric analysis, such as in repeated measures ANOVA, but are new to discrete choice. The managerial implications are substantial. The bivariate beta binomial is in its own right a useful new distribution but it also paves the way for a more general model for use with most discrete choice experiments with many attributes with many levels.
Finite mixture of binary logistic regression analysis on labour supply of mothers with disabled children
Australia has experienced a growing rate of child disability, with the rate of 9.3% for children aged 14 and under in 1981 increasing to 13.2% in 1998 and 20% in 2003. This paper studies the economic effect of child disability on mother’s labor force participation outcome. Examination of the population heterogeneity forms important part of our studies. We formulate an econometric model, which allows for the possible existence of heterogeneous groups of mothers, whose status in labor force are attributed to different explanatory mechanisms in terms of different sets of explanatory factors and different interactions among factors. Our findings based on the recent Australian Bureau of Statistics’ survey data present strong evidence on existence of such the heterogeneity. A two- step model selection procedure is proposed for estimating the number of heterogeneous groups and selecting explanatory variables within groups. Some theoretical aspects concerning the procedure are studied
A New Paradigm for Asset Pricing.
This presentation will show how to fuse two pieces of theory to make a tractable model for asset pricing. The first is the theory of asset pricing using state price density processes (or stochastic discounting function processes) for asset pricing. This will be reveiwed. The second is to use Hidden Markov Models (HMMs) to model uncertainty in an economy (rather than some other Markov process or time series model). It turns out that with an elegant representation of HMMs introduced by R.J.Elliott, these models can be calibrated and asset valuation given. We will discuss implications for interest rate models, stock price models, futures pricing, exchange rates.
All at sea with spectral analysis – modal analysis of sea keeping trials
Andrew Metcalfe, Rany Thach, Tim Svenson (University of Adelaide) , & Grant Hearn (University of Southampton)
Data from sea keeping trials of a 24m ship in the North Sea are available. The ship sailed an octagonal course, each leg took over 20 minutes and data were recorded at a 0.1s resolution. The data are analysed to compare the H1 and H2 estimators of the linear transfer functions. The heave amplitude response function, in particular, showed a substantial subsidiary peak. Possible explanations will be discussed. The adequacy of linear model for the ship response will be considered, and some results of a non-linear analysis will be presented.
The Square Root Problem of Kato for Elliptic Operators: Survey, Solution and Sequel
About 1960 Tosio Kato, during his investigation of the evolution of
physical systems, was led to pose a key question about the square roots of
elliptic partial differential operators. A positive answer to his question
implies that the square root is stable under small perturbations, this being
useful in solving related hyperbolic
equations with time-varying coefficients. The one-dimensional problem was
solved by Coifman, McIntosh and Meyer in 1982, while it was only in 2001
that the question was fully answered by Auscher, Hofmann, Lacey, McIntosh
and Tchamitchian. The speaker will survey this development, and discuss
further progress made with Axelsson and Keith.
1. An Introduction to Quantum Control
This talk will present an introduction to quantum control, with a
particular emphasis on feedback control. Quantum mechanical models are
discussed, using the language of quantum probability. In particular, the
theory of quantum measurement and filtering is discussed due to its
importance in measurement-based feedback control. Some examples from our
current work are described.
2. Quantum Networks: Modelling, Analysis and Design
The focus of this talk is networks consisting of quantum and classical
components. Such networks cover a wide range of situations relevant to
quantum technologies including feedback systems, quantum information and
computing systems, device modelling, etc. We begin by describing how
components can be connected using algebraic and graphical tools, analogous
to classical circuit theory. We then discuss dissipation in quantum systems
in a manner which combines perspectives from physics and engineering using a
network framework. We show how Willems' control by interconnection
paradigm can be implemented using quantum network models.
Towards a Theory of Information for Control Systems
There has been a long held view that some form of information theory holds the key to a rigorous understanding of control problems which are subject to non-classical information patterns. In this talk we will review this idea and present recent results which connect information theory and stabilization theory. We discuss the so called data-rate theorem for classical stochastic linear systems and then present new results on the 'lowest data-rate' stabilization of interconnected large scale systems.
Director the
International Center for
Decision and Risk Analysis
University of Texas, USA
Hedging Contingent Claims with portfolios submitted to constraints and frictions
A contingent claim is a random financial commitment to be fulfilled at some future time. This entails risk and opportunities. Black-Scholes-Merton approach consists in providing a way to benefit from opportunities without taking risks. It is based on hedging the contingent claim with a portfolio of stocks valued on the market. With some initial investment, it is possible to guarantee a sufficient wealth at the time of commitment to pay the contingent claim in all circumstances. This wealth is provided by an adequate portfolio, which evolves according to market changes. However, the approach is based on many assumptions, which are not in general satisfied. One of them is the absence of constraints on admissible portfolios. A lot of efforts has been devoted to extend the approach to take into account constraints and frictions on admissible portfolios. We will review some of the ideas to treat this question, and emphasize the interest of an approach based on penalty techniques.
