Past Industrial and Interdisciplinary Workshops

This will be on the topic of the CASE project Thales will be sponsoring from Oct '11.

We apply the novel method of potential analysis to study climatic records. The method comprises (i) derivation of the number of climate states from time series, (ii) derivation of the potential coefficients. Dynamically

monitoring patterns of potential analysis yields indications of possible bifurcations and transitions of the system.

The method is tested on artificial data and then applied to various climatic records [1,2]. It can be applied to a wide range of stochastic systems where time series of sufficient length and temporal resolution are available and transitions or bifurcations are surmised. A recent application of the method in a model of globally coupled bistable systems [3] confirms its general applicability for studying time series in statistical physics.

[1] Livina et al, Climate of the Past, 2010.

[2] Livina et al, Climate Dynamics (submitted)

[3] Vaz Martins et al, Phys. Rev. E, 2010

There will be three problems discussed all of which are open for consideration as MSc projects.

1. Reduction of Ndof in Adaptive Signal Processing

2. Calculus of Convex Sets

3. Dynamic Response of a disc with an off centre hole(s)

This is the session for industrial sponsors of the MSc in MM and SC to present the project ideas for 2010-11 academic year. Potential supervisors should attend to clarify details of the projects and meet the industrialists.

Please note the earlier than usual start-time!

POSTPONED!!!

PLEASE NOTE THAT THIS WORKSHOP IS TO BE HELD IN 21 BANBURY ROAD BEGINNING AT 9AM! \\

We will give three short presentations of current work here on small scale mechanics :

1) micron-scale cantilever testing and nanoindentation - Dave Armstrong

2) micron-scale pillar compression – Ele Grieveson

3) Dislocation loop shapes – Steve Fitzgerald

These should all provide fuel for discussion, and I hope ideas for future collaborative work.\\

The meeting will be in the committee room in 21 Banbury Rd (1st floor, West end).

John Allen: The Bennett Pinch revisited

Abstract: The original derivation of the well-known Bennett relation is presented. Willard H. Bennett developed a theory, considering both electric and magnetic fields within a pinched column, which is completely different from that found in the textbooks. The latter theory is based on simple magnetohydrodynamics which ignores the electric field.

The discussion leads to the interesting question as to whether the possibility of purely electrostatic confinement should be seriously considered.

Angela Mihai: A mathematical model of coupled chemical and electrochemical processes arising in stress corrosion cracking

Abstract: A general mathematical model for the electrochemistry of corrosion in a long and narrow metal crack is constructed by extending classical kinetic models to also incorporate physically realistic kinematic conditions of metal erosion and surface film growth. In this model, the electrochemical processes are described by a system of transport equations coupled through an electric field, and the movement of the metal surface is caused, on the one hand, by the corrosion process, and on the other hand, by the undermining action of a hydroxide film, which forms by consuming the metal substrate. For the model problem, approximate solutions obtained via a combination of analytical and numerical methods indicate that, if the diffusivity of the metal ions across the film increases, a thick unprotective film forms, while if the rate at which the hydroxide produces is increased, a thin passivating film develops.

We will try to cover the following problems in the workshop:

(1) Modelling of aortic aneurisms showing the changes in blood flow / wall loads before and after placements of aortic stents;

(2) Modelling of blood flows / wall loads in interracial aneurisms when flow diverters are used;

(3) Metal artefact reduction in computer tomography (CT).

If we run out of time the third topic may be postponed.

9:45 DH common room coffee

This workshop is half-seminar, half-workshop. \\ \\ HSBC have an on-going problem and they submitted a proposal for an MSc in Applied Stats project on this topic. Unfortunately, the project was submitted too late for this cohort of students. Eurico will talk about "the first approach at the problem" but please be aware that it is an open problem which requires further work. Eurico's abstract is as follows. \\ \\

This article examines modelling yield curves through chaotic dynamical systems whose dynamics can be unfolded using non-linear embeddings in higher dimensions. We then refine recent techniques used in the state space reconstruction of spatially extended time series in order to forecast the dynamics of yield curves.

We use daily LIBOR GBP data (January 2007-June 2008) in order to perform forecasts over a 1-month horizon. Our method seems to outperform random walk and other benchmark models on the basis of mean square forecast error criteria.

Puck Rombach;

"Weighted Generalization of the Chromatic Number in Networks with Community Structure",

Christopher Lustri;

"Exponential Asymptotics for Time-Varying Flows,

Alex Shabala

"Mathematical Modelling of Oncolytic Virotherapy",

Martin Gould;

"Foreign Exchange Trading and The Limit Order Book"

'Compressive sampling' is a topic of current interest. It relies on data being sparse in some domain, which allows what is apparently 'sub Nyquist' sampling so that the quantities of data which must be handled become more closely related to the information rate. This principal would appear to have (at least) three applications for radar and electronic warfare: \\

The most modest application is to reduce the amount of data which we must handle: radar and electronic warfare receivers generate vast amounts of data (up to 1Gbit/second or even 10Gbit.sec). It is desirable to be able to store this data for future analysis and it is also becoming increasingly important to be able to share it between different sensors, which, prima facie, requires vast communication bandwidths and it would be valuable to be able to find ways to handle this more efficiently. \\

The second advantage is that if suitable data domains can be identified, it may also be possible to pre-process the data before the analogue to digital converters in the receivers, to reduce the demands on these critical components. \\

The most ambitious use of compressive sensing would be to find ways of modifying the radar waveforms, and the electronic warfare receiver sampling strategies, to change the domain in which the information is represented to reduce the data rates at the receiver 'front ends', i.e. make the data at the front end better match the information we really want to acquire.\\

The aim of the presentation will be to describe the issues with which we are faced, and to discuss how compressive sampling might be able to help. A particular issue which will be raised is how we might find domains in which the data is sparse.

9:50am Welcome \\

10:00am Malcolm McCulloch (Engineering, Oxford), "Dual usage of land: Solar power and cattle grazing"; \\

10:45am Jonathan Moghal (Materials, Oxford), “Anti-reflectance coatings: ascertaining microstructure from optical properties”; \\

11:15am (approx) Coffee \\

11:45am Agnese Abrusci (Physics, Oxford), "P3HT based dye-sensitized solar cells"; \\

12:15pm Peter Foreman (Destertec UK), "Concentrating Solar Power and Financial Issues" \\

1:00pm Lunch.

Andrew Stewart -

The role of the complete Coriolis force in ocean currents that cross the equator

Large scale motions in the atmosphere and ocean are dominated by the Coriolis force due to the Earth's rotation. This tends to prevent fluid crossing the equator from one hemisphere to the other. We investigate the flow of a deep ocean current, the Antarctic Bottom Water, across the equator using a shallow water model that includes the Earth's complete Coriolis force. By contrast, most theoretical models of the atmosphere and ocean use the so-called traditional approximation that neglects the component of the Coriolis force associated with the locally horizontal component of the Earth's rotation vector. Using a combination of analytical and numerical techniques, we show that the cross-equatorial transport of the Antarctic Bottom Water may be substantially influenced by the interaction of the complete Coriolis force with bottom topography.

NO WORKSHOP - 09:45 coffee in DH Common Room for those attending the OCIAM Meeting

• Amy Smith presents: “Multiscale modelling of coronary blood flow derived from the microstructure”

• Laura Gallimore presents: “Modelling Cell Motility”

• Jean-Charles Seguis presents: “Coupling the membrane with the cytosol: a first encounter”

This will not be a normal workshop with a single scientist presenting an unsolved problem where mathematics may help. Instead it is more of a discussion meeting with a few speakers all interested in a single theme. So far we have:

Lenny Smith (LSE) on Using Empirically Inadequate Models to inform Your Subjective Probabilities: How might Solvency II inform climate change decisions?

Dan Rowlands (AOPP, Oxford) on "objective" climate forecasting;

Tim Palmer (ECMWF and AOPP, Oxford) on Constraining predictions of climate change using methods of data assimilation;

Chris Farmer (Oxford) about the problem of how to ascertain the error in the equations of a model when in the midst of probabilistic forecasting and prediction.

Synthetic Aperture Radars (SARs) produce high resolution images over large areas at high data rates. An aircraft flying at 100m/s can easily image an area at a rate of 1square kilometre per second at a resolution of 0.3x0.3m, i.e. 10Mpixels/sec with a dynamic range of 60-80dB (10-13bits). Unlike optical images, the SAR image is also coherent and this coherence can be used to detect changes in the terrain from one image to another, for example to detect the distortions in the ground surface which precede volcanic eruptions.

It is clearly very desirable to be able to compress these images before they are relayed from one place to another, most particularly down to the ground from the aircraft in which they are gathered.

Conventional image compression techniques superficially work well with SAR images, for example JPEG 2000 was created for the compression of traditional photographic images and optimised on that basis. However there is conventional wisdom that SAR data is generally much less correlated in nature and therefore unlikely to achieve the same compression ratios using the same coding schemes unless significant information is lost.

Features which typically need to be preserved in SAR images are:

o texture to identify different types of terrain

o boundaries between different types of terrain

o anomalies, such as military vehicles in the middle of a field, which may be of tactical importance and

o the fine details of the pixels on a military target so that it might be recognised.

The talk will describe how Synthetic Aperture Radar images are formed and the features of them which make the requirements for compression algorithms different from electro-optical images and the properties of wavelets which may make them appropriate for addressing this problem. It will also discuss what is currently known about the compression of radar images in general.