Past Industrial and Interdisciplinary Workshops

The behaviour of complex processing systems is often controlled by large numbers of parameters.  For example, one Thales radar processor has over 2000 adjustable parameters.  Evaluating the performance for each set of parameters is typically time-consuming, involving either simulation or processing of large recorded data sets (or both).  In processing recorded data, the optimum parameters for one data set are unlikely to be optimal for another.

We would be interested in discussing mathematical techniques that could make the process of optimisation more efficient and effective, and what we might learn from a more mathematical approach.

VerdErg Renewable Energy Ltd is developing a new hydropower unit for cost-effective energy generation at very low heads of pressure. The device is called the VETT after the underlying technology – Venturi Enhanced Turbine Technology. Flow into the VETT is split into two. The larger flow at low head transfers its energy to the smaller flow at a greater head. The smaller flow powers a conventional turbo-generator which can be a smaller, faster unit at an order of magnitude lower cost. Further, there are significant environmental benefits to fish and birds compared to the conventional hydropower solution. After several physical model test programmes* in the UK, France and The Netherlands along with CFD studies the efficiency now stands at 50%. We wish to increase that by understanding the major loss mechanisms and how they might be avoided or minimised.

The presentation will explain the VETT’s working principles and key relationships, together with some possible ideas for improvement. The comments of attendees on problem areas, potential solutions and how an enhanced understanding of key phenomena may be applied will be most welcome.

*(One was observed by Prof John Ockendon who identified a fairly extreme flow condition in a region previously thought to be benign.)

Most sensing systems exhibit so-called ‘sidelobe’ responses, which can be interpreted as an inevitable effect in one domain of truncation of the signal in the Fourier-complement domain.  Perhaps the best-known example is in antenna theory where sidelobes are an inevitable consequence of the fact that the antenna aperture must be finite.  The effect also appears in many other places, for example in time-frequency conversions and in the range domain of a pulse-compressed radar which radiates a signal only over a finite frequency band.  In the range domain these sidelobes extend over twice the length of the transmitted pulse.  For a conventional radar with relatively short pulses the effect of these unwanted returns is thus confined to a relatively short part of the range swathe.

Some of the most modern radar techniques, however, use continuous, noise-like transmissions.  ‘Primary’ noise-modulated radars are in their infancy but so-called ‘Passive’ radars using broadcast transmissions as their power source receive similar signals.  The sidelobes of even a small target at very short range can be larger than the main return from a target at much greater range.  This limits the dynamic range of the radar.

Since, however, the sidelobe pattern is predictable if the illuminating signal is known sufficiently accurately, the expected sidelobes due to a large target can be estimated and removed to tidy up the image.  This approach was first described formally in:

Hoegbom, J. A., ‘Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines,’ Astrom. Astrophys. Suppl. 15, pp417-26, 1974.

And is generally known by the name of the ‘CLEAN’ algorithm.

The seminar will outline the problem, outline the basic form of the algorithm and ask questions about what is possible with non-iterative versions of the algorithms, how to process the data coherently and how to understand any stability issues associated with the algorithm.

We are looking for a better understanding of how a lithium wall can improve energy confinement in a tokamak plasma. Improved energy confinement can make a big difference to the minimum size of tokamak that could produce a fusion power gain.

Details: 

1) Shape optimization of a paddle for density-viscosity measurements in oilfield environment;

2) Phenomenology of Kapitza thermal resistance with coupling at the MD to macroscopic scale.

Abstract:

(i) We consider the modelling of freezing of fluids which contain particulates and fibres (imagine orange juice “with bits”) flowing in channels. The objective is to design optimum geometry/temperatures to accelerate freezing.

(ii) We present the challenge of setting-up a model for lithium or sodium ion stationary energy storage cells and battery packs to calculate the gravimetric and volumetric energy density of the cells and cost. Depending upon the materials, electrode content, porosity, packing electrolyte and current collectors. There is a model existing for automotive called Batpac.

Topics:

1) Marine Acoustics;

2) Air and water quality discharge and emission modelling;

3) Geospatial mapping, remote sensing and ecosystem services.

We’ll discuss applications of big data in financial services, LBG’s assets, architecture and analytics techniques as well as specific use cases within  LBG

The four topics are:

1. Thermal interface materials

2. Low temperature joining technology

3. Nano Ag materials

4. Status of PV technology

An important military task in a high-technology environment is to understand the set of radars present in it, since the radars will be, to a greater or lesser extent, indicative of the ships, aircraft and other military units which are present.

The transmissions of the different radars typically overlap in most of the dimensions which characterise then, such as frequency and bearing, and their pulses are interleaved in time. If, however, we are able to separate the individual pulse trains which are present then not only does this allow us to know how many different radars are present, but the characteristics of the pulse train are indicative of the type of the radar.

The problem of recognising the pulse trains is not trivial, because many radars 'jitter' their transmissions and pulses may be missing or two pulses may occur together, causing the characteristics of the pulse to be 'garbled.' The jittering may be used as a way to reject mutual interference between the radars, to resolve ambiguities in measurements of range or velocity or to make it harder to jam the radar.

The problems caused by pulses overlapping are likely to become more severe in the future because the pulses of the individual radars are becoming longer.

Although solutions currently exist which can cope, to at least some extent, with most of these issues, the purpose of bringing this topic to the seminar is to allow a fresh look at the problem from first principles.

NbTi-based superconducting wires have widespread use in engineering applications of superconductivity such as MRI and accelerator magnets. Tolerance to the effects of interactions with changing (external) magnetic fields is an important consideration in wire design, in order to make the most efficient use of the superconducting material. This project aims to develop robust analytical models of the power dissipation in real conductor geometries across a broad frequency range of external field changes, with a view to developing wire designs that minimise these effects.

Seismic exploration in the oil industry is one example where wave equations are used as models. When the wave speed is spatially varying one is naturally concerned with questions of homogenisation or upscaling, where one would like to calculate an effective or average wave speed. As a canonical problem this short workshop will introduce the one-dimensional acoustic wave equation with a rapidly varying wave speed, perhaps even a periodic variation. Three questions will be asked: (i) how do you calculate a sensible average wave speed (ii) does the wave equation suffice or is there a change of form after averaging and (iii) if one can induce any particular excitation at one end of a finite one-dimensional medium, and make any observations that we like at that end, what - if anything - can be inferred about the spatial variability of the wave speed?

This topic was the subject of an OCIAM workshop on 8th March 2013

given by Nick Hall Taylor . The presentation will start with a review

of the physical problem and experimental evidence. A mathematical

model leading to a hydrodynamic free boundary problem has been derived

and some mathematical and computational results will be described.

Finally we will assess the results so far and list a number of

interesting open problems.

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After the workshop and during coffee at 11:30, we will also give a preview of the

upcoming problems at the Malaysian Study Group (Mar. 17-21). Problem

descriptions can be found here:

www.maths.ox.ac.uk/~trinh/2014_studygroup_problems.pdf.

This talk is intended to explain the link between some relatively straightforward mathematical concepts, in terms of linear programming and optimisation over a convex set of feasible solutions, and questions for the organisation of the power sector and hence for energy policy.

Both markets and centralised control systems should in theory optimise the use of the current stock of generation assets and ensure electricity is generated at least cost, by ranking plant in ascending order of short run marginal cost (SRMC), sometimes known as merit order operation. Wholesale markets, in principle at least, replicate exactly what would happen in a perfect but centrally calculated optimal dispatch of plant. This happens because the SRMC of each individual plant is “discovered” through the market and results in a price equal to “system marginal cost” (SMC), which is just high enough to incentivise the most costly plant required to meet the actual load.

More generally, defining the conditions for this to work - “decentralised prices replicate perfect central planning” - is of great interest to economists. Quite apart from any ideological implications, it also helps to define possible sources of market failure. There is an extensive literature on this, but we can explain why it has appeared to work so well, and so obviously, for merit order operation, and then consider whether the conditions underpinning its success will continue to apply in the future.

The big simplifying assumptions, regarded as an adequate approximation to reality, behind most current power markets are the following:

• Each optimisation period can be considered independent of all past and future periods.

• The only relevant costs are well defined short term operating costs, essentially fuel.

• (Fossil) plant is (infinitely) flexible, and costs vary continuously and linearly with output.

• Non-fossil plant has hitherto been intra-marginal, and hence has little impact

The merit order is essentially very simple linear programming, with the dual value of the main constraint equating to the “correct” market price. Unfortunately the simplifying assumptions cease to apply as we move towards types of plant (and consumer demand) with much more complex constraints and cost structures. These include major inflexibilities, stochastic elements, and storage, and many non-linearities. Possible consequences include:

• Single period optimisation, as a concept underlying the market or central control, will need to be abandoned. Multi period optimisation will be required.

• Algorithms much more complicated than simple merit order will be needed, embracing non-linearities and complex constraints.

• Mathematically there is no longer a “dual” price, and the conditions for decentralisation are broken. There is no obvious means of calculating what the price “ought” to be, or even knowing that a meaningful price exists.

The remaining questions are clear. The theory suggests that current market structures may be broken, but how do we assess or show when and how much this might matter?

Droplet snap-off and coalescence are very rich hydrodynamic phenomena that are even richer in liquid crystals where both the bulk phase and the interface have anisotropic properties. We studied both phenomena in suspensions of colloidal platelets with isotropic-nematic phase coexistence.

We observed two different scenarios for droplet snap-off depending on the relative values of the elastic constant and anchoring strength, in both cases markedly different from Newtonian pinching.[1] Furthermore, we studied coalescence of nematic droplets with the bulk nematic phase. For small droplets this qualitatively resembles coalescence in isotropic fluids, while larger droplets act as if they are immiscible with their own bulk phase. We also observed an interesting deformation of the director field inside the droplets as they sediment towards the bulk phase, probably as a result of flow inside the droplet. Finally, we found that mutual droplet coalescence is accompanied by large droplet deformations that closely resemble coalescence of isotropic droplets.[2]

[1] A.A. Verhoeff and H.N.W. Lekkerkerker, N. J. Phys. 14, 023010 (2012)

[2] M. Manga and H.A. Stone, J. Fluid Mech. 256, 647 (1993)

The problem is based on real time computation for 4D (3D+time) trajectory planning for unmanned vehicles (UVs). The ability to quickly predict a 4D trajectory/path enables safe, flexible, efficient use of UVs in a collaborative space is a key objective for autonomous mission and task management. 

The problem/topic proposal will consist of 3 challenges: 
1.      A single UV 4D path planning problem.
2.      Multi UV 4D path planning sharing the same space and time.
3.      Assignment of simultaneous tasks for multiple UVs based on the 4D path finding solution.

A projectile travelling supersonically in air creates a shock wave in the shape of a cone, with the projectile at the tip of the Mach cone. When the projectile travels over an array of microphones the shock wave is detected with different times of arrival at each microphone. Given measurements of the times of arrival, we are trying to calculate the azimuth direction of travel of the projectile. We have found a solution when the speed of the projectile is known. However the solution is ambiguous, and can take one of two possible values. Therefore we are seeking a new mathematical approach to resolve the ambiguity and thus find the azimuth direction of travel.