Past Industrial and Interdisciplinary Workshops

Micron-sized bacteria or algae operate at very small Reynolds numbers.

In this regime, inertial effects are negligible and, hence, efficient

swimming strategies have to be different from those employed by fish

or bigger animals. Mathematically, this means that, in order to

achieve locomotion, the swimming stroke of a microorganism must break

the time-reversal symmetry of the Stokes equations. Large ensembles of

bacteria or algae can exhibit rich collective dynamics (e.g., complex

turbulent patterns, such as vortices or spirals), resulting from a

combination of physical and chemical interactions. The spatial extent

of these structures typically exceeds the size of a single organism by

several orders of magnitude. One of our current projects in the Soft

and Biological Matter Group aims at understanding how the collective

macroscopic behavior of swimming microorganisms is related to their

microscopic properties. I am going to outline theoretical and

computational approaches, and would like to discuss technical

challenges that arise when one tries to derive continuum equations for

these systems from microscopic or mesoscopic models.

I have reconstructed multiple palaeoecological records from sites across the British Isles; this work has resulted in detailed time series that demonstrate changes in vegetation, herbivore density, nitrogen cycling, fire levels and air temperature across an 8,000 year time span covering the end of the last glacial period. The aim of my research is to use statistics to infer the relationships between vegetation changes and changes in the abiotic and biotic environment in which they occurred. This aim is achieved by using a model-fitting and model-selection method whereby sets of ordinary differential equations (ODE) are ‘fitted’ to the time series data via maximum likelihood estimation in order to find the model(s) that provide the closest match to the data. Many of the differential equation models that I have used in this study are well established in the theoretical ecology literature (i.e. plant – resource dynamics and plant – herbivore dynamics); however, there are no existing ODE models of fire or temperature dynamics that were appropriate for my data. For this workshop, I will present the palaeoecological data that I collected along with the models that I have chosen to work with (including my first attempt at models for fire and temperature dynamics) and I hope to get your feedback on these models and suggestions for other useful modelling methods that could be used to represent these dynamics.

The significance of the effects of non-healing wounds has been the topic of many research papers and lectures during the last 25 years. Efforts have been made to understand the effects of long-standing venous hypertension, diabetes, the prevalence of wounds in such conditions with as well as the difficulties faced in managing such wounds with some success. Successful efforts to define standard care regimes have also been made. However, attempts to introduce innovative therapy have been much less successful. Is this merely because we have not understood the intricacies of the problem? And would system based modelling be an untried technique?

Venous ulcers are the majority of lower extremity wounds, and a clinical challenge. A previously developed model of venous ulcers permits some understanding of why compression bandaging is successful but fails to accommodate complications such as exudate and infection. Could this experimental model be improved by system based modelling?

Chronic wounds need to be modelled however the needs for such models should be examined in order that the outcome permits advances in our thinking as well in clinical management.

Trevor Wishart writes "I realise 'irrational' means something very specific to a mathematician, and I'm not using the word in that sense."

Abstract:

Trevor Wishart will discuss the use of Digital Signal Processing as a tool in musical composition, ranging from the application of standard analysis procedures (e.g. windowed Fourier Transforms), and common time-domain methods (Brassage), to more unconventional approaches (e.g. waveset distortion, spectral tracing, iterative-extension). He will discuss the algorithms involved and illustrate his talk with musical examples taken from his own work.

This workshop is linked to a musical performance of "Two Women" and "Globalalia" by Trevor Wishart in the Jacqueline du Pre concert hall that evening (5th Feb) at 8pm as part of the Music Department's "New Music Forum". Tickets are £12 (or £8 concession) but if you are interested please let me know (Rebecca Gower, @email or 152312) as we may be able to negotiate a much lower price for members of the Mathematical Institute in a group associated with his workshop.

Trevor will also be giving two lectures in the Denis Arnold Hall, Faculty of Music on the 3rd and 4th Feb which are open to the public and admission is free.

McBurnie: “Sound propagation through bubbly liquids”.

Hewett: "Switching on a time-harmonic acoustic source".

When the human eye looks at a distant object, the lens is held in a state of tension by a set of fibres (known as zonules) that connect the lens to the ciliary body. To view a nearby object, the ciliary muscle (which is part of the ciliary body) contracts. This reduces the tension in the zonules, the lens assumes a thicker and more rounded shape and the optical power of the eye increases.

This process is known as accommodation.

With increased age, however, the accommodation mechanism becomes increasingly ineffective so that, from an age of about 50 years onwards, it effectively ceases to function. This condition is known as presbyopia. There is considerable interest in the ophthalmic community on developing a better understanding of the ageing processes that cause presbyopia. As well as being an interesting scientific question in its own right, it is hoped that this improved understanding will lead to improved surgical procedures (e.g. to re-start the accommodation process in elderly cataract patients).

Each problem to be solved at the study group will be discussed.

• “Two Problems Relating to Sand Dune Formation” by Andrew Ellis

• “Interface Sharpening with a Lattice Boltzmann Equation” by Tim Reis

• “A Dual Porosity Model for the Uptake of Nutrients by Root Hairs” by Kostas Zygalakis

Atomistic computer simulation models are constructed to study a range of materials in which

the atoms appear in novel environments. Two key research areas are considered:

• The Growth and Structure Inorganic Nanotubes. A range of materials have been

observed to form nanotubular structures (inorganic nanotubes - INTs) analogous to those

well known for carbon. These INTs, which may have unique low-dimensional morphologies

not simply related to known bulk polymorphs, potentially offer unique mechanical and electronic properties. A useful synthetic pathway is to use carbon nanotubes as templates using

molten salts. Atomistic simulation models, in which the atom interactions are treated utilizing relatively simple potential energy functions, are developed and applied to understand

the INT formation and stability. INT morphologies are classified by reference to folding

two dimensional sheets. The respective roles of thermodynamics and kinetics in determining

INT morphology are outlined and the atomistic results used to develop an analytic model to

predict INT diameters.

• Ordering on Multiple Length-Scales in Network-forming Liquids. Intermediate-range order (IRO), in which systems exhibit structural ordering on length-scales beyond

the nearest-neighbour (short-range), has been identified in a wide range of materials and is

characterised by the appearance of the so-called first sharp diffraction peak (FSDP) at low

scattering angles. The precise structural origin of such ordering remains contentious and a full

understanding of the factors underlying this order is vital if such materials (many of which are

technologically significant) are to be produced in a controlled manner. Simulation models,

in which the ion-ion interactions are represented by relatively simple potential functions

which incorporate (many-body) polarisation and which are parameterised by reference to

well-directed electronic structure calculations, have been shown to reproduce such IRO and

allow the precise structural origin of the IRO to be identified. Furthermore, the use of

relatively simple (and hence computationally tractable) models allows for the study of the

relatively long length- and time-scales required. The underlying structures are analysed with

reference to both recent (neutron scattering) experimental results and high level electronic

structure calculations. The role of key structural units (corner and edge sharing polyhedra)

in determining the network topology is investigated in terms of the underlying dynamics and

the relationship to the glass transition considered.

HSBC Currency Trading has collaborated with the Oxford Maths Institute for over six years and is now working with its third DPhil student. In this workshop, we will look at the some of the academic research which has directly benefited the trading operation.

Thin films of low refractive index nanoparticles are being developed for use as anti-reflection coatings for solar cells and displays. Although these films are deposited as a single layer, the comparison between a simple theoretical model and the experimental data shows that the coating cannot be treated as a such, but rather as a layer with an unknown refractive index gradient. Approaches to modelling the reflectance from such coatings are sought. Such approaches would allow model refractive index gradients to be fitted to the experimental data and would allow better understanding of how the structure of the films develops during fabrication.

Collaborators from Industry will speak to us about their proposed projects for the MSc in Math Modelling and Scientific Computation. Potential supervisors should attend. All others welcome too.

The aim is to explore whether we can extend the work of PM Woodward first published many years ago, to see if we can extract more information than we do to date from our radar returns. A particular interest is in the information available for target recognition, which requires going beyond Woodward's assumption that the target has no internal structure.

Understanding the critical parameters controlling the stability of solidification interfaces in colloidal systems is a necessary step in many domains were the freezing of colloids is present, such as materials science or geophysics. What we understand so far of the solidification of colloidal suspensions is derived primarily from the analogies with dilute alloys systems, or the investigated behaviour of single particles in front of a moving interface and is still a subject of intense work. A more realistic, multi-particles model should account for the particles movement, the various possible interactions between the particles and the multiple interactions between the particles and the solid/liquid cellular interface. In order to bring new experimental observations, we choose to investigate the stability of a cellular interface during directional solidification of colloidal suspensions by using X-ray radiography and tomography. I will present recent experimental results of ice growth (ice lenses) and particle redistribution observations, their implications, and open the discussion regarding the limitations of the technique and the potential for further progress in the field using this approach.

Anthony Lock will speak on "A Column Model of Moist Convection".

Preview of problems to be solved at the study Group in Limerick taking place in the following week.

Inverse problems arise with regularity (sic!) in the context of our study of the deformation of solids, and its characterisation (in terms of diffraction and imaging) using radiation (neutrons and X-rays).

I wish to introduce several examples where the advancement of inverse problem methods can make a significant impact on applicatins.

1. Inverse eigenstrain analysis of residual stress states

2. Strain tomography

3. Strain image correlation

Depending on the time available, I may also mention (a) Rietveld refinement of diffraction patterns from polycrystalline aggregates, and
(b) Laue pattern indexing and energy dispersive detection for single grain strain analysis.

PROBLEM STATEMENT:

Consider a set of measurements made by many sensors placed in a noisy environment, the noise is both temporally and spatially correlated and has time varying statistics. Given this environment, characterised by spatial and temporal scales of correlation, the challenge is to detect the presence of a weak, stationary signal described by smaller scales of temporal and spatial correlation.

Many current and future challenges involve detection of signals in the presence of other, similar, signals. The signal environment is extremely busy and thus the traditional process of detection of a signal buried in noise at reducing signal to noise ratio is no longer sufficient. Signals of interest may be at high SNR but need to be detected, classified, isolated and analysed as close to real time as is possible. All interfering signals are potentially signals of interest and all overlap in time and frequency.

Can the performance of signal detection algorithms be parameterised by some characteristic(s) of the signal environment?

A problem exists to detect and classify multiple signal types, but with a very low duty cycle for the receiver. In certain circumstances, very short windows of opportunity exist where the local signal environment can be sampled and the duty cycle of observation opportunities can be as low as 10%. The signals to be detected may be continuous or intermittent (burst) transmissions. Within these short windows, it is desirable to detect and classify multiple transmissions in terms of signal type (e.g. analogue or digital comms, navigation etc.) and location of transmitters. The low duty cycle of observations for the receiver makes this a challenging prospect.

Again, can the performance of signal detection algorithms be parameterised by some characteristic(s) of the signal environment?

About a third of us will have a cancer during our lives, and we all know someone with the disease. Despite enormous progress in recent years, so that being diagnosed with cancer is not the death sentence that it once was, treatment can be aggressive, leading to short and long term reductions in quality of life. Cancer and its treatment is still feared, and rightly so - it is a major health concern. Destroying cancer non-invasively using protons or charged light ions such as carbon (Particle Therapy Cancer Research or PTCR) offers advantages over conventional radiotherapy using x-rays, since far lower radiation dose is delivered to healthy normal tissues. PT is also an alternative to radical cancer surgery. Most radiotherapy uses a small electron linear accelerator to accelerate an electron beams to a few million volts and then to generate hard x-rays, whereas CPT uses cyclotrons or synchrotrons to accelerate protons to a few hundred million volts, which themselves sterilise the tumour. More recently, a new concept in accelerators – the “non-scaling Fixed Field Alternating Gradient” accelerator – has been advanced, which offers the prospect of developing relatively compact, high acceleration rate accelerators for a variety of purposes, from neutrino factories and muon acceleration to cancer therapy. However, there are formidable technical challenges to be overcome, including resonance crossing. We have recently been awarded funding in the UK to construct a demonstrator non-scaling FFAG at the Daresbury laboratory (EMMA, the Electron Model with Many Applications), and to design a prototype machine for proton and carbon ion cancer therapy (PAMELA, the Particle Accelerator for MEdicaL Applications). I will describe some of the motivations for developing this new type of accelerator. Finally, although the physics of CPT says that it should be qualitatively and quantitatively better than conventional radiotherapy, the robust clinical analyses (for example, randomised control trials) have not been done, and the meta-analyses seem to suffer from large sample biases. The Particle Therapy Cancer Research Institute (part of the James Martin 21st Century School in Oxford) will study the clinical effectiveness of charged particle therapy to treat cancer, promoting its use in the UK and elsewhere on the basis of robust clinical evidence and analysis.