All seminars (unless otherwise stated) will take place on Mondays at 3.00 pm in Room 500 which is located on the 5th floor of the Mathematics Department. See Where to Find Us for further details. There will be tea afterwards in room 606.

If you require any more information on the Applied seminars please contact Professor Yaroslav Kurylev e-mail: y.kurylev AT ucl.ac.uk or tel: 020-7679-7896.

## 19 January 2009

Professor S. D. Griffiths - University of Leeds

##### Global modelling of ocean tides

Abstract

A longstanding challenge in oceanography is the production of accurate global maps of the amplitude and phase of the ocean tides, from simple hydrodynamical equations with appropriate astronomical forcing and global topography. Over the last forty years, such prognostic models have improved in accuracy, partly due to increases in computing power, but also as the role of supposedly secondary physical processes have been recognised. Here, the development of a new prognostic global tidal model is discussed, with special emphasis upon implementing physically reasonable parameterized drag (due to bottom friction, and internal waves). Having demonstrated the integrity of this model by comparison with data-constrained tidal models, we use it to predict the form of the tides during the last Ice Age, when the ocean depth and coastal configuration were quite different to those of today.

## 26 January 2009

Professor E. Benilov - University of Limerick

##### Drops climbing uphill on an oscillating substrate

Abstract

We examine the dynamics of a drop on an inclined plate vibrating vertically.Using several simplifying assumptions (the lubrication approximation, two-dimensionality, quasi-steadiness), it is shown that, if the vibration-induced inertial force involves a narrow/deep 'trough' and a relatively wide/low 'plateau', the drop can climb uphill.

## 09 February 2009

Professor H. Ammari - Ecole Polytechnique, Palaiseau, France

##### Asymptotic spectral imaging

Abstract

The aim of this talk is to present an asymptotic theory for eigenvalue problems with applications in the fields of inverse problems and optimal design. Our general approach combines layer potentials techniques with the elegant theory of Ghoberg and Sigal on meromorphic operator-valued functions.

## 16 February 2009

NO SEMINAR - READING WEEK

## 23 February 2009

Professor W. Lionheart - University of Manchester

##### Uniqueness and Reconstruction algorithms for Photoelastic Tomography

Abstract

We consider the problem of determination of a weakly anisotropic permittivity tensor field from measurements of polarized light. In applications this is used in photoelastic tomography where the stress tensor is determined by optical measurement. In the usual experimental setting a measurement of the overall phase change of the light passing through the material is not available and the problem reduces to the inversion of the Truncated Transverse Ray Transform.

Recent work with Sharafutdinov shows that there is an explicit reconstruction method using data only from rays parallel to three planes, and a stable reconstruction algorithm for data parallel to siz planes.

Recent joint work with Szotten gives derivation of an algorithm of Aben for solenoidal tensor fields, and a simple method for potential tensor fields.

## 02 March 2009

Dr M. Blyth - University of East Anglia

##### Electrified film flow over topography

Abstract

Film flow over topography arises in numerous practical applications such as industrial coating flows. Topographical features like a protrusion or a depression lead to an uneven film surface which may be unacceptable in a finished product. In this talk, it is demonstrated how an electric field can be used to manipulate film flow over topography to mitigate this problem. In particular, it is shown through numerical calculations how a uniform electric field of sufficient intensity can be used to iron out the so-called capillary ridge arising when a liquid film flows over a rectangular trench. The numerical observations are confirmed through an asymptotic analysis conducted in the limit of small trench depth. The effect of focusing the electric field on a particular part of the flow using an isolated, shaped electrode

held over the flow is also discussed.

## 09 March 2009 - at 4:30pm (Room 500)

Professor C. Alexander - ICMA Centre, Henley Business School at Reading

##### ROM Simulation

Abstract: to follow

ROM simulation is a new approach to multivariate simulation based on random, orthogonal matrices. Unlike Monte Carlo methods there is no simulation error in the means, variances and correlations of the

simulations. The higher sample moments are precisely targeted and no distributional assumptions are made. We realise a sample from a given covariance matrix using an L-Matrix, which is a new class of orthogonal matrix, and explain how to change the features of the sample (e.g. higher moments, volatilty clustering) using different classes of random orthogonal matrices. Applications to finance are described.

## 23 March 2009 (NOT 16 March)

Dr S. Guillas - Dept. of Statistics, UCL

##### Bivariate Splines for Spatial Functional Regression Models

Abstract

We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, with bounded or normal noise. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with or without a penalization term. Under the assumptions that the regressors in the sample are bounded and span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the US that illustrates the predictive skills of the method.