Applied Mathematics Seminars 

Autumn 2016

All seminars (unless otherwise stated) will take place on Tuesdays at 3.00pm in Room Physics A1/3 (Physics Building, Gower Street). See the map for further details. There will be tea afterwards in Mathematics Room 606 (25 Gordon Street). If you require any more information on the Applied seminars please contact Prof Slava Kurylev e-mail: y.kurylev AT or tel: 020-7679-7896.

4 October 2016

Berangere Delourme (Paris 13 University, France)

Title: Homogenization of a thin perforated wall of finite length

This talk deals with the resolution of a scattering problem in a domain made of a thin and periodic layer of finite length placed into an homogeneous medium. The presence of this thin periodic layer of holes is responsible for the appearance of two different kinds of singular behaviors. First, a highly oscillatory boundary layer appears in the vicinity of the periodic layer. Additionaly, since the thin periodic layer has a finite length, corners singularities come up in the neighborhood of its extremities. Based on an approach mixing matched asymptotic expansions and (surface) periodic homogenization, we provide and justify a high order asymptotic expansion which takes into account these two phenomena. Numerical experiments are carried out to illustrate the method.

11 October 2016

Prof Ivan Graham (University of Bath)

Title: High dimensional problems arising from PDE with random coefficients

We consider non-uniformly elliptic problems with  coefficients given as lognormal random fields.  We focus on  the forward problem of assessing how uncertainty propagates from data to solution, which leads to very high-dimensional parametrised systems of PDEs. We combine the fast realisation of data via circulant embedding techniques with quasi-Monte Carlo methods for dealing with high dimension. We prove rates of convergence independent of dimension and illustrate the results on some problems motivated by flow in porous media.

This is joint work with Rob Scheichl (Bath) and Frances Kuo and Ian Sloan (New South Wales)

18 October 2016

Dr Rhodri Nelson (Imperial College of London)

Title: Potential problems in multiply-connected domains

The talk will begin by briefly introducing the Schottky-Klein Prime (SKP) function and following this a new and efficient method for computing this function and its derivatives will be presented. This SKP function is then used as the basis of a calculus for solving potential problems in multiply-connected domains. Some examples, including the motion of vortex patches in multiply-connected domains and waterflooding in an oil resevoir, are then given.

25 October 2016

Please see the Departmental Colloquia webpage

1 November 2016

Dr Hanne Kekkonen (Warwick University)

Title: Posterior consistency and convergence rates for Bayesian inversion

We consider an indirect noisy measurement of an unknown physical quantity of interest. The measurement, the additive noise and the unknown are treated as random variables. We are interested to know what happens to the approximate solution of the unknown when the noise amplitude goes to zero. The analysis of small noise limit, also known as the theory of posterior consistency, has attracted a lot of interest in the last decade. However, much remains to be done. Developing a comprehensive theory is important since posterior consistency justifies the use of the Bayesian approach the same way convergence results do the use of regularisation techniques.

15 November 2016

Prof Jonathan Healey (Keelee University)

Title: On the mechanisms, and control, of boundary layer instability

The stability of laminar boundary layers has been investigated intensively for a long time, and remains central to the fundamental problem of predicting and controlling transition to turbulence. And yet some aspects are not easily explained, like why does viscosity destabilize flows? We present a new interpretation of the Orr-Sommerfeld equation (which describes shear layer instabilities) as a coupled oscillator system, and show how it leads to suggestions for flow modifications with strong stabilizing properties, even when the modifications create inflexion points.