Applied Mathematics Seminars Autumn 2009

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.

28 September 2009 - NOW AT 3:30PM IN 500

Professor A. G. Ramm - Kansas State University

Implicit function theorem via Dynamical Systems Method (DSM)

05 October 2009

Dr S. Soussi - University of Limerick 

Transparent boundary conditions for exterior periodic media

12 October 2009

Dr O. Dorn - University of Manchester 

Solving structural inverse problems with level sets

19 October 2009

Dr I Didenkulova - Talinn, Estonia

Analytical theory of long wave runup on a beach

Abstract:

A modern view on the analytical theory of the long sea wave runup on a plane beach is presented. This theory is based on rigorous solutions of nonlinear shallow-water equations. The dynamics of the moving shoreline is studied in detail. The key and novel results presented here are: i) parameterization

of basic formulas for extreme runup characteristics for bell-shape waves, showing that they weakly depend on the initial wave shape, which is usually unknown in real sea conditions; ii) runup analysis of periodic asymmetric waves with a steep front, as such waves are penetrating inland over large distances and with larger velocities than symmetric waves; iii) statistical analysis of irregular wave runup demonstrating that wave nonlinearity nearshore does not influence on the probability distribution of the velocity of the moving shoreline and its moments, and influences on the vertical displacement of the moving shoreline (runup). Wave runup on convex beaches and in narrow bays, which allow abnormal wave amplification, are also discussed. Described analytical results are used for explanation of observed tsunami wave runups on different coasts.

26 October 2009

Dr. P. Dellar - Oxford

Lattice Boltzmann formulation of Braginskii magnetohydrodynamics

Abstract: There’ll be a fair bit of boundary-layer-type analysis of the channel flow problem in Braginskii magnetohydrodynamics as well, but I thought putting that in the title would make it too long.

02 November 2009

Prof. O. Kounchev - Bonn, Germany

Multidimensional Moment problem, Inverse Potential theory, and Gauss type Cubature formulas

Abstract.

The Moment problem and the related theory of Orthogonal polynomials and Quadrature formulas in one dimension were historically one of the main sources for establishing the modern Functional Analysis, and in particular Spectral theory, in the works of Riesz, Nevanlinna, Carleman, M. Stone and others. Later it played a basic role in the Inverse Scattering problem, in the works of Gelfan-Levitan, Marchenko, M. Krein, M. Kac, and others. However the developments in the multidimensional Moment problem and a related theory of multidimensional Orthogonality and Cubature have remained very far from the standards raised by the one-dimensional case. We present a new “PDE” approach to the Multidimensional Moment problem which is related to the Inverse Potential theory; we call this Pseudopositive Moment problem. This setting allows for a generalization of the Gauss quadrature formula and many other classical results in the one-dimensional case.

09 November 2009

NO SEMINAR - READING WEEK

16 November 2009

Professor B. McLeod - University of Oxford 

The motion of protein motors

Abstract

Protein motors are an essential ingredient in life as they enable the body to repair and replicate DNA. The lecture will discuss how to model the motion of protein motors and then discuss some mathematical analysis of the resulting equations.

23 November 2009

Prof V. Smyshlyaev - Bath

Waves in highly heterogeneous media: dispersion and localisation via a”non-classical” homogenization

Abstract: 

We review a “non-classical” homogenization which, in contrast to its classical counterpart, deals with explicit limit asymptotic descriptions which remain multiscale ones. This leads to interesting effects physically (e.g. frequency or “directional” localisation, dispersion etc), and mathematically requires developing novel versions of e.g. multiscale convergence and of the theory of compensated compactness.

30 November 2009 - SEMINAR CANCELLED - RESCHEDULED FOR 18 JAN 2010 

Professor M. Dafermos - University of Cambridge

The black hole stability problem

07 December 2009

Professor A. Korobkin - University of East Anglia 

Impulsive motion of floating plate

14 December 2009

Professor D. Papageorgiou - Imperial College, London

Dynamics of falling film flows: Electrostatic and topographical effects

Abstract:

Viscous liquid films on inclined substrates can be unstable if the angle of inclination is sufficiently large. The ensuing phenomenon has been called “interfacial turbulence” due to the complex dynamics of the free surface even at small Reynolds numbers. In this talk we will derive and study mathematical models that support such observations. In particular we will incorporate the effects of instability, dispersion and high- wavenumber stabilization due to surface tension in order to arrive at an evolution equation of the dissipative-dispersive type. The effects of electric fields will also be included.

Computational and analytical aspects of the model equations will be described. Recent work on analogous problems over topography will also be discussed