Applied Mathematics Seminars Autumn 2010
TBC
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.
04 October 2010
Prof E. Volkov - Lebedev Physical Institute, Moscow
Multirhythmicity generated by phase-repulsive coupling
Abstract:
The dynamical behavior of coupled identical or near identical oscillators of different nature are considered. It is well known that the type of coupling may define the set of stable attractors which exist and coexist in such ensembles. Using the different examples the role of phase-repulsive coupling, which is realized as local or global diffusion of slow (recovery) variable of oscillator, will be presented. Special attention will be paid to the quenching of oscillation due to coupling, so called “oscillation death”, which is a result of pitchfork bifurcation providing the coexistence of homogeneous oscillation and inhomogeneous steady states.
11 October 2010
Dr. M. Turner - University of Brighton
Cat’s eyes in two-dimensional vortices and their link to quasi-modes
Abstract:
We examine the response of a two-dimensional Gaussian vortex when placed in a rotating strain field. If the amplitude of the strain is large enough it can be switched off and cat’s eyes will persist in the vortex. If the strain amplitude is below some threshold value then the perturbation generated will decay away exponentially with a decay rate that is linked to the quasi-mode of the linear inviscid problem. The talk will also include other results from this topic, depending upon how much time remains.
18 October 2010
Prof. T. Phillips - Cardiff University
On the Effect of Viscoelasticity on Cavitation and Bubble Dynamics
Abstract:
In this talk the effect of viscoelasticity on bubble dynamics is investigated using a boundary element method. Viscoelastic effects are incorporated into the mathematical model through the normal stress balance across the surface of the bubble. A number of situations are modelled including bubble growth, collapse near rigid and free surfaces and rising bubbles. Predictions include damped oscillation with time for spherical dynamics, jet prevention in bubble collapse near boundaries and the cusp at the trailing end of a rising bubble. Consideration is given to the cause of the jump discontinuity in the rise velocity, which is observed once the bubble exceeds a certain critical volume.
25 October 2010
Dr. A. D. Zarnescu - University of Oxford
Mathematical problems of the Q-tensor theory of nematic liquid crystals
Abstract:
The challenge of modelling the complexity of nematic liquid crystals through a model that is both comprehensive and simple enough to manipulate efficiently has led to the existence of several major competing theories. Despite its popularity with physicists, the Q-tensor theory, proposed
by de the Nobel medalist P.G. de Gennes, has received little attention from mathematicians, until a few years ago. In this talk we describe the progress done in the recent years on its mathematical study.
01 November 2010
Dr. D. Dos Santos Ferreira - Paris 13 University
Carleman estimates and anisotropic inverse problems
Abstract:
Calderón’s inverse problem is concerned with the question of determining an electric conductivity from boundary measurements. In this talk, I will first present the method developed by Sylvester and Uhlmann (based on Calderón’s first insights) to prove the identifiability of an isotropic electric conductivity. The method relies on the construction of complex geometrical optics solutions to the
Schrödinger equation. Then I will explain to which extent those techniques can be generalized to anisotropic settings and what are the obstructions that one can encounter. This talk is based on a joint work with Carlos Kenig, Mikko Salo and Gunther Uhlmann.
08 November 2010
READING WEEK - NO SEMINAR
15 November 2010
Prof R. Knops - Heriot-Watt University
Uniqueness in affine boundary value problems for the nonlinear elastic dielectric
Abstract:
An integral identity, constructed from properties of the energy momentum tensor, is used to demonstrate uniqueness of smooth solutions to the title problem on interior and exterior star-shaped and cone-like regions that include the whole and half-space. It is supposed that the electric enthalpy is variously rank-one and quasi-convex, and that certain asymptotic conditions are satisfied for unbounded regions. The methods of proof develop those introduced by Pucci and Serrin, by Knops and Stuart, and by Esteban and Lions.
22 November 2010
Peter A. Markowich - Cambridge and Vienna
On Wigner and Bohmian Measures
Abstract:
TBA
29 November 2010
José A. Carrillo de la Plata - Barcelona
Keller-Segel, Fast-Diffusion and Functional Inequalities
Abstract:
It will be shown how the critical mass classical Keller-Segel system and the critical displacement convex fast-diffusion equation in two dimensions are related. On one hand, the critical fast diffusion entropy functional helps to show global existence around equilibrium states of the critical mass Keller-Segel system. On the other hand, the critical fast diffusion flow allows to show functional inequalities such as the Logarithmic HLS inequality in simple terms who is essential in the behavior of the subcritical mass Keller-Segel system. HLS inequalities can also be recovered in several dimensions using this procedure. It is crucial the relation to the GNS inequalities obtained by DelPino and Dolbeault. This talk corresponds to two works with E. Carlen and A. Blanchet, and with E. Carlen and M. Loss.
06 December 2010
Prof. P. Gritzmann - Munich University of Technology
On Clustering Bodies, Gravity Polytopes and Power Diagrams: Computational Convexity in Agriculture
Abstract:
In geometric clustering, m objects in some R^d have to be partitioned into k clusters according to certain balancing constraints so as to optimize some distance-based objective function. The most prominent example in our context is that of the consolidation of farmland.
In particular, we present new structural and algorithmic results for underlying convex sets and diagrams that are at the basis of surprisingly tight approximation algorithms for optimal clusterings.
13 December 2010
Dr. R.Hoyle - Surrey
Stochastic effects in a two-component signalling system
Abstract:
Two-component signal transduction is a mechanism frequently used by bacteria to adapt to changing environmental signals. Motivated by the desire to understand switching behaviour, such as that involved in the transition between rapid growth and dormancy in Mycobacterium tuberculosis, we compare deterministic and stochastic approaches - including equation-free methods - to the analysis of such a system. We show that the so-called `mixed mode’ response is an intrinsically stochastic phenomenon, and that stochasticity also results in an `all-or-none’ bistable response being observed over a much wider range of external signals than would be expected on deterministic grounds.