Applied Mathematics Seminars Spring 2016

All seminars (unless otherwise stated) will take place on Tuesdays at 3.00pm in Room 505 in the Mathematics Department (25 Gordon Street). See see how to find us for further details. There will be tea afterwards in Mathematics Room 606. If you require any more information on the Applied seminars please contact Prof Slava Kurylev e-mail: y.kurylev AT ucl.ac.uk or tel: 020-7679-7896.

Special Applied Seminar, Monday 11 January 2016 in Room G10, 1-19 Torrington Place

José da Silva (Porto University, Portugal)

Title: SAR imaging of Wave Tails: recognition of second mode internal wave patterns and some mechanisms of their formation

Abstract:
Please click here for José da Silva’s abstract

12 January 2016

Sarah Harris (Leeds University)

Title: Modelling Biomacromolecules with Supercomputers: From atomistic length-scales up to the continuum limit

Abstract:
Computational models have huge potential to provide insight into molecular biology by providing detailed animations of biomolecules and their interactions. In principle, these simulations act as a “computational microscope”, so long as the results that are obtained can be validated against experimental data. Molecular simulation can show how the shapes of biomolecules change due to their thermal motion, how the structure of individual biomolecules is affected by subjecting them to mechanical stress and the possible biological consequences conformational diversity. However, the computational expense of the calculations, which require high performance supercomputer facilities, places serious limitations on the length and time-scales that can be accessed. I shall describe the successes and the challenges of simulations of biomacromolecules at the atomistic level using examples from our own research and present a new algorithm we are developing that uses continuum mechanics to model biomolecular complexes that are far too large to be simulated at the atomistic level. I will conclude by commenting on future prospects for computer simulation in molecular biology.

19 January 2016

Eugene Benilov (Univ. of Limerick, Ireland)

Title: A new model for gas-liquid phase transitions

Abstract:
We examine a rarefied gas with inter-molecular attraction. It is argued that the attraction force amplifies random density fluctuations by pulling molecules from lower-density regions into high-density regions and, thus, may give rise to an instability. To describe this effect, we use a kinetic equation where the attraction force is taken into account similarly to how electromagnetic forces in plasma are treated in the Vlasov model. It is demonstrated that the instability occurs when the temperature drops below a certain threshold value depending on the gas density. It is further shown that, even if the temperature is only marginally lower than the threshold, the instability generates ‘clusters’ with density much higher than that of the gas.

These results suggest that the instability found should be interpreted as gas-liquid phase transition, with the temperature threshold being the temperature of saturated vapour and the high-density clusters representing liquid droplets.

26 January 2016

Andreas Dedner (Warwick University)

Title: Discontinuous Galerkin methods for surface PDEs

Abstract:
The Discontinuous Galerkin (DG) method has been used to solve a wide range of partial differential equations. Especially for advection dominated problems it has proven very reliable and accurate. But even for elliptic problems it has advantages over continuous finite element methods, especially when parallelization and local adaptivity are considered.

After introducing the notation and analysis for DG methods in Euclidean spaces, we will extend the DG method to general surfaces. The surface finite-element method with continuous ansatz functions was analysed some time ago; we extend this results to a wide range of DG methods for stationary advection-diffusion problems. The non-smooth approximation of the surface introduces some additional challenges not observed when using continuous ansatz spaces. Both a-prioir and a-posteriori analysis of the DG is presented together with numerical experiments.

2 February 2016

David Silvester (Manchester University)

Title: Adaptive algorithms for PDEs with random data

Abstract:
An efficient adaptive algorithm for computing stochastic Galerkin finite element approximations of elliptic PDE problems with random data will be outlined in this talk. The underlying differential operator will be assumed to have affine dependence on a large, possibly infinite, number of random parameters. Stochastic Galerkin approximations are sought in a tensor-product space comprising a standard $h-$ finite element space associated with the physical domain, together with a set of multivariate polynomials  characterising a $p-$ finite-dimensional manifold of the (stochastic) parameter space.

Our adaptive strategy is based on computing distinct error estimators associated with the two sources of discretisation error. These estimators, at the same time, will be shown to provide effective estimates of the error reduction for enhanced approximations.  Our algorithm  adaptively `builds’ a polynomial space over a low-dimensional manifold of the infinitely-dimensional parameter space by reducing the energy of the combined discretisation error in an optimal manner. Convergence of the adaptive algorithm will be demonstrated numerically.

9 February 2016 -Colloquium Talk

Prof Malwina Luczak (Queen Mary, University of London)

- please see the Departmental Colloquia webpage

16 February 2016

READING WEEK - NO SEMINAR

23 February 2016

Christian Klettner (UCL)

Title: The effect of a uniform through-surface flow on a cylinder and sphere

Abstract:
The effect of a uniform through-surface flow on a rigid cylinder and sphere fixed in a free stream  is analysed analytically and numerically. The flow is characterised by a dimensionless blow velocity  and Reynolds number. High resolution numerical calculations are compared against theoretical predictions.

When there is strong suction, the flow is viscously dominated in a thin boundary layer adjacent to the rigid surface. The flow downstream of the body is irrotational so the wake volume flux is zero and the drag force can be determined by a global momentum analysis. A dissipation argument is applied to analyse the drag force; the rate of working of the drag force is balanced by viscous dissipation, flux of energy and rate of work by viscous stresses due to sucking. 

When there is a blowing flow, the boundary layer thickness initially grows linearly with time as vorticity is blown away from the rigid surface. For large blow velocity, the vorticity is swept into two well-separated shear layers and the maximum vorticity decreases due to diffusion. The drag force is related exactly to the vorticity distribution on the body surface and an approximate expression can be derived by considering the first term of a Fourier expansion in the surface vorticity.

1 March 2016

Gareth Parry (Nottingham University)

Title: Discrete structures in continuum descriptions of defective crystals

Abstract:
I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular I provide a quite general list of ‘plastic strain variables’, which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification.

8 March 2016

Franco Florini (Instituto Balseiro, Argentina)

Title: Some regular aspects of Born-Infeld gravity

Abstract:
In this talk, I will review some of the regularity properties of a new deformed scheme for the description of the gravitational field known as Born-Infeld determinantal gravity. Apart from the early success achieved within this framework concerning the regularization of the Big Bang singularity in FRW-like cosmological scenarios, I will discuss more subtle regularization mechanisms emerging from this theory. In particular, and going over through a number of specific examples, I will focus on how geodesic completeness emerges out sometimes within this context. Finally, I will comment on some lines of current research and a few open problems I would like to share with the audience.

Special Applied Seminar, Friday 11 March 2016 in Room 505 at 4pm

Wooyoung Choi (New Jersey Institute of Technology)

Title: Predicting highly nonlinear ocean waves with breaking - is it possible?

Abstract:
The accurate prediction of nonlinear ocean waves is a challenging task due to complicated nonlinear interactions among waves of different spatial scales ranging from centimeters up to kilometers. Another source of difficulty lies in a lack of our understanding of various physical processes in the ocean including wave breaking and wind forcing. In this talk, our recent efforts to develop theoretical models to describe the evolution of nonlinear ocean waves will be described. Validation of the models with laboratory experiments will be presented and some remaining challenges will be discussed.

15 March 2016 - CANCELLED

Ivan Graham (Bath University)

Title: Non-uniformly elliptic problems with random coefficients

Abstract:
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).

**This seminar has been cancelled.**

22 March 2016

Roger Grimshaw (UCL)

Title: Depression and elevation tsunami waves in the framework of the Korteweg-de Vries equation 

Abstract:
Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. Here we use a variable-coefficient Korteweg-de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each.  We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train, and find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a prefactor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave.