Applied Mathematics Seminars
These seminars take place on Tuesdays, in Room M/2.06, Senghennydd Road, Cardiff from 4pm, unless otherwise stated.
When a seminar is not scheduled there is a collaborative workshop with other groups within the College of Physical Sciences & Engineering or a SIAM Chapter Meeting. Further details can be found on the School Diary.
For more information or if you wish to give a talk, please contact the programme organiser Dr Angela Mihai.
15 October 2013
Speaker: Thomas Lessinnes (University of Oxford).
Title: Birods: theory and applications.
Abstract: Nature abounds with filamentary, rod-like structures. Be it trunks, stems, rhubarb stalks, pollen tubes, arteries, neurons, microtubules, or linear macromolecules, filaments are known to exhibit similar instabilities and mechanical behaviours. In this seminar I will give a rapid introduction to Kirchhoff's rod theory and show how growth and remodeling is usually incorporated in it. Often in practical applications (of which I will consider a few) growth is spatially limited by walls or attachment to different mechanical bodies. This incompatibility leads to various buckling and makes for a rich landscape of shape formation. A framework will be presented that allows to practically treat "morphoelastic rods problems" and a couple of examples will be developed to illustrate how to apply it.
29 October 2013
Speaker: Andrew Wathen (University of Oxford).
Title: Iterative linear solvers for PDE-constrained optimization involving fluid flow.
Abstract: Many control problems for PDEs can be expressed as Optimization problems with the relevant PDEs acting as constraints. As is being discovered in other areas such as multi-physics, there seem to be distinct advantages to tackling such constrained Optimization problems all-at-once' or with a `one-shot' method. That is, decoupling of the overall problem in some loosely coupled iterative fashion appears to be a rather poorer approach than to compute on the fully coupled problem.
The use of iterative methods for the relavant linear algebra is crucial here since the overall dimensions (including the Optimization and PDE) are usually very large, but matrix vector products as required in Krylov subspace methods such as MINRES are still readily computed. The work to ensure rapid convergence is in preconditioning and it is this topic that we will mostly focus on in this talk.
We will describe our general approach via block preconditioning and demonstrate its use for the control of Poisson and Stokes problems and also for the fully time-dependent heat equations.
5 November 2013
Speaker: Tomasz Koziara (University of Durham).
Title: Some basic of the Discrete Element Method and how it can be improved (does anybody know, please?).
Abstract: I am going to share some thoughts on a "large brushstrokes" program of the refinement of DEM, idealistically aimed at more realistic/efficient simulations driven by less material parameters. I will try to sketch the avenue from the rigid particle - deformable interface law paradigm towards the deformable particle - rigid interface law one. I will show some old and, hopefully, some new preliminary results.
12 November 2013
Speaker: Alison Ramage (University of Strathclyde, Glasgow).
Title: Efficient iterative solvers for director-based models of liquid crystal devices.
Abstract:Whenever Lagrange multipliers are used for the pointwise unit-vector constraints in director modelling of liquid crystals, or in both director and order tensor models when an electric field that stems from a constant voltage is present, the resulting discretised equations take the form of saddle-point problems. For the construction of bifurcation diagrams illustrating the various types of behaviour a particular device exhibits, these equations must be solved many times, so it is important that this is done as efficiently as possible. In this talk we discuss a preconditioned iterative solver particularly suited to director models and illustrate its performance on a model of a Twisted Nematic device. This is joint work with Eugene C. Gartland, Jr., Department of Mathematical Sciences, Kent State University.
19 November 2013
Speaker: Hamid Ghasemi (Bauhaus University Weimar, Germany).
Title: Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach.
Abstract: A comprehensive stochastic optimization algorithm for finding the optimum fiber content and its distribution in solid composites characterized by uncertain design parameters is presented. Firstly, the optimum amount of fiber in a FRC structure with uniformly distributed fibers is conducted in the framework of Reliability Based Design Optimization (RBDO) problem. Secondly, the fiber distribution optimization having the aim to increase the structure reliability more is performed by defining a fiber dispersion function through a Non-Uniform Rational B-Spline (NURBS) surface. These two stages iterate sequentially and interactively till satisfying convergence criterion. The target parameter provided by the proposed computational procedure is the reliability index (a measure for probability of structural failure) of the final structure with optimum fiber content and optimum fiber distribution. First order reliability method has been implemented in order to approximate the limit state function while a homogenization approach, based on the assumption of random orientation of fibers in the matrix, has been adopted. A number of static loading test examples are conducted to demonstrate the capability and reliability of the present model.
3 December 2013
Speaker: Peter Stewart (University of Glasgow).
Title: Coalescence and fracture of gas-liquid foams.
Abstract: We construct a large-scale network model for the dynamics and stability of gas-liquid foams which explicitly incorporates hydrodynamic effects in the liquid films between adjacent gas bubbles. We use two example problems to demonstrate how these microscale flows can play a significant role in determining the macroscale behaviour of the foam. Firstly, we consider batch processing of high-porosity metallic solids from molten metal foams (produced without surfactant) where the liquid bridges separating adjacent bubbles drain rapidly and break due to inter-molecular attractions, leading to bubble coalescence. We characterise this coalescence process over both short and long timescales, and demonstrate that the evolution of the foam is remarkably self-similar over a wide range of parameter space. Secondly, we consider the fracture of (aqueous) gas-liquid foams under an applied driving pressure, elucidating the two distinct fracture modes observed in experiment which are analogous to the brittle and ductile failure mechanisms of crystalline solids.
Co-Host: Maurice Blount
11 February 2014
Speaker: David Silvester (University of Manchester).
Title: A posteriori error estimation for stochastic Galerkin approximation.
18 February 2014
Speaker: Adrian Hill (University of Bath).
Title: Sharp Bounds on a Matrix Function.
25 February 2014
Speaker: Paul Ledger (Swansea University).
Title: Characterising the shape and material properties of hidden targets from magnetic induction data.
4 March 2014
Speaker: Jennifer Pestana (University of Manchester).
Title: Solving saddle point systems: the Batman factorisation and preconditioners.
11 March 2014
Speaker: David Kay (University of Oxford).
Title: A Porous-Elastic Model of the Lung.
8 April 2014
Speaker: Rebecca Lingwood (University of Cambridge).
Title: The rotating-disk boundary layer: edge effects and other recent results.
Co-Host: Chris Davies