University of Bath

Liquid crystals are classical examples of mesophases or materials that are intermediate in character between conventional solids and liquids. There are different classes of liquid crystals and we focus on the simplest and most widely used nematic liquid crystals. Nematic liquid crystals are simply put, anisotropic liquids with distinguished directions and are the working material of choice for the multi-billion dollar liquid crystal display industry. In this workshop, we briefly review the mathematical theories for nematic liquid crystals, the modelling framework and some recent work on modelling experiments on confined liquid crystalline systems conducted by the Aarts Group (Chemistry Oxford) and experiments on nematic microfluidics by Anupam Sengupta (ETH Zurich). This is joint work with Alexander Lewis, Peter Howell, Dirk Aarts, Ian Griffiths, Maria Crespo Moya and Angel Ramos.
We conclude with a brief overview of new experiments on smectic liquid crystals in the Aarts laboratory and questions related to the recycling of liquid crystal displays originating from informal discussions with Votechnik ( a company dealing with automated recycling technologies , http://votechnik.com/).
 

Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretised, they lead to ill-conditioned linear systems, often of huge dimensions: regularisation consists in replacing the original system by a nearby problem with better numerical properties, in order to find meaningful approximations of its solution. In this talk we will explore the regularisation properties of many iterative methods based on Krylov subspaces. After surveying some basic methods such as CGLS and GMRES, innovative approaches based on flexible variants of CGLS and GMRES will be presented, in order to efficiently enforce nonnegativity and sparsity into the solution.

In this talk I will present a recent result on the characterisation of the equilibrium measure for a nonlocal and non-radial energy arising as the Gamma-limit of discrete interacting dislocations.

Some models for climate change, the good the bad and the ugly

Modelling climate presents huge challenges for mathematicians and scientists, and has a large effect on policy makers.  Climate models themselves vary from simple to complex with a huge range in between.  But how good and/or reliable are they?

In this talk I will describe some of the various mathematical models of climate that are both used to understand past climate and also to predict future climate.  I will also try to show that an understanding of non-smooth effects in dynamical systems can give us useful insights into the behaviour and analysis of these models.

The requirement to compute Jordan blocks for multiple eigenvalues arises in a number of physical problems, for example panel flutter problems in aerodynamical stability, the stability of electrical power systems, and in quantum mechanics. We introduce a general method for computing a 2-dimensional Jordan block in a parameter-dependent matrix eigenvalue problem based on the so called Implicit Determinant Method. This is joint work with Alastair Spence (Bath).