University of Durham

Composite materials make up over 50% of recent aircraft constructions. They are manufactured from very thin fibrous layers  (~10^-4 m) and even  thinner resin interfaces (~10^-5 m). To achieve the required strength, a particular layup sequence of orientations of the anisotropic fibrous layers is used. During manufacturing, small localised defects in the form of misaligned fibrous layers can occur in composite materials, adding an additional level of complexity. After FE discretisation the model exhibits multiple scales and large spatial variations in model parameters. Thus the resultant linear system of equations can be very ill-conditioned and extremely large. The limitations of commercially available modelling tools for solving these problems has led us to the implementation of a robust and scalable preconditioner called GenEO for parallel Krylov solvers. I will discuss using the GenEO coarse space as an effective multiscale model for the fine-scale displacement and stress fields. For the coarse space construction, GenEO computes generalised eigenvectors of the local stiffness matrices on the overlapping subdomains and builds an approximate coarse space by combining the smallest energy eigenvectors on each subdomain via a partition of unity.

A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact @email.

Topological spaces and manifolds are commonly used to model configuration
spaces of systems of various nature. However, many practical tasks, such as
those dealing with the modelling, control and design of large systems, lead
to topological problems having mixed topological-probabilistic character
when spaces and manifolds depend on many random parameters.
In my talk I will describe several models of stochastic algebraic topology.
I will also mention some open problems and results known so far.

While studying growth of lattices in semisimple Lie groups we

encounter many interesting number theoretic problems. In some cases we

can show an equivalence between the two classes of problems, while in

the other the true relation between them is unclear. On the talk I

will give a brief overview of the subject and will then try to focus

on some particularly interesting examples.

Trevor Wishart writes "I realise 'irrational' means something very specific to a mathematician, and I'm not using the word in that sense."

Abstract:

Trevor Wishart will discuss the use of Digital Signal Processing as a tool in musical composition, ranging from the application of standard analysis procedures (e.g. windowed Fourier Transforms), and common time-domain methods (Brassage), to more unconventional approaches (e.g. waveset distortion, spectral tracing, iterative-extension). He will discuss the algorithms involved and illustrate his talk with musical examples taken from his own work.

This workshop is linked to a musical performance of "Two Women" and "Globalalia" by Trevor Wishart in the Jacqueline du Pre concert hall that evening (5th Feb) at 8pm as part of the Music Department's "New Music Forum". Tickets are £12 (or £8 concession) but if you are interested please let me know (Rebecca Gower, @email or 152312) as we may be able to negotiate a much lower price for members of the Mathematical Institute in a group associated with his workshop.

Trevor will also be giving two lectures in the Denis Arnold Hall, Faculty of Music on the 3rd and 4th Feb which are open to the public and admission is free.

I will describe a topological approach to the motion planning problem of

robotics which leads to a new homotopy invariant of topological spaces

reflecting their "navigational complexity". Technically, this invariant is

defined as the genus (in the sense of A. Schwartz) of a specific fibration.

Meeting to mark Sir Roger Penrose's 75th Birthday