School of Mathematics

Events

SoM Colloquium: Prof. David Abrahams (Cambridge, INI)

October 4th 14:05 - 15:05

Description: SoM Colloquium Fri, Oct 4th, 2019Time: 2:05 -- 3:00Location: JCMB 6206Prof. David Abrahams NM Rothschild & SonsProfessor of Mathematical SciencesDirector, Isaac Newton Institute forĀ  Mathematical Sciences, University of Cambridge, UK https://idabrahams.weebly.com/https://www.newton.ac.uk/about/history/abrahamsTitle: Complex analytic methods for determining effective wave propagation in compositesAbstract: This talk will cover a variety of topics which hopefully shall offer a flavour of applied mathematical methods to characterise the effective properties of multi-phase materials. Such composites appear everywhere, from electromagnetics through modern engineering laminates to granular materials. Determining the wave propagation characteristics for such composites may be required for evaluation, inspection or design purposes, and this is the principal objective of the present research.In order to increase the interest and accessibility of the talk, we shall focus on the use of complex variable methods for tackling problems in this area, and focus on simple one-dimensional and two-dimensional models that exhibit behaviour similar to that found in more complicated cases.We shall commence the talk with a look at the Wiener-Hopf technique, its solution procedure and limitations, and then discuss how this may be useful for certain simple wave models. We sketch the approach for materials with periodically arranged microstructure, and then to the scaterring properties at the surface of random composites. The latter shall be approached by use of ensemble averaging and the quasi-crystalline approximation. The main conclusion of the talk will be the recently-found result that random composites permit more than a single effective wave, and that all such waves are required to accurately predict the scattering coefficients in any given case.This talk will be accessible to a wide mathematics audience including students.