Geometry and Topology Seminar: Asymptotic analysis of partially degenerating multi-scale variational problems
27 April 2017 13:00 in CM221
A recent class of composite materials, known as Metamaterials, have gained much attention and interest in the Mathematics and Physics community over the last decade or so. These composites can roughly be characterised as exhibiting much more pronounced physical properties than their constituent components. These responses are due to scale-interaction effects.Mathematically, such metamaterial type effects could be rigorously justified and explained due to 'partial degeneracies' in underlying multi-scale continuum models.
In this talk, we shall introduce a notion of a partial degeneracy in parameter-dependent variational systems, motivated by examples from classical and semi-classical homogenisation theory, and present an approach to study the leading-order asymptotics of such systems. The determined asymptotics of the variational system can serve as effective models for phenomena due to multi-scale interactions and are given with order-sharp error estimates in the uniform operator topology.
This is joint work with Dr Ilia Kamotski(UCL) and Prof. Valery Smyshlyaev(UCL).