Developing mathematics of new composites of metamaterials

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According to the World Health Organisation and the European Commission, at least 100 million people are affected and 1.6 million healthy years of life are lost every year in Europe due to environmental noise. We aim to reduce the burden of noise pollution by developing new panels made of special materials (metamaterials) combined together. Acoustic metamaterials are a prime example of a new technology that is designed in collaboration between the mathematical, physical and material sciences. Metamaterials are engineered materials which exhibit breathtaking properties not found in nature.Importantly, the potential of metamaterials has been first discovered theoretically and then shown to be practically possible by Sir John Pendry. Metamaterials are usually modelled through the periodic arrangement of some unit cells in a 3-D or a 2-D fashion. Metamaterials are much thinner and lighter than conventional materials while achieving the same noise reduction, a property highly valued in their practical use. Their main limitation is the relative narrow frequency band width of the noise absorption. This project aims to develop the fundamental mathematics which would allow to combine different metamaterials in one composite absorbing panel of enhanced properties. Creating such composites is a complicated problem with many factors to consider. Analytic methods, an inexpensive way of rapidly exploring different design possibilities, are particularly suited to this challenge. They also offer insights into the underlying physical mechanisms and are hence key to tailored adaptations. The fundamental problems explored analytically in this new area will form the cornerstones for further experimental and numerical investigations.