Developing mathematics of new composites of metamaterials

根据世界卫生组织和欧盟委员会的数据，由于环境噪音，欧洲每年至少有1亿人受到影响，160万健康寿命损失。我们的目标是通过开发由特殊材料（超材料）组合而成的新型面板来减轻噪音污染的负担。声学超材料是数学、物理和材料科学合作设计的新技术的一个典型例子。超材料是一种工程材料，具有自然界中没有的惊人特性。重要的是，超材料的潜力首先在理论上被发现，然后由约翰·彭德里爵士证明是可行的。超材料通常是通过三维或二维方式的一些单元格的周期性排列来建模的。超材料比传统材料更薄更轻，同时实现相同的降噪效果，这是一种在实际应用中非常受重视的特性。它们的主要限制是噪声吸收的相对窄的频带宽度。这个项目的目的是发展基础数学，这将允许联合收割机不同的超材料结合在一个复合吸收板的增强性能。创建这样的复合材料是一个复杂的问题，需要考虑许多因素。分析方法是一种快速探索不同设计可能性的廉价方法，特别适合这一挑战。它们还提供了对潜在物理机制的见解，因此是有针对性的适应的关键。在这一新领域中，分析探讨的基本问题将成为进一步实验和数值研究的基石。

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.