Developing mathematics of new composites of metamaterials
Lead Research Organisation:
University of Manchester
Department Name: Mathematics
Abstract
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.
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.
Organisations
Publications
Assier R
(2023)
A contribution to the mathematical theory of diffraction: a note on double fourier integrals
in The Quarterly Journal of Mechanics and Applied Mathematics
Davey R
(2022)
An Efficient Semi-Analytical Scheme for Determining the Reflection of Lamb Waves in a Semi-Infinite Elastic Waveguide
in Applied Sciences
Kunz V
(2023)
Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
in Quarterly Journal of Mechanics and Applied Mathematics
Nethercote M
(2022)
Diffraction of Acoustic Waves by a Wedge of Point Scatterers
in SIAM Journal on Applied Mathematics
Nethercote M
(2022)
Array scattering resonance in the context of Foldy's approximation
in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Nethercote MA
(2023)
Diffraction of acoustic waves by multiple semi-infinite arraysa).
in The Journal of the Acoustical Society of America
Description | New understanding has been obtained how to model complicated material which might be able to absorb unwanted sound. There is additional funding from other sources to investigate this further. |
Exploitation Route | In the long run this could be used to reduce unwanted noise. |
Sectors | Manufacturing, including Industrial Biotechology |
Description | Volunteer at New Scientist Live on the UK Acoustics Network stand |
Geographic Reach | National |
Policy Influence Type | Influenced training of practitioners or researchers |
Impact | Some of the exhibits in our stand were very popular with older generations and school children alike because of their seemingly impossible features. Because of this, it is highly likely that we have played an active role in convincing many youngs minds, from age 4 to 18 to pursue interests in science and engineering. |
Description | David Crighton Fellowship |
Amount | £4,000 (GBP) |
Organisation | University of Cambridge |
Sector | Academic/University |
Country | United Kingdom |
Start | 01/2023 |
End | 04/2023 |
Description | Enhanced Research Expenses |
Amount | £80,000 (GBP) |
Organisation | The Royal Society |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 04/2023 |
End | 01/2024 |
Description | Presentation at the Isaac Newton Institute |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | A gathering of academic researchers from around the world to engage in a week long workshop on canonical scattering problems at the Isaac Newton Institute in Cambridge University. This was part of a six month long programme to discuss current research and ways forward in multiple wave scattering problems. |
Year(s) Of Engagement Activity | 2023 |
URL | https://www.newton.ac.uk/seminar/38379/ |