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A novel application of parametric resonance (PR) is described, which has improved the effectiveness of a vibrating screen used for size-sorting of crushed rock. These improvements have had an economic impact on the Ukrainian company that makes the screens: the mathematics developed in Aberystwyth permits a stable, high amplitude PR-regime to be found, reducing the damage to the screen mesh and increasing its longevity. This new technology is allowing the company to reduce costs and equipment downtime and is enabling them to gain a market advantage by being able to sort wetter materials than previously.
Large-amplitude horizontally propagating internal solitary waves commonly occur in the interior of the ocean. This case study presents evidence to demonstrate the impact of research conducted by Professor Grimshaw at Loughborough University on the development and utilisation of Korteweg- de Vries (KdV) models of these waves, which has formed the paradigm for the theoretical modelling and practical prediction of these waves.
These waves are highly significant for sediment transport, continental shelf biology and interior ocean mixing, while their associated currents cause strong forces on marine platforms, underwater pipelines and submersibles, and the strong distortion of the density field has a severe impact on acoustic signalling.
The theory developed at Loughborough University has had substantial impact on the strategies developed by marine and naval engineers and scientists in dealing with these issues.
The US National Institute of Science & Technology (NIST) "Digital Library of Mathematical Functions" (DLMF) available at http://dlmf.nist.gov/ is an online resource which informs the general public by making detailed properties of elementary and higher functions freely available to all. The DLMF together with its print companion, the new NIST Handbook of Mathematical Functions, published by Cambridge University Press (CUP, 2010), replaces and updates the National Bureau of Standards Handbook of Mathematical Functions (Abramowitz & Stegun), a classic source which is one of the best-selling mathematics texts of all time. The fact that the 10-year DLMF project has been led and funded by NIST, part of the US Department of Commerce, is a measure of the economic importance of making this information publically available, so that science and engineering practitioners can use it freely. In addition, CUP has already received considerable benefit through the strong sales of the NIST Handbook since its publication, and prestige from the praise that the DLMF has already received from the US government and industrial societies.
A chapter of the new Handbook has been contributed by a member of the School of Mathematics, Statistics and Actuarial Science, and is based on research carried out at Kent. The provision of this information in an interactive format raises awareness and understanding, and enhances the work of practitioners such as industrial scientists and teachers in disciplines outside mathematics, by allowing them easy and immediate access to the most relevant and up to date research results in this area.
A software package called CPO has been developed that simulates the motion of charged particles in electromagnetic fields. More than 200 benchmark tests have established CPO as the gold standard in low-energy charged-particle optics. A spin-off company was formed to market CPO, [text removed for publication]
Professor Peter Giblin (Department of Mathematical Sciences at the University of Liverpool), together with collaborators, used methods from singularity theory to develop an approach for recovering 3-d information from 2-d images, such as photos. In the past decade, these have been implemented and built upon by software engineers, leading to significant cultural, economic and societal impacts. These include the creation of an innovative 25m high sculpture of the human body in the Netherlands by the sculptor Antony Gormley and the virtual modelling of clothing on online clothing websites such as Tesco's (Virtual Changing Room by Tesco/F&F). These have reached thousands of consumers worldwide and represent a significant commercial success for the company which developed the software.