Log in
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.
It is well-known that certain bridges are susceptible to potentially dangerous uncontrolled vibrations; recent examples include London's Millennium Bridge and the Volga Bridge in Volgograd. Correcting such problems after the construction of the bridge can be extremely expensive and time-consuming. Research in the Department of Mathematical Sciences at the University of Liverpool has led to a novel approach for predicting such behaviour in advance and then modifying the bridge design so as to avoid it. During the period 2011-12 this research has been incorporated into standard design procedures by industrial companies involved in bridge design. There is an economic impact for the companies concerned (avoiding costly repairs after bridge construction) and a societal impact (improvements in public safety and also avoiding the inconvenience of long-term closure of crucial transport links).
The research is based on a novel, highly non-trivial approach that has been developed to study properties of elastic waves in complex engineered structures with a multi-scale pattern. The work has been taken up by the industrial construction company ICOSTRADE S.R.L. Italy, whose design engineer Dr Gian Felice Giaccu integrated the innovative research ideas into their standard design procedures for complex structures such as multiply supported bridges. Novel designs of wave by- pass systems developed by the Liverpool group have also been embedded in standard algorithms by the industrial software company ENGINSOFT, in the framework of a project led by their project manager Mr. Giovanni Borzi.
This case study describes the impact of research at Loughborough University from 2009-2012 into the mathematical modelling of the dynamics of ions using perturbation theory of Hamiltonian systems of equations. Outcomes from this research have been incorporated into software used for the performance modelling of a series of high-precision Fourier Transform Mass Spectrometers manufactured by Thermo Fisher Scientific GbmH and branded as OrbitrapTM with an average price $0.5 million. The derived methodology reduces the time of numerical modelling of the behaviour of charged particles in an OrbitrapTM instrument by a factor of 100 to 1000. This reduction is of significant benefit to the Life Science Mass Spectrometry, Scientific Instrumentation Division of Thermo Fisher Scientific and indirectly the users of the instrument.
Since 1995, Loughborough's research into vibro-impact systems (VIS) has made handheld breaker tools safer for operators and has also increased machining efficiency. Users have been prone to detrimental `hand arm vibration' effects of multiple impacts, including the debilitating condition `white finger'. JCB applied the research findings in its HM25LV breaker design, introduced in 2008, which despite being more powerful exhibits half the hand arm vibration of competitors. JCB has sold more than 1,800 units in the UK and abroad.
University of Bradford research has enabled a material manufacturing company, Armacell, to reuse up to 95% of its production waste to produce new, high-value acoustic products with up to 50% better acoustic performance than any competition products of similar size. We protected the developed IP through several international patents and set up a spin-off company, Acoutechs Ltd, to explore this technology commercially. These materials are now used to reduce noise levels below the recommended limits and to improve the general acoustic quality of spaces at home and work for the benefit of public health. The products generate an annual turnover of more than €4 million for Armacell and prevent more than 500 tonnes of plastic waste from going into landfill annually.
Spatial decomposition methods have been extended to apply to spatial, scale, and temporal domains as a result of work at the Numerical and Applied Mathematics Research Unit (NAMU) at the University of Greenwich. This work has led to a numerical framework for tackling many nonlinear problems which have been key bottlenecks in software design and scientific computing. The work has benefitted the welding industry in the UK because these concepts are now embedded, with parallel computing, in the industry's modern welding design process software.
A new hybrid analysis method, arising from research at the University of Cambridge Department of Engineering (DoEng), unites Statistical Energy Analysis (SEA) with Finite Element Analysis (FEA) to enable full-spectrum vibro-acoustic analysis of large and complex structures with modest computing resources for the first time. The method also allows for uncertainties in the manufacturing process. This research breakthrough has been exploited by ESI Group (ESI), which is a company that provides virtual prototyping solutions, in commercial software licensed to more than 600 companies across a wide range of industrial sectors to improve product design and performance with regard to vibrations and noise. Typical applications include the prediction and reduction of interior noise in automotive and aerospace structures, and the assessment of launch- induced vibration levels in satellite structures.
This study demonstrates how Bayes linear methodologies developed at Durham University have impacted on industrial practice. Two examples are given. The approach has been applied by London Underground Ltd. to the management of bridges, stations and other civil engineering assets, enabling a whole-life strategic approach to maintenance and renewal to reduce costs and increase safety. The approach has won a major award for innovation in engineering and technology. The methodology has also been applied by Unilever and Fera to improve methods of assessing product safety and in particular the risk of chemical ingredients in products causing allergic skin reactions.