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https://dspace.lboro.ac.uk/2134/89
2015-11-29T01:38:23ZBook review of "Algebra teaching around the world" edited by Frederick Koon Shing Leung, Kyungmee Park, Derek Holton and David Clarke.
https://dspace.lboro.ac.uk/2134/19567
Title: Book review of "Algebra teaching around the world" edited by Frederick Koon Shing Leung, Kyungmee Park, Derek Holton and David Clarke.
Authors: Jones, Ian
Abstract: Book review of: Book review of "Algebra teaching around the world" edited by Frederick Koon Shing Leung, Kyungmee Park, Derek Holton and David Clarke. Rotterdam: Sense Publishers, ISBN 99789462097070
Description: This paper is in closed access until 22nd Oct 2016.2015-01-01T00:00:00ZLocal normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics
https://dspace.lboro.ac.uk/2134/19554
Title: Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics
Authors: Bolsinov, Alexey V.; Matveev, Vladimir S.; Rosemann, Steffan
Abstract: Two Kähler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arbitrary signature and use this description to prove the classical Yano-Obata conjecture: we show that on a closed connected Kähler manifold of arbitrary signature, any c-projective vector field is an affine vector field unless the manifold is CPn with (a multiple of) the Fubini-Study metric. As a by-product, we prove the projective Lichnerowicz conjecture for metrics of Lorentzian signature: we show that on a closed connected Lorentzian manifold, any projective vector field is an affine vector field.
Description: This pre-print was submitted to arXiv on 1 Oct 2015.2015-01-01T00:00:00ZCritical control in transcritical shallow-water flow over two obstacles
https://dspace.lboro.ac.uk/2134/19523
Title: Critical control in transcritical shallow-water flow over two obstacles
Authors: Grimshaw, Roger H.J.; Maleewong, Montri
Abstract: The nonlinear shallow-water equations are often used to model flow over topography. In this paper we use these equations both analytically and numerically to study flow over two widely separated localised obstacles, and compare the outcome with the corresponding flow over a single localised obstacle. Initially we assume uniform flow with constant water depth, which is then perturbed by the obstacles. The upstream flow can be characterised as subcritical, supercritical and transcritical, respectively. We review the well-known theory for flow over a single localised obstacle, where in the transcritical regime the flow is characterised by a local hydraulic flow over the obstacle, contained between an elevation shock propagating upstream and a depression shock propagating downstream. Classical shock closure conditions are used to determine these shocks. Then we show that the same approach can be used to describe the flow over two widely spaced localised obstacles. The flow development can be characterised by two stages. The first stage is the generation of upstream elevation shock and downstream depression shock from each obstacle alone, isolated from the other obstacle. The second stage is the interaction of two shocks between the two obstacles, followed by an adjustment to a hydraulic flow over both obstacles, with criticality being controlled by the higher of the two obstacles, and by the second obstacle when they have equal heights. This hydraulic flow is terminated by an elevation shock propagating upstream of the first obstacle and a depression shock propagating downstream of the second obstacle. A weakly nonlinear model for sufficiently small obstacles is developed to describe this second stage. The theoretical results are compared with fully nonlinear simulations obtained using a well-balanced finite-volume method. The analytical results agree quite well with the nonlinear simulations for sufficiently small obstacles.
Description: Closed access until 01 April 20162015-01-01T00:00:00ZModelling of nonlinear wave scattering in a delaminated elastic bar
https://dspace.lboro.ac.uk/2134/19501
Title: Modelling of nonlinear wave scattering in a delaminated elastic bar
Authors: Khusnutdinova, Karima R.; Tranter, Matthew R.
Abstract: Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of the structure. Can nonlinear waves help us to control the quality of layered structures? In this paper, we numerically model the dynamics of a long longitudinal strain solitary wave in a split, symmetric layered bar. The recently developed analytical approach, based on matching two asymptotic multiple-scales expansions and the integrability theory of the Korteweg–de Vries equation by the inverse scattering transform, is used to develop an effective semi-analytical numerical approach for these types of problems. We also employ a direct finite-difference method and compare the numerical results with each other, and with the analytical predictions. The numerical modelling confirms that delamination causes fission of an incident solitary wave and, thus, can be used to detect the defect.
Description: This is an Open Access article published under the Creative Commons Attribution licence (CC BY 4.0).2015-01-01T00:00:00Z