Mathematics
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The Department was founded in 1845. It runs undergraduate programmes in Mathematics, in Computing and in Financial Mathematics. It also offers masters programmes in Mathematics and has a number of PhD students. Details of these programmes can be found on the page for future students.
The Department carries out research in Algebra, Analysis, Geometry/Topology, and Statistics. Details are given on the Department's research page. There is also a weekly seminar. Furthermore, the De Brun Centre is dedicated to computational algebra.
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A refinement of a conjecture of Quillen
(Elsevier ScienceDirect, 201509)We present some new results on the cohomology of a large scope of SL2 groups in degrees above the virtual cohomological dimension, yielding some partial positive results for the Quillen conjecture in rank one. We combine ... 
Incremental equations for soft fibrous materials
(Springer, 2015)The general theory of nonlinear anisotropic elasticity is extended to describe smallamplitude motions and static deformations that can be superimposed on large prestrains of fibrereinforced solids. The linearised ... 
Interface waves in prestressed incompressible solids
(Springer, 2007)We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semiinfinite solid. With a view to model loaded elastomers and soft ... 
Mechanical properties of excised human skin
(Springer Verlag, 2010)In this study we have investigated in influence of location, gender and orientation on the deformation characteristics of 55 samples of human excised skin. Uniaxial tensile tests were carried out at a strain rate of ... 
Multiples of Pfister forms
(Elsevier, 20160301)The isotropy of multiples of Pfister forms is studied. Some classical results are recalled and their consequences presented, with certain of these statements being previously known but hitherto unpublished. In particular, ... 
Toward a predictive assessment of stabpenetration forces
(Lippincott, Williams & Wilkins, 201509)Collaborative research between the disciplines of forensic pathology and biomechanics was undertaken to investigate the hyperelastic properties of human skin, to determine the force required for sharp instrument penetration ... 
ENDOCOM: Abdominal aortic aneurysm test bench for in vitro simulation
(IEEE, 2007)An abdominal aortic aneurysm (AAA) is a dilatation of the aorta at the abdominal level, whose rupture is a life threatening complication. Recent treatment procedures of AAA consists in endovascular treatment with covered ... 
Finiteamplitude Love waves in a prestressed neoHookean material
(2008)In the context of the nonlinear elasticity theory we consider a model for compressible solids called compressible neoHookean material . We show how (exact) finiteamplitude inhomogeneous plane wave solutions and ... 
Uniform transmural strain in prestressed arteries occurs at physiological pressure
(Elsevier, 20120621)Residual deformation (strain) exists in arterial vessels, and has been previously proposed to induce homogeneous transmural strain distribution. In this work, we present analytical formulations that predict the existence ... 
A combined experimental and numerical study of stabpenetration forces
(Elsevier, 201312)The magnitude of force used in a stabbing incident can be difficult to quantify, although the estimate given by forensic pathologists is often seen as 'critical' evidence in medicolegal situations. The main objective of ... 
On stressdependent elastic moduli and wave speeds
(Oxford University Press, 2013)On the basis of the general nonlinear theory of a hyperelastic material with initial stress, initially without consideration of the origin of the initial stress, we determine explicit expressions for the stressdependent ... 
On anisotropic elasticity and questions concerning its Finite Element implementation
(Springer, 20130521)We give conditions on the strainenergy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated ... 
Mechanical characterization of brain tissue in simple shear at dynamic strain rates
(Elsevier, 201312)During severe impact conditions, brain tissue experiences a rapid and complex deformation, which can be seen as a mixture of compression, tension and shear. Diffuse axonal injury (DAI) occurs in animals and humans when ... 
Shear instability in skin tissue
(Oxford University Press, 2013)We propose two toymodels to describe, predict and interpret the wrinkles appearing on the surface of skin when it is sheared. With the first model, we account for the lines of greatest tension present in human skin by ... 
Influence of preservation temperature on the measured mechanical properties of brain tissue
(Elsevier, 20130426)The large variability in experimentally measured mechanical properties of brain tissue is due to many factors including heterogeneity, anisotropy, age dependence and postmortem time. Moreover, differences in test protocols ... 
Deficiencies in numerical models of anisotropic nonlinearly elastic materials
(Springer, 201308)Incompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying ... 
Gent models for the inflation of spherical balloons
(Elsevier, 2015)We revisit an iconic deformation of nonlinear elasticity: the inflation of a rubber spherical thin shell. We use the 3parameter Mooney and GentGent (GG) phenomenological models to explain the stretchstrain curve of a ... 
At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials
(Springer, 20130418)The modelling of offaxis simple tension experiments on transversely isotropic nonlinearly elastic materials is considered. A testing protocol is proposed where normal force is applied to one edge of a rectangular specimen ... 
Extreme softness of brain matter in simple shear
(Elsevier, 20150313)We show that porcine brain matter can be modelled accurately as a very soft rubberlike material using the MooneyRivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments ... 
Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis
(Springer, 20150220)We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the ...