Browsing Mathematics (Scholarly Articles) by Title
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Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations
(The Royal Society, 20110708)We study the propagation of twodimensional finiteamplitude shear waves in a nonlinear prestrained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The ... 
Seismic Rayleigh waves on an exponentially graded, orthotropic halfspace
(The Royal Society, 2007)Efforts at modelling the propagation of seismic waves in halfspaces with continuously varying properties have mostly been focused on shearhorizontal waves. Here, a sagittally polarized (Rayleigh type) wave travels along ... 
Simple shear is not so simple
(201203)For homogeneous, isotropic, nonlinearly elastic materials, the form of the homogeneous deformation consistent with the application of a Cauchy shear stress is derived here for both compressible and incompressible materials. ... 
Slight compressibility and sensitivity to changes in Poisson's ratio
(2012)Finite element simulations of rubbers and biological soft tissue usually assume that the material being deformed is slightly compressible. It is shown here that, in shearing deformations, the corresponding normal stress ... 
Small amplitude waves and stability for a prestressed viscoelastic solid
(Springer, 2009)We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material of differential type. We use bulk waves and surface waves to address the questions of ... 
Solitary and compactlike shear waves in the bulk of solids
(American Physical Society, 200606)We show that a model proposed by Rubin, Rosenau and Gottlieb J. Appl. Phys. 77 4054 (1995) for dispersion caused by an inherent material characteristic length belongs to the class of simple materials. Therefore, it is ... 
Some Generalizations of the MacMahon Master Theorem
(2011)We consider a number of generalizations of the $\beta$extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations ... 
Some Irrational Generalised Moonshine from Orbifolds
(2002)We verify the Generalised Moonshine conjectures for some irrational modular functions for the Monster centralisers related to the HaradaNorton, Held, $M_{12}$ and $L_3(3)$ simple groups based on certain orbifolding ... 
Some results on finite amplitude elastic waves propagating in rotating media
(Springer, 200412)Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic halfspace put into uniform rotation? It is seen that nonlinear ... 
The speed of interfacial waves polarized in a symmetry plane
(Elsevier, 200601)The surfaceimpedance matrix method is used to study interfacial waves polarized in a plane of symmetry of anisotropic elastic materials. Although the corresponding Stroh polynomial is a quartic, it turns out to be ... 
Stoneley waves and interface stability for Bell materials in compression; comparison with rubber
(2005)Two semiinfinite bodies made of prestressed, homogeneous, Bellconstrained, hyperelastic materials are perfectly bonded along a plane interface. The halfspace have been subjected to finite pure homogeneous predeformations, ... 
The stress field in a pulled cork and some subtle points in the semiinverse method of nonlinear elasticity
(The Royal Society, 20071108)In an attempt to describe corkpulling, we model a cork as an incompressible rubberlike material and consider that it is subject to a helical shear deformation superimposed onto a shrink fit and a simple torsion. It turns ... 
The subgroup measuring the defect of the Abelianization of SL_2(Z[i])
(Springer, 20130210)There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 torsion of the Abelianization of SL2(Z) ... 
Surface acoustic waves in rotating orthorhombic crystals
(The Royal Society, 20040208)The propagation of surface (Rayleigh) waves over a rotating orthorhombic crystal is studied. The crystal possesses three crystallographic axes, normal to the symmetry planes: the half¿space is cut along a plane normal to ... 
Surface waves and surface stability for prestretched, unconstrained, nonlinearly elastic halfspace
(Elsevier, 200906)An unconstrained, nonlinearly elastic, semiinfinite solid is maintained in a state of large static plane strain. A power¿law relation between the prestretches is assumed and it is shown that this assumption is well ... 
Surface waves in a deformed isotropic hyperelastic material subject to an isotropic internal constraint
(Elsevier, 2004)An isotropic elastic halfspace is prestrained so that two of the principal axes of strain lie in the bounding plane, which itself remains free of traction. The material is subject to an isotropic constraint of arbitrary ... 
Surface waves in a stretched and sheared incompressible elastic material
(2005)In this paper, we analyze the effect of a combined pure homogeneous strain and simple shear in a principal plane of the latter on the propagation of surface waves for an incompressible isotropic elastic halfspace whose ... 
Surface waves in deformed Bell materials
(2003)Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semiinfinite body made of Bell constrained material. The predeformation corresponds to a finite static pure ... 
Surface waves in orthotropic incompressible materials
(Acoustical Society of America, 20010417)The secular equation for surface acoustic waves propagating on an orthotropic incompressible halfspace is derived in a direct manner, using the method of first integrals. 
The Szegö Kernel on a Sewn Riemann Surface
(2010)We describe the Szegö kernel on a higher genus Riemann surface in terms of Szegö kernel data coming from lower genus surfaces via two explicit sewing procedures where either two Riemann surfaces are sewn together or a ...