the uniqueness of hill s spherical vortex the mathematical description of steady vortex rings in an ideal fluid occupying the whole space r3 can be approached in various ways the physical basis of the problem its history up to 1973 and several formulations are outlined in 12 pp 14 21 another quite different formulation and the plan for a corresponding existence theory are presented in 6 further existence theorems variational principles and results are to be found in 3 7 11 13 and 20 here we state only definitions and equations that seem relevant to our immediate purpose

a constrained variational problem for an existence theorem of a steady vortex pair in two phase shear flow abstract we prove an existence theorem for a steady vortex pair in two phase shear flow in a planar domain the method used is a variational principle in which the kinetic energy is maximised subject to the vorticity belonging to the weak closure of the set of rearrangements of a prescribed function and subject to another functional representing the generalised impulse having a prescribed value we prove also that when the prescribed value of the generalised impulse is large enough the constrained maximiser of the kinetic energy is in fact a rearrangement of the prescribed function

a hypersingular boundary integral method for two dimensional screen and crack problems we analyze hypersingular integral equations on a curved open smooth arc in r 2 that model either curved cracks in an elastic medium or the scattering of acoustic and elastic waves at a hard screen by using the mellin transformation we obtain sharp regularity results for the solution of these equations in sobolev spaces in the form of singular expansions in particular we show that the expansions do not contain logarithmic singularities

a boundary element method for anisotropic inhomogeneous elasticity this paper is concerned with obtaining boundary integral equations for the numerical solution of the partial differential equations governing static deformations of inhomogeneous anisotropic elastic materials the elastic parameters for the inhomogeneous materials are assumed to vary continuously with the spatial variables

wave propagation in anisotropic layered media the determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques such computations require great effort the method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices for which the eigenvalues can be found with great speed and accuracy the technique is then illustrated by means of an example involving a cross anisotropic gibson solid

the scaled boundary finite element method analytical solution in frequency domain the scaled boundary finite element equation a system of ordinary differential equations in the radial coordinate is solved analytically applying a series expansion an eigenvalue problem of a hamiltonian matrix is solved when the difference of two eigenvalues is an even number besides the power series logarithmic functions occur two sets of independent solutions are obtained the scaled boundary finite element method is thus a semi analytical procedure to solve partial differential equations with the polynomial approximation of finite elements in the two circumferential directions and a closed form solution in the radial direction applications to bounded and unbounded domains demonstrate excellent accuracy

the non homogeneous biharmonic plate equation fundamental solutions abstract real materials and structural components are often non homogeneous either by design or because of the physical composition and imperfections in the underlying material thus analytical solutions for non homogeneous materials under mechanical loads are of considerable interest to engineers and have widespread applications given the prevalence of these materials in fields as diverse as aerospace construction electronics etc more precisely those are essentially composites with carefully manufactured properties that yield desirable mechanical characteristics and properties such as optimal arrangement of the material minimum weight etc to this end the displacement fundamental solution or green s function corresponding to a point force for the non homogenous biharmonic equation in two dimensions are derived in this work by employing a conformal mapping technique in conjunction with the radon transformation these functions besides being useful in their own right can also be used within the context of integral equation formulations for the solution of boundary value problems finally a series of numerical examples that deal with the non homogeneous plate on elastic foundation problem serve to illustrate the present method

steady vortex pairs in two phase shear flow of an ideal fluid this study proves an existence of a steady vortex pairs in two phase shear flow in plane domain the method was used is a variational principle in which a functional related to the kinetic energy can be maximised over the set where the vorticity being a rearrangement of a prescribed function

a class of rearrangement optimization problems involving the p laplacian abstract we investigate two optimization problems related to a quasilinear boundary value problem involving the p laplace operator these optimization problems are formulated relative to the rearrangement of a fixed function under some suitable assumptions we show that both problems are solvable

a fast volume integral equation method for elastic wave propagation in a half space abstract a fast method for solving the volume integral equation is developed for scattering analysis of elastic wave propagation in a half space the proposed method applies the fast generalized fourier transform and inverse transform formulated in the present study to the krylov subspace method the amount of calculations required for the proposed method is o nlogn where n is the number of grid points used to model the elastic half space furthermore the mpi parallel algorithm for the generalized fourier transform is presented for further reduction of the cpu time numerical calculations are performed in order to examine the effects of the number of sampling grid points as well as their intervals on the solutions of the volume integral equation and the cpu time required for the analysis in addition comparisons of the proposed method with the previous method based on the trapezoidal approach touhei 2009 are also performed in order to discuss the properties of the solution of the present method

time domain fundamental solution to biot s complete equations of dynamic poroelasticity part i two dimensional solution abstract this paper develops transient fundamental solution for biot s full dynamic two dimensional equations of poroelasticity an explicit well posed laplace transform domain fundamental solution is obtained for the governing differential equations which are established in terms of solid displacements and fluid pressure in some limiting cases the solutions are shown to reduce to those of classical elastodynamics and steady state poroelasticity thus ensuring the validity of our result the closed form transient fundamental solutions both for the limiting case early time approximation and for the general case are derived from corresponding ones in the laplace transform domain by means of laplace transform techniques they represent the very first satisfactory fundamental solutions in the real time domain for full dynamic poroelasticity some characteristics of the solutions are investigated selected numerical results are presented to demonstrate the features of the waves and the accuracy of the solution is established by comparing them with laplace transform domain solutions to complete the ingredients for developing the bem the betti s reciprocal theorem is extended to the full dynamic poroelasticity based on which a time domain boundary integral equation is obtained

spin nilhecke algebras of classical type abstract we formulate and study the spin nilhecke algebras nh n b and nh n d of type b d which differ from the usual nilhecke algebras by some odd signs the type b spin nilhecke algebra is a nil version of the spin type b hecke algebra introduced earlier by the second author and khongsap but not for the type d one we construct faithful polynomial representations pol n of the nilhecke algebras via odd demazure operators we formulate the spin schubert polynomials and use them to show that the spin nilhecke algebras are matrix algebras with entries in a subalgebra of pol n consisting of spin symmetric polynomials all these results have their counterparts for the usual nilhecke algebras over the rational field our work is a generalization of results of lauda and ellis khovanov lauda in usual spin type a

wave scattering by cracks in inhomogeneous continua using biem elastic wave scattering by cracks in inhomogeneous geological continua with depth dependent material parameters and under conditions of plane strain is studied in this work a restricted case of inhomogeneity is considered where poisson s ratio is fixed at one quarter while both shear modulus and density profile vary with depth but proportionally to each other furthermore time harmonic conditions are assumed to hold for this type of material the body wave speeds remain macroscopically constant and it becomes possible to recover exact green functions for the crack free inhomogeneous continuum by using an algebraic transformation method proposed in earlier work as a first step in a subsequent step the complete elastodynamic fundamental solution along with its spatial derivatives and an asymptotic expansion for small argument are all derived in closed form using the radon transform next a non hypersingular traction based boundary integral equation method biem formulation for solving boundary value problems with internal cracks is presented specifically the biem is used for computing stress intensity factors and scattered wave displacement amplitudes for an inclined line crack in an otherwise inhomogeneous continuum that is being swept by either pressure waves or vertically polarized shear waves at an arbitrary angle of incidence with respect to the horizontal direction the numerical results obtained herein reveal substantial differences between homogeneous and continuously inhomogeneous materials containing a crack in terms of their dynamic response where the latter case is assumed to give a more realistic representation of geological deposits compared to the former one finally these types of examples plus the benchmark case used for validation serve to illustrate the present approach and to show its potential for solving complex problems not just in geophysics but also in mechanics

elastic wave scattering around cavities in inhomogeneous continua by the bem this work examines elastic wave scattering around cavities embedded in a continuum with depth dependent shear modulus and under conditions of plane strain a restricted case of inhomogeneity is considered where the poisson ratio is fixed at 0 25 and where the density profile also varies but proportionally to the shear modulus for this specific case the wave speeds remain macroscopically constant and it becomes possible to recover the exact green functions by using an algebraic transformation method these functions are subsequently used as kernels in a standard 2d boundary element formulation defined in the laplace transform domain the final step involves an inverse laplace transformation whereby the transient behavior of cavities in the aforementioned inhomogeneous continuum can be recovered two basic examples are solved namely the circular cylindrical cavity under sudden internal explosion and under a pressure wave sweep in the latter case it is possible to investigate the effect that the angle of wave incidence has on the displacement and stress that develop along the cavity s perimeter given the fact that the shear modulus is changing along the vertical direction these examples serve to illustrate the present approach and to reveal some interesting differences that are observed in transient wave scattering phenomena between homogeneous and continuously inhomogeneous models where the latter models yield a more realistic representation of geological formations

multivalued fixed point index and nonlocal problems involving relative rearrangement abstract we apply the fixed point index theory for multivalued problems to nonlocal problems involving relative rearrangement mappings these applications need an extension of the almgren lieb theorem and an improvement of the strong continuity of the relative rearrangement mapping on arbitrary open sets bounded or not the proofs of these results are based on some pointwise equations relating the relative rearrangement of the gradient and the weighted de giorgi perimeter

type a blocks of super category o we show that every block of category oo for the general linear lie superalgebra glm n k glm n k is equivalent to some corresponding block of category oo for the queer lie superalgebra qm n k qm n k this implies the truth of the kazhdan lusztig conjecture for the so called type a blocks of category oo for the queer lie superalgebra as formulated by cheng kwon and wang

effects of material gradients on transient dynamic mode iii stress intensity factors in a fgm abstract this paper presents a transient dynamic crack analysis for a functionally graded material fgm by using a hypersingular time domain boundary integral equation method the spatial variations of the material parameters of the fgm are described by an exponential law a numerical solution procedure is developed for solving the hypersingular time domain traction bie to avoid the use of time dependent green s functions which are not available for general fgm a convolution quadrature formula is adopted for approximating the temporal convolution while a galerkin method is applied for the spatial discretization of the hypersingular time domain traction bie numerical results for the transient dynamic stress intensity factors for a finite crack in an infinite and linear elastic fgm subjected to an impact anti plane crack face loading are presented and discussed the effects of the material gradients of the fgm on the transient dynamic stress intensity factors and their dynamic overshoot over the corresponding static stress intensity factors are analyzed