c1 continuous stress recovery in finite element analysis abstract a penalized discrete least squares pdls variational principle is employed to recover c 1 continuous smooth stress fields from finite element stresses the error functional involves discrete least squares with a penalty constraint to enforce c 1 continuity of the recovered stresses the recovery procedure uses a smoothing element analysis sea with element based interpolation functions to minimize the error functional sea pdls recovers a superconvergent stress field of higher accuracy and continuity than the underlying consistent finite element stress field general and specialized formulations of the functional are given and an appropriate discretization strategy for the sea is discussed numerical results for both one and two dimensional stress fields are presented and compared with the corresponding solutions for the superconvergent patch recovery spr method of zienkiewicz and zhu the results demonstrate that in addition to achieving a higher degree of continuity sea pdls produces generally more accurate stresses than spr although an additional global analysis is required results indicate that two coarse mesh analyses finite element and smoothing produce solutions comparable to a single finite element analysis with a much greater degree of refinement and more computational effort the procedure is unique in that the recovered stress field is essentially c 1 continuous the results are shown to be insensitive to the value of the penalty parameter above a threshold and hence uncertainty in the choice of an appropriate penalty value is eliminated

exact operator solution of the calogero sutherland model the wave functions of the calogero sutherland model are known to be expressible in terms of jack polynomials a formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived the creation operators that enter in this formula of rodrigues type for the jack polynomials involve dunkl operators

patch recovery based on superconvergent derivatives and equilibrium in this paper a postprocessing technique is developed for determining first order derivatives fluxes stresses at nodal points based on derivatives in superconvergent points it is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu in contrast to that technique all flux or stress components are interpolated at the same time coupled by equilibrium equations at the superconvergent points the equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries

simple wzw currents a complete classification of simple currents of wzw theories is obtained the proof is based on an analysis of the quantum dimensions of the primary fields simple currents are precisely the primaries with unit quantum dimension for wzw theories explicit formulae for the quantum dimensions can be derived so that an identification of the fields with unit quantum dimension is possible

an improved variational method for finite element stress recovery and a posteriori error estimation abstract a new variational formulation is presented which serves as a foundation for an improved finite element stress recovery and a posteriori error estimation in the case of stress predictions interelement discontinuous stress fields from finite element solutions are transformed into a c 1 continuous stress field with c 0 continuous stress gradients these enhanced results are ideally suited for error estimation since the stress gradients can be used to assess equilibrium satisfaction the approach is employed as a post processing step in finite element analysis the variational statement used herein combines discrete least squares penalty constraint and curvature control functionals thus enabling automated recovery of smooth stresses and stress gradients the paper describes the mathematical foundation of the method and presents numerical examples including stress recovery in two dimensional structures and built up aircraft components and error estimation for adaptive mesh refinement procedures

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

recursive construction for a class of radial functions ii superspace we extend the recursion formula for matrix bessel functions which we obtained previously to superspace it is sufficient to do this for the unitary orthosymplectic supergroup by direct computations we show that fairly explicit results can be obtained at least up to dimension 8 8 for the supermatrices since we introduce a new technique we discuss various of its aspects in some detail

algebraic equations determining quantum dimensions we show that a quantum dimension dq lambda for a representation rho of uq g a quantized universal enveloping algebra of a compact and simple lie group g is computed from the algebraic equations which we found recently in studying 2 1 dimensional chern simons theory we solve the equations explicitly for the typical examples of all compact and simple lie groups this method can be applied to super lie groups such as su m n and osp m n

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

integrability of two interacting n dimensional rigid bodies a new class of integrable euler equations on the lie algebra so 2n describing twon dimensional interacting rigid bodies is found a lax representation of equations of motion which depends on a spectral parameter is given and complete integrability is proved the double hamiltonian structure and the lax representation of the general flow is discussed

the superconvergent patch recovery spr and adaptive finite element refinement abstract the error estimation processes which have been developed by the authors depend on the accuracy with which stresses gradients can be recovered the recovery methods available currently such as the l 2 projection and averaging are inaccurate and an improved process is needed this paper presents a very much improved recovery process yielding superconvergent values throughout the domain details of this method named the superconvergent patch recovery are presented with test results showing its efficiency examples of adaptive h based refinement are given showing high local and overall efficiency indices for error estimation

explicit computation of the spectrum of the deformed calogero model by yukawa like potential we study the quantum spectrum of the one dimensional calogero model deformed by a yukawa like potential using special features of the uv and ir behaviour of the deformed potential symmetry of classical hamiltonian as well as the expansion method of the wavefunction we compute the explicit expression of the discrete energy spectrum and the corresponding eigenfunctions n

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

singularity complexity and quasi integrability of rational mappings we investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models by exploiting their nature of birational transformations of projective spaces we give an algorithmic analysis of the structure of invariants of such mappings we discuss some characteristic conditions for their quasi integrability and in particular its links with their singularities in the 2 plane finally we describe some of their propertiesqua dynamical systems making contact with arnol d s notion of complexity and exemplify remarkable behaviours

uniqueness of ϕ minimal hypersurfaces in warped product manifolds abstract we show that generalized minimal graphs in a warped product with density over a parabolic manifold are fibers under appropriate conditions on the density the proof employs appropriate test functions

the structure of phi stable minimal hypersurfaces in manifolds of nonnegative p scalar curvature suppose n n g is an n dimensional riemannian manifold with a given smooth measure m the p scalar curvature is defined as p g r m infty g r g 2 delta g rm log phi nabla g rm log phi g 2 where dm phi dvol g and r g is the scalar curvature of n n g in this paper under a technical assumption on phi we prove that phi stable minimal oriented hypersurface in the three dimensional manifold with nonnegative p scalar curvature must be conformally equivalent to either the complex plane mathbb c or the cylinder mathbb r times mathbb s 1

a new integrable case of the motion of the 4 dimensional rigid body a lax pair for a new family of integrable systems on so 4 is presented the construction makes use of a twisted loop algebra of theg 2 lie algebra we also describe a general scheme producing integrable cases of the generalized rigid body motion in an external field which have a lax representation with spectral parameter several other examples of multi dimensional tops are discussed

a variational method for finite element stress recovery and error estimation abstract a variational method for obtaining smoothed stresses from a finite element derived non smooth stress field is presented the method is based on minimizing a functional involving discrete least squares error plus a penalty constraint that ensures smoothness of the stress field an equivalent accuracy criterion is developed for the smoothing analysis which results in a c1 continuous smoothed stress field possessing the same order of accuracy as that found at the superconvergent optimal stress points of the original finite element analysis application of the smoothing analysis to residual error estimation is also demonstrated

on inter element forces in the fem displacement formulation and implications for stress recovery this paper describes a new technique for the determination of the inter element forces and tractions as well as stress state at nodes as a post processing step after the solution of standard fe displacement calculation the work is motivated in the context of a broader development of a procedure to simulate fracture processes using a discrete approach without the need of double noded interface elements the technique easily implementable is based on the double minimization of an objective function representing the error between the inter element stress tractions and the projection of the best fit stress tensor t along the planes of the interfaces converging at an element corner node the formulation is illustrated with some basic examples in which the resulting stress tensors and inter element forces are compared to theoretical solutions and to the results obtained by using a traditional stress average smoothing method

superconvergent derivatives a taylor series analysis an analysis based on the use of taylor series expansions is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite element interpolant or approximation the analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates superconvergence moreover it leads directly to a class of post processing strategies for the derivatives and offers a more direct constructive approach to the subject

the calogero moser equation system and the ensemble average in the gaussian ensembles from random matrix theory it is known that for special values of the coupling constant the calogero moser cm equation system is nothing but the radial part of a generalized harmonic oscillator schrodinger equation this allows an immediate construction of the solutions by means of a rodriguez relation the results are easily generalized to arbitrary values of the coupling constant by this the cm equations become nearly trivial as an application an expansion for eitr xy in terms of eigenfunctions of the cm equation system is obtained where x and y are matrices taken from one of the gaussian ensembles and the brackets denote an average over the angular variables

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

quantum group invariants and link polynomials a general method is developed for constructing quantum group invariants and determining their eigenvalues applied to the universal matrix this method leads to the construction of a closed formula for link polynomials to illustrate the application of this formula the quantum groups uq es uq so 2m 1 and uq gl m are considered as examples and corresponding link polynomials are obtained