monopoles and the gibbons manton metric we show that in the region where monopoles are well separated the l 2 metric on the moduli space of n monopoles is exponentially close to the l 2 invariant hyperkahler metric proposed by gibbons and manton the proof is based on a description of the gibbons manton metric as a metric on a certain moduli space of solutions to nahm s equations and on twistor methods in particular we show how the twistor description of monopole metrics determines the asymptotic metric the construction of the gibbons manton metric in terms of nahm s equations yields a class of interesting pseudo hyperkahler metrics for example we show for each semisimple lie group g and a maximal torus t g the existence of a g t invariant pseudo hyperkahler manifold whose hyperkahler quotients by t are precisely kronheimer s hyperkahler metrics on g t a similar result holds for kronheimer s ale spaces

a note on monopole moduli spaces we discuss the structure of the framed moduli space of bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact lie groups we show that each stratum is a union of submanifolds for which we conjecture that the natural l2 metric is hyper kahler the dimensions of the strata and of these submanifolds are calculated and it is found that for the latter the dimension is always a multiple of four

approximation by solutions of elliptic equations in semilocal spaces in the present work we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain by solutions of the same equations in a larger domain we construct an abstract framework which allows us to deal with such density questions simultaneously for various norms more specifically we study approximations with respect to the norms of semilocal banach spaces of distributions these spaces are required to satisfy certain postulates we establish density results for elliptic operators with constant coefficients which unify and extend previous results in our density results may possess holes and it is required to satisfy the segment condition we observe that analogous density results do not hold in spaces where the infinitely smooth functions are not dense finally we provide applications related to the method of fundamental solutions

monopoles and rational maps a note on a theorem of donaldson in a recent paper donaldson gave a description of the moduli space of su 2 monopoles in terms of rational maps this was done indirectly via the associated solution of nahm s equations we give here an interpretation of these rational maps in terms of the monopole s spectral curve and then as scattering data for the monopole itself

updated lagrangian formulation of a flat triangular element for thin laminated shells an updated lagrangian formulation of a three node flat triangular shell element is presented for geometrically nonlinear analysis of laminated plates and shells the flat shell element is obtained by combining the discrete kirchhoff theory plate bending element and a membrane element that is similar to the allman element but a derivative of the linear strain triangular element results are presented for large rotation static response analysis of a cantilever beam under end moment cylindrical shell under pinching and stretching loads a hemispherical shell under pinching and stretching loads and a ring plate under a line load for dynamic response analysis of a cylindrical panel and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel to estimate the accuracy of the present formulation in predicting the nonlinear response of large flexible structures static analysis of an apex loaded circular arch is performed the arch is a building block of a large inflatable structure the results are in good agreement with those available in the existing literature and those obtained using the commercial finite element software abaqus demonstrating the accuracy of the present formulation he two most widely adopted approaches in the finite element analysis of shells are use of curved shell elements based on a suitable shell theory and approximation of the curved structure by an assemblage of flat shell elements in which the membranebending coupling is brought about as a result of material anisotropy and transformation of the element stiffness matrices computed in a local coordinate system to the global coordinate system prior to assembly the curved shell elements can be computationally very expensive especially in the case of nonlinear analysis because of the complexity of the formulation and the need to compute the curvature information flat shell elements are more attractive because of their simplicity and the ease with which they can be built from alreadyexisting familiar membrane and plate bending elements though a large number of elements are required to accurately model curved structures the analysis is computational ly less expensive because of extremely simple formulation updated lagrangian formulations have been predominantly used in the flat shell formulations available in the existing literature in an updated lagrangian formulation all of the variables are referred to a known configuration the reference configuration which is updated continuously during the deformation process if the rigid body modes are removed from the total or incremental displacements the resulting deformational translations and rotations are very small and hence a linearized incremental formulation1 can be used in a linearized incremental formulation the stresses are computed using linear strain displacement relations the tangent stiffness matrix contains only the linear stiffness matrix and the initial stress matrix the stiffness matrices resulting from the nonlinear terms in the strain displacement relations are neglected resulting in very economical analysis if the rigid body modes are not removed all nonlinear terms in the strain displacement relations will have to be considered for computing the stresses and the tangent stiffness matrix a three node flat triangular shell element was introduced by argyris et al 2 for nonlinear elastic stability problems this formula

applicability and applications of the method of fundamental solutions in the present work we investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic systems more specifically we study whether linear combinations of fundamental solutions can approximate the solutions of the boundary value problems under consideration in our study the singularities of the fundamental solutions lie on a prescribed pseudo boundary the boundary of a domain which embraces the domain of the problem under consideration we extend previous density results of kupradze and aleksidze and of bogomolny to more general domains and partial differential operators and with respect to more appropriate norms our domains may possess holes and their boundaries are only required to satisfy a rather weak boundary requirement namely the segment condition our density results are with respect to the norms of the spaces c l analogous density results are obtainable with respect to holder norms we have studied approximation by fundamental solutions of the laplacian biharmonic and m harmonic and modified helmholtz and poly helmholtz operators in the case of elliptic systems we obtain analogous density results for the cauchy navier operator as well as for an operator which arises in the linear theory of thermo elasticity we also study alternative formulations of the method of fundamental solutions in cases when linear combinations of fundamental solutions of the equations under consideration are not dense in the solution space finally we show that linear combinations of fundamental solutions of operators of order m 4 with singularities lying on a prescribed pseudo boundary are not in general dense in the corresponding solution space

a note on a symplectic structure on the space of g monopoles let g be a semisimple complex lie group with a borel subgroup b let x g b be the flag manifold of g let be the projective line let the moduli space of g monopoles of topological charge is naturally identified with the space of based maps from c to x b of degree the moduli space of g monopoles carries a natural hyperkahler structure and hence a holomorphic symplectic structure it was explicitly computed by r bielawski in case g sln we propose a simple explicit formula for another natural symplectic structure on it is tantalizingly similar to r bielawski s formula but in general rank 1 the two structures do not coincide let p g be a parabolic subgroup the construction of the poisson structure on generalizes verbatim to the space of based maps in most cases the corresponding map is not an isomorphism i e splits into nontrivial symplectic leaves these leaves are explicilty described

bosonic representations of yangian double with on the basis of the rtt ttr formalism we introduce the quantum double of the yangian for with a central extension the gauss decomposition of the t matrices gives us the so called drinfel d generators using these generators we present some examples of both finite and infinite dimensional representations that are quite natural deformations of their corresponding affine counterpart

min max theory for the yang mills higgs equations in each monopole sector there exist an infinite number of finite energy solutions to the prasad sommerfield limit of the su 2 yang mills higgs equations on 3 whose energy is greater than any finite number

comultiplication for shifted yangians and quantum open toda lattice abstract we study a coproduct in type a quantum open toda lattice in terms of a coproduct in the shifted yangian of sl 2 at the classical level this corresponds to the multiplication of scattering matrices of euclidean s u 2 monopoles we also study coproducts for shifted yangians for any simply laced lie algebra

dynamic finite element analysis of viscoelastic composite plates in the time domain numerical procedures for analysing transient responses of anisotropic viscoeiastic composite plates have been developed in the time domain using variational principles and a direct time integration method recursion relationships have been formulated in order to reduce computer storage substantially the method developed herein requires only two previous lime solutions to evaluate the next time solution and the necessary storage is independent of the number of the time steps verification studies were conducted to evaluate the accuracy and convergence of the present numerical algorithm and they show that the numerical solutions agree well with analytical ones as examples dynamic transient responses of viscoeiastic composite plates subjected to unit step loads were calculated using the presently developed procedure

on the numerical solution of some 2 d electromagnetic interface problems by the boundary collocation method abstract the boundary collocation method is used to solve some 2 d interface problems of microwave heating the choice of subspace of particular solutions and the selection of collocation points are discussed numerical examples are presented

hyperkahler quotient construction of bps monopole moduli spaces we use the hyperkahler quotient of flat space to obtain some monopole moduli space metrics in explicit form using this new description we discuss their topology completeness and isometries we construct the moduli space metrics in the limit when some monopoles become massless which corresponds to non maximal symmetry breaking of the gauge group we also introduce a new family of hyperkahler metrics which depending on the mass parameter being positive or negative tend to either the asymptotic metric on the moduli space of many su 2 monopoles or to previously unknown metrics these new metrics are singular or complete depending on the particular choice of the level set of the moment map the singular metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups finally we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow

gaiotto witten superpotential and whittaker d modules on monopoles abstract let g be an almost simple simply connected group over c for a positive element of the coroot lattice of g let z denote the space of maps from p 1 to the flag variety b of g sending p 1 to a fixed point in b of degree this space is known to be isomorphic to the space of framed g monopoles on r 3 with maximal symmetry breaking at infinity of charge in 6 a system of etale rational coordinates on z is introduced in this note we compute various known structures on z in terms of the above coordinates as a byproduct we give a natural interpretation of the gaiotto witten superpotential studied in 8 and relate it to the theory of whittaker d modules discussed in 9

the classification of monopoles for the classical groups by studying a construction of nahm we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forsu n so n andsp n these are found to be equivalent to spaces of holomorphic maps from 1 into flag manifolds

matrix decomposition mfs algorithms for elasticity and thermo elasticity problems in axisymmetric domains in this work we propose an efficient matrix decomposition algorithm for the method of fundamental solutions when applied to three dimensional boundary value problems governed by elliptic systems of partial differential equations in particular we consider problems arising in linear elasticity in axisymmetric domains the proposed algorithm exploits the block circulant structure of the coefficient matrices and makes use of fast fourier transforms the algorithm is also applied to problems in thermo elasticity several numerical experiments are carried out

method of fundamental solutions in micromechanics of elastic random structure composites abstract one considers linearly elastic composite media which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non canonical i e nonellipsoidal shape the new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities the method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals that makes it possible to reconsider basic concepts of micromechanics such as effective field hypothesis quasi crystalline approximation and the hypothesis of ellipsoidal symmetry the results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape some new effects are detected that are impossible in the framework of a classical background of micromechanics

monopoles and clusters we define and study certain hyperkahler manifolds which capture the asymptotic behaviour of the su 2 monopole metric in regions where monopoles break down into monopoles of lower charges the rate at which these new metrics approximate the monopole metric is exponential as for the gibbons manton metric

on the construction of monopoles for the classical groups forg a classical group an equivalence is exhibited between a g monopoles over 3 with maximal symmetry breaking at infinity b families of rank g algebraic curves int 1 along with divisors on those curves satisfying certain constraints c solutions of nahm s equations over rank g intervals satisfying the appropriate boundary conditions a and b are linked by twistor techniques b and c via the krichever method for solving non linear differential equations and a and c via the adhmn construction providing a unified picture of techniques for solution amongst other things an asymptotic formula for the higgs field of the monopole is computed

the method of fundamental solutions for the cauchy problem in two dimensional linear elasticity in this paper the application of the method of fundamental solutions to the cauchy problem in two dimensional isotropic linear elasticity is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularised by employing the first order tikhonov functional while the choice of the regularisation parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries as well as for constant and linear stress states the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

fundamental solutions method for elliptic boundary value problems we consider a procedure for solving boundary value problems for elliptic homogeneous equations known as the fundamental solutions method we prove its applicability for some second order operators as well as for fourth order ones the boundary conditions of an elliptic problem are approximated by using fundamental solutions of the corresponding operator with singularities located outside the domain of interest in a specific case of the laplacian an estimate shows that the method discussed possesses convergence properties as good as those of any method using harmonic polynomials as trial functions numerical examples are given among which are simple signorini s problems for harmonic and lame operators

higgs bundles gauge theories and quantum groups the appearance of the bethe ansatz equation for the nonlinear schrodinger equation in the equivariant integration over the moduli space of higgs bundles is revisited we argue that the wave functions of the corresponding two dimensional topological u n gauge theory reproduce quantum wave functions of the nonlinear schrodinger equation in the n particle sector this implies the full equivalence between the above gauge theory and the n particle sub sector of the quantum theory of the nonlinear schrodinger equation this also implies the explicit correspondence between the gauge theory and the representation theory of the degenerate double affine hecke algebra we propose a similar construction based on the g g gauged wzw model leading to the representation theory of the double affine hecke algebra

on the construction of monopoles we show that any self dual su 2 monopole may be constructed either by ward s twistor method or nahm s use of the adhm construction the common factor in both approaches is an algebraic curve whose jacobian is used to linearize the non linear ordinary differential equations which arise in nahm s method we derive the non singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions

bethe subalgebras in yangians and the wonderful compactification let mathfrak g be a complex simple lie algebra we study the family of bethe subalgebras in the yangian y mathfrak g parameterized by the corresponding adjoint lie group g we describe their classical limits as subalgebras in the algebra of polynomial functions on the formal lie group g 1 t 1 in particular we show that for regular values of the parameter these subalgebras are free polynomial algebras with the same poincare series as the cartan subalgebra of the yangian next we extend the family of bethe subalgebras to the de concini procesi wonderful compactification overline g supset g and describe the subalgebras corresponding to generic points of any stratum in overline g as bethe subalgebras in the yangian of the corresponding levi subalgebra in mathfrak g in particular we describe explicitly all bethe subalgebras corresponding to the closure of the maximal torus in the wonderful compactification

isomorphism of two realizations of quantum affine algebra u_q widehat mathfrak g mathfrak l text n text we establish an explicit isomorphism between two realizations of the quantum affine algebra u q widehat mathfrak g mathfrak l text n text given previously by drinfeld and reshetikhin semenov tian shansky our result can be considered as an affine version of the isomorphism between the drinfield jimbo and the faddeev reshetikhin takhtajan constructions of the quantum algebra u q mathfrak g mathfrak l n

geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites a triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale in addition to the usual hygrothermal loads recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads the nonlinear deformation process is computed using an incremental iterative approach with the newton raphson method used to find the incremental displacements in each step the presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation independent mechanical loads deformation dependent pressure loads and thermal loads unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times both creep buckling and snap through examples are presented here in some cases viscoelastic results are also obtained using the quasielastic method in which load history effects are ignored and time varying viscoelastic properties are simply used in a series of elastic problems the presented numerical examples demonstrate the capability and accuracy of the formulation

stress intensity factor computation using the method of fundamental solutions mixed mode problems the method of fundamental solutions is applied to the computation of stress intensity factors in linear elastic fracture mechanics the displacements are approximated by linear combinations of the fundamental solutions of the cauchy navier equations of elasticity and the leading terms for the displacement near the crack tip two algorithms are developed one using a single domain and one using domain decomposition numerical results are given copyright 2006 john wiley sons ltd

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

monopoles and harmonic maps recently jarvis has proved a correspondence between su n monopoles and rational maps of the riemann sphere into flag manifolds furthermore he has outlined a construction to obtain the monopole fields from the rational map in this paper we examine this construction in some detail and provide explicit examples for spherically symmetric su n monopoles with various symmetry breakings in particular we show how to obtain these monopoles from harmonic maps into complex projective spaces the approach extends in a natural way to monopoles in hyperbolic space and we use it to construct new spherically symmetric su n hyperbolic monopoles

on a class of representations of the yangian and moduli space of monopoles a new class of infinite dimensional representations of the yangians yopen image in new window and yopen image in new window corresponding to a complex semisimple algebra open image in new window and its borel subalgebra open image in new window is constructed it is based on the generalization of the drinfeld realization of open image in new window in terms of quantum minors to the case of an arbitrary semisimple lie algebra open image in new window the poisson geometry associated with the constructed representations is described in particular it is shown that the underlying symplectic leaves are isomorphic to the moduli spaces of g monopoles defined as the components of the space of based maps of 1 into the generalized flag manifold open image in new window thus the constructed representations of the yangian may be considered as a quantization of the moduli space of the monopoles

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

asymptotic metrics for su n monopoles with maximal symmetry breaking we compute the asymptotic metrics for moduli spaces of su n monopoles with maximal symmetry breaking these metrics are exponentially close to the exact monopole metric1 as soon as for each simple root the individual monopoles corresponding to that root are well separated we also show that the estimates can be differentiated term by term in natural coordinates which is a new result even for su 2 monopoles

mathematical foundation of the mfs for certain elliptic systems in linear elasticity the method of fundamental solutions mfs is a trefftz type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental solutions with singularities placed on a pseudo boundary i e a surface embracing the domain of the problem under consideration in this work we develop a mathematical framework for the numerical implementation of the mfs in elliptic systems we obtain density results with respect to the c l norms which establish the applicability of the method in certain systems arising from the theory of elastostatics and thermo elastostatics the domains in our density results may possess holes and they satisfy the segment condition

on the choice of finite rotation parameters in this work we discuss some aspects of the three dimensional finite rotations pertinent to the formulation and computational treatment of the geometrically exact structural theories among various possibilities to parameterize the finite rotations special attention is dedicated to a choice featuring an incremental rotation vector some computational aspects pertinent to the implementation of the newton iterative scheme and the newmark time stepping algorithm applied to solving these problems are examined representative numerical simulations are presented in order to illustrate the performance of the proposed formulation

gelfand zeitlin actions and rational maps we observe that the analogue of the gelfand zeitlin action on mathfrak g mathfrak l n mathbb c which exists on any symplectic manifold m with an hamiltonian action of gl n mathbb c has a natural interpretation as a residual action after we identify m with a symplectic quotient of m times prod i 1 n t ast gl i mathbb c we also show that the gelfand zeitlin actions on t ast gl n mathbb c and on the regular part of mathfrak g mathfrak l n mathbb c can be identified with natural hamiltonian actions on spaces of rational maps into full flag manifolds while the gelfand zeitlin action on the whole mathfrak g mathfrak l n mathbb c corresponds to a natural action on a space of rational maps into the manifold of half full flags in mathbb c 2n

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3