a contact model based on the sqp algorithm and engineering application a kind of improvement contact frictional model based on traditional coulomb friction model is adopted corresponding contact element also is given detail contact algorithm based on sequential quadratic programming sqp and augmented lagrange method is introduced and applied on complex contact friction problem successfully the results of test example and the actual engineering case all show that the algorithm of the model is efficient

flat g bundles with canonical metrics on considere la relation entre la theorie invariante des actions de groupes algebriques semi simples sur des varietes algebriques complexes et le comportement de l application de moment et des donnees quantiques fournies par une structure symplectique associee on etudie un exemple de dimension infinie comprenant des fibres plats sur des varietes de riemann compactes

a new frictional time integration algorithm for large slip multi body frictional contact problems in this paper a new frictional time integration suitable for large slip multibody frictional contact problems is presented the algorithm is introduced within the simple context of a model problem the sliding motion of a particle onto a rough surface time integration of frictional traction is performed introducing a new slip path parametrization which is defined independently of the local surface finite element parametrization used in the spatial triangularization the key point of the algorithm is that now in presence of large slips problems associated with slip motions such that a full incremental slip path is not within a single surface element are completely bypassed remarkably the algorithm is defined on the sole basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization geometrically the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path the algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a newton raphson iterative solution scheme the algorithm can easily be extended to large slip multi body frictional contact problems involving finite strains

hitchin kobayashi correspondence quivers and vortices a twisted quiver bundle is a set of holomorphic vector bundles over a com plex manifold labelled by the vertices of a quiver linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles labelled by the arrows when the manifold is kahler quiver bundles admit natural gauge theoretic equations which unify many known equations for bundles with extra structure in this paper we prove a hitchin kobayashi correspondence for twisted quiver bundles over a compact kahler manifold relating the existence of solutions to the gauge equations to a stability criterion and con sider its application to a number of situations related to higgs bundles and dimensional reductions of the hermitian einstein equations

a numerical scheme for impact problems i the one dimensional case we consider a mechanical system with impact and one degree of freedom the system is not necessarily lagrangian the representative point is subject to the constraint u t in er for all t we assume that at impact the velocity is reversed and multiplied by a given coefficient of restitution e in 0 1 we define a numerical scheme which enables us to approximate the solutions of the cauchy problem this is an ad hoc scheme which does not require a systematic search for the times of impact we prove the convergence of this numerical scheme to a solution many of the features of this proof will be reused in the nonconvex multidimensional case written in generalized coordinates given in the companion paper l paoli and m schatzman siam j numer anal 40 2002 pp 734 768 we present some numerical results obtained with the scheme for a spring dashpot system and we compare them to the results obtained by impact detection and penalization

the moduli of flat pu p p structures with large toledo invariants for a compact riemann surface x of genus g 1 rm hom pi 1 x rm pu p q rm pu p q is the moduli space of flat rm pu p q connections on x there are two invariants the chern class c and the toledo invariant tau associated with each element in the moduli the toledo invariant is bounded in the range 2min p q g 1 le tau le 2min p q g 1 this paper shows that the component associated with a fixed tau 2 max p q 1 g 1 resp tau 2 max p q 1 g 1 and a fixed chern class c is connected the restriction on tau implies p q

coupled vortex equations and moduli deformation theoretic approach and kahler geometry we investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact kahler manifold x these solutions are known to be related to polystable triples via a kobayashi hitchin type correspondence using a characterization of infinitesimal deformations in terms of the cohomology of a certain elliptic double complex we construct a hermitian structure on these moduli spaces this hermitian structure is proved to be kahler the proof involves establishing a fiber integral formula for the hermitian form we compute the curvature tensor of this kahler form when x is a riemann surface the holomorphic bisectional curvature turns out to be semi positive it is shown that in the case where x is a smooth complex projective variety the kahler form is the chern form of a quillen metric on a certain determinant line bundle

algorithmic symmetrization of coulomb frictional problems using augmented lagrangians abstract a major drawback of most implicit algorithmic treatments of coulomb frictional contact problems is the nonsymmetry of the algorithmic tangent operator which emanates from the nonassociativity of the slip flow rule reliable algorithms leading to symmetric equation systems are highly desirable especially in three dimensional problems where the computational cost is dominated by equation solving in this paper such an algorithm symmetrization is proposed the method is derived from the augmented lagrangian treatment of friction given by simo and laursen comput structures 42 1992 97 116 and exploits the iterative nature of the classical method of multipliers more specifically symmetrization is achieved by a modified multiplier update scheme in which all nonassociativity is removed from the solution phase and placed in the multiplier update phase the result is an algorithm involving only the solution of symmetric equations which maintains the attributes of an augmented lagrangian method

generalized newton s methods for the approximation and resolution of frictional contact problems in elasticity abstract in this paper some new generalized newton s methods for the resolution of elastostatic frictional contact problem approximated by finite elements are presented and compared to existing ones a numerical experimentation is performed to compare the different methods especially with respect to the sensitivity to the method parameter two different strategies to approximate the contact and friction condition are considered a nodal and an integral one existence and uniqueness results of the solution to the discretized problem are also discussed

a robust consistent configuration framework and formulation for 3d finite strain dynamic impact problems as a first step towards the next generation of computational tools for contact impact applications a robust consistent configuration dynamic formulation for frictional contact impact dynamic problems is described based on a newly developed decoupled point to segment gap vector projection and decoupled contact model in conjunction with the so called arbitrary reference configuration arc formulation for finite elastic inelastic deformation and the forward incremental displacement central difference time integration scheme for the equation of motion as a consequence the resulting normal and tangential contact boundary formulations are easy to be solved and the contact constraints are satisfied exactly this formulation is highly robust and efficient for the numerical simulation of finite deformation elastic inelastic frictional contact impact dynamic applications numerical results with comparisons to available experimental data and those obtained from other codes are also presented thereby demonstrating the inherent advantages

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

the intersection form on moduli spaces of twisted pgl_n higgs bundles vanishes hausel and rodriguez villegas conjectured that the intersection form on the moduli space of stable textsf pgl n higgs bundles on a curve vanishes if the degree is coprime to n in this note we prove this conjecture along the way we show that moduli spaces of stable chains are irreducible for stability parameters larger than the stability condition induced form stability of higgs bundles

moduli spaces of holomorphic triples over compact riemann surfaces a holomorphic triple over a compact riemann surface consists of two holomorphic vector bundles and a holomorphic map between them after fixing the topological types of the bundles and a real parameter there exist moduli spaces of stable holomorphic triples in this paper we study non emptiness irreducibility smoothness and birational descriptions of these moduli spaces for a certain range of the parameter our results have important applications to the study of the moduli space of representations of the fundamental group of the surface into unitary lie groups of indefinite signature 5 7 another application that we study in this paper is to the existence of stable bundles on the product of the surface by the complex projective line

numerical simulation of the dynamics of an impacting bar we calculate numerically the motion of a slender bar dropped on a rigid foundation for the computation the bar is discretized by a system of rigid bodies linked by spiral springs or by a pair of linear springs we assume that the impact is frictionless and we model it by newton s law we compute the motion by using either an event driven method based on the detection of impacts or a time stepping scheme avoiding the detection of impacts we calculate also the apparent restitution coefficient and we compare our results with the experimental and numerical results of stoianovici and hurmuzlu

an analysis of metal forming processes using large deformation elastic plastic formulations a concise survey of the literature related to the large deformation elasto plasticity problems including unilateral contact and friction is presented together with an extension of the friction law for large deformation analysis starting from the principle of virtual work the so called total lagrangian and updated lagrangian formulations are derived based on some fundamental assumptions in linearizing the nonlinear equations by introducing the zaremba jaumann co rotational increment to the cauchy stress tensor the classical prandtl reuss equations are generalized for describing the elastic plastic material behavior to allow a proper consideration of the contact conditions in the incremental analysis a general friction law with an associated isotropic coulomb sliding rule is obtained by the similarity between dry friction and plasticity finite element discretizations and approximations are applied to the resulting formulation of the updated lagrangian approach four example problems are solved to test the formulations developed in this paper the emphasis is made toward the numerical accuracy of the finite element solutions

surface group representations and u p q higgs bundles using the l2 norm of the higgs field as a morse function we study the moduli spaces of u p q higgs bundles over a riemann surface we require that the genus of the surface be at least two but place no constraints on p q a key step is the identification of the function s local minima as moduli spaces of holomorphic triples in a companion paper 7 we prove that these moduli spaces of triples are nonempty and irreducible because of the relation between flat bundles and fundamental group representations we can interpret our conclusions as results about the number of connected components in the moduli space of semisimple pu p q representations the topological invariants of the flat bundles are used to label subspaces these invariants are bounded by a milnor wood type inequality for each allowed value of the invariants satisfying a certain coprimality condition we prove that the corresponding subspace is nonempty and connected if the coprimality condition does not hold our results apply to the closure of the moduli space of irreducible representations 1 members of vbac vector bundles on algebraic curves which is partially supported by eager ec fp5 contract no hprn ct 2000 00099 and by edge ec fp5 contract no hprn ct 2000 00101 2 partially supported by the national science foundation under grant dms0072073 3 partially supported by the ministerio de ciencia y tecnolo ia spain under grant bfm2000 0024 4 partially supported by the fundacao para a ciencia e a tecnologia portugal through the centro de matematica da universidade do porto and through grant no sfrh bpd 1606 2000 5 partially supported by the portugal spain bilateral programme acciones integradas grant nos hp2000 0015 and ai 01 24 6 partially supported by a british epsrc grant october december 2001 received 11 27 2002

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

conjugate gradient type algorithms for frictional multi contact problems applications to granular materials abstract this paper presents gradient type algorithms to solve frictional multi contact problems written as quasi optimization problems a single loop scheme formally close to the classical conjugate gradient method is proposed with some adaptations of the iterate corrections and gradient projections since the convergence is difficult to prove various tests in the field of granular media are performed with comparison with the non linear gauss seidel scheme

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

twisted harmonic maps and the self duality equations si m est une surface de riemann compacte on utilise des resultats de la theorie des applications harmoniques pour trouver une solution aux equations d auto dualite associees a une representation irreductible p 1 m psl 2 c