exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

a new dissipative time stepping algorithm for frictional contact problems formulation and analysis this paper presents a new time stepping algorithm for frictional contact problems that exhibits unconditional positive energy dissipation more specifically the proposed scheme preserves a priori stability estimates of the continuum problem for both frictionless and frictional contact leading to improved numerical stability properties in particular for the normal contact component the algorithm exhibits full energy conservation between released states while the energy does not increase over its initial value due to the enforcement of the normal contact constraint during persistent contact a penalty regularization is considered to this purpose a new regularization of the stick conditions is considered for the frictional part the new scheme is shown rigorously to exhibit positive energy dissipation like the continuum physical problem in this frictional case coulomb friction is assumed complete analyses of these considerations as well as a detailed description of their finite element implementation are included in the general finite deformation range representative numerical simulations are presented to assess the performance of the newly proposed methods

the classification of automorphism groups of rational elliptic surfaces with section abstract in this paper we give a classification of regular automorphism groups of relatively minimal rational elliptic surfaces with section over the field c which have non constant j maps the automorphism group aut b of such a surface b is the semi direct product of its mordell weil group mw b and the subgroup aut b of the automorphisms preserving the zero section of the rational elliptic surface b the configuration of singular fibers on the surface determines the mordell weil group as has been shown by oguiso and shioda 1991 and aut b also depends on the singular fibers the classification of automorphism groups in this paper gives the group aut b in terms of the configuration of singular fibers on the surface in general aut b is a finite group of order less than or equal to 24 which is a z 2 z extension of either z n z z 2 z z 2 z d n the dihedral group of order 2n or a 4 the alternating group of order 12 the configuration of singular fibers does not determine the group aut b uniquely however we list explicitly all the possible groups aut b and the configurations of singular fibers for which each group occurs

configurations of kodaira fibers on rational elliptic surfaces i n t r o d u c t i o n l legend 6 the list 7 i d i s c r i m i n a n t cons ide ra t i ons 14 if po l a r s of p lane curves 16 ili in t r ins ic g e o m e t r y on g e n u s two curves 19 iv ell iptic qua r t i c s 25 v r a t i o n a l qua r t i c s 30 the reduc ib le case 43 to r s ion g r o u p s of ra t iona l elliptic surfaces 43 epi logue 46 references 46

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part ii second order methods we present in this paper the formulation of a new high frequency dissipative time stepping algorithm for nonlinear elastodynamics that is second order accurate in time the new scheme exhibits unconditional energy dissipation and momentum conservation and thus the given name of energy dissipative momentum conserving second order scheme edmc 2 leading also to the conservation of the relative equilibria of the underlying physical system the unconditional character of these properties applies not only with respect to the time step size but equally important with respect to the considered elastic potential moreover the dissipation properties are fully controlled through an algorithmic parameter reducing to existing fully conserving schemes if desired the design of the new algorithm is described in detail including a complete analysis of its dissipation conservation properties in the fully nonlinear range of finite elasticity to motivate the different constructions that lead to the dissipative properties of the final scheme the same arguments are used first in the construction of new linear time stepping algorithms for the system of linear elastodynamics including first and second order schemes the new schemes exhibit a rigorous decay of the physical energy with the second order schemes formulated in a general two stage formula accommodating the aforementioned control parameter in the dissipation of the energy a complete spectral analysis of the new schemes is presented in this linear range to evaluate their different numerical properties in particular the dissipative character of the proposed schemes in the high frequency range is fully demonstrated in fact it is shown that the new second order scheme is l stable most remarkably the extension of these ideas to the nonlinear range is accomplished avoiding the use of multi stage formulae given the freedom gained in using general nonlinear relations while preserving the conservation laws of the momenta and the corresponding relative equilibria several representative numerical simulations are presented in the context of nonlinear elastodynamics to evaluate the performance of the newly proposed schemes

regularizations of products of residue and principal value currents let f 1 and f 2 be two functions on some complex n manifold and let be a test form of bidegree n n 2 assume that f 1 f 2 defines a complete intersection the integral of f 1 f 2 on f 1 2 e lunate 1 f 2 2 e lunate 2 is the residue integral i f1 f 2 e lunate 1 e lunate 2 it is in general discontinuous at the origin let 1 and 2 be smooth functions on 0 such that j 0 0 and j 1 we prove that the regularized residue integral defined as the integral of over 1 over 2 f 1 f 2 where j j f j 2 e lunate j is holder continuous on the closed first quarter and that the value at zero is the coleff herrera residue current acting on in fact we prove that if is a test form of bidegree n n 1 then the integral of 1 over 2 f 1 f 2 is holder continuous and tends to the over potential 1 f 1 over 1 f 2 of the coleff herrera current acting on more generally let f 1 and f 2 be sections of some vector bundles and assume that f 1 f 2 defines a complete intersection there are associated principal value currents u f and u g and residue currents r f and r g the residue currents equal the coleff herrera residue currents locally one can give meaning to formal expressions such as e g u f r g in such a way that formal leibnitz rules hold our results generalize to products of these currents as well 2006 elsevier inc all rights reserved

on the derived category of the classical godeaux surface abstract we construct an exceptional sequence of length 11 on the classical godeaux surface x which is the z 5 z quotient of the fermat quintic surface in p 3 this is the maximal possible length of such a sequence on this surface which has grothendieck group z 11 z 5 z in particular the result answers kuznetsov s nonvanishing conjecture which concerns hochschild homology of an admissible subcategory in the negative the sequence carries a symmetry when interpreted in terms of the root lattice of the simple lie algebra of type e 8 we also produce explicit nonzero objects in the right orthogonal to the exceptional sequence

exceptional collections of line bundles on the beauville surface abstract we construct quasi phantom admissible subcategories in the derived category of coherent sheaves on the beauville surface s these quasi phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on s we prove that there are exactly 6 exceptional collections consisting of line bundles up to a twist and these collections are spires of two helices

a variational formulation of constitutive models and updates in non linear finite viscoelasticity the purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime the approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment the set of internal variables is strain based and employs according to the specific model chosen a multiplicative decomposition of strain into elastic and viscous components the present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity such as the solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration however instead of using the classical decomposition of inelastic strains into amplitude and direction we take advantage of a spectral decomposition that provides additional facilities to accommodate into simple analytical expressions a wide set of specific models moreover appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature the final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large scale fem analyses copyright 2005 john wiley sons ltd

explicit serre duality on complex spaces abstract in this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization as well as a new analytic proof of serre duality on any reduced pure n dimensional paracompact complex space x at the core of the paper is the introduction of certain fine sheaves b x n q of currents on x of bidegree n q such that the dolbeault complex b x n becomes in a certain sense a dualizing complex in particular if x is cohen macaulay then b x n is an explicit fine resolution of the grothendieck dualizing sheaf

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

energy dissipative momentum conserving time stepping algorithms for finite strain multiplicative plasticity abstract this paper presents a new energy dissipative momentum conserving algorithm for multiplicative models of finite strain plasticity the proposed scheme preserves exactly the conservation laws of linear and angular momenta and leads to the exact energy dissipation between the two computed solutions in a given time step in particular the energy is exactly conserved if the step is elastic thus recovering existing energy momentum conserving schemes in the purely elastic range extensions accommodating a strictly non negative numerical energy dissipation in the high frequency to handle the numerical stiffness of the problem are also discussed briefly these conservation dissipation properties are proven rigorously in the very nonlinear setting of multiplicative finite strain plasticity in fact the analysis drives the design of the new return mapping algorithm proposed to integrate the plastic evolution equations so the above dissipation conservation properties hold these analyses account for the spatial discretization of the problem in the context of the finite element method several representative numerical simulations are presented to illustrate the performance of the new algorithm

variational time integrators for finite dimensional thermo elasto dynamics without heat conduction this paper focuses on the formulation of variational integrators vis for finite dimensional thermo elastic systems without heat conduction the dynamics of these systems happen to have a hamiltonian structure after thermal displacements are introduced it is then possible to formulate integrators by taking advantage of standard methods in vi the class of integrators we construct have some remarkable features a they are symplectic b they exactly conserve the entropy of the system or in other words they exactly satisfy the second law of the thermodynamics for reversible adiabatic processes c they nearly exactly conserve the value of the energy for very long times and d they exactly conserve linear and angular momentum we first describe how to adapt any vi for the classical mechanical systems to integrate adiabatic thermo elastic ones and then formulate three new types of integrators the first class based on a generalized trapezoidal rule gives rise to two first order explicit integrators and a second order implicit one by composing then the two first order integrators we construct a second order explicit one finally we formulate a fourth order implicit integrator which is a symplectic partitioned runge kutta method the performance of these new algorithms is showcased through numerical examples copyright 2011 john wiley sons ltd

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

exceptional collections on dolgachev surfaces associated with degenerations abstract dolgachev surfaces are simply connected minimal elliptic surfaces with p g q 0 and of kodaira dimension 1 these surfaces are constructed by logarithmic transformations of rational elliptic surfaces in this paper we explain the construction of dolgachev surfaces via q gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities this construction is based on the paper 25 also some exceptional bundles on dolgachev surfaces associated with q gorenstein smoothing have been constructed based on the idea of hacking 12 in the case if dolgachev surfaces were of type 2 3 we describe the picard group and present an exceptional collection of maximal length finally we prove that the presented exceptional collection is not full hence there exists a nontrivial phantom category in the derived category

del pezzo orders on projective surfaces abstract in this paper we generalise the notion of del pezzo surfaces to orders on surfaces we show that these del pezzo orders have del pezzo centre if the centre is normal gorenstein and the order has finite representation type we proceed to classify these del pezzo orders the main result is that if the centre is not p 1 p 1 or the quadric cone then these del pezzo orders can be obtained from del pezzo orders on p 2 finally we classify del pezzo orders on p 2 p 1 p 1 and the quadric cone

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part i low order methods for two model problems and nonlinear elastodynamics abstract we present in this paper the development of a class of time stepping algorithms for nonlinear elastodynamics that exhibits the controllable numerical dissipation in the high frequency range required for the robust solution of the resulting numerically stiff systems to motivate and illustrate better the developments in this general case we present first the formulation and analysis of these methods for two simple model problems namely we consider a nonlinear elastic spring mass system and a simplified model of thin elastic beams as it is discussed in detail in this paper the conservation by the numerical algorithm of the momenta and corresponding relative equilibria of these characteristic hamiltonian systems with symmetry is of the main importance these conservation properties lead for a fixed and finite time step to a correct qualitative picture of the phase space where the discrete dynamics takes place even in the presence of the desired and controlled numerical dissipation of the energy this situation is contrasted with traditional dissipative numerical schemes which are shown through rigorous analyses to not only lose their dissipative character in the general nonlinear range but also the aforementioned conservation properties thus leading to a qualitatively distorted approximation of the phase dynamics the key for a successful algorithm in this context is the incorporation of the numerical dissipation in the internal modes of the motion while not affecting the group motions of the systems the algorithms presented in this work accomplish these goals the focus in this first part is given to first order methods representative numerical simulations ranging from applications in nonlinear structural dynamics to nonlinear continuum three dimensional elastodynamics are presented in the context of the finite element method to illustrate these ideas and results

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

log canonical models of elliptic surfaces abstract we classify the log canonical models of elliptic surface pairs f x c s f a where f x c is an elliptic fibration s is a section and f a is a weighted sum of marked fibers in particular we show how the log canonical models depend on the choice of the weights we describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes in addition we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers this is the first step in constructing compactifications of moduli spaces of elliptic surfaces using the minimal model program

a systematic method for constructing discrete painleve equations in the degeneration cascade of the e8 group we present a systematic and quite elementary method for constructing discrete painleve equations in the degeneration cascade for e8 1 starting from the invariant for the autonomous limit of the e8 1 equation one wishes to study the method relies on choosing simple homographies that will cast this invariant into certain judiciously chosen canonical forms these new invariants lead to mappings the deautonomisations of which allow us to build up the entire degeneration cascade of the original mapping we explain the method on three examples two symmetric mappings and an asymmetric one and we discuss the link between our results and the known geometric structure of these mappings

various approaches to products of residue currents abstract we describe various approaches to coleff herrera products of residue currents r j of cauchy fantappie leray type associated to holomorphic mappings f j more precisely we study to which extent exterior products of natural regularizations of the individual currents r j yield regularizations of the corresponding coleff herrera products our results hold globally on an arbitrary pure dimensional complex space

combinatorial aspects of exceptional sequences on rational surfaces we investigate combinatorial aspects of exceptional sequences in the derived category of coherent sheaves on certain smooth and complete algebraic surfaces we show that to any such sequence there is canonically associated a complete toric surface whose torus fixpoints are either smooth or cyclic t singularities in the sense of wahl of type frac 1 r 2 1 kr 1 we also show that any exceptional sequence can be transformed by mutation into an exceptional sequence which consists only of objects of rank one

the construction of numerically calabi yau orders on projective surfaces abstract in this paper we construct a vast collection of maximal numerically calabi yau orders utilising a noncommutative analogue of the well known commutative cyclic covering trick such orders play an integral role in the mori program for orders on projective surfaces and although we know a substantial amount about them there are relatively few known examples

mckay correspondence for canonical orders canonical orders introduced in the minimal model program for orders are simultaneous generalisations of kleinian singularities k s t g g sl 2 and their associated skew group rings k s t g in this paper we construct minimal resolutions of canonical orders via non commutative cyclic covers and skew group rings this allows us to exhibit a derived equivalence between minimal resolutions of canonical orders and the skew group ring form of the canonical order in all but one case the fourier mukai transform used to construct this equivalence allows us to make explicit the numerical version of the mckay correspondence for canonical orders noted in chan hacking and ingalls which relates the exceptional curves of the minimal resolution to the indecomposable reflexive modules of the canonical order

energy consistent algorithms for dynamic finite deformation plasticity abstract this paper addresses the theoretical development and numerical implementation of energy consistent algorithms for dynamic elastoplasticity emphasizing finite strain constitutive formulations so that unconditional stability of the algorithms is assured even in the fully nonlinear regime the key concept behind energy consistency is the requirement that the discretized system obey an a priori stability estimate which may be derived in general using the first and second laws of thermodynamics this approach to computational dynamic plasticity differs from typical application of traditional algorithms such as newmark or hilber hughes taylor methods where local time integration schemes for plasticity laws are developed somewhat independently from the global time integration scheme for the equations of motion without explicit consideration of thermodynamical restrictions two algorithms based on both additive and multiplicative finite deformation plasticity model are formulated within the energy consistent framework both algorithms possess the desirable feature of nonlinear stability of previous energy momentum algorithms for elastodynamics

grobner geometry of vertex decompositions and of flagged tableaux we relate a classic algebro geometric degeneration technique dating at least to hodge 1941 to the notion of vertex decompositions of simplicial com plexes the good case is when the degeneration is reduced and we call this a geometric vertex decomposition our main example in this paper is the family of vexillary matrix schubert vari eties whose ideals are also known as one sided ladder determinantal ideals us ing a diagonal term order to specify the grobner degeneration we show that these have geometric vertex decompositions into simpler varieties of the same type from this together with the combinatorics of the pipe dreams of fomin kirillov 1996 we derive a new formula for the numerators of their multigraded hilbert series the double grothendieck polynomials in terms of flagged set valued tableaux this unifies work of wachs 1985 on flagged tableaux and buch 2002 on set valued tableaux giving geometric meaning to both this work focuses on diagonal term orders giving results complementary to those of knutson miller 2004 where it was shown that the generating minors form a grobner basis for any antidiagonal term order and any matrix schubert va riety we show here that under a diagonal term order the only matrix schubert varieties for which these minors form grobner bases are the vexillary ones reach ing an end toward which the ladder determinantal literature had been building contents

automorphisms of elliptic surfaces inducing the identity in cohomology abstract we give a numerical classification for pairs s g consisting of complex nonsingular projective surfaces s of kodaira dimension one and subgroups g of automorphisms of s inducing trivial actions on h 2 s q

twelve points on the projective line branched covers and rational elliptic fibrations the following divisors in the space rm sym 12 mathbb p 1 of twelve points on mathbb p 1 are actually the same mathcal a the possible locus of the twelve nodal fibers in a rational elliptic fibration i e a pencil of plane cubic curves mathcal b degree 12 binary forms that can be expressed as a cube plus a square mathcal c the locus of the twelve tangents to a smooth plane quartic from a general point of the plane mathcal d the branch locus of a degree 4 map from a hyperelliptic genus 3 curve to mathbb p 1 mathcal e the branch locus of a degree 3 map from a genus 4 curve to mathbb p 1 induced by a theta characteristic and several more the corresponding moduli spaces are smooth but they are not all isomorphic some are finite etale covers of others we describe the web of interconnections among these spaces and give monodromy rationality and prym related consequences enumerative consequences include i the degree of this locus is 3762 e g there are 3762 rational elliptic fibrations with nodes above 11 given general points of the base ii if c rightarrow mathbb p 1 is a cover as in mathcal d then there are 135 different such covers branched at the same points iii the general set of 12 tangent lines that arise in mathcal c turn up in 120 essentially different ways some parts of this story are well known and some other parts were known classically to zeuthen zariski coble mumford and others the unified picture is surprisingly intricate and connects many beautiful constructions including recillas trigonal construction and shioda s e 8 mordell weil lattice

exceptional collections and the neron severi lattice for surfaces abstract we work out properties of smooth projective varieties x over a not necessarily algebraically closed field k that admit collections of objects in the bounded derived category of coherent sheaves d b x that are either full exceptional or numerically exceptional of maximal length our main result gives a necessary and sufficient condition on the neron severi lattice for a smooth projective surface s with o s 1 to admit a numerically exceptional collection of maximal length consisting of line bundles as a consequence we determine exactly which complex surfaces with p g q 0 admit a numerically exceptional collection of maximal length another consequence is that a minimal geometrically rational surface with a numerically exceptional collection of maximal length is rational

non classical godeaux surfaces a non classical godeaux surface is a minimal surface of general type with k2 1 but with h01 0 we prove that such surfaces fulfill h01 1 and they can exist only over fields of positive characteristic at most 5 like non classical enriques surfaces they fall into two classes the singular and the supersingular ones we give a complete classification in characteristic 5 and compute their hodge hodge witt and crystalline cohomology including torsion finally we give an example of a supersingular godeaux surface in characteristic 5

on the jordan holder property for geometric derived categories abstract we prove that the semiorthogonal decompositions of the derived category of the classical godeaux surface x do not satisfy the jordan holder property more precisely there are two maximal exceptional sequences in this category one of length 11 the other of length 9 assuming the noetherian property for semiorthogonal decompositions one can define following kuznetsov the clemens griffiths component cg d for each fixed maximal decomposition d we then show that d b x has two different maximal decompositions for which the clemens griffiths components differ moreover we produce examples of rational fourfolds whose derived categories also violate the jordan holder property

conservation properties of a time fe method part i time stepping schemes forn body problems in the present paper one step implicit integration algorithms for the n body problem are developed the time stepping schemes are based on a petrov galerkin finite element method applied to the hamiltonian formulation of the n body problem the approach furnishes algorithmic energy conservation in a natural way the proposed time finite element method facilitates a systematic implementation of a family of time stepping schemes a particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals the influence of various standard as well as non standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements copyright 2000 john wiley sons ltd

arithmetic fake projective spaces and arithmetic fake grassmannians in a recent paper we have classified fake projective planes natural higher dimensional generalization of these surfaces are arithmetic fake bf p n 1 c and arithmetic fake bf gr m n in this paper we show that arithmetic fake bf p n 1 c can exist only if n 3 5 and an arithmetic fake bf gr m n can exist with n3 odd only if n 5 here we construct four distinct arithmetic fake bf p 4 c and four distinct fake arithmetic bf gr 2 5 furthermore we use certain results and computations of py to exhibit five irreducible arithmetic fake bf p 2 c times bf p 2 c all these are connected smooth complex projective shimura varieties

energy decaying scheme for non linear beam models abstract this paper is concerned with the time integration of the equations of motion describing the non linear dynamic response of beams desirable characteristics of integration schemes for structural dynamics problems include unconditional stability accuracy and high frequency numerical dissipation several schemes exist that present all these features when applied to linear problems though the application of those schemes to non linear problems is often successful proofs of unconditional stability are rarely derived a finite difference integration scheme is derived in this paper for the non linear dynamic response of beams though of a finite difference nature the proposed scheme mimics the integration scheme obtained by applying the time discontinuous galerkin methodology to a single degree of freedom linear oscillator a formal proof of unconditional stability for the non linear problem is derived based on an energy decay argument numerical examples using the proposed scheme are given and the results are compared with the predictions of other available schemes the accuracy of the proposed scheme and its high frequency numerical dissipation characteristics are demonstrated in these examples

density of rational points on del pezzo surfaces of degree one we state conditions under which the set s k of k rational points on a del pezzo surface s of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is zariski dense for example it suffices to require that the elliptic fibration s p 1 induced by the anticanonical map has a nodal fiber over a k rational point of p 1 it also suffices to require the existence of a point in s k that does not lie on six exceptional curves of s and that has order 3 on its fiber of the elliptic fibration this allows us to show that within a parameter space for del pezzo surfaces of degree 1 over r the set of surfaces s defined over q for which the set s q is zariski dense is dense with respect to the real analytic topology we also include conditions that may be satisfied for every del pezzo surface s and that can be verified with a finite computation for any del pezzo surface s that does satisfy them c 2014 elsevier inc all rights reserved

an energy momentum conserving algorithm using the variational formulation of visco plastic updates in this paper we use the variational formulation of elasto plastic updates proposed by ortiz and stainier comput methods appl mech eng 1999 171 419 444 in the context of consistent time integration schemes we show that such a formulation is well suited to obtain a general expression of energy momentum conserving algorithms moreover we present numerical examples that illustrate the efficiency of our developments copyright 2005 john wiley sons ltd

global representation of segre numbers by monge ampere products on a reduced analytic space x we introduce the concept of a generalized cycle which extends the notion of a formal sum of analytic subspaces to include also a form part we then consider a suitable equivalence relation and corresponding quotient mathcal b x that we think of as an analogue of the chow group and a refinement of de rham cohomology this group allows us to study both global and local intersection theoretic properties we provide many mathcal b analogues of classical intersection theoretic constructions for an analytic subspace v subset x we define a mathcal b segre class which is an element of mathcal b x with support in v it satisfies a global king formula and in particular its multiplicities at each point coincide with the segre numbers of v when v is cut out by a section of a vector bundle we interpret this class as a monge ampere type product for regular embeddings we construct a mathcal b analogue of the gysin morphism

computational schemes for non linear elasto dynamics this paper deals with the development of computational schemes for the dynamic analysis of non linear elastic systems the focus of the investigation is on the derivation of unconditionally stable time integration schemes presenting high frequency numerical dissipation for these types of problem at first schemes based on galerkin and time discontinuous galerkin approximations applied to the equations of motion written in the symmetric hyperbolic form are proposed though useful these schemes require casting the equations of motion in the symmetric hyperbolic form which is not always possible furthermore this approaches to unacceptably high computational costs next unconditionally stable schemes are proposed that do not rely on the symmetric hyperbolic form both energy preserving and energy decaying schemes are derived numerical examples are presented to demonstrate the accuracy and efficiency of the proposed schemes copyright 1999 john wiley sons ltd

existence of terminal resolutions of geometric brauer pairs of arbitrary dimension abstract a geometric brauer pair is a pair x where x is a smooth quasi projective variety over an algebraically closed field and is an element in the 2 torsion part of the brauer group of the function field of x a geometric brauer pair y is a terminal pair if the brauer discrepancy of y is positive we show that given a geometric brauer pair x there is a terminal pair y with a birational morphism y x in short any geometric brauer pair admits a terminal resolution

mirror symmetry for del pezzo surfaces vanishing cycles and coherent sheaves we study homological mirror symmetry for del pezzo surfaces and their mirror landau ginzburg models in particular we show that the derived category of coherent sheaves on a del pezzo surface x k obtained by blowing up 2 at k points is equivalent to the derived category of vanishing cycles of a certain elliptic fibration w k m k with k 3 singular fibers equipped with a suitable symplectic form moreover we also show that this mirror correspondence between derived categories can be extended to noncommutative deformations of x k and give an explicit correspondence between the deformation parameters for x k and the cohomology class b i h 2 m k

a first order energy dissipative momentum conserving scheme for elasto plasticity using the variational updates formulation abstract in a previous paper l noels l stainier j p ponthot an energy momentum conserving algorithm using the variational formulation of visco plastic updates int j numer methods engrg 65 2006 904 942 the authors demonstrated the efficiency of the variational formulation of elasto plastic updates to develop energy momentum conserving time integration algorithms indeed within such a framework the stress tensor always derives from an incremental potential even when plastic behavior is considered therefore the verification of the conservation of energy in the non linear range can easily be demonstrated the sum of the reversible stored energy and irreversible dissipated energy exactly corresponds to the work of the external forces applied to the structure although this formulation was shown to be accurate and robust the introduction of numerical dissipation for high frequency numerical modes can be necessary to simulate complex phenomena in this work we propose a modification of the variational updates framework to introduce this numerical property leading to a new energy dissipative momentum conserving time integration algorithm for elasto plasticity

exceptional bundles associated to degenerations of surfaces in 1981 j wahl described smoothings of surface quotient singularities with no vanishing cycles w81 5 9 1 given a smoothing of a projective surface x of this type we construct an associated exceptional vector bundle on the nearby fiber y in the case h2 0 y h1 y 0 if y p2 we show that our construction establishes a bijective correspondence between the possible degenerate surfaces x and exceptional bundles on y modulo a natural equivalence relation if y is of general type then our construction establishes a connection between components of the boundary of the moduli space of surfaces deformation equivalent to y and exceptional bundles on y let n a be positive integers such that a n and a n 1 consider the cyclic quotient singularity

energy preserving decaying schemes for non linear beam dynamics using the helicoidal approximation abstract we develop two unconditionally stable displacement based time stepping schemes for the non linear dynamic response of beams the first algorithm guarantees the exact discrete conservation of energy and momentum the second is associated with an energy decay inequality that achieves control of the unresolved frequencies by means of a numerical dissipation mechanism both schemes emanate from a weak form of the equations of dynamic equilibrium referred to a fixed pole space and time discretizations are based on the exponential parameterization of motion this implies that the beam reference line and the trajectories of the beam nodes are helicoids in space the exponential mapping approach allows a unified treatment of translations and rotations greatly simplifying the derivation of the algorithms and their analysis the capabilities and performance of the new schemes are demonstrated and discussed with the aid of numerical simulations

conservation properties of a time fe method part ii time stepping schemes for non linear elastodynamics in the present paper one step implicit integration algorithms for non linear elastodynamics are developed the discretization process rests on galerkin methods in space and time in particular the continuous galerkin method applied to the hamiltonian formulation of semidiscrete non linear elastodynamics lies at the heart of the time stepping schemes algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals we newly introduce the assumed strain method in time which enables the design of energy momentum conserving schemes and which can be interpreted as temporal counterpart of the well established assumed strain method for finite elements in space the numerical examples deal with quasi rigid motion as well as large strain motion copyright 2001 john wiley sons ltd

energy momentum consistent finite element discretization of dynamic finite viscoelasticity this paper is concerned with energy momentum consistent time discretizations of dynamic finite viscoelasticity energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics the discretization is energy momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations the performed approximation is based on a three field formulation in which the deformation field the velocity field and a strain like viscous internal variable field are treated as independent quantities the new non linear viscous evolution equation satisfies a non negative viscous dissipation not only in the continuous case but also in the fully discretized system the initial boundary value problem is discretized by using finite elements in space and time thereby the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments incremental objectivity although the present approach makes possible to design schemes of arbitrary order the focus is on finite elements relying on linear lagrange polynomials for the sake of clearness the discrete energy momentum consistency is based on the collocation property and an enhanced second piola kirchhoff stress tensor the obtained coupled non linear algebraic equations are consistently linearized the corresponding iterative solution procedure is associated with newly proposed convergence criteria which take the discrete energy consistency into account the iterative solution procedure is therefore not complicated by different scalings in the independent variables since the motion of the element is taken into account for solving the viscous evolution equation representative numerical simulations with various boundary conditions show the superior stability of the new time integration algorithm in comparison with the ordinary midpoint rule both the quasi rigid deformations during a free flight and large deformations arising in a dynamic tensile test are considered copyright 2009 john wiley sons ltd

derived categories of burniat surfaces and exceptional collections we construct an exceptional collection varupsilon of maximal possible length 6 on any of the burniat surfaces with k x 2 6 a 4 dimensional family of surfaces of general type with p g q 0 we also calculate the dg algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all burniat surfaces the semiorthogonal complement mathcal a of varupsilon is an almost phantom category it has trivial hochschild homology and k 0 mathcal a mathbb z 2 6

a simply connected surface of general type with p g 0 and k 2 2 in this paper we construct a simply connected minimal complex surface of general type with pg 0 and k2 2 using a rational blow down surgery and a gorenstein smoothing theory

a consistent time fe method for large strain elasto plasto dynamics in the present paper energy consistent momentum conserving time stepping schemes for geometrically nonlinear multiplicative elasto plasto dynamics referred to as ecmc cg methods are developed in this context the entire discretisation procedure of the global equations of motion is based on galerkin methods in space and time whereby special emphasis is placed on the desired conservation properties related to the approximation of time integrals to guarantee energy consistency also for higher order finite elements in time a thermodynamically motivated enhanced stress tensor which defines a non standard quadrature rule is derived for elasto plastic material behaviour concerning the integration of the local evolution equations in time exemplarily a well established first order accurate exponential update is applied and adapted according to the global time stepping scheme based on linear finite elements in time the performance of the resulting scheme is demonstrated by means of several representative numerical examples whereby it is shown that global energy consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

segre numbers a generalized king formula and local intersections let mathcal j be an ideal sheaf on a reduced analytic space x with zero set z we show that the lelong numbers of the restrictions to z of certain generalized monge ampere products dd c log f 2 k where f is a tuple of generators of mathcal j coincide with the so called segre numbers of mathcal j introduced independently by tworzewski achilles manaresi and gaffney gassler more generally we show that these currents satisfy a generalization of the classical king formula that takes into account fixed and moving components of vogel cycles associated with mathcal j a basic tool is a new calculus for products of positive currents of bochner martinelli type we also discuss connections to intersection theory

semiorthogonal decompositions and birational geometry of del pezzo surfaces over arbitrary fields we study the birational properties of geometrically rational surfaces from a derived categorical perspective in particular we give a criterion for the rationality of a del pezzo surface s over an arbitrary field namely that its derived category decomposes into zero dimensional components when s has degree at least 5 we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of s from brauer classes and chern classes associated to these vector bundles

optimal bounds for t singularities in stable surfaces abstract we explicitly bound t singularities on normal projective surfaces w with one singularity and k w ample this bound depends only on k w 2 and it is optimal when w is not rational we classify and realize surfaces attaining the bound for each nonnegative kodaira dimension of the minimal resolution of w this answers effectiveness of bounds see 1 2 17 for those surfaces