a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

space time finite element techniques for computation of fluid structure interactions we describe the space time finite element techniques we developed for computation of fluid structure interaction fsi problems among these techniques are the deforming spatial domain stabilized space time dsd sst formulation and its special version and the mesh update methods including the solid extension mesh moving technique semmt also among these techniques are the block iterative quasi direct and direct coupling methods for the solution of the fully discretized coupled fluid and structural mechanics equations we present some test computations for the mesh moving techniques described we also present numerical examples where the fluid is governed by the navier stokes equations of incompressible flows and the structure is governed by the membrane and cable equations overall we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of fsi problems 2005 elsevier b v all rights reserved

a glimm effros dichotomy for borel equivalence relations a basic dichotomy concerning the structure of the orbit space of a transformation group has been discovered by glimm g12 in the locally compact group action case and extended by effros e 1 e2 in the polish group action case when additionally the induced equivalence relation is f it is the purpose of this paper to extend the glimm effros dichotomy to the very general context of an arbitrary borel equivalence relation not even necessarily induced by a group action despite the totally classical descriptive set theoretic nature of our result our proof requires the employment of methods of effective descriptive set theory and thus ultimately makes crucial use of computability or recursion theory on the integers

the smooth ideal we give a classical proof of the generalization of the characterization of smoothness to quotients of polish spaces by borel equivalence relations as an application we describe the extent to which any given borel equivalence relation on a polish space is encoded by the corresponding ideal generated by the family of borel sets on which it is smooth

essential countability of treeable equivalence relations we establish a dichotomy theorem characterizing the circumstances under which a treeable borel equivalence relation e is essentially countable under additional topological assumptions on the treeing we in fact show that e is essentially countable if and only if there is no continuous embedding of e1 into e our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations and allow us to show that up to continuous kakutani embeddability there is a minimum borel function which is not essentially countable to one

perturbation technique for non self adjoint systems with repeated eigenvalues the reanalysis of non self adjoint systems is computationally very expensive in the design of structural dynamics an effective even if approximate evaluation of the eigensolutions of a modified system is valuable to designers in a paper by meirovitch and ryland meirovitch l and ryland g a perturbation technique for gyroscopic systems with small internal and external damping journal of sound and vibration vol 100 no 3 1985 pp 393408 a perturbation technique was used to derive the perturhed solutions of a damped gyroscopic system with distinct eigenvalues that approach is extended to the case of systems with repeated eigenvalues a numerical example is presented to verify the present method and satisfactory results are observed

the classification problem for torsion free abelian groups of finite rank in 1937 baer 5 introduced the notion of the type of an element in a torsion free abelian group and showed that this notion provided a complete invariant for the classification problem for torsion free abelian groups of rank 1 since then despite the efforts of such mathematicians as kurosh 23 and malcev 25 no satisfactory system of complete invariants has been found for the torsion free abelian groups of finite rank n 2 so it is natural to ask whether the classification problem is genuinely more difficult for the groups of rank n 2 of course if we wish to show that the classification problem for the groups of rank n 2 is intractible it is not enough merely to prove that there are 2 such groups up to isomorphism for there are 2 pairwise nonisomorphic groups of rank 1 and we have already pointed out that baer has given a satisfactory classification for this class of groups in this paper following friedman stanley 11 and hjorth kechris 15 we shall use the more sensitive notions of descriptive set theory to measure the complexity of the classification problem for the groups of rank n 2 recall that up to isomorphism the torsion free abelian groups of rank n are exactly the additive subgroups of the n dimensional vector space qf which contain n linearly independent elements thus the collection of torsion free abelian groups of rank 1 r n can be naturally identified with the set s qn of all nontrivial additive subgroups of qn notice that s qn is a borel subset of the polish space p qn of all subsets of qn and hence s qn can be regarded as a standard borel space i e a polish space equipped with its associated o algebra of borel subsets here we are identifying p qn with the space 2 qn of all functions h qn 0 1 equipped with the product topology furthermore the natural action of gln q on the vector space qn induces a corresponding borel action on s qn and it is easily checked that if a b c s qn then a v b iff there exists an element f e gln q such that p a b it follows that the isomorphism relation on s qn is a countable borel equivalence relation if x is a standard borel space then a borel equivalence relation on x is an equivalence relation e c x2 which is a borel subset of x2 the borel equivalence relation e is said to be countable iff every e equivalence class is countable

approximate method for eigensensitivity analysis of a defective matrix based on the exact modal expansion method an arbitrary high order approximate method is developed for calculating the second order eigenvalue derivatives and the first order eigenvector derivatives of a defective matrix the numerical example shows the validity of the method if the different eigenvalues m 1 m q of the matrix are arranged so that m 1 m q and satisfy the condition that m q 1 m q 1 1 for some q 1

multi domain parallel computation of wake flows abstract we present a new multi domain parallel computational method for simulation of unsteady flows involving a primary object a long wake region and possibly a secondary object affected by the wake flow the method is based on the stabilized finite element formulation of the time dependent navier stokes equations of incompressible flows in the multi domain computational method the entire simulation domain is divided into an ordered sequence of overlapping subdomains the flow data computed over the leading subdomain is used for specifying the inflow boundary conditions for the next subdomain the subdomain corresponding to the wake would not involve any objects hence the mesh constructed over this domain would be structured a special purpose finite element implementation for structured meshes is used for the wake domain to achieve much higher computational speeds compared to a general purpose implementation we present verification studies for the multi domain method and special purpose implementation followed by two numerical examples the first example is the wake behavior behind a circular cylinder the second one is the aerodynamic effect of tip vortices released from a leading wing on a trailing wing placed in the far wake

generalized galerkin method for modal testing of structure with pseudomaterials this paper presents a generalized galerkin method based on the dynamic flexibility matrix expansion technique the main objective is to develop an analysis to predict the modes and frequencies of a real structure when the design verification methods used to conduct on the ground tests can only be performed on a pseudomaterial structure it is critical to develop analytical methods that correctly predict the dynamic behavior of real structure in order to guarantee a successful design of complex structures oftentimes a full scale spacecraft modal test cannot be performed on the real model due to hazardous payloads it carries stable and relatively inexpensive materials are often used to replace these hazardous materials during the test the basic idea for analyzing these test modes of pseudomaterial structures is based on eigenvalue reanalysis techniques this method is relatively easy to understand and can be implemented into the existing method it is numerically accurate and efficient and can be applied to assist in large complex space structure designs

parachute fluid structure interactions 3 d computation abstract we present a parallel computational strategy for carrying out 3 d simulations of parachute fluid structure interaction fsi and apply this strategy to a round parachute the strategy uses a stabilized space time finite element formulation for the fluid dynamics fd and a finite element formulation derived from the principle of virtual work for the structural dynamics sd the fluid structure coupling is implemented over compatible surface meshes in the sd and fd meshes large deformations of the structure are handled in the fd mesh by using an automatic mesh moving scheme with remeshing as needed

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

countable abelian group actions and hyperfinite equivalence relations an equivalence relation e on a standard borel space is hyperfinite if e is the increasing union of countably many borel equivalence relations e n where all e n equivalence classs are finite in this article we establish the following theorem if a countable abelian group acts on a standard borel space in a borel manner then the orbit equivalence relation is hyperfinite the proof uses constructions and analysis of borel marker sets and regions in the space 2 mathbb z omega this technique is also applied to a problem of finding borel chromatic numbers for invariant borel subspaces of 2 mathbb z n

the classification of hypersmooth borel equivalence relations this paper is a contribution to the study of borel equivalence relations in standard borel spaces i e polish spaces equipped with their borel structure a class of such equivalence relations which has received particular attention is the class of hyperfinite borel equivalence relations these can be defined as the increasing unions of sequences of borel equivalence relations all of whose equivalence classes are finite or as it turns out equivalently those induced by the orbits of a single borel auto morphism hyperfinite equivalence relations have been classified in djk under two notions of equivalence borel bi reducibility and borel isomorphism

the classification problem for s local torsion free abelian groups of finite rank abstract suppose that n 2 and that s t are sets of primes then the classification problem for the s local torsion free abelian groups of rank n is borel reducible to the classification problem for the t local torsion free abelian groups of rank n if and only if s t

fluid structure interactions of a parachute crossing the far wake of an aircraft abstract in this paper we describe a computational technique for simulation of the fluid structure interactions of a parachute crossing the far wake of an aircraft this technique relies on using the long wake flow data already computed in our case with the multi domain method mdm we developed earlier the fluid structure interaction computations are carried out over a domain enclosing the parachute and moving with the payload this domain functions as one of the subdomains of the mdm designed specifically for the parachute fluid structure interactions considered here the boundary conditions for this subdomain are extracted from the long wake flow data at locations corresponding to the positions of those boundaries in the subdomain over which the wake flow data were computed the navier stokes equations of incompressible flows governing the fluid dynamics are solved with the deforming spatial domain stabilized space time dsd sst formulation which can handle changes in the spatial domain occupied by the fluid this formulation is coupled to the finite element formulation used for solving the membrane equations governing the structural mechanics of the parachute canopy and the equations governing the mechanics of the suspension lines the numerical example included demonstrates how the technique described here functioning as a component of the mdm enables us to simulate the fluid structure interactions of a parachute crossing an aircraft wake

smooth sets for a borel equivalence relation we study some properties of smooth borel sets with respect to a borel equivalence relation showing some analogies with the collection of countable sets from a descriptive set theoretic point of view we found what can be seen as an analog of the hyperarithmetic points in the context of smooth sets we generalize a theorem of weiss from z actions to actions by arbitrary countable groups we show that the ci ideal of closed smooth sets is ill non borel

orbit equivalence for cantor minimal ℤd systems we show that every minimal action of any finitely generated abelian group on the cantor set is topologically orbit equivalent to an af relation as a consequence this extends the classification up to orbit equivalence of minimal dynamical systems on the cantor set to include af relations and d actions

linear algebraic groups and countable borel equivalence relations this paper is a contribution to the study of borel equivalence relations on standard borel spaces i e polish spaces equipped with their borel structure in mathematics one often deals with problems of classification of objects up to some notion of equivalence by invariants frequently these objects can be viewed as elements of a standard borel space x and the equivalence turns out to be a borel equivalence relation e on x a complete classification of x up to e consists of finding a set of invariants i and a map c x i such that xey c x c y for this to be of any interest both i and c must be explicit or definable and as simple and concrete as possible the theory of borel equivalence relations studies the set theoretic nature of possible invariants and develops a mathematical framework for measuring the complexity of such classification problems

uniformly recurrent subgroups and simple c algebras we study uniformly recurrent subgroups urs introduced by glasner and weiss 18 answering their query we show that any urs z of a finitely generated group is the stability system of a minimal z proper action we also show that for any sofic urs z there is a z proper action admitting an invariant measure we prove that for a urs z all z proper actions admits an invariant measure if and only if z is coamenable in the second part of the paper we study the separable c algebras associated to urs s we prove that if a urs is generic then its c algebra is simple we give various examples of generic urs s with exact and nuclear c algebras and an example of a urs z for which the associated simple c algebra is not exact and not even locally reflexive in particular it admits both a uniformly amenable trace and a nonuniformly amenable trace

orbit equivalence for cantor minimal mathbb z 2 systems we show that every minimal action of any finitely generated abelian group on the cantor set is topologically orbit equivalent to an af relation as a consequence this extends the classification up to orbit equivalence of minimal dynamical systems on the cantor set to include af relations and d actions

on the complexity of the uniform homeomorphism relation between separable banach spaces we investigate the uniform homeomorphism relation between separable banach spaces and the related relation of local equivalence we completely characterize the descriptive complexity of local equivalence in the borel reducibility hierarchy this also provides a lower bound for the complexity of the uniform homeomorphism

a perturbation technique for gyroscopic systems with small internal and external damping abstract the response of linear damped gyroscopic systems can be obtained by means of techniques of linear systems theory which involves the computation of the transition matrix the response is in terms of complex quantities which is likely to cause computational difficulties as the order of the system increases in the absence of damping it is possible to derive the response of a linear gyroscopic system with relative ease by working with real quantities alone when damping is small one can use a perturbation approach to produce the response by regarding the undamped gyroscopic system as the unperturbed system in a previous paper a perturbation analysis was used to derive the response of a gyroscopic system with small internal damping this paper extends the approach to the case of external damping which is characterized not only by symmetric coefficients multiplying velocities but also by skew symmetric coefficients multiplying displacements where the latter terms are known as circulatory a numerical example is presented

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

the structure of hyperfinite borel equivalence relations we study the structure of the equivalence relations induced by the orbits of a single borel automorphism on a standard borel space we show that any two such equivalence relations which are not smooth i e do not admit borel selectors are borel embeddable into each other this utilizes among other things work of effros and weiss using this and also results of dye varadarajan and recent work of nadkarni we show that the cardinality of the set of ergodic invariant measures is a complete invariant for borel isomorphism of aperiodic nonsmooth such equivalence relations in particular since the only possible such cardinalities are the finite ones countable infinity and the cardinality of the continuum there are exactly countably infinitely many isomorphism types canonical examples of each type are also discussed

dichotomy theorems for families of non cofinal essential complexity we prove that for every borel equivalence relation e either e is borel reducible to mathbb e 0 or the family of borel equivalence relations incompatible with e has cofinal essential complexity it follows that if f is a borel equivalence relation and cal f is a family of borel equivalence relations of non cofinal essential complexity which together satisfy the dichotomy that for every borel equivalence relation e either e in cal f or f is borel reducible to e then cal f consists solely of smooth equivalence relations thus the dichotomy is equivalent to a known theorem

on the complexity of the isomorphism relation for finitely generated groups working within the framework of descriptive set theory we show that the isomorphism relation for finitely generated groups is a universal essentially countable borel equivalence relation we also prove the corresponding result for the conjugacy relation for subgroups of the free group on two generators the proofs are group theoretic and we refer to descriptive set theory only for the relevant definitions and for motivation for the results

generic dynamics and monotone complete c algebras soit r une relation d equivalence generique denombrable ergodique sur un espace parfait polonais x modulo un sous ensemble maigre de x r peut s identifier a la relation d equivalence d orbite suivant une action canonique de z

derivatives of eigenvalues and eigenvectors of a general complex matrix a survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non hermitian matrices is presented in addition a modification of one method based on a better normalizing condition is proposed methods are classified as direct or adjoint and are evaluated for efficiency operation counts are presented in terms of matrix size number of design variables and number of eigenvalues and eigenvectors of interest the effect of the sparsity of the matrix and its derivatives is also considered and typical solution times are given general guidelines are established for the selection of the most efficient method

a parallel 3d computational method for fluid structure interactions in parachute systems abstract we present a parallel finite element computational method for 3d simulation of fluid structure interactions fsi in parachute systems the flow solver is based on a stabilized finite element formulation applicable to problems involving moving boundaries and governed by the navier stokes equations of incompressible flows the structural dynamics sd solver is based on the total lagrangian description of motion with cable and membrane elements the nonlinear equation system is solved iteratively with a segregated treatment of the fluid and sd equations the large linear equation systems that need to be solved at every nonlinear iteration are also solved iteratively the parallel implementation is accomplished using a message passing programming environment as a test case the method is applied to computation of the equilibrium configuration of an anchored ram air parachute placed in an air stream

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

borel chromatic numbers we study in this paper graph coloring problems in the context of descriptive set theory we consider graphs g x r where the vertex set x is a standard borel space i e a complete separable metrizable space equipped with its algebra of borel sets and the edge relation r x 2 is definable i e borel analytic co analytic etc a borel n coloring of such a graph where 1 n n 0 is a borel map c x y with card y n such that xry c x c y if such a borel coloring exists we define the borel chromatic number of g in symbols x b g to be the smallest such n otherwise we say that g has uncountable borel chromatic number in symbols x b g n 0

universal perturbation technique for reanalysis of non self adjoint systems a novel matrix perturbation technique for modal dynamic reanalysis of non self adjoint systems is presented this technique is established first by performing complex eigensubspace condensation and orthogonal decomposition procedure the lower order perturbations of eigensolutions i e complex eigenvalues complex left and right eigenvectors are obtained by solving two reduced eigenvalue problems the higher order perturbations of eigensolutions are then derived by implementing the successive approximation process the proposed technique is a kind of universal dynamic reanalysis method because it is universally applicable to systems with all of the three cases distinct repeated and closely spaced eigenvalues illustrative examples are given to verify the present method and satisfactory results are observed

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100