spinors and diffeomorphisms we discuss the action of diffeomorphisms on spinors on an oriented manifoldm to do this we first describe the action of the diffeomorphism groupd m on the set h1 m z2 of inequivalent spin structures and show that it is affine we argue that in the presence of spinors the gauge group of gravity is a certain double cover ofd m which depends on the spin structure we explicitly compute the action ofd m on whenm is a closed riemann surface is seen to consist of exactly two orbits corresponding to even and odd spin structures

iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi minimal residual algorithm abstract finite element discretizations of time harmonic acoustic wave problems in exterior domains result in large sparse systems of linear equations with complex symmetric coefficient matrices in many situations these matrix problems need to be solved repeatedly for different right hand sides but with the same coefficient matrix recently freund and malhotra have proposed a block quasi minimal residual bl qmr algorithm 13 for the iterative solution of non hermitian linear systems with multiple right hand sides the bl qmr algorithm is a block krylov subspace iterative method that incorporates deflation to delete linearly and almost linearly dependent vectors in the underlying block krylov sequences in this paper we describe a j symmetric variant of the bl qmr algorithm that introduces important simplifications for the case when the coefficient matrix is symmetric with respect to a bilinear form induced by a certain matrix j in particular the j symmetric variant includes the complex symmetric form of bl qmr as a special case we identify suitable preconditioners for the bl qmr algorithm applied to multiple radiation and scattering problems our numerical tests with the preconditioned bl qmr algorithm for such multiple linear systems show that instead of solving each of the linear systems individually it is significantly more efficient to employ the block version of the iterative method moreover the numerical results clearly illustrate the importance of deflation and its effect on iterative convergence

calculation of brs cohomology with spectral sequences a method for finding the general form of the brs cohomology spaceh for the various gauge and supersymmetry theories is presented the method is adapted for use in the space of integrated local polynomials of the gauge fields and ghosts with arbitrary numbers of fields and dervivatives the technique uses the hodge decomposition in a fock space with a euclidean inner product and combines this with spectral sequences to generate simple and soluble equations whose solutions span a simple spacee isomorphic to the complicated spaceh the technique is illustrated for pedagogic purposes by the detailed calculation of the ghost charge zero and one sectors ofh for yang mills theory with gauge groupso 32 in ten dimensions the method is appropriate for supersymmetric theories gravity supergravity and superstrings where higher order terms with many derivatives occur naturally in the effective action

preconditioning harmonic unsteady potential flow calculations this paper considers finite element discretizations of the helmholtz equation and its generalization arising from harmonic acoustic perturbations to a nonuniform steady potential flow a novel elliptic positive definite preconditioner with a multigrid implementation is used to accelerate the iterative convergence of krylov subspace solvers both theory and numerical results show that for a model 1 d helmholtz test problem the preconditioner clusters the discrete system s eigenvalues and lowers its condition number to a level independent of grid resolution for the 2 d helmholtz equation grid independent convergence is achieved using a quasi minimal residual krylov solver significantly outperforming the popular symmetric successive over relaxation preconditioner impressive results are also presented on more complex domains including an axisymmetric aircraft engine inlet with nonstagnant mean flow and modal boundary conditions

local anomalies and local equivariant cohomology the locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology this interpretation allows us to solve the problem proposed by singer in 31 and consists in defining an adequate notion of local cohomology to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the atiyah singer index theorem moreover using the relation between local cohomology and the cohomology of jet bundles studied in 19 we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies

a multigrid preconditioner for stabilised discretisations of advection diffusion problems abstract this paper is concerned with the iterative solution of linear systems arising from stabilised discretisations of advection diffusion problems on stretched finite element grids using nonuniform grids of this type leads in general to very badly conditioned matrix problems we therefore consider using gmres in conjunction with a multigrid mg preconditioning strategy in particular we show that in order to achieve the grid size independent convergence which is characteristic of mg methods it is essential to use an effective stabilisation strategy at each level of the mg structure

smoothness of the action of the gauge transformation group on connections the nlf lie group structure of the group g of the gauge transformations defined as the group of sections of the bundle p g associated to the principal bundle p m g is discussed other current definitions of the group of gauge transformations are shown to admit a nontrivial smooth structure only in the case of compact g the space c of principal connections as well is given the structure of local affine nlf manifold after identifications of connections with sections of a convenient vector bundle on m finally the smoothness of the action of g on c is proved in general in the case of compact m the group g becomes a tame frechet lie group and the action a tame smooth action

determinants torsion and strings we apply the results of bf1 bf2 on determinants of dirac operators to string theory for the bosonic string we recover the holomorphic factorization of belavin and knizhik witten s global anomaly formula is used to give sufficient conditions for anomaly cancellation in the heterotic string for arbitrary background spacetimes to prove the latter result we develop certain torsion invariants related to characteristic classes of vector bundles and to index theory

b r s algebras analysis of the consistency equations in gauge theory we compute all possible anomalous terms in quantum gauge theory in the natural class of polynomials of differential forms by using the appropriate cohomological and algebraic methods we do it for all dimensions of spacetime and all structure groups with reductive lie algebras

chern simons forms on principal superfiber bundles a graded weil homomorphism is defined for principal superfiber bundles and the related transgression or chern simons forms are introduced as an example of the application of these concepts a superextension of the dirac monopole is discussed

efficient preconditioning of the linearized navier stokes equations for incompressible flow we outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of navier stokes equations we describe a very general strategy for preconditioning that has two basic building blocks a multigrid v cycle for the scalar convection diffusion operator and a multigrid v cycle for a pressure poisson operator we present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid robust with respect to the time step and only deteriorates very slowly as the reynolds number is increased

transversal dirac families in riemannian foliations we describe a family of differential operators parametrized by the transversal vector potentials of a riemannian foliation relative to the clifford algebra of the foliation this family is non elliptic but in certain ways behaves like a standard dirac family in the absolute case as a result of its elliptic like regularity properties the analytic and topological indices of this family are defined as elements of k theory in the parameter space we indicate how the cohomology of the parameter space is described via suitable maps to fredholm operators we outline the proof of a theorem of vafa witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument a determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation with respect to a generalized coupled dirac yang mills system we indicate how chiral anomalies are located relative to the foliation

methodology for a nullcline based model from direct experiments applications to electrochemical reaction models abstract a method is proposed for the construction of simple yet accurate mathematical models for description of dynamics of nonlinear systems based on the concept of nullclines the nullclines are functional relationships between the essential variables of a dynamical system where the rate of change of a species is constrained to zero when the time scales of the essential variables are separated the dynamics can often be described by motion along nullclines of the fast variable we propose a methodology with which the nullclines can be obtained from direct control experiments the goal is achieved by a combination of an adaptive and proportional controller acting on the fast and the slow variables of the system it is demonstrated in the numerical simulations of two and three variable electrochemical models that the nullclines can be extracted from control of experimentally feasible control parameters circuit potential and rotation rate as an extension of the methodology we propose a nullcline based technique which is capable of reproducing the temporal behavior of the system s variables e g waveform of the oscillations the numerical simulations indicate that the nullcline based model information from direct experiments can effectively predict the system s dynamics and thus the technique holds promise for an alternative modeling route to traditional kinetics mass transfer based approaches

gravitational anomalies and the family s index theorem we discuss the use of the family s index theorem in the study of gravitational anomalies the geometrical framework required to apply the family s index theorem is presented and the relation to gravitational anomalies is discussed we show how physics necessitates the introduction of the notion oflocal cohomology which is distinct from the ordinary topological cohomology the recent results of alvarez gaume and witten are derived by using the family s index theorem

on the bundle of connections and the gauge orbit manifold in yang mills theory in an appropriate mathematical framework we supply a simple proof that the quotienting of the space of connections by the group of gauge transformations in yang mills theory is ac principal fibration the underlying quotient space the gauge orbit space is seen explicitly to be ac manifold modelled on a hilbert space

gerbes simplicial forms and invariants for families of foliated bundles the notion of smooth deligne cohomology is conveniently reformulated in terms of the simplicial derham complex in particular the usual chern weil and chern simons theory is well adapted to this framework and rather easily gives rise to characteristic deligne cohomology classes associated to families of bundles and connections in turn this gives invariants for families of foliated bundles the construction provides representing cocycles in the usual cech derham model for smooth deligne cohomology called gerbes with connection as they generalize usual hermitian line bundles with connection a special case is the quillen line bundle associated to families of flat su 2 bundles

universal bundle for gravity local index theorem and covariant gravitational anomalies consistent and covariant lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity this bundle is explicitly constructed and its geometrical structure will be studied by means of the local index theorem for families of bismut and freed the consistent gravitational anomalies are calculated covariant gravitational anomalies are shown to be related with secondary characteristic classes of the universal bundle and a new set of descent equations which also contains the covariant schwinger terms is derived the relation between consistent and covariant anomalies is studied finally a geometrical realization of the gravitational brs anti brs transformations is presented which enables the formulation of a kind of covariance condition for covariant gravitational anomalies

the evaluation map in field theory sigma models and strings ii in this paper we examine specifically the role of the evaluation map in sigma models and strings we discuss the difference between sigma models and field theory as far as anomaly cancellation is concerned the introduction of the wess zumino terms in different sigma models is considered anomalies in string theory are discussed with special attention to the conformal anomalies and to the sigma model anomalies for the imbedded or immersed world sheet of the string conformal anomalies in two dimensions are connected to holomorphic and gravitational anomalies in order to have the cancellation of the sigma model anomalies of the string certain topological conditions must be satisfied by the ambient manifold the role of the evaluation map in the calculations of global anomalies is also discussed both for field theories and for sigma models in particular global anomalies are connected with the differential characters of cheeger and simons we show that the absence of global anomalies in sigma models is guaranteed by the absence of torsion in suitable homology groups of the target space

adaptive control of unknown unstable steady states of dynamical systems a simple adaptive controller based on a low pass filter to stabilize unstable steady states of dynamical systems is considered the controller is reference free it does not require knowledge of the location of the fixed point in the phase space a topological limitation similar to that of the delayed feedback controller is discussed we show that the saddle type steady states cannot be stabilized by using the conventional low pass filter the limitation can be overcome by using an unstable low pass filter the use of the controller is demonstrated for several physical models including the pendulum driven by a constant torque the lorenz system and an electrochemical oscillator linear and nonlinear analyses of the models are performed and the problem of the basins of attraction of the stabilized steady states is discussed the robustness of the controller is demonstrated in experiments and numerical simulations with an electrochemical oscillator the dissolution of nickel in sulfuric acid a comparison of the effect of using direct and indirect variables in the control is made with the use of the controller all unstable phase space objects are successfully reconstructed experimentally

rational homotopy of the space of sections of a nilpotent bundle we show that an algebraic construction proposed by sullivan is indeed a model for the rational homotopy type of the space of sections of a nilpotent bundle in his paper uhomologie des espaces fonctionnels r thom studied the homotopy type of the space f of continuous maps of x into f homotopic to a given map starting from a postnikov decomposition of f he built the functional space f step by step he also indicated how one could construct a differential graded algebra describing the rational homotopy type of f later on sullivan gave an algebraic model which mirrors this construction in terms of a dg algebra representing x and the minimal model of f the aim of this paper is to show following the method of thom that the model of sullivan is indeed a model for the functional space under suitable restrictions as in 3 we consider the slightly more general problem of the determination of the rational homotopy type of the space of sections ts of a nilpotent fiber space p y x homotopic to a given section s in 1 we explain thorn s geometric construction in 2 we describe an algebraic model for an abelian galois covering of a nilpotent space in 3 we show how the model of sullivan fits with the geometry i thank the referee for many improvements of this paper 1 a postnikov factorization of the space of sections 1 1 let g be a finitely generated abehan group and let x be a path connected space whose cohomology groups hk x g are finitely generated for each k to avoid difficulties with the topologies cf 4 we can work in the category of simplicial sets proposition thom 4 the space k g m x of continuous maps of x in the eilenberg mac lane complex k g m is homotopically equivalent to the product nr ra fthe eilenberg mac lane spaces ki k hm x g i more precisely let x g hm k g m g be the fundamental class of k g m if e k g m x xx k g m

on accuracy conditions for the numerical computation of waves abstract the helmholtz equation k 2 n 2 u f with a variable index of refraction n and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems such problems can be solved numerically by first truncating the given unbounded domain imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization for example using a finite element method in practical applications the mesh size h and the wave number k are not independent but are constrained by the accuracy of the desired computation it will be shown that the number of points per wavelength measured by kh 1 is not sufficient to determine the accuracy of a given discretization for example the quantity k 3 h 2 is shown to determine the accuracy in the l 2 norm for a second order discretization method applied to several propagation models

adaptive detection of instabilities an experimental feasibility study abstract we implement a practical protocol for the active on line detection of bifurcations in experimental systems based on real time identification and feedback control ideas current experimental practice for the detection of bifurcations typically requires long observation times in the vicinity of marginally stable solutions as well as frequent re settings of the experiment for the detection of turning point or subcritical bifurcations the approach exemplified here addresses these issues drawing from numerical bifurcation detection procedures the main idea is to create an augmented experiment using the experimental bifurcation parameter s as additional state variables we implement deterministic laws for the evolution of these new variables by coupling the experiment with an on line computer assisted identification feedback protocol the augmented experiment the closed loop system thus actively converges to what for the original experiment the open loop system is a bifurcation point we apply this method to the real time computer assisted detection of period doubling bifurcations in an electronic circuit the method succeeds in actively driving the circuit to the bifurcation points even in the presence of modest experimental uncertainties noise and limited resolution the active experimental tracing of a codimension 1 bifurcation boundary in two parameter space is also demonstrated

the chiral determinant and the eta invariant for y ye a one parameter family of invertible weyl operators of possibly non zero index acting on spinors over an even dimensional compact manifoldx we express the phase of the chiral determinant det in terms of the invariant of a dirac operator acting on spinors over x

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

the analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems we prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems we provide results for the so called symmetric multigrid schemes we show that for the variable v script cycle and the w script cycle schemes multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns provided that the initial grid is sufficiently fine we show that the v script cycle algorithm also converges under appropriate assumptions on the coarsest grid but at a rate which may deteriorate as the number of levels increases this deterioration for the v script cycle may occur even in the case of full elliptic regularity finally the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory

four dimensional yang mills theory as a deformation of topological bf theory the classical action for pure yang mills gauge theory can be formulated as a deformation of the topological bf theory where beside the two form field b one has to add one extra field given by a one form which transforms as the difference of two connections the ensuing action functional gives a theory that is both classically and quantistically equivalent to the original yang mills theory in order to prove such an equivalence it is shown that the dependency on the field can be gauged away completely this gives rise to a field theory that for this reason can be considered as semi topological or topological in some but not all the fields of the theory the symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections a mathematical analysis of this group action and of the relevant brst complex is discussed in detail

on the weil petersson metric on teichmuller space teichmuller space for a compact oriented surface m without boundary is described as the quotient ji b0 where s is the space of almost complex structures on m compatible with a given orientation and 8 0 are those c diffeomorphisms homotopic to the identity there is a natural 3 0 invariant l2 riemannian structure on si which induces a riemannian structure on si 3 n infinitesimally this is the bilinear pairing suggested by andre weil the weil petersson riemannian struc ture the structure is shown to be kahler with respect to a naturally induced complex structure on s0