classical states and the brst charge the role played by the brst charge in isolating the physical states in a classical first class constrained system is analysed contrary to popular belief the cohomological argument used to characterize the physical observables in such a system does not extend to the classical states it is shown that in order to recover the physical states the brst charge must be augmented with a new charge of ghost number minus one constructed out of a set of gauge fixing conditions for the original constraints the relevance of this construction to the quantum theory is discussed

covariant factor ordering of gauge systems using ghost variables ii states and observables the aim of any constraint quantization procedure is to be able to recover the physical content of a system after quantizing on the extended state space which will include both physical and unphysical configurations within the dirac approach to such problems there is no guarantee that the resulting quantum theory will be equivalent to the quantized physical theory and one has to be content with a case by case analysis of its applicability in this paper it is shown that for finite dimensional systems with first class constraints linear in momenta invariance under constraint rescaling and point transformations is sufficient to ensure a consistent quantization as discussed in the preceding paper j math phys 30 xxx 1989 in order to become a manifest symmetry constraint rescaling requires ghost variables it is now shown how the associated brst charge is constructed and how it is used to describe the physical states and observables in the constrained system the extension of this construction to

the extended phase space of the brs approach the origin of the classical brs symmetry is discussed for the case of a first class constrained system consisting of a 2n dimensional phase spaces with free action of a lie gauge groupg of dimensionm the extended phase spacesext of the fradkin vilkovisky approach is identified with a globally trivial vector bundle overs with fibrel g l g wherel g is the lie algebra ofg andl g its dual it is shown that the structure group of the frame bundle of the supermanifoldsext is the orthosymplectic group osp m m 2n which is the natural invariance group of the super poisson bracket structure on the function spacec sext the action of the brs operator is analyzed for the cases r2n with constraints given by pure momenta the breaking of the osp m m 2n invariance down to sp 2n 2m occurs via an intermediate osp m 2n m starting from a 2n 2m dimensional system with orthosymplectic invariance different choices for the brs operator correspond to choosing different 2n dimensional constraint supermanifolds insext which in general characterize different constrained systems there is a whole family of physically equivalent brs operators which can be used to describe a particular constrained system

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

geometric quantization of the brst charge in the first half of this paper sects 1 4 we generalise the standard geometric quantization procedure to symplectic supermanifolds in the second half sects 5 6 we apply this to two examples that exhibit classical brst symmetry i e we quantize the brst charge and the ghost number more precisely in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with ad equivariant moment map in the second example we consider a foliated configuration space whose cotangent bundle admits the construction of a brst charge associated to this foliation we show that the classical brst symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space and that geometric quantization gives us a super unitary representation of this supergroup finally we point out how these results are related to reduction at the quantum level as compared with the reduction at the classical level

the batalin fradkin and vilkovisky formalism for higher order theories the generalized batalin fradkin and vilkovisky bfv formalism was developed as a method for determining the ghost structure for theories such as gravity and supergravity whose hamiltonian formalism has constraints not related to a lie algebra action previously the classical dynamical content of the bfv description of yang mills theory was investigated there it was found that this approach had a homological interpretation derived from the lie algebra cohomology of the gauge group which allowed one to understand the construction in terms of the dirac approach to constrained systems in this paper the dynamical consequences of the generalized bfv formalism are investigated it is found that even though one no longer has a lie algebra structure associated with the constraints one can still develop a homology theory that reproduces the dirac analysis and from which the generalized bfv formalism can be derived some of the consequences of this approach are discussed

isometries of the toeplitz matrix algebra abstract we study the structure of isometries defined on the algebra a of upper triangular toeplitz matrices our first result is that a continuous multiplicative norm preserving map a m n c must be of the form either a u a u or a u a u where a is the complex conjugation and u is a unitary matrix in our second result we use a range of ideas in operator theory and linear algebra to show that every linear isometry a m n c is of the form a u a v where u and v are two unitary matrices this implies in particular that every such an isometry is a complete isometry and that a unital linear isometry a m n c is necessarily an algebra homomorphism

isomorphisms of certain csl algebras abstract we show that an isomorphism between two reflexive operator algebras on hilbert space with commutative subspace lattices csl is automatically continuous and induces an isomorphism between the lattices for such algebras with completely distributive subspace lattices cdc algebras the quasi spatially implemented isomorphisms are shown to be exactly those that preserve the rank of all finite rank operators we present some examples of nonspatial isomorphisms and discuss some sufficient conditions on the lattices that ensure that all isomorphisms be spatially implemented the relationship between isomorphisms and derivations of csl algebras is also investigated

large eddy simulation of turbulent obstacle flow using a dynamic subgrid scale model we apply the dynamic subgrid scale model to a large eddy simulation of turbulent channel flow with a square rib mounted on one wall the reynolds number re is 3 21 x 10 3 based on the mean velocity above the obstacle and the obstacle s height near wall structures are resolved with the no slip boundary condition the results show better agreement with direct numerical simulation than large eddy simulation with a fixed model constant verifying the value of the dynamic subgrid scale model for simulating complex turbulent flows arge eddy simulation les is an accurate method of simulating complex turbulent flows in which the large flow structures are computed while small scales are modeled the rationale behind this method is based on two observations most of the turbulent energy is in the large structures and the small scales are more isotropic and universal therefore les may be more general and less geometry dependent than reynolds averaged modeling although it comes at higher cost even though les has been used by many investigators most research has been limited to flows with simple geometry in engineering applications however one encounters more complicated geometries here we shall consider a rectangular parallelepiped mounted on a flat surface related flows are those over surfaces protruding from submarines conning towers or control fins wind flows around buildings and airflows over computer chips among others the most distinctive features associated with these flows are three dimensionality flow separation due to protruding surfaces and large scale unsteadiness as a model flow we consider a plane channel flow in which a two dimensional obstacle is mounted on one surface see fig 1 this relatively simple geometry contains flow separation and reattachment flow in this geometry has been studied by tropea and gackstatter1 for low re and werner and wengle2 and dimaczek et al 3 for high re among others recently germano et al 4 suggested a dynamic subgridscale model dsgsm in which the model coefficient is dynamically computed as computation progresses rather than specified a priori this approach is based on an algebraic identity between the subgrid scale stresses at two different filter levels and the resolved turbulent stresses they applied the model to transitional and fully turbulent channel flows and showed that the model contributes nothing in laminar flow and exhibits the correct asymptotic behavior in the nearwall region of turbulent flows without an ad hoc damping function this is a significant improvement over conventional subgrid scale modeling

covariant factor ordering of gauge systems using ghost variables i constraint rescaling a dynamical consequence of local gauge invariance is the existence of first class constraints that are linear in momenta by studying finite dimensional systems with this constraint structure one finds that in order to quantize such theories it is not enough to find a consistent factor ordering rather one must also maintain covariance under rescaling of the constraints point transformations and weak changes to the observables within the standard dirac constraint formalism covariance under these symmetries obstructs a full hilbert space description it is shown how this difficulty may be overcome by the use of ghost variables in the present paper i an analysis of the becchi rouet stora tyutin brst structure of such systems is presented the constraint rescaling is shown to be implemented by a canonical transformation on the super phase space that can be evaluated to a unitary transformation on a suitably defined state space in the following paper ii j math phys 30 xxx 1989 these tech

homological perturbation theory and the algebraic structure of the antifield antibracket formalism for gauge theories the algebraic structure of the antifield antibracket formalism for both reducible and irreducible gauge theories is clarified this is done by using the methods of homological perturbation theory hpt a crucial ingredient of the construction is the koszul tate complex associated with the stationary surface of the classical extremals the koszul tate differential acts on the antifields and is graded by the antighost number it provides a resolution of the algebraa of functions defined on the stationary surface namely it is acyclic except at degree zero where its homology group reduces toa acyclicity only holds because of the introduction of the ghosts of ghosts and provides an alternative criterion for what is meant by a proper solution of the master equation the existence of the brst symmetry follows from the techniques of hpt the classical lagrangian brst cohomology is completely worked out and shown to be isomorphic with the cohomology of the exterior derivative along the gauge orbits on the stationary surface the algebraic structure of the formalism is identical with the structure of the hamiltonian brst construction the role played there by the constraint surface is played here by the stationary surface only elementary quantum questions general properties of the measure are addressed

existence theorem for gauge algebra a general gauge action is defined by postulating a minimum of its properties necessary for the existence of loop expansion in the quantum theory the structure of the general gauge algebra is derived from these postulates the proof of existence of the structure functions lacking in previous works is given the question of uniqueness is also completely cleared up some unsolved problems are discussed in connection with the covariant quantization conjecture

isometries for unitarily invariant norms a survey of linear isometries for unitarily invariant norms on real or complex rectangular matrices is given which includes some latest development on the topic a result on isometries for unitarily invariant norms without the linearity assumption is presented related results and problems are discussed

brst cohomology and phase space reduction in deformation quantization in this article we consider quantum phase space reduction when zero is a regular value of the momentum map by analogy with the classical case we define the brst cohomology in the framework of deformation quantization we compute the quantum brst cohomology in terms of a quantum chevalley eilenberg cohomology of the lie algebra on the constraint surface to prove this result we construct an explicit chain homotopy both in the classical and quantum case which is constructed out of a prolongation of functions on the constraint surface we have observed the phenomenon that the quantum brst cohomology cannot always be used for quantum reduction because generally its zero part is no longer a deformation of the space of all smooth functions on the reduced phase space but in case the group action is sufficiently nice e g proper which is the case for all compact lie group actions it is shown for a strongly invariant star product that the brst procedure always induces a star product on the reduced phase space in a rather explicit and natural way simple examples and counterexamples are discussed

implicit large eddy simulation of non wall bounded turbulent flows based on the multiscale properties of a high order finite volume method in this paper it is presented the application of a higher order finite volume method based on moving least squares approximations fv mls to the resolution of non wall bounded compressible turbulent flows our approach is based on the monotonically implicit large eddy simulation miles the main idea of miles methodology is the absence of any explicit subgrid scale sgs model in the numerical algorithm to solve turbulent flows in the case of the fv mls method we take advantage of the multiresolution properties of moving least squares approximations and we show that they can be used as an implicit sgs model the numerical results are encouraging the third order fv mls method is able to reproduce the inertial subrange and it obtains better results than other usual numerical schemes in les computations such as the muscl scheme we note that in the present state of this research the numerical method is not yet suited for wall bounded flows this paper is the first step in the application of the fv mls method to general turbulent flows

a novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows abstract this paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models the approximate deconvolution ad procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the smagorinsky and leith models the novel idea here is to estimate the modeling parameters using the ad method rather than the traditionally used test filtering approach first a priori and a posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem the proposed model is then applied to a wind driven quasigeostrophic four gyre ocean circulation problem which is a standard prototype of more realistic ocean dynamics results show that the proposed model captures the quasi stationary ocean dynamics and provides the time averaged four gyre circulation patterns taking locally resolved flow characteristics into account the model dynamically provides higher eddy viscosity values for lower resolutions

isometries of certain reflexive operator algebras abstract we consider linear surjective isometries acting on reflexive operator algebras with commutative completely distributive subspace lattices such isometries come in two types those implemented by unitary operators and conjugations acting on the hilbert space and those implemented by unitaries alone it is shown that every isometry is a direct sum of these types

algebraic structure of the brst symmetry an explicit construction of the brst symmetry is presented in the hamiltonian approach the construction is based on the splitting homotopy and the transference problem

isometries of non self adjoint operator algebras abstract we study isometries of certain non self adjoint operator algebras by means of the structure of the complete holomorphic vector fields on their unit balls and the associated partial jordan triple products we show that isometries of nest sub algebras of b h are of the form t utw or t ujt jw where u w are suitable unitary operators and j a fixed involution of h

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