compact composition operators on weighted hilbert spaces of analytic functions we characterize the compactness of composition operators acting on a large family of hilbert spaces of analytic functions which lie between bergman and dirichlet spaces our characterization is given in terms of generalized nevanlinna counting functions

hausdorff measures capacities and compact composition operators it is shown that there exist analytic self maps of the unit disc inducing compact composition operators on the hardy space 1 p such that the hausdorff dimension of the set is one sharpening a classical result due to schwartz moreover the same holds in the weighted dirichlet spaces with 0 1 as a consequence we deduce that there exist symbols inducing compact composition operators on such that the capacity of e is positive which is no longer true for those just inducing hilbert schmidt composition operators on

compact composition operators on h 2 and hardy orlicz spaces abstract we compare the compactness of composition operators on h 2 and on orlicz hardy spaces h we show that for every 1 p there exists an orlicz function such that h p e h h p for every e 0 and a composition operator c which is compact on h p and on h p e but not on h we also show that for every orlicz function which does not satisfy condition 2 there is a composition operator c which is compact on h 2 but not on h and that when grows fast enough there is a function such that c is in all schatten classes s p for p 0 but is not compact on h

three dimensional unstructured multigrid for the euler equations the three dimensional euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy the driving algorithm consists of an explicit vertex based finite element scheme which employs an edge based data structure to assemble the residuals the multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady state of the fine grid solution variables residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation the addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm the preprocessing operation is shown to require a negligible fraction of the cpu time required by the overall solution procedure whereas gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350 000 vertices solutions using globally regenerated fine meshes as well as adaptively refined meshes are given

time domain identification of loads on plate like structures using an array of acoustic velocity sensors the fat force analysis technique method has been developped to identify loads on beams or plates from the knowledge of their flexural displacements the method is based on a local discretisation of the differential operator of the studied structure all derivatives of the displacement field are assessed at a given point from a finite difference scheme the estimation of the operator gives as an output the value of the force distribution up to now applications of the fat method have been made in the frequency domain scanning the studied structure with accelerometers or with a laser vibrometer and using phase references to get the phase relation between different points the aim of the present study is to show that the fat method allows to identify loads in the time domain this operation requires the simultaneous measurement of at least 13 points on the plate that can be realized without contact using an array of acoustic velocity sensors in the very near field of the plate the method has been app

compact composition operators on bergman orlicz spaces we construct an analytic self map of the unit disk and an orlicz functionfor which the composition operator of symbol is compact on the hardy orlicz space h but not on the bergman orlicz space b for that we first prove a carleson embedding theorem and then characterize the compact ness of composition operators on bergman orlicz spaces in terms of carleson function of order 2 we show that this carleson function is equivalent to the nevanlinna counting function of order 2 mathematics subject classification primary 47b33 secondary 30d50 30d55 46e15

implicit multiple grid solution of the compressible navier stokes equations using k epsilon turbulence closure in the present work an algorithm for the numerical solution of the two dimensional mass weighted ensemble averaged compressible navier stokes equations is presented turbulence closure for the reynolds stresses is obtained using a low reynolds n umber two equation k s model which includes near wall effects the same algorithm is used for the integration of both the navier stokes and the turbulence transport equations the algorithm consists of a basic explicit finite volume scheme whose convergence is accelerated using local time step ping and multiple grid techniques convergence is further enhanced by the use of an implicit residual smoothing technique applied both in the fine and the coarser grids the application of the numerical scheme to the solution of the k s equations is examined in detail comparisons of computations with experimental data are presented for three shock wave turbulent boundary layer interaction flows algorithm convergence rate and cpu time require ments are discussed he numerical solution of the navier stokes equations for the simulation of turbulent flowfields is a subject of intense research and code development work 1 interest is focused both on code applicability to variegated config urations and on computational rapidity although direct simulation of turbulent flows2 or large eddy numerical sim ulations using subgrid turbulence modeling 3 4 have appeared in the literature current status of algorithm development and computer power indicate that for practical applications the ensemble averaged navier stokes equations should be used in conjunction with transport equations for turbulence closure 5 7 algebraic or mixing length models may provide satisfactory results for relatively simple flow geometries8 but require the determination of the shear layer thickness and of the distance of each grid point from the solid boundary thus they lack both geometric invariance and locality which are highly desirable properties from a computational viewpoint when addressing complex flowfields with many interacting solid boundaries although research on reynolds stre ss transport closure appears quite promising 9 10 its extension to three dimensions involves considerable increase of the number of transport equations to be solved also further research con cerning wall effects is required the more so since the use of wall functions is considered inadequate 11 on the other hand the use of two equation closures such as a 12 14 is quite widespread notwithstanding the fact that the use of the boussinesq hypothesis15 introduces a question able simplification of the flow physics 16 the major drawback of the k s model is probably the near wall formulation which fails to reproduce correctly the effects of the solid boundary on turbulence several variants of the original jones launder model12 have been developed in an attempt to improve upon near wall modeling some ten such models have been thor oughly examined in a critical review article by patel et al 17 who concluded that the models of launder and sharma 14

reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering the localization and the magnitude of acting steady states forces resulting from the dynamic response of a cylindrical shell are investigated the derivatives present in the equation of motion are expressed in terms of displacements using finite difference schemes displacements of the structure are introduced into the equation of motion in order to calculate the distribution of these forces numerical simulations show that when the force distribution is calculated using well defined displacements the exact position of the force is easily determined however when the displacements are mixed with uncertainties noise appears and the real force is relatively inaccurate in order to handle this instability in the inverse problem a regularization method based on signal processing techniques such as windowing and filtering in the spatial wavenumber domain should be performed numerical examples that illustrate the regularization process show that when the local filtering is applied to the force distribution calculated from noisy data reasonable results are obtained experiments are performed on a cylindrical shell in order to measure its velocities unfortunately using the displacements derived from measured velocities high sensitivity to the noise in the measurements is observed overall the experimental identification gives also good results when the same technique of filtering is applied to the force distribution

vibration source identification using corrected finite difference schemes abstract this paper addresses the problem of the location and identification of vibration excitations from the measurement of the displacement field of a vibrating structure it constitutes an improvement of the force analysis technique published several years ago the development is based on the use of the motion equation which is discretized by finite difference schemes approximating spatial derivatives of the displacement in a first instance the error due to this approximation is analytically calculated in the case of beams and the low pass filtering effect of the finite difference schemes in the wavenumber domain is shown this filter also contains singularities implying bias errors especially if the spacing between sensors is chosen in order to regularize the problem in a second instance a corrected value is applied to the classic schemes used in the force analysis technique which suppresses completely the singularities of the filter after the complete description of the corrected force analysis technique on beams the extension to plates is described where simulations with noisy data show the very good accuracy one can obtain without the requirement of an added regularization for the excitation identification

near wall k e computation of transonic turbomachinery flows with tip clearance acomputational methodforthenumericalintegration ofthefavre reynolds averaged three dimensionalcompressible navier stokes equations in axial turbomachinery using the launder sharma near wall k turbulence closure is developed the mean e ow and turbulence transport equations are discretized using a e nite volume method based on muscl van leere ux vector splitting with van albada limiters and are integrated in time using a fully coupled approximately factored implicit backward euler method the resulting scheme is robust and was found stable for local time steps of courant friedrichs lewy number cfl 20 the computational domain is discretized using a basic h o h grid the tip clearance gap is discretized using a e ne o type grid the radial distribution ofnodeswithin thetip clearancegap is independent of theblade rowo grid and a bufferoverlap grid is used to convey information boundary conditions at periodicity boundaries and at domain interfaces are treated using e ve phantom nodes this procedure ensures stability at high cfl results are presented for the nasa 37 rotor at an operating point near surge computations are compared with measurements both for blade to blade mach number contours and pitchwise distributions and for radial distributions downstream of the blades results are obtained using three grids of 10 6 2 10 6 and 3 10 6 points with 21 31 and 41 radial stations within the tip clearancegap respectively demonstratingthatresultsaregridindependent comparisonwithmeasurementsis satisfactory with theexception of pressureratio overestimation due to unsatisfactory prediction ofe ow separation by the turbulence model

exceptional sets and hilbert schmidt composition operators it is shown that an analytic map phi of the unit disk into itself inducing a hilbert schmidt composition operator on the dirichlet space has the property that the set e phi e i0 is an element ofpartial derivatived phi e 10 1 has zero logarithmic capacity we also show that this is no longer true for compact composition operators on the dirichlet space moreover such a condition is not even satisfied by hilbert schmidt composition operators on the hardy space

simulation of three dimensional turbulent flows on unstructured meshes a three dimensional navier stokes flow solver is developed on unstructured tetrahedral meshes for a turbulence closure a standard high reynolds number k e model with a wall function boundary condition is used the seven equations of motion are discretized and integrated in a tightly coupled manner the time integration is achieved using an explicit runge kutta time stepping scheme the inviscid flux terms are discretized based on a cell centered finite volume formulation with roe s flux difference splitting the numerical method is applied for flows on a two dimensional backward facing step and a three dimensional turbomachinery geometry the results are compared with analytical and experimental data for validations

some examples of composition operators and their approximation numbers on the hardy space of the bi disk we give examples of composition operators c phi on h 2 d 2 showing that the condition phi infty 1 is not sufficient for their approximation numbers a n c phi to satisfy lim n to infty a n c phi 1 sqrt n 1 contrary to the 1 dimensional case we also give a situation where this implication holds we make a link with the monge amp ere capacity of the image of phi

trace ideal criteria for toeplitz operators for a complex measure on the open unit disk u define an operator t on a hilbert space h of analytic functions with reproducing kernel k z w by u for a certain scale of hilbert spaces h 1 which includes the hardy space h2 and weighted bergman spaces a2 conditions are obtained which imply t belongs to a schatten ideal sp if is a positive measure then these conditions are necessary and sufficient application to composition operators and restriction operators are indicated

level sets and composition operators on the dirichlet space abstract we consider composition operators in the dirichlet space of the unit disc in the plane various criteria on boundedness compactness and hilbert schmidt class membership are established some of these criteria are shown to be optimal

nevanlinna counting function and carleson function of analytic maps we show that the maximal nevanlinna counting function and the carleson function of analytic self maps of the unit disk are equivalent up to constants

compact composition operators on the dirichlet space and capacity of sets of contact points we prove several results about composition operators on the dirichlet space d for every compact set k d of logarithmic capacity capk 0 there exists a schur function both in the disk algebra a d and in d such that the composition operator c is in all schatten classes sp d p 0 and for which k eit eit 1 eit eit 1 for every bounded composition operator c on d and every d the logarithmic capacity of eit eit is 0 every compact composition operator c on d is compact on b 2 and on h 2 in particular c is in every schatten class sp p 0 both on h2 and on b2 there exists a schur function such that c is compact on h 2 but which is not even bounded on d there exists a schur function such that c is compact on d but in no schatten class sp d

some examples of compact composition operators on h2 abstract we construct in an essentially explicit way various composition operators on h 2 and study their compactness or their membership in the schatten classes we construct non compact composition operators on h 2 whose symbols have the same modulus on the boundary of d as symbols whose composition operators are in various schatten classes s p with p 2 compact composition operators which are in no schatten class but whose symbols have the same modulus on the boundary of d as symbols whose associated composition operators are in s p for every p 2

stability of explicit navier stokes procedures using k e and k e algebraic reynolds stress turbulence models abstract a three dimensional explicit navier stokes procedure has been developed for application to compressible turbulent flows including rotation effects in the present work a numerical stability analysis of the discrete coupled system of seven governing equations is presented order of magnitude arguments are presented for flow and geometric properties typical of internal flows including turbomachinery applications to ascertain the relative importance of grid stretching rotation and turbulence source terms and effective diffusivity on the stability of the scheme it is demonstrated through both analysis and corroborative numerical experiments that 1 it is quite feasible to incorporate efficiently a two equation k turbulence model in an explicit time marching scheme provided certain numerical stability constraints are enforced 2 the role of source terms due to system rotation on the stability of the numerical scheme is not significant when appropriate grids are used and realistic rotor angular velocities are specified 3 the direct role of source terms in the turbulence transport equations on the stability of the numerical scheme is not significant when appropriate grids are used and realistic freestream turbulence quantities are specified except in the earliest stages of iteration a result which is contrary to that generally perceived 4 there is no advantage to numerically coupling the two equation model system to the mean flow equation system in regard to convergence or accuracy 5 for some flow configurations including turbomachinery blade rows it is useful to incorporate the influence of artificial dissipation in the prescription of a local timestep 6 explicit implementation of an algebraic reynolds stress model arsm is intrinsically stable provided that the discrete two equation transport model which provides the necessary values of k and is itself stable