quantitative error estimate in modeling the laminar stationary flow of a bingham fluid we present a quantitative a posteriori error estimate when the linear laminar stationary flow of a bingham fluid in a cylindrical pipe is modeled as a newtonian fluid the estimate is proved by using a complementary variational principle for the bingham fluid flow examples show that the estimate is effective

moment method analysis of finite rectangular waveguide phased arrays a method of moments formulation for small finite planar phased arrays of rectangular waveguides in an infinite ground plane is investigated piecewise sinusoidal uniform surface patches are used as the basis and testing functions for the unknown equivalent magnetic currents of each aperture the block toeplitz symmetry property for rectangular grid arrays is utilized in the solution of the system of equations data are presented for 11 times 11 arrays with various element sizes element spacings and scan angles good agreement with data in the literature is shown the analysis is particularly efficient for e plane and h plane scans for arrays having rectangular waveguide fed apertures excited by the dominant mode

definable relations and first order query languages over strings we study analogs of classical relational calculus in the context of strings we start by studying string logics taking a classical model theoretic approach we fix a set of string operations and look at the resulting collection of definable relations these form an algebra a class of n ary relations for every n closed under projection and boolean operations we show that by choosing the string vocabulary carefully we get string logics that have desirable properties computable evaluation and normal forms we identify five distinct models and study the differences in their model theory and complexity of evaluation we identify a subset of these models that have additional attractive properties such as finite vc dimension and quantifier elimination once you have a logic the addition of free predicate symbols gives you a string query language the resulting languages have attractive closure properties from a database point of view while sql does not allow the full composition of string pattern matching expressions with relational operators these logics yield compositional query languages that can capture common string matching queries while remaining tractable for each of the logics studied in the first part of the article we study properties of the corresponding query languages we give bounds on the data complexity of queries extend the normal form results from logics to queries and show that the languages have corresponding algebras expressing safe queries

flow of a bingham fluid in contact with a newtonian fluid abstract we study the problem modeling the flow of a bingham fluid in contact with a newtonian fluid playing the role of lubricant this is a free boundary problem coupled by means of diffraction conditions with a boundary value problem of parabolic type we examine the steady state solutions the evolutive case with particular regard for the asymptotic behaviour of the solution and a regularized model related to the appearance of a new rigid zone

error estimates for the numerical approximation of time dependent flow of bingham fluid in cylindrical pipes by the regularization method the flow of a bingham fluid in a cylindrical pipe can give rise to free boundary problems the fluid behaves like a viscous fluid if the shear stress expressed as a linear function of the shear rate exceeds a yield value and like a rigid body otherwise the surfaces dividing fluid and rigid zones are the free boundaries therefore the solution for such highly nonlinear problems can in general only be obtained by numerical methods considerable progress has been made in the development of numerical algorithms for bingham fluids 2 20 27 29 30 32 however very little research can be found in the literature regarding the rate of convergence of the numerical solution to the true continuous solution that is the error estimate of these numerical methods error estimates are a critically important issue because they tells us how to control the error by appropriately choosing the grid sizes and other related parameters this paper concerns the error estimates of a unsteady bingham fluid modeled as a variational inequality due to duvaut lions 16 and glowinski 30 the difficulty both in the analytical and numerical treatment of the mathematical model is due to the fact that it contains a nondifferentiable term a common technique called the regularization method is to replace the non differentiable term by a perturbed differentiable term which depends on a small regularization parameter the regularization method effectively reduces the variational inequality to an equation a regularized problem which is much easier to cope with this paper has achieved the following 1 error estimates are derived for a continuous time galerkin method in suitable norms 2 we give an estimate of the difference between the true solution and the regularized solution in terms of 3 some regularity properties for both regularized solution and the true solution are proved 4 the error estimates for full discretization of the regularized problem using piecewise linear finite elements in space and backward differencing in time are established for the first time by coupling the regularization parameter and the discretization parameters h and t 5 we are able to improve our estimates in the one dimensional case or under stronger regularity assumptions on the true solution the estimates for the one dimensional case are optimal and confirmed by numerical experiment the estimates from 4 and 5 provide very important information on the measure of the error and give us a powerful mechanism to properly choose the parameters h t and in order to control the error see corollary 4 4 the above estimates extend the error bounds derived in glowinski lions and tremolieres 32 chapter 5 pp 348 404 for the stationary bingham fluid to the time dependent one which is the main contribution of this paper

anl2 error estimate for an approximation of the solution of a parabolic variational inequality we estimate the order of the difference between the numerical approximation and the solution of a parabolic variational inequality the numerical approximation is obtained using a finite element discretization in space and a finite difference discretization in time which is more general than is used in the literature we obtain better error estimates than those given in the literature the error estimates are compared with numerical experiments

error estimates for the approximation of semicoercive variational inequalities an abstract error estimate for the approximation of semicoercive variational inequalities is obtained provided a certain condition holds for the exact solution this condition turns out to be necessary as is demonstrated analytically and numerically the results are applied to the finite element approximation of poisson s equation with signorini boundary conditions and to the obstacle problem for the beam with no fixed boundary conditions for second order variational inequalities the condition is always satisfied whereas for the beam problem the condition holds if the center of forces belongs to the interior of the convex hull of the contact set applying the error estimate yields optimal order of convergence in terms of the mesh size h the numerical convergence rates observed are in good agreement with the predicted ones

singular integral equation analysis of flange mounted rectangular waveguide radiators the authors analyze rigorously single and twin radiating waveguides by means of a singular integral equation approach which includes the edge condition on the apertures from the start the above inclusion has an important bearing on convergence and matrix size enabling highly accurate solutions to be obtained with few test functions typically two to four this becomes particularly important in the case of multiple coupled radiators where matrix sizes increase as the product of the number of radiators times the number of test functions theoretical and experimental results are compared for the two important cases of two radiators with parallel narrow walls and with parallel broad walls and are found to be in very good agreement

a bi projection method for bingham type flows we propose and study a new numerical scheme to compute the isothermal and unsteady flow of an incompressible viscoplastic bingham medium the main difficulty for both theoretical and numerical approaches is due to the non differentiability of the plastic part of the stress tensor in regions where the rate of strain tensor vanishes this is handled by reformulating the definition of the plastic stress tensor in terms of a projection a new time scheme based on the classical incremental projection method for the newtonian navier stokes equations is proposed the plastic tensor is treated implicitly in the first sub step of the projection scheme and is computed by using a fixed point procedure a pseudo time relaxation is added into the bingham projection whose effect is to ensure a geometric convergence of the fixed point algorithm this is a key feature of the bi projection scheme which provides a fast and accurate computation of the plastic tensor stability and error analyses of the numerical scheme are provided the error induced by the pseudo time relaxation term is controlled by a prescribed numerical parameter so that a first order estimate of the time error is derived for the velocity field a second order cell centred finite volume scheme on staggered grids is applied for the spatial discretisation the scheme is assessed against previously published benchmark results for both newtonian and bingham flows in a two dimensional lid driven cavity for reynolds number equals 1000 moreover the proposed numerical scheme is able to reproduce the fundamental property of cessation in finite time of a viscoplastic medium in the absence of any energy source term in the equations for a fixed value 100 of the bingham number various numerical simulations for a range of reynolds numbers up to 200000 were performed with the bi projection scheme on a grid with 1024 2 mesh points the effect of this physical parameter on the flow behaviour is discussed

analysis of an infinite periodic array of slot radiators with dielectric loading an efficient numerical procedure for determining the radiation characteristics of an infinite periodic array of slots in a conducting screen is presented the procedure employs a novel mixed potential integral equation formulation and is solved by the method of moments subdomain type basis functions are used to provide the flexibility to model arbitrarily shaped slots analysis is carried out to account for dielectric layers ground planes or cavities placed on either side of the slot series acceleration techniques are employed to reduce significantly the computation time required to sum the series representing the periodic green s function the numerical scheme developed is applied to obtain quantities such as the slot field distribution and input admittance as a function of the array scan angle where possible numerical results obtained are compared with data available in the literature data for the half space case are found to agree with those of a y grinev et al 1978 except for the case of multilayer dielectric loading

radiation from a flanged rectangular waveguide the radiation from a rectangular waveguide with a perfectly conducting infinite flange is rigorously studied by using the method of the kobayashi potential kp the fields in the waveguide and half space are expanded in terms of the waveguide modes and the weber schafheitlin discontinuous integrals respectively continuity of the tangential aperture fields yields matrix equations for the expansion coefficients and the matrix elements consist of double infinite integrals and double infinite series of bessel functions which are calculated efficiently by applying the asymptotic approximation of the bessel function numerical results are presented for various physical quantities such as the aperture admittance reflection coefficient of the incident wave and magnitudes of higher order mode waves as well as the far radiation pattern and aperture fields to verify the validity of our method the results are compared with other methods and excellent agreement is obtained

finite queries do not have effective syntax a relational query is called finite or sometimes safe iff it yields a finite answer in every database state the set of finite queries of relational calculus is known to be unsolvable however in many cases it is possible to impose syntactical restrictions on the class of queries that guarantee finiteness and do not reduce the expressive power of the calculus we show that unfortunately this is not always the case as we construct a recursive domain with decidable theory where any solvable or enumerable for that matter subclass of queries either contains an infinite query or misses a finite one we show that although any domain can always be extended to a domain with an effective syntax for finite queries such extensions of our domain necessarily have undecidable theories the reason decidability of domain matters is that this property is in effect equivalent to the ability to answer queries effectively using the same example we further show undecidability of the problem of relative finiteness which is given a query and a database state to decide upon finiteness of the query in this state this settles two long standing open problems in the theory of relational databases

sharpl error estimates for semilinear elliptic problems with free boundaries a numerical scheme to approximate a semilinear pde involving a singular maximal monotone graph is analyzed inl a preliminary regularization is combined with piecewise linear finite elements defined on a triangulation which is not assumed to be acute the discrete maximum principle is thus avoided sharp pointwise error estimates are derived for both the smoothing and the discretization procedures an optimal choice of the regularization parameter as a function of the mesh size leads to a sharp global rate of convergence these error estimates for solutions in conjunction with nondegeneracy properties of continuous problems provide sharp interface error estimates two model examples are discussed the obstacle problem and a combustion equation

calculation of the field radiated by horn antennas using the mode matching method methods employed for evaluating fields radiated by horn antennas like the aperture field method and the spherical wave expansion have not taken into account the contribution by fields existing outside the horn aperture e g along the outer walls of the horn the use of the mode matching technique for analyzing the transition from horn antenna to free space makes it possible to include in the analysis even those fields which exist outside e g behind the horn aperture when determining the far as well as the near field furthermore the effects of the finite wall thickness and the discontinuity caused by the transition from waveguide to free space are also taken into account a suitable development of the fields at the transition of the conical corrugated horn to free space using the mode matching technique is presented two different convergence diagrams depending on the kind of modes excited in the horn antenna are given they show the results from extensive convergence investigations with the help of these diagrams a reliable evaluation of the fields radiated by horn antennas is guaranteed practical measurements of the fields radiated by horn antennas confirm the field distributions gained through analysis

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

l error estimate for an approximation of a parabolic variational inequality almost optimall convergence of an approximation of a variational inequality of parabolic type is proved under regularity assumptions which are met by the solution of a one phase stefan problem the discretization employs piecewise linear finite elements in space and the backward euler scheme in time by means of a maximum principle the problem is reduced to an error estimate for an auxiliary parabolic equation the latter bound is obtained by using the smoothing property of the galerkin method

error analysis for implicit approximations to solutions to cauchy problems exact error analyses for two implicit approximation schemes to the cauchy problem du t dt mathcal a u t mathrel backepsilon 0 u 0 u 0 in d mathcal a are presented the operator mathcal a is required to be maximal monotone on a hilbert space mathcal h the approximations considered are u h kh i h mathcal a k u 0 and solutions u lambda to the approximating problems du lambda t dt mathcal a lambda u lambda 0 u lambda 0 u 0 where a lambda is the yosida approximation of mathcal a the special case of a being a subgradient is considered and tight estimates of the convergence of both u h and mathcal a h u h or u h and a h u h are given the new results in this case are the linear rates of convergence of u h in l infty 0 infty mathcal h and in the energy norm and the sublinear rate of convergence of a h u h in l 2 0 infty mathcal h applications to both linear and

application of a first order operator splitting method to bingham fluid flow simulation abstract we discuss here a first order operator splitting method for the solution of the time dependent variational inequality modeling the flow of a bingham visco plastic medium at each time step we shall have to solve a nonlinear elliptic problem then a nondifferentiable minimization problem and finally a stokes type problem the first problem is solved by a fixed point method the second one happens to be a saddle point problem for a lagrangian functional and we shall use an uzawa algorithm to solve it the last problem is solved by a conjugate gradient method we have applied this splitting method to two test problems the first one has a forcing term with homogeneous dirichlet boundary conditions while the second one concerns the simulation of the flow of a bingham fluid in a wall driven cavity our results compare very well with the ones obtained by solving directly the variational inequality mentioned above

orderings for term rewriting systems abstract methods of proving that a term rewriting system terminates are presented they are based on the intuitive notion of simplification orderings orderings in which any term that is syntactically simpler than another is smaller than the other as a consequence of kruskal s tree theorem any nonterminating system must be self embedding in the sense that it allows for the derivation of some term from a simpler one thus termination is guaranteed if every rule in the system is a reduction in some simplification ordering most of the orderings that have been used for proving termination are indeed simplication orderings using this notion often allows for much easier proofs a particularly useful class of simplification orderings the recursive path orderings is defined examples of the use of simplication orderings in termination proofs are given

monadic decomposition monadic predicates play a prominent role in many decidable cases including decision procedures for symbolic automata we are here interested in discovering whether a formula can be rewritten into a boolean combination of monadic predicates our setting is quantifier free formulas whose satisfiability is decidable such as linear arithmetic here we develop a semidecision procedure for extracting a monadic decomposition of a formula when it exists

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

numerical solution of the obstacle problem by the penalty method part ii time dependent problems in a previous paper we considered the possibility of using the penalty method to get approximations of the solution of elliptic variational inequalities in this note we show that the same idea can be used for the treatment of parabolic problems by coupling the penalty parameter e and the discretization parametersh and t quasi optimal error estimates are derived in suitable norms

semi discrete stabilized finite element methods for navier stokes equations with nonlinear slip boundary conditions based on regularization procedure based on the pressure projection stabilized methods the semi discrete finite element approximation to the time dependent navier stokes equations with nonlinear slip boundary conditions is considered in this paper because this class of boundary condition includes the subdifferential property then the variational formulation is the navier stokes type variational inequality problem using the regularization procedure we obtain a regularized problem and give the error estimate between the solutions of the variational inequality problem and the regularized problem with respect to the regularized parameter varepsilon which means that the solution of the regularized problem converges to the solution of the navier stokes type variational inequality problem as the parameter varepsilon longrightarrow 0 moreover some regularized estimates about the solution of the regularized problem are also derived under some assumptions about the physical data the pressure projection stabilized finite element methods are used to the regularized problem and some optimal error estimates of the finite element approximation solutions are derived

a hybrid mom solution of scattering from finite arrays of cylindrical cavities in a ground plane in this paper we propose a novel hybrid space spectral domain method of moments mom calculation of canonical plane wave scattering from finite periodic structures comprised of dissimilar cylindrical cavities in an infinite ground plane covered by a dielectric superstrate we take full advantage of analyzing this particular type of problem comprised of a canonical geometry by employing a set of entire domain basis functions waveguide modes which truly span the hilbert space in which the desired solution resides the convergence behavior of a solution using said functions is quite robust results show that typically only a few basis functions are required to adequately represent the aperture fields with fidelity we have also reformulated the conventional magnetic field integral equation in a hybrid fashion whereby the exterior unbounded half space mom interaction terms have been cast in the spectral domain and the interior cavity interactions cast in the space domain directly the spectral representation allows us to trivially include a superstrate layer in the geometry and additionally leads to an efficient evaluation of the interaction integrals due to an overall reduction in the spatial dimensionality the interior interactions are readily handled in the space domain where we take advantage of the orthogonality property of waveguide modes most importantly the technique is significantly more accurate than purely numerical methods i e those in which a discretization of the geometry is necessary

convergence analysis of finite element method for a parabolic obstacle problem abstract a conforming finite element method is proposed and analyzed for numerical approximation of the solution of a parabolic variational inequality of the obstacle problem the model problem which is originally proposed using a general obstacle is reframed as a model problem with zero obstacle but with non homogeneous dirichlet boundary conditions subsequently the discrete problem is reframed and the error analysis proving the convergence of the method is performed the analysis requires a positive preserving interpolation with non homogeneous dirichlet boundary condition and a post processed solution that satisfies the boundary conditions sharply the results in the article extend the results of johnson sinum 1976 for a zero obstacle function to a more general obstacle function