an inventory model with limited production capacity and uncertain demands ii the discounted cost criterion this paper considers a single item periodic review inventory model with uncertain demands we assume a finite production capacity in each period with stationary data a convex one period cost function and a continuous demand distribution we show under a few additional unrestrictive assumptions that a modified basic stock policy is optimal under the discounted cost criterion both for finite and infinite planning horizons in addition we characterize the optimal base stock levels in several ways

efficient calculation of large finite periodic structures based on surface wave analysis the electromagnetic modeling of practical finite periodic structures is a topic of growing interest due to the truncation of infinite periodic structures surface waves will be excited and localized near discontinuous interfaces leading to the edge effect in this work surface waves are numerically extracted and their magnitudes and decay rates are analyzed for different materials and geometries based on the exponential decay of the surface wave a novel method is developed by connecting the solution to the large finite array problem with that to a relatively small one to achieve low complexity and memory consumption the method numerically reconstructs propagating bloch waves and surface waves according to the bloch floquet theorem of periodic structures and translation invariant properties of semi infinite periodic structures respectively numerical examples are shown for near field distributions and far field radiation patterns the results obtained from small finite periodic structures capture the edge effect and agree well with the results by the rigorous element by element approach

acceleration of fast multipole method for large scale periodic structures with finite sizes using sub entire domain basis functions an acceleration technique to the fast multipole method fmm has been proposed to handle large scale problems of periodic structures in free space with finite sizes based on the accurate sub entire domain basis functions in the proposed algorithm only nine or 27 elements in the whole impedance matrix are required to be computed and stored for a two dimensional or three dimensional periodic structure and the matrix vector multiply can be performed efficiently using the combination of fast fourier transform and fmm the theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of o n with small constants where n is the total number of unknowns

an efficient computation scheme for the free space green s function of a two dimensional semiinfinite phased array a simple scheme is developed to compute the green s function of a periodic semiinfinite array in free space it is based on the spectral representation of the fields radiated by an infinite linear array of dipoles results related to successive linear arrays are added in the space domain this summation can be accelerated tremendously by using an elementary extrapolation technique the resulting formulation converges everywhere in the plane containing the array and the number of terms required to achieve a given precision increases slowly away from this plane

parameterizing quasi periodicity generalized poisson summation and its application to modified fibonacci antenna arrays the fairly recent discovery of quasi crystals whose x ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity has motivated studies of the wave dynamical implications of aperiodic order within the context of the radiation properties of antenna arrays an instructive novel canonical example of wave interactions with quasi periodic order is illustrated here for one dimensional array configurations based on the modified fibonacci sequence with utilization of a two scale generalization of the standard poisson summation formula for periodic arrays this allows for a quasi floquet analytic parameterization of the radiated field which provides instructive insights into some of the basic wave mechanisms associated with quasi periodic order highlighting similarities and differences with the periodic case examples are shown for quasi periodic infinite and spatially truncated arrays with brief discussion of computational issues and potential applications

accelerating the convergence of value iteration by using partial transition functions abstract this work proposes an algorithm that makes use of partial information to improve the convergence properties of the value iteration algorithm in terms of the overall computational complexity the algorithm iterates on a series of increasingly refined approximate models that converges to the true model according to an optimal linear rate which coincides with the convergence rate of the original value iteration algorithm the paper investigates the properties of the proposed algorithm and features a series of switchover queue examples which illustrates the efficacy of the method

asymptotic floquet mode investigation over two dimensional infinite array antennas phased to radiate near zone focused fields this paper extends the previous work in to consider the radiation from an infinite 2 d antenna array for the near field focus applications it employs the poisson sum formula to expand the radiation into floquet modes which may exhibit a class of wave phenomena in terms of geometrical ray fields this analysis automatically reduces to the conventional case of a linearly phased antenna array and results in consistent radiation phenomena it can be considered as a generalization of phased array analysis theoretical investigations as well as numerical illustrations are presented

element free galerkin method for wave propagation and dynamic fracture abstract element free galerkin method efg is extended to dynamic problems efg method which is based on moving least square interpolants mls requires only nodal data no element connectivity is needed this makes the method particularly attractive for moving dynamic crack problems since remeshing can be avoided in contrast to the earlier formulation for static problems by authors the weak form of kinematic boundary conditions for dynamic problems is introduced in the implementation to enforce the kinematic boundary conditions with this formulation the stiffness matrix is symmetric and positive semi definite and hence the consistency conergence and stability analyses of time integration remain the same as those in finite element method numerical examples are presented to illustrate the performance of this method the relationship between the element free galerkin method and the smooth particle hydrodynamics sph method is also discussed in this paper results are presented for some one dimensional problems and two dimensional problems with static and moving cracks

stability and optimality of a multi product production and storage system under demand uncertainty this work develops a discrete event model for a multi product multi stage production and storage p s problem subject to random demand the intervention problem consists of three types of possible decisions made at the end of one stage which depend on the observed demand or lack of for each item i to proceed further with the production of the same product ii to proceed with the production of another product or iii to halt the production the intervention problem is formulated in terms of dynamic programming dp operators and each possible solution induces an homogeneous markov chain that characterizes the dynamics however solving directly the dp problem is not a viable task in situations involving a moderately large number of products with many production stages and the idea of the paper is to detach from strict optimality with monitored precision and rely on stability the notion of stochastic stability brought to bear requires a finite set of positive recurrent states and the paper derives necessary and sufficient conditions for a policy to induce such a set in the studied p s problem an approximate value iteration algorithm is proposed which applies to the broader class of control problems described by homogeneous markov chains that satisfy a structural condition pointed out in the paper this procedure iterates in a finite subset of the state space circumventing the computational burden of standard dynamic programming to benchmark the approach the proposed algorithm is applied to a simple two product p s system

some characteristics of radiation from linearly phased sequentially excited periodic rectangular arrays of dipoles floquet wave and element by element summation representations are implemented to investigate the radiation from a periodic rectangular array of linearly phased sequentially pulsed dipoles in the frequency and time domains a synthetic aperture type formulation for floquet wave representation and an asymptotic formulation for the element by element summation representation are developed numerical results are presented to demonstrate the efficiency of the floquet wave representation in terms of radiating non radiating and diffracted wave constituents and then validated via comparison with direct summation over the contributions of individual dipole radiations

time domain green s function for an infinite sequentially excited periodic planar array of dipoles the present paper is a continuation of previous explorations by the authors aimed at gaining a basic understanding of the time domain td behavior of large periodic phased i e sequentially turned on array antennas and related configurations our systematic investigation of the relevant canonical td dipole excited green s functions has so far included those for infinite and truncated sequentially pulsed line periodic arrays parameterized in terms of radiating propagating and nonradiating evanescent conical td floquet waves fw and truncation induced td fw modulated tip diffractions the present contribution extends these investigations to an infinite periodic sequentially pulsed planar array which generates pulsed plane propagating and evanescent fw starting from the familiar frequency domain fd transformation of the linearly phased element by element summation synthesis into summations of propagating and evanescent fws we access the time domain by fourier inversion the inversion integrals are manipulated in a unified fashion into exact closed forms which are parameterized by the single nondimensional quantity spl eta c v sup p sub u1 where v sup p sub u1 and c are the excitation phase speed along a preferred phasing direction u sub 1 in the array plane and the ambient wave speed respectively the present study deals with the practically relevant rapidly phased propagating case spl eta 1 regime for a future manuscript numerical reference data generated via element by element summation over the fields radiated by the individual dipoles with ultrawide band limited excitation are compared with results obtained much more efficiently by inclusion of a few td fws physical interpretation of the formal td fw solutions is obtained by recourse to asymptotics instantaneous frequencies and wavenumbers and related constructs of special interest is the demonstration that the td fws emerge along equal delay ellipses from the array plane this furnishes a novel and physically appealing interpretation of the planar array td fw phenomenology

application of haar wavelet based multiresolution time domain schemes to electromagnetic scattering problems the multiresolution time domain mrtd algorithm is applied to the problem of general two dimensional electromagnetic scattering a haar wavelet expansion is utilized a parallel between haar mrtd and the classic yee finite difference time domain fdtd algorithm is discussed and results of simulations on canonical targets are shown for comparison we focus on the incident field implementation which in our case consists of a pulsed plane wave also we consider scattering in a half space environment with application to subsurface sensing the results illustrate the advantage of the haar mrtd method as compared with the classic fdtd which consists of reduced memory and execution time requirements without sacrificing accuracy

scheduling multiple part types in an unreliable single machine manufacturing system quadratic approximations to the differential cost to go function which yield linear switching curves have been extensively studied in the literature in this paper we provide solutions to the partial differential equations associated with the components of the steady state probability density function of the buffer levels for two part type single machine flexible manufacturing systems under a linear switching curve lsc policy when there are more than two part types we derive the probability density function under a prioritized hedging point php policy by decomposing the multiple part type problem into a sequence of two part type problems the analytic expression for the steady state probability density function is independent of the cost function therefore for average cost functions we can compute the optimal php policy or the more general optimal lsc policy for two part type problems

a combined approach of efgm and precise algorithm in time domain solving viscoelasticity problems in this paper element free galerkin efg method is combined with a precise algorithm in the time domain for solving viscoelasticity problems by expanding variables at discretized time intervals an initial boundary value problem is converted into a series of recurrent boundary value problems which can be conveniently solved by efg efg fe with a self adaptive computing process there is no requirement of iteration for the solution of non linear cases satisfactory numerical results are obtained for both static and dynamical viscoelasticity problems

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays ii generalization to 3 d cases for pt i see ibid vol 48 no 3 p 594 600 2000 this paper deals with the generalization to three dimensional 3 d arrays of the truncated floquet wave tfw diffraction method for the full wave analysis of large arrays this generalization potentially includes arrays consisting of microstrip excited slots cavity backed apertures and patches the formulation is carried out first by deriving an appropriate fringe integral equation ie and next by defining entire domain basis functions in terms of global array functions shaped as tfw diffracted rays whose analytical expression is derived on the basis of prototype canonical problems the efficiency and the accuracy of this method is demonstrated by comparison with the results of an element by element full wave approach for a rectangular slot array

solving average cost markov decision processes by means of a two phase time aggregation algorithm abstract this paper introduces a two phase approach to solve average cost markov decision processes which is based on state space embedding or time aggregation in the first phase time aggregation is applied for policy optimization in a prescribed subset of the state space and a novel result is applied to expand the evaluation to the whole state space this evaluation is then used in the second phase in a policy improvement step and the two phases are then alternated until convergence is attained some numerical experiments illustrate the results

shaped beam synthesis of real antenna arrays via finite element method floquet modal analysis and convex programming a shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region and constraints on the sidelobe and cross polar levels is proposed in this paper a previously developed synthesis formulation for designing finite impulse response fir filters by transforming a nonconvex synthesis problem to a convex optimization scheme enforcing conjugate symmetric excitation weights is extended to real and coupled radiating elements of complex geometry taking into account mutual coupling effects the optimization procedure is integrated with a finite array approach simulating different array environments this approach is based on the infinite array model through a floquet modal and general scattering matrix gsm based analysis where the periodic radiating element is characterized from a hybrid and full wave analysis procedure combining the fem modal analysis and domain decomposition technique numerical results of different synthesized beam patterns are presented for arrays of open ended apertures and microstrip antennas

optimal time domain detection of a deterministic target buried under a randomly rough interface we consider pulsed plane wave scattering from targets buried under a rough air ground interface the properties of the interface are parametrized as a random process with known statistics and therefore the fields scattered from a particular surface constitute one realization of an ensemble characterized by corresponding statistics moreover since the fields incident upon a buried target must first penetrate the rough interface they and the subsequent scattered fields are random processes as well based on this understanding an optimal detector is formulated accounting for the clutter and target signature statistics the former due to scattering at the rough surface and the latter due to transmission the statistics of these two processes are in general different the detector performance is compared to that of a matched filter which assumes the target signature is known exactly i e nonrandom the results presented here as a function of angle and polarization demonstrate that there is often a significant gain in detector performance if the target signature is properly treated as a random process

exact eigenvalue calculations for structures with rotationally periodic substructures on considere 2 classes de sous structures a symetrie cyclique autour d un axe longitudinal l une n est reliee a sa structure mere qu aux extremites de son axe tandis que l autre est reliee par un nombre quelconque de n uds a sa structure mere qui partage alors sa periodicite rotationnelle

optimal feedback production planning in a stochastic n machine flowshop we consider a production planning problem in an n machine flowshop subject to breakdown and repair of machines and to non negativity constraints on work in process the machine capacities and demand processes are assumed to be finite state markov chains the problem is to choose the rates of production on the n machines over time to minimize the expected discounted cost of production and inventory backlog over an infinite horizon it is formulated as a stochastic dynamic programming problem we show that the value function of the problem is locally lipschitz and is a solution to a dynamic programming equation together with a certain boundary condition we provide an interpretation of the boundary condition we also prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the value function finally we obtain a deterministic optimal control problem that is equivalent to the stochastic production planning problem under consideration

network oriented dyadic time domain green s function for a sequentially excited infinite planar array of dipoles in free space during the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas infinite periodic structures frequency selective surfaces and related applications with emphasis on gaining physical insight into the phenomenology of short pulse radiation the present contribution shows the current status of our network oriented dyadic time domain green s function td gf for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short pulsed radiation by infinite periodic arrays the dispersive effects of the td floquet waves fw and the consequences of a te and tm field decomposition are discussed in details in this network formulation the equivalent td transmission line tl voltages and currents excited by equivalent td current generators are determined an expression for the tm voltage tl gf is provided for the first time in terms of incomplete lipschitz hankel integrals and bessel functions together with some remarks for its evaluation as shown in previous publications for the scalar potentials real td physical observables are determined by pairing td floquet waves with positive and negative indices it is shown that the vectorial td radiated field is reconstructed at any time with the superposition of a few td fws

edge effects in axial arrays of circular rings a boundary value problem is solved for the current induced by any source in particular for an incident plane wave on any number of identical rings that are arranged to form an axisymmetric linear array the net aperture distribution along the finite array is approximated by a combination of three physically identifiable components a term from the related infinite array plus contributions from two independent edge effect waves that originate from each of the two ends however if individually resonant loops are closer than a critical spacing the entire structure exhibits a wild resonance and the simple approximation becomes invalid

floquet mode phenomena of infinite phased array antennas in near field focus applications this paper presents a theoretical investigation on the radiation of an infinite one dimensional antenna array which is phased to radiate electromagnetic fields focused in the near zone of the array aperture in particular the wave phenomena in each of the floquet modes obtained by applying the poisson sum formula to the array excitations are investigated the analysis reduces to the case of a conventional phased antenna array when the radiation is focused in the far zone and exhibits consistent phenomena theoretical investigations as well as numerical illustrations are presented

time harmonic and transient scattering by finite periodic flat strip arrays hybrid ray floquet mode mom algorithm a frequency and short pulse sp time domain td study of two dimensional plane wave scattering from a finite periodic array of thin flat coplanar perfectly conducting strips is presented rigorous analytical numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments mom followed by frequency inversion the analytical portion is approximated so as to yield via high frequency asymptotics for a sufficiently large number of strips a hybrid ray floquet mode mom algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution of special interest are the td floquet modes with their space time dependent frequencies and wave numbers by superposition they can synthesize the highly resolved pulse train return under sp conditions attention is given also to direct sp td synthesis and to processing options for sp td data

truncated floquet wave full wave analysis of large phased arrays of open ended waveguides with a nonuniform amplitude excitation recently an efficient hybrid asymptotic method of moments mom approach has been proposed for the analysis of large periodic planar arrays of elements excited with equal amplitude and linear phase the aforementioned method which is based on a floquet wave diffraction representation of the array green s function agf is here extended to treat arrays with tapered amplitude excitation to this end the asymptotic agf is refined by introducing additional slope diffraction contributions an appropriate fringe integral equation solved via a mom scheme provides the effects of array truncation in addition to the infinite array solution the dimension of the corresponding linear algebraic system is independent of the number of elements of the array numerical results are provided to prove the accuracy and the efficiency of this method with respect to an ordinary element by element mom

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

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

a hybrid spectral spatial method to evaluate the active green s function of large planar rectangular arrays a combined asymptotic numerical algorithm the article illustrates a formulation to evaluate the array green s function agf of large finite planar phased array for observation points on the array plane possibly close to the array contour the procedure is based on the agf representation in terms of a double spectral integral whose integration paths are properly deformed to have an exponential attenuation of the integrand the diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges this latter comprises higher order contributions thanks to the convergence properties the final algorithm is numerically accurate stable and more efficient with respect to the individual element summation for large arrays it also constitutes the basic step for the efficient evaluation of the agf of a multilayer environment

periodicity induced generalized fourier transform pair the field radiated by an infinite periodic structure can be expressed in terms of floquet waves fws both in the frequency domain fd and time domain td see felsen l b and capolino f ieee trans antennas propagat vol 48 p 921 31 2000 a new periodicity induced generalized fourier transform ft pair is derived relating fd fws to td fws and vice versa based on tabulated transforms and physical conditions at infinity the new fts are directly related to the simple canonical problem of a line array of sequentially excited dipoles that is a basic building block for more general phased periodic structures

an eigencurrent approach for the analysis of finite antenna arrays an accurate description of typical finite array behavior such as edge effects and array resonances is essential in the design of various types of antennas the analysis approach proposed in this paper is essentially based on the concept of eigencurrents and is capable of describing finite array behavior in the approach numerical simulation is carried out first by computing element eigencurrents from chosen expansion functions and second by expanding a limited set of array eigencurrents in terms of element eigencurrents that contribute to the mutual coupling in the array both types of eigencurrents are eigenfunctions of an impedance operator that relates the current to the excitation field highlighting both mathematical and physical features we describe the basic concepts of the approach in particular the relation between eigenvalues and mutual coupling we illustrate these features for uniform linear arrays of loops and dipoles and demonstrate that the approach provides significant improvements in terms of computation time and memory use

analysis of symmetric or partially symmetric structures this paper combines group theoretic methods with substructuring techniques to treat the symmetric or partially symmetric structures subjected to arbitrary loads first for a given substructure module whose symmetry group is g it gives a method to find the generalized displacements associated with irreducible representations of g based on some concepts presented in this paper and then points out that for these displacements the analysis problem for a substructure module can be divided into a series of uncoupled subproblems for each subproblem the triangularization as well as condensation can be carried out individually finally a simplified calculation formula of condensed stiffness coefficients for the original displacements is established in which only the coefficients relating to the displacements in the basic region are necessary to be calculated a series of computer programs has been developed by the methods presented in this paper 1 4 these programs enable us to reduce the cpu time and save the memory noticeably

wave propagation and sampling theory part ii sampling theory and complex waves morlet et al 1982 this issue showed the advantages of using complex values for both waves and characteristics of the media we simulated the theoretical tools we present here using the goupillaud kunetz algorithm now we present sampling methods for complex signals or traces corresponding to received waves and sampling methods for complex characterization of multilayered or heterogeneous media regarding the complex signals we present a twodimecsional 2 d method of sampling in the time frequency domain using a special or extended gabor expansion on a set of basic wavelets adapted to phase preservation such a 2 d expansion permits us to handle in a proper manner instantaneous frequency spectra we show the differences between wavelet resolution and sampling grid resolution we also show the importance of phase preservation in high resolution seismic regarding the media we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution analytical studies of wave propagation in periodic structures are well known in solid state physics and lead to the so called bloch waves the introduction of complex waves leads to replacing the classical wave equation by a schriidinger equation finally we show that complex wave equations gabor expansion and bloch waves are three different ways of introducing the tools of quantum mechanics in highresolution seismic gabor 1946 kittel 1976 morlet 1975 and conversely the goupillaud kunetz algorithm and an extended gabor expansion may be of some use in solid state physics

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

analysis of the rayleigh pulse seismologists make frequent use of wavelets also referred to as signals signatures or pulses particularly in such fields as seismic filtering wavelet processing wave propagation modeling and trace inversion whenever possible the actual seismic wavelet of the real source should be considered hosken 1988 however frequently particularly in wave propagation modeling one must consider a synthetic source wavelet this should if possible be given by a simple mathematical formula and possess an easy description for its most important spectral properties e g amplitude and phase spectrum main frequency hilbert transform etc moreover the mathematical expression should be such that with a minimum number of parameters a large flexibility in the form of the wavelet can be obtained

truncated floquet wave full wave t fw sup 2 analysis of large periodic arrays of rectangular waveguides a new hybrid technique has been recently proposed for the analysis of large periodic arrays this method is based on a high frequency representation of the active green s function of a finite array involving a floquet wave fw expansion with the relevant edge and vertex diffracted ray fields originating at the array border using this representation the unknown current of an appropriate fringe integral equation is expanded in terms of a few basis functions shaped as fw induced diffracted rays this representation drastically reduces the numerical effort and provides a physical insight into the mechanism of the array truncation in this paper this method is applied to the analysis of large arrays of rectangular waveguides opened on an infinite ground plane numerical results are shown to demonstrate the effectiveness and the numerical efficiency of the method

the use of cyclic symmetry in efg analysis for heat transfer problems rotationally periodic or cyclic symmetry is exploited in the element free galerkin efg analysis for heat transfer problems of two dimensional systems it is proved that the coefficient matrices of the global efg equations are block circulant furthermore a partitioning algorithm is presented and the computational convenience and efficiency are demonstrated a technique dealing with asymmetric boundary conditions is developed to extend the application of the proposed approach numerical examples are given to illustrate the advantages of such exploitation of symmetry in the context copyright 2004 john wiley sons ltd

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

asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers we consider a production planning problem for a jobshop with unreliable machines producing a number of products there are upper and lower bounds on intermediate parts and an upper bound on finished parts the machine capacities are modelled as finite state markov chains the objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production finding an optimal control policy for this problem is difficult instead we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity the asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities the value function for the original problem is shown to converge to the value function of the limiting problem the convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established

analysis of large complex structures with the synthetic functions approach an innovative procedure is presented that allows the method of moments mom analysis of large and complex antenna and scattering problems at a reduced memory and cpu cost bounded within the resources provided by a standard 32 bit personal computer the method is based on the separation of the overall geometry into smaller portions called blocks and on the degrees of freedom of the field the blocks need not be electrically unconnected on each block basis functions are generated with support on the entire block that are subsequently used as basis functions for the analysis of the complete structure only a small number of these functions is required to obtain an accurate solution therefore the overall number of unknowns is drastically reduced with consequent impact on storage and solution time these entire domain basis functions are called synthetic functions they are generated from the solution of the electromagnetic problem for the block in isolation under excitation by suitably defined sources the synthetic functions are obtained from the responses to all sources via a procedure based on the singular value decomposition because of the strong reduction of the global number of unknowns one can store the mom matrix and afford a direct solution the method is kernel free and can be implemented on existing mom codes

edge born waves in connected arrays a finite times infinite analytical representation connected arrays constitute one of the most promising options for wideband phased arrays like most phased arrays they are designed using infinite array theory however when finiteness is included edge effects perturb their behavior these effects are more severe when the arrays are designed to operate over very broad frequency ranges since the mutual coupling between the elements facilitates the propagation of edge born waves that can become dominant over large portions of the arrays finite array simulations which would predict these behaviors are computationally unwieldy in this paper we present a green s function based procedure to assess edge effects in finite connected arrays first the electric current distribution on the array is rigorously derived later on the introduction of a few simplifying assumptions allows the derivation of an analytical approximation for the current distribution this latter provides meaningful insights in the induced dominant edge wave mechanism the efficiency of connected arrays as a function of their dimension in terms of the wavelength and of the loading feed impedances is investigated

hermite rodriguez uwb circular arrays pulsed circular arrays are collecting growing interest in radar applications such as automotives and indoor navigations this contribution presents the analytic derivation of the space time and energy patterns of pulsed circular arrays in terms of geometrical and electrical parameters as well as of the signal distortion produced by the antennas response it is shown that the field emitted by circular arrays with many elements can be represented as a summation of a practically finite set of high order hermite rodriguez waveforms while the energy pattern is a generalized hypergeometric function the angular and temporal resolutions are finally related through handy formulas to the array size the input signals and to the antenna types

time domain weyl s identity and the causality trick based formulation of the time domain periodic green s function time domain floquet modes for analyzing scattering radiation from periodically arranged planar scatterers sources have been presented recently in a series of papers by felsen and capolino in these papers they have investigated phenomenological details of transient scattering radiation by such structures typically time domain floquet modes are derived either by fourier transforming their frequency domain counterparts or using spatial synthesis using poisson summation this paper proposes an alternative means to develop similar expressions and is motivated by the possibility of easily extending the method to the analysis of periodic structures in a layered medium as will be shown the time domain weyl s identity can be used to construct the periodic green s function using both homogeneous and inhomogeneous plane waves we will also derive expressions using the causality trick this technique involves using time symmetric non causal signals however it yields much simpler expressions that involve only homogeneous time domain plane waves and the results are identical to those obtained using the time domain weyl s identity for the time region of interest finally we will use the whittaker formulation which relies on real signals to derive time domain floquet modes this formulation is applicable for simultaneous excitation only

frequency and time domain green s functions for a phased semi infinite periodic line array of dipoles we extend a previous prototype study of felsen and capolino see ibid vol 48 p 921 931 june 2000 of frequency domain fd and time domain td green s functions for an infinite periodic phased line array of dipoles to account for the effects of truncation as modeled by a semi infinite array these canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular td plane phased arrays in the presentation we rely on the analytic results and phenomenologies pertaining to the infinite array which are reviewed major emphasis is then placed on the modifications introduced by the truncation finite poisson summation is used to convert the individual dipole radiations into collective truncated wavefields the fd and td floquet waves fw in the td exact closed form solutions are obtained and are examined asymptotically to extract fd and td periodicity matched conical truncated fw fields both propagating and nonpropagating corresponding tip diffracted periodicity matched spherical waves and uniform transition functions connecting both across the fd and td fw truncation boundaries these new effects can again be incorporated in a fw modulated geometrical theory of diffraction a numerical example of radiation from a finite phased td dipole array with band limited excitation demonstrates the accuracy and efficiency of the fw diffracted field asymptotic algorithm when compared with an element by element summation reference solution

the use of cyclic symmetry in two dimensional elastic stress analysis by bem abstract rotationally periodic or cyclic symmetry is exploited in the elastic stress analysis of two dimensional structures under arbitrary load conditions by the bem it is proved that the coefficient matrices of the global boundary element equations for the rotationally periodic system are block circulant so long as a kind of symmetry adapted reference coordinate system is adopted furthermore the computational convenience and efficiency which can be achieved by exploiting this property and the structural geometric symmetry in the different phases of numerical implementation is demonstrated and an efficient algorithm is presented numerical examples are given to illustrate the advantages of such exploitation of symmetry in the context of the bem

semi infinite arrays of isotropic point scatterers a unified approach we solve the two dimensional problem of acoustic scattering by a semi infinite pe riodic array of identical isotropic point scatterers i e objects whose size is negligible compared to the incident wavelength and which are assumed to scatter incident waves uniformly in all directions this model is appropriate for scatterers on which dirichlet boundary conditions are applied in the limit as the ratio of wavelength to body size tends to infinity the problem is also relevant to the scattering of an e polarized electromagnetic wave by an array of highly conducting wires the actual geometry of each scatterer is characterized by a single parameter in the equations related to the single body scattering problem and determined from a harmonic boundary value problem using a mixture of analytical and numerical techniques we confirm that a number of phenomena reported for specific geometries are in fact present in the general case such as the presence of shadow boundaries in the far field and the vanishing of the circular wave scattered by the end of the array in certain specific directions we show that the semi infinite array problem is equivalent to that of inverting an infinite toeplitz matrix which in turn can be formulated as a discrete wiener hopf problem numerical results are presented which compare the amplitude of the wave diffracted by the end of the array for scatterers having different shapes