diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions the three dimensional problem of diffraction of a skew incident plane wave by a wedge with anisotropic impedance boundary conditions is explicitly solved by the probabilistic random walk method the problem is formulated in terms of two certain components of the electric and magnetic fields which satisfy independent helmholtz equations but are coupled through the first order boundary conditions the solution is represented as a superposition of the geometric waves that are completely determined by elementary methods and of the waves diffracted by the apex of the wedge the diffracted field is explicitly represented as the mathematical expectation computed over the trajectories of a two state random motion which runs in a complex space and switches states under the control of stochastic equations determined by the problem s geometry and by the boundary conditions

arbitrarily oriented perfectly conducting wedge over a dielectric half space diffraction and total far field complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field in this paper we describe a complete procedure to study this problem with possible developments in radar technologies like gpr antenna development or electromagnetic compatibility tips near substrates the diffraction of an incident plane wave by a perfectly conducting pec wedge over a dielectric half space is studied using generalized wiener hopf equations gwhes and the solution is obtained using analytical and numerical analytical approaches that reduce the wiener hopf wh factorization to integral equations ies the mathematical aspects are described in a unified and consistent theory for angular and layered region problems the proposed procedure is valid for the general case and the paper focuses on e polarization at normal incidence the solutions are given in terms of geometrical uniform theory of diffraction gtd utd diffraction coefficients and total far fields for engineering applications this paper presents several numerical test cases that show the validity of the proposed method

efficient algorithms for computing sommerfeld integral tails sommerfeld integrals sis are ubiquitous in the analysis of problems involving antennas and scatterers embedded in planar multilayered media it is well known that the oscillating and slowly decaying nature of their integrands makes the numerical evaluation of the si real axis tail segment a very time consuming and computationally expensive task therefore si tails have to be specially treated in this paper we compare two recently developed techniques for their efficient numerical evaluation first a partition extrapolation method in which the integration then summation procedure is combined with a new version of the weighted averages wa extrapolation technique is summarized the previous variants of wa technique are also discussed then a review of double exponential de quadrature formulas for direct integration of the si tails is presented the efficient way of implementing the algorithms their pros and cons as well as comparisons of their performance are discussed in detail

fast computation of sommerfeld integral tails via direct integration based on double exponential type quadrature formulas a direct integration algorithm based on double exponential type quadrature rules is presented for the efficient computation of the sommerfeld integral tails arising in the evaluation of multilayered green s functions the proposed scheme maintains the error controllable nature of the so called partition extrapolation methods often used to tackle this problem whereas it requires substantially reduced computational time moreover the proposed method is very easy to implement since the associated weights and abscissas can be precomputed the overall behavior of the proposed method both in terms of accuracy and efficiency is demonstrated through a series of representative numerical experiments where compared with one of the most proven methods available in the literature

the weighted averages algorithm revisited the classic weighted averages wa algorithm for the evaluation of sommerfeld like integrals is reviewed and reappraised as a result a new version of the wa algorithm called generalized wa is introduced the new version can be considered as a generalization of the well established holder and cesaro means used to sum divergent series generalized wa exhibits a more compact formulation devoid of iterative and recursive steps and a wider range of applications it is more robust as it provides a unique formulation valid for monotonic and oscillating functions the implementation of the new version is easier and more economical in terms of basic operations preliminary numerical examples show that generalized wa also outperforms in terms of accuracy the classic wa algorithm which is currently recognized as the most competitive algorithm to evaluate sommerfeld integral tails

on the solution of two coupled wiener hopf equations vector wiener hopi equations previously solved in closed form by using different techniques involve matrices having a particular structure a general procedure is given to factorize these matrices it leads to an approach which even if sometimes cumbersome is uniform and allows the solution of new problems in addition a new method is proposed which transforms simultaneous wiener hopf equations in the form of fredholm integral equation of the second kind

the wiener hopf technique for impenetrable wedges having arbitrary aperture angle diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the wiener hopf w h technique a system of functional equations called generalized wiener hopf equations gwhe is obtained only for certain values of the aperture angle are these equations recognizable as standard or classical wiener hopf equations cwhe however in all cases a mapping is found that reduces the gwhe to cwhe it means that the diffraction by an impenetrable wedge always reduces to a standard w h factorization the solution for the diffraction by a wedge with given face impedances the malyuzhinets problem is obtained in closed form by an explicit factorization of the kernel

wiener hopf solution for impenetrable wedges at skew incidence a new wiener hopf approach for the solution of impenetrable wedges at skew incidence is presented mathematical aspects are described in a unified and consistent theory for angular region problems solutions are obtained using analytical and numerical analytical approaches several numerical tests from the scientific literature validate the new technique and new solutions for anisotropic surface impedance wedges are solved at skew incidence the solutions are presented considering the geometrical and uniform theory of diffraction coefficients total fields and possible surface wave contributions

gossiping in minimal time the gossip problem involves communicating a unique item from each node in a graph to every other node this paper studies the minimum time required to do this under the weakest model of parallel communication which allows each node to participate in just one communication at a time as either sender or receiver a number of topologies are studied including the omplete graph grids hypercubes and rings definitive new optimal time algorithms are derived for complete graphs rings regular grids and toroidal grids that significantly extend existing results in particular an open problem about minimum time gossiping in complete graphs is settled specifically for a graph with n nodes at least log rho n communication steps where the logarithm is in the base of the golden ratio rho are required by any algorithm under the weakest model of communication this bound which is approximately 1 44 log 2 n can be realized for some networks and so the result is optimal

a general multisegment artificial neural network architecture for the efficient evaluation of electromagnetic plane wave wedge diffraction a multisegment artificial neural network ann is proposed as an interpolation technique for the evaluation of the electromagnetic field diffracted at the edge of anisotropic impedance wedges under plane wave illumination at oblique incidence multisegmentation is needed as the high frequency wedge diffracted field is characterized by a number of discontinuities at the shadow boundaries of the geometrical optics and surface wave fields the proposed approach is applied as a test case to the problem of an anisotropic impedance right angled wedge illuminated by a skewly incident plane wave some exact analytical solutions valid for specific surface impedance tensors are used to obtain numerical data for the ann training phase as well as to show the interpolation capabilities of the implemented ann nevertheless the proposed ann structure is general and can be trained with data obtained from other available solutions analytical perturbative numerical valid for more general wedge configurations eventually leading to a single software tool encompassing all of them and providing accurate approximations of the wedge diffracted field in a relatively short time comparable to that of a closed form analytical solution

electromagnetic diffraction by arbitrary angle impedance wedges the problem of the diffraction of a plane electromagnetic wave incident at an oblique angle on a wedge of arbitrary angle with general tensor impedance boundary conditions is solved using a semi an

fast gossiping for the hypercube the gossip problem involves communicating a unique item from every node in a graph to every other node the minimum time required to do this for the binary hypercube under two models of communication is studied in the first model all communication links may be used concurrently but each may only carry information in one direction at a time in the second weaker model each node may be involved in only one communication at a time either as sender or receiver in both cases simple algorithms exist that are close to optimal this paper shows that neither of these algorithms is optimal by exhibiting faster algorithms in the first case an optimal algorithm is obtained

on the non commutative factorization of wiener hopf kernels of khrapkov type there are a great many problems in mathematical physics and engineering which when modelled mathematically are reduced to wiener hopf functional equations defined in some region of a complex plane in simple models this equation is scalar but in more complicated situations inherent coupling etc can often give rise to coupled systems of equations and so the resulting wiener hopf kernels are of matrix form the crucial step in the solution of any wiener hopf equation is to decompose the kernel which can be a quite general function of the complex transform variable into a product of two factors which are regular in overlapping half planes this can be accomplished explicitly for scalar kernels and may be generalized to a particular class of matrix kernels namely those which permit a commutative decomposition although this class is wide and therefore contains some valuable physical problems it is found that many such kernels yield factorization elements with exponentially large behaviour at infinity in their half planes of analyticity this prevents a later step in the wiener hopf procedure being carried through and therefore introduces a serious limitation to the usefulness of khrapkov s approach previous researchers have offered schemes to eliminate the exponential behaviour of the khrapkov factors but for reasons discussed herein these have problems in their successful implementation this article offers a new procedure for quenching the exponential growth which is based on a method proposed recently by the author for fully coupled kernels which do not have commutative factors the approach is two step first a commutative factorization is obtained which is algebraic at infinity as required but which has spurious branch cuts in the regions of intended analyticity second an approximate procedure is used to eliminate the offending branch points by introduction of pade approximants for a certain scalar function and by inclusion of a regularizing meromorphic matrix for one particular example kernel in which an exact factorization happens to be known the explicit approximate kernel factors thus derived are shown to yield very close agreement to the exact factors the application of this work to problems in the area of fluid structural interaction is discussed

efficient evaluation of the finite part of pole free sommerfeld integrals in half space problems with predefined accuracy this communication presents a novel simple and robust approach for the computation of the finite part of pole free sommerfeld integrals sis in half space problems with high and controllable accuracy over a large range of source observer distances the approach includes the following techniques 1 cancellation of the branch point singularities based on the square root change of variables for numerical integration 2 approximation of real axis integration path in order to enhance the singularity cancellation for arbitrary low loss dielectrics 3 thresholds for truncation of the interval of integration for given accuracy which improve the efficiency of computation and 4 prediction formulas that estimate the required number of integration points for a given accuracy up to 1000 wavelengths of source observer distance the proposed approach is verified through numerical examples and comparison to reference methods

electromagnetic diffraction of an obliquely incident plane wave by a right angled anisotropic impedance wedge with a perfectly conducting face the diffraction of an arbitrarily polarized electromagnetic plane wave obliquely incident on the edge of a right angled anisotropic impedance wedge with a perfectly conducting face is analyzed the impedance tensor on the loaded face has its principal anisotropy axes along directions parallel and perpendicular to the edge exhibiting arbitrary surface impedance values in these directions the proposed solution procedure applies both to the exterior and the interior right angled wedges the rigorous spectral solution for the field components parallel to the edge is determined through the application of the sommerfeld maliuzhinets technique a uniform asymptotic solution is provided in the framework of the uniform geometrical theory of diffraction utd the diffracted field is expressed in a simple closed form involving ratios of trigonometric functions and the utd transition function samples of numerical results are presented to demonstrate the effectiveness of the asymptotic expressions proposed and to show that they contain as limit cases all previous three dimensional 3 d solutions for the right angled impedance wedge with a perfectly conducting face

wave diffraction by wedges having arbitrary aperture angle abstract the problem of plane wave diffraction by a wedge sector having arbitrary aperture angle has a very long and interesting research background in fact we may recognize significant research on this topic for more than one century despite this fact up to now no clear unified approach was implemented to treat such a problem from a rigourous mathematical way and in a consequent appropriate sobolev space setting in the present paper we are considering the corresponding boundary value problems for the helmholtz equation with complex wave number admitting combinations of dirichlet and neumann boundary conditions the main ideas are based on a convenient combination of potential representation formulas associated with weighted mellin pseudo differential operators in appropriate sobolev spaces and a detailed fredholm analysis thus we prove that the problems have unique solutions with continuous dependence on the data which are represented by the single and double layer potentials where the densities are solutions of derived pseudo differential equations on the half line

exact solution to diffraction problem by wedges with a class of anisotropic impedance faces oblique incidence of a plane electromagnetic wave this paper studies diffraction of an obliquely incident arbitrarily polarized plane electromagnetic wave by an anisotropic impedance wedge with an opening angle 2 spl phi between 0 and 2 spl pi and presents a closed form exact solution to a class of impedance wedge faces and the related uniform asymptotic solution uas on use of a unitary similarity transform the boundary conditions on the wedge faces is brought into a form which makes the exactly soluble class of impedance faces evident the exact solution is found with help of the sommerfeld malyuzhinets 1896 1958 technique a generalized malyuzhinets function spl chi sub spl phi and the so called s integrals a standard procedure yields therefrom the uas the exact solution agrees with known analytical results in special cases and the numerical results of uas are confirmed by that of parabolic equation method pem

communication complexity of fault tolerant information diffusion this paper considers problems of fault tolerant information diffusion in a network with cost function we show that the problem of determining the minimum cost necessary to perform fault tolerant gossiping among a given set of participants is np hard and give approximate with respect to the cost fault tolerant gossiping algorithms we also analyze the communication time and communication complexity of fault tolerant gossiping algorithms finally we give an optimal cost fault tolerant broadcasting algorithm and apply our results to the atomic commitment problem

evaluation of weakly singular integrals via generalized cartesian product rules based on the double exponential formula various weakly singular integrals over triangular and quadrangular domains arising in the mixed potential integral equation formulations are computed with the help of novel generalized cartesian product rules the proposed integration schemes utilize the so called double exponential quadrature rule originally developed for the integration of functions with singularities at the endpoints of the associated integration interval the final formulas can easily be incorporated in the context of singularity subtraction singularity cancellation and fully numerical methods often used for the evaluation of multidimensional singular integrals the performed numerical experiments clearly reveal the superior overall performance of the proposed method over the existing numerical integration methods

exact closed form expression of a sommerfeld integral for the impedance plane problem a sommerfeld integral for an impedance half plane is one of the classical problems in electromagnetic theory in this paper the integral is evaluated into two series representations which are expressed in terms of the exponential integral and the lommel function respectively it is shown that the series expansions absolutely converge for any parameters such as distance or surface impedance then based on the lommel function expansion an exact closed form expression of the integral is formulated this expression is written in terms of incomplete weber integrals which are directly related to incomplete cylindrical functions such as incomplete lipschitz hankel integrals additionally a complete asymptotic series of the integral is obtained based on the exponential integral expansion with conventional methods such as steepest descent method it is cumbersome to derive the divergent series the validity of all the formulations derived in this paper is demonstrated through a comparison with a numerical integration of the integral for various situations

application of the fast fourier transform to the computation of the sommerfeld integral for a vertical electric dipole above a half space the fast fourier transform fft is used in conjunction with analytical techniques to obtain an approximate expression for the sommerfeld integral associated with a vertical electric dipole above a half space the resulting expression which is an analytic function of the source and observation locations can be used in lieu of a numerical integration of the sommerfeld integral it can be used in either the near zone or the far zone and it can even be applied for observation angles close to grazing the accuracy of the expansion directly depends on the number of terms used in the fft results obtained using the expansion are compared with those obtained both from a direct numerical integration of the sommerfeld integral and the reflection coefficient method

a robust method for the computation of green s functions in stratified media closed form green s functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves the methodology is based on a two level approximation of the spectral domain representation of green s functions this robust efficient and fully numerical approach does not call for an analytical extraction of ldquoproblematicrdquo behaviors such as the quasi static terms and the surface wave poles prior to the spectrum fitting instead the spatial domain green s functions derived in this paper provide an accurate description of both the near field singularity in the vicinity of the source and the far field dominant behavior of the surface waves

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

a new representation for the green s function of multilayer media based on plane wave expansion in this paper a new representation for the space domain green s function of general multilayer media is presented this approach is based on an efficient plane wave expansion of the source incident field using the transmission line model for the multilayer medium the effect of the layered medium on the incident plane waves is determined by a transmission coefficient and the amplitude and phase of each plane wave at the field point are obtained the total field is evaluated by summing the resultant plane waves at the field point the main advantage of the proposed method is that the spatial domain green s function of multilayer media can be obtained easily as a summation of simple exponential functions without the need for sommerfeld integration or complex image approximation the plane wave approximation is independent of the parameters of the medium and is valid over a wide frequency range furthermore the exponential form of the plane wave solution makes it possible to compute the method of moments matrix elements analytically for most important types of basis functions in multilayer problems

a utd solution for the scattering by a wedge with anisotropic impedance faces skew incidence case asymptotic expressions for the fields scattered by an anisotropic impedance wedge at oblique incidence are derived in the context of the uniform geometrical theory of diffraction utd they are obtained by resorting to a perturbative approach considering the normal incidence case as the imperturbed configuration we observe that the limits of applicability of this approximate analytical solution extend far beyond those of standard perturbative approaches allowing us to account for deviations from the normal incidence case of 20 spl deg to 30 spl deg

note on optimal gossiping in some weak connected graphs abstract the problems of gossiping and broadcasting in one way communication mode are investigated optimal algorithms for gossip problem are known only for the complete graphs paths some simple trees and cycles in this paper some lower bounds on gossiping in graphs with bridges or with edge disjoint cycles are proved a direct consequence of these lower bounds is the construction of optimal gossip algorithms for some families of weak connected graphs another question considered here is the relationship between the gossip problem and the broadcast problem gossiping cannot be more than twice as hard as broadcasting and only for trees it is known that gossiping is exactly two times harder than broadcasting using the above mentioned l lower bounds some other graphs having cycles with this property are found

the wiener hopf solution of the isotropic penetrable wedge problem diffraction and total field the diffraction of an incident plane wave by an isotropic penetrable wedge is studied using generalized wiener hopf equations and the solution is obtained using analytical and numerical analytical approaches that reduce the wiener hopf factorization to fredholm integral equations of second kind mathematical aspects are described in a unified and consistent theory for angular region problems the formulation is presented in the general case of skew incidence and several numerical tests at normal incidence are reported to validate the new technique the solutions consider engineering applications in terms of gtd utd diffraction coefficients and total fields