an efficient closed form derivation of spatial green s function for finite dielectric structures using characteristic green s function rational function fitting method a uniform and closed form spatial green s function for finite dielectric structures is derived by using a combination of the characteristic green s function cgf and rational function fitting method rffm employing the concept of quasi leaky waves cgf rffm represents both of the discrete and continuous spectrum contributions efficiently by using the modified vectfit algorithm the method is examined for 2 d truncated dielectric slab while it can be implemented for 3 d structure straightforwardly an error of less than 0 2 is achieved compared with the direct numerical integration of the spectral integral the derived green s function is exact for separable structures while it is approximate for nonseparable structures like truncated dielectric substrates where the corner regions are replaced with fictitious materials to obtain more accurate results mode conversions due to the surface waves sws incident on the end facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes the main advantage of this method lies in its speed as well as accuracy excellent agreements with the rigorous method of moments mom are shown in several examples

efficient calculation of the green s function for multilayered planar periodic structures an efficient calculation scheme is presented for the periodic green s function in planar multilayered structures the proposed method is based on the static complex image conversion and the ewald sum technique and it converts the slowly convergent green s function into the sum of two rapidly convergent series

yang lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 d 7 we have extended in most cases through 24th order the series expansions of the dimer density in powers of the activity in the case of bipartite hyper simple cubic and hyper body centered cubic lattices of dimensionalities 2 d 7 a numerical analysis of these data yields estimates of the exponents characterizing the yang lee edge singularities for lattice ferromagnetic spin models as d varies between the lower and the upper critical dimensionalities our results are consistent with but more extensive and sometimes more accurate than those obtained from the existing dimer series or from the estimates of related exponents for lattice animals branched polymers and fluids we mention also that it is possible to obtain estimates of the dimer constants from our series for the various lattices

an improved discrete complex image method based on a special sampling path a special sampling path is proposed to improve the accuracy of the discrete complex image method dcim in evaluating the lateral wave different from all the previous dcim implementations the proposed sampling path goes through the branch point directly which helps to evaluate its contribution to the lateral wave more accurately in this communication different sampling paths of dcim have been implemented and compared it is found that in the situations where the lateral wave dominates the far field region dcim with the new path gives more accurate and stable results

numerical approximation of electromagnetic signals arising in the evaluation of geological formations the integration of complicated oscillatory functions arises in computational electromagnetics when evaluating signals produced by the propagation of electromagnetic radiation through the anisotropic layers of a geological formation the computation of exact integrals involves the evaluation of sommerfeld integrals the matrix pencil method is used for the numerical approximation of such signals numerical results show accuracy and robustness of the method for the approximation of these signals and efficiency in their numerical integration sampling frequency is discussed and numerical efficiency is improved by down sampling

green s functions in lossy layered media integration along the imaginary axis and asymptotic behavior this paper presents an efficient technique for evaluating green s functions associated to layered media when formulated as sommerfeld integrals in the space domain the key step in the formulation is that sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane it is shown that with this original choice of the integration contour the numerical effort usually involved in the evaluation of sommerfeld integrals can be greatly reduced specially when large source observer distances are involved one asset of this technique is that it can be easily incorporated into integral equation based cad packages for the efficient analysis of complex printed microwave circuit and antennas in addition the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media green s functions for large source observer distances

a new approach to dyadic green s function in spectral domain a new method is proposed to derive the dyadic green s function for stratified dielectric layers from the wave equation in spectral domain the result is a clear equivalent circuit of the whole structure which combines the te and tm modes by hybrid block matrices it is simple to apply and evaluate the relation to the conventional immittance approach is shown by means of a similarity transform which diagonalizes the submatrices the simplicity of the method is demonstrated in the application to the well known example of a single microstrip patch on a grounded dielectric layer as well as structures with multiple layers and metallizations in arbitrary interfaces

closed form green s function representations in cylindrically stratified media for method of moments applications closed form green s function cfgf representations for cylindrically stratified media which can be used as the kernel of an electric field integral equation are developed the developed cfgf representations can safely be used in a method of moments solution procedure as they are valid for almost all possible source and field points that lie on the same radial distance from the axis of the cylinder such as the air dielectric and dielectric dielectric interfaces including the axial line rho rho and phi phi which has not been available before in the course of obtaining these expressions the conventional spectral domain green s function representations are rewritten in a different form so that i we can attack the axial line problem and ii the method can handle electrically large cylinders available acceleration techniques that exist in the literature are implemented to perform the summation over the cylindrical eigenmodes efficiently lastly the resulting expressions are transformed to the spatial domain using the discrete complex image method with the help of the generalized pencil of function method where a modified two level approach is used numerical results are presented in the form of mutual coupling between two current modes to assess the accuracy of the final spatial domain cfgf representations

a hybrid time domain technique that combines the finite element finite difference and method of moment techniques to solve complex electromagnetic problems this paper describes a hybrid technique directly operating in time domain that combines the finite element time domain fetd the finite difference time domain fdtd and the integral equation based method of moments in the time domain momtd techniques to analyze complex electromagnetic problems involving thin wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary the method brings together the ability of the fdtd scheme to deal with arbitrary material properties the versatility of the fetd to accurately model curved geometries and that of the mom to analyze thin wire structures working in the time domain provides wide band information from a single execution of the marching on in time procedure and simplifies the interfacing of the fe and mom methods with the fdtd an approach specifically designed for time domain analysis numerical results that validate the hybrid method and show its capabilities are presented in the paper

monomer dimer model in two dimensional rectangular lattices with fixed dimer density the classical monomer dimer model in two dimensional lattices has been shown to belong to the p complete class which indicates the problem is computationally intractable we use exact computational method to investigate the number of ways to arrange dimers on mxn two dimensional rectangular lattice strips with fixed dimer density rho for any dimer density 0 rho 1 we find a logarithmic correction term in the finite size correction of the free energy per lattice site the coefficient of the logarithmic correction term is exactly 12 this logarithmic correction term is explained by the newly developed asymptotic theory of pemantle and wilson the sequence of the free energy of lattice strips with cylinder boundary condition converges so fast that very accurate free energy f 2 rho for large lattices can be obtained for example for a half filled lattice f 2 12 0 633195588930 while f 2 14 0 4413453753046 and f 2 34 0 64039026 for rho 0 65 f 2 rho is accurate at least to ten decimal digits the function f 2 rho reaches the maximum value f 2 rho 0 662798972834 at rho 0 6381231 with 11 correct digits this is also the monomer dimer constant for two dimensional rectangular lattices the asymptotic expressions of free energy near close packing are investigated for finite and infinite lattice widths for lattices with finite width dependence on the parity of the lattice width is found for infinite lattices the data support the functional form obtained previously through series expansions

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

rational modeling by pencil of functions method pole zero modeling of signals such as an electromagnetic scatterer response is considered in this paper it is shown by use of the pencil of functions theorem that a the true parameters can be recovered in the ideal case where the signal is the impulse reponse of a rational function h z and b the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error although the computations are more involved than in all pole modeling they are considerably less than those required in iterative schemes of pole zero modeling the advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer the paper also includes very recent and promising results on a new approach to noise correction in contradistinction with spectral subtraction techniques where only amplitude information is emphasized and phase is ignored we propose a method that a estimates the noise spectral density for the data frame and then b performs the subtraction of the noise correlation matrix from the gram matrix of the signal

accurate and efficient computation of layered medium doubly periodic green s function in matrix friendly formulation this communication proposes a novel approach to evaluate the doubly periodic green s function for layered medium in matrix friendly formulation several techniques including factorization of the green s function generalized pencil of function method and high order taylor expansion are employed in a delicate manner to derive the high order asymptotic expressions which are then evaluated by new fast convergent series derived from ewald transformation this approach delivers fast and highly accurate results as well as high order convergence and also allows fast frequency sweep for calculating brillouin diagram in eigenvalue problem and for normal incidence in scattering problem

enhanced mom analysis of the scattering by periodic strip gratings in multilayered substrates the method of moments mom is applied to the analysis of the scattering of a multilayered periodic strip grating by a plane wave with oblique incidence and arbitrary polarization although this problem has been traditionally solved by means of the mom in the spectral domain this is an approach which leads to the computation of slowly convergent infinite summations in this paper the problem is solved by means of the mixed potential integral equation mpie formulation of the mom in the spatial domain while applying the mom in the spatial domain two improvements are introduced which lead to important cpu time savings first the multilayered periodic green s functions are accurately interpolated in terms of chebyshev polynomials second half the integrals involved in the computation of the mom matrix entries are obtained in closed form as a consequence of these two improvements the spatial domain version of the mom presented in this paper turns out to be between one and two orders of magnitude faster than the conventional spectral domain version when basis functions that account for edge singularities are used in the modeling of the current density on the metallizations

perturbation analysis of tk method for harmonic retrieval problems the authors present a first order perturbation analysis of the tufts kumaresan tk 1980 method used to estimate frequencies of complex sinusoids in small additive noise several fundamental properties are presented and proved further illustrations are provided through numerical examples

a pfaffian formula for monomer dimer partition functions we consider the monomer dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights with the restriction that the only non zero monomer weights are those on the boundary we prove a pfaffian formula for the corresponding partition function as a consequence of this result multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics our proof is based on the celebrated kasteleyn theorem combined with a theorem on pfaffians proved by one of the authors and a careful labeling and directing procedure of the vertices and edges of the graph

extension and optimization of the axisymmetric 2 5 d eigensolver toward far field calculations in stratified backgrounds we extend and optimize the axisymmetric 2 5 d eigensolver to calculate the far field results of axisymmetric structures in stratified backgrounds sbs which is useful and practical for optical design and engineering two kinds of near field to far field transformations nfffts are proposed one is called closed surface transformation which is based on the dipole radiations in sbs the other is called open surface transformation which is based on the analytic continuation this transformation can provide the far field results of any axisymmetric structure including backgrounds the far field results achieved by these two transformations are in good agreement with each other and with analytical ones moreover in order to obtain accurate near field results we optimize the perfectly matched layer pml setting of the 2 5 d eigensolver corresponding optimization rules are proposed and discussed

dual gpof dcim for fast computation of sommerfeld integrals and em scattering from an object partially embedded in dielectric half space a novel approach of dual gpof general pencil of functions combined with the dcim the discrete complex image method is developed to accelerate the sommerfeld integral evaluation when the mixed potential integral equation mpie is applied to numerically calculate scattering from a conductive object partially embedded in a dielectric half space where the field and source points are located in different media firstly the factors related with the field point are separated from the spectrum function and the gpof is used to find the complex image parameters at finite discrete source points secondly the gpof is used again to fit the functional relationship of each complex image parameter with the source positions to evaluate the complex image parameters for any source position in a closed functional summation comparing numerical results of dual gpof and direct numerical integration this dual gpof process is proved highly effective finally dual gpof dcim is applied to computation of electromagnetic scattering from a pec spherical object partially embedded in a dielectric half space medium and numerical scattering results upon different model parameters are presented and analyzed

closed form green s function representations for mutual coupling calculations between apertures on a perfect electric conductor circular cylinder covered with dielectric layers closed form green s function cfgf representations are developed for tangential magnetic current sources to calculate the mutual coupling between apertures on perfectly conducting circular cylinders covered with dielectric layers the new representations are obtained by first rewriting the corresponding spectral domain green s function representations in a different form so that accurate results for electrically large cylinders and along the axial line of a cylinder can be obtained then the summation over the cylindrical eigenmodes is calculated efficiently finally the resulting expressions are transformed to the spatial domain using a modified two level generalized pencil of function method numerical results are presented showing good agreement when compared to cst microwave studio results

a novel analysis of microstrip structures using the gaussian green s function method a novel closed form expression is derived for spatial green s functions of microstrip structures by expanding the spectral green s function into a gaussian series this innovative method is called the gaussian green s function ggf method due to the gaussian form in the closed form green s function representation the main advantage of the ggf method lies in its precision as well as rapid convergence to demonstrate the versatility of this method the current distribution of a microstrip antenna is achieved via the combination of the method of moments mom and ggf method it is shown that this method can be computationally very efficient with less than 1 error compared to the numerical integration of the spectral integral also the results of the ggf method have been compared to the results of the commercial full wave software of agilent ads

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

combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution the purpose of this work is to combine an extrapolation technique with the method of moments mom to solve scattering problems involving large bodies it has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms based on this concept a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer complemented by subdomain basis functions near edges and discontinuities an extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional mom next a set of entire domain basis functions whose behaviour could be extrapolated with an increase in the size of the scatterer is extracted from this original solution the procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased allowing for large scatterers to be handled with a relatively small number of unknowns the extrapolation technique is applied to scattering problems from bodies of revolution bors and numerical results for an open cylinder and a barrel shaped bor are presented

an efficient asymptotic extraction approach for the green s functions of conformal antennas in multilayered cylindrical media asymptotic expressions are derived for the dyadic green s functions of antennas radiating in the presence of a multilayered cylinder where analytic representation of the asymptotic expansion coefficients eliminates the computational cost of numerical evaluation as a result the asymptotic extraction technique has been applied only once for a large summation order in addition the hankel function singularity encountered for source and evaluation points at the same radius has been eliminated using analytical integration

upper bound on the energy gap in terms of the localization in tight binding systems we present an upper bound on the energy gap above the ground energy in terms of the variance of the particle position in one particle tight binding systems our inequality gives a complementary relationship between the energy gap and the localization of the particle that is the energy gap narrows as the ground state spreads spatially while the energy gap can broaden as the ground state becomes localized we first consider the ground state in one dimensional tight binding systems and relate the energy gap to the variance of the particle position in the ground state we then extend the result to higher dimensional systems we compare our upper bound with the exact energy gap as calculated numerically in one and two dimensions this comparison confirms that our upper bound places a tight restriction on the energy gap

monomer dimer problem on some networks abstract zhang et al 2012 obtained the exact formula for the number of all possible monomer dimer arrangements and the asymptotic growth constant on a scale free small world network in this note we generalize this result and obtain the exact solution on the monomer dimer model on many networks particularly we prove that these networks have the same asymptotic growth constant of the number of monomer dimer arrangements

application of dcim on marine controlled source electromagnetic survey the discrete complex image method dcim is used to calculate the mixed potential electric field integral equation the dcim has been used broadly in high frequency domain and now is successfully introduced to the extremely low frequency situation of marine controlled source electromagnetic mcsem survey the integral path in high frequency situation does not hold valid for extremely low frequency situation the reason can be ascribed to the change of wave number formulas a new integral path suitable for the extremely low frequency situation is proposed the appropriate ranges of the parameters used in dcim are given the computation is stable at these considerably large ranges the results of a five layer model calculated with dcim are compared with those with the filter method and the direct integral method the computation time with dcim is comparable to the time with filter method the effects of water depth upper sediment thickness and oil layer thickness are studied with dcim the results show that electric field varies with the change of thickness the effects accord to the physical meanings of mcsem survey it is safe to conclude that the dcim with the new path is valid in mcsem survey

representation of electromagnetic responses in time domain using state space system identification method this paper presents a control system methodology based on system identification si to derive state matrices and system dynamics for the extrapolation of simulated time domain electromagnetic em responses using both input and output data the method is applied to model transient responses for a dielectric resonator and a wideband slot antenna computed by the finite integration method using non gaussian excitation pulses typically employed in digital signals using state space si formulation a compact representation of the output time domain signal is derived including the early time transient responses and its numerical implementation depicts no instability in late time responses plotted well beyond the steady state furthermore all the system poles are found to lie within the unit circle in the complex plane excellent model corroboration is achieved with independently computed frequency domain data or measured results using modest computer resources

dimer monomer model on the sierpinski gasket abstract we present the numbers of dimer monomers m d n on the sierpinski gasket s g d n at stage n with dimension d equal to two three and four the upper and lower bounds for the asymptotic growth constant defined as z s g d lim v ln m d n v where v is the number of vertices on s g d n are derived in terms of the results at a certain stage as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of z s g d can be evaluated with more than a hundred significant figures accurate from the results for d 2 3 4 we conjecture the upper and lower bounds of z s g d for general dimension the corresponding results on the generalized sierpinski gasket s g d b n with d 2 and b 3 4 are also obtained

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

two dimensional multidomain pseudospectral time domain algorithm based on alternating direction implicit method in order to deal with the stability problem restricted by the finite difference time domain fdtd and conventional pseudospectral time domain pstd the multidomain pstd algorithm based on alternating direction implicit adi technique is proposed in this paper this algorithm improves the stability and efficiency of conventional pstd while it maintains the accuracy and flexibility of conventional pstd for an accurate treatment of arbitrarily curved objects a compact matrix form is derived to effectively describe two dimensional adi multidomain pseudospectral time domain adi mpstd algorithm numerical results show an excellent agreement with analytical solutions as well as results obtained by the fdtd algorithm and fully demonstrate a remarkable improvement in stability and efficiency

a technique for approximating the location of surface and leaky wave poles for a lossy dielectric slab an approximation technique for locating the surface and leaky wave poles for a lossy dielectric slab is presented the problem is reduced to the simultaneous solution of two transcendental equations for each of the perfect magnetic conductor pmc and perfect electric conductor pec cases which is shown to yield a simple approximate solution for the poles and which can subsequently be refined using numerical optimization the technique yields both surface wave and leaky wave poles and results are presented for a typical example to demonstrate the approach the greatest approximation accuracy was observed for surface wave and leaky wave poles well removed from the spectral gap for poles either within or in close proximity to the spectral gap an alternative iterative technique is proposed expressions for the number of proper plus improper surface wave poles in a given problem are also derived

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

a novel approach for the efficient computation of 1 d and 2 d summations a novel computational method is proposed to evaluate 1 d and 2 d summations and integrals which are relatively difficult to compute numerically the method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials for a convergent summation the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation since the procedure requires the evaluation of relatively small number of terms the computation time for the evaluation of the summation is reduced significantly in addition by using the proposed method very accurate and convergent results are obtained for the summations which are not even absolutely convergent the efficiency and accuracy of the method are verified by evaluating some challenging 1 d and 2 d summations and integrals

shape from moments an estimation theory perspective this paper discusses the problem of recovering a planar polygon from its measured complex moments these moments correspond to an indicator function defined over the polygon s support previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given in this paper we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given similar to methods found in array processing system identification and signal processing we discuss a set of possible estimation procedures that are based on the prony and the pencil methods relate them one to the other and compare them through simulations we then present an improvement over these methods based on the direct use of the maximum likelihood estimator exploiting the above methods as initialization finally we show how regularization and thus maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon

utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival in this study we use the matrix pencil mp method to compute the direction of arrival doa of the signals using a very efficient computational procedure in which the complexity of the computation can be reduced significantly by using a unitary matrix transformation this method applies the technique directly to the data without forming a covariance matrix simulation results show that the variance of the estimate approaches to the cramer rao lower bound using real computations through the unitary transformation for the mp method leads to a very efficient computational methodology for real time implementation on a digital signal processor chip a unitary transform can convert the complex matrix to a real matrix along with their eigenvectors and thereby reducing the computational cost at least by a factor of four without sacrificing accuracy this reduction in the number of computations is achieved by using a transformation which maps centro hermitian matrices to real matrices this transformation is based on lee s work on centro hermitian matrices

closed form green s function of a 2 d rectangular room closed form enough accurate green s function for wave propagation modeling in a rectangular 2 d room is presented using the characteristic green s function technique this green s function is first developed in an integral form then its spatial domain closed form is obtained using three fast methods in the first method the integral is computed by the stationary phase method in the second one the integral is computed analytically by expanding the integrand into a complex exponential series in the third method the integrand is approximated by a series of rational functions and the integral is computed using cauchy s residue theorem the results of these three methods are studied and compared in an example the results show that the methods are fast while preserving accuracy

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

an improved pencil of functions method and comparisons with traditional methods of pole extraction prony s method is usually used for the determination of poles from experimental data in the singularity expansion method sem literature it is the aim here to show that this is not the best method and that jain s pencil of functions pof method can be generalized to provide a better method an example of such a method is given

on the application of parametric models to the transient analysis of resonant and multiband antennas the transient responses of a resonant antenna and a fractal multiband antenna both formed by conducting surfaces are calculated the surfaces are modeled by planar triangular patches and the study is carried out by solving the time domain electric field integral equation td efie linear parametric modeling techniques are applied to considerably reduce the computation time numerical results are compared with experimental measurements

the analysis of arbitrarily shaped aperture coupled patch antennas via a mixed potential integral equation a mixed potential integral equation mpie is formulated for the electric and magnetic currents on a multilayered aperture coupled patch antenna the integral equation is solved via the method of moments mom using subsectional basis functions that allow the analysis of nonrectangular aperture and patch shapes the input impedance and radiation efficiency of various aperture coupled elements are calculated using the proposed technique and compared to measured results the advantages and disadvantages of several aperture and patch configurations are discussed and six methods of numerically de embedding the element s input impedance are compared

a robust method for the computation of green s functions in cylindrically stratified media closed form green s functions for cylindrically stratified media are derived in terms of spherical waves and surface wave contributions the methodology is based on a two level approximation of the spectral domain green s functions in the first step the large argument behavior of the zeroth order hankel functions is used for the extraction of the quasistatic images from the spectral domain green s functions with the use of the sommerfeld identity in the second step the remaining part of the green s functions are approximated in terms of pole residue expressions via the rational function fitting method this robust efficient and fully numerical approach does not call for an analytical cumbersome extraction of the surface wave poles prior to the spectrum fitting moreover it can be applied in both the near and far field numerical results for the green s functions of one layer and two layer structures are presented to verify the accuracy and efficiency of this approach

comparative evaluation of absorbing boundary conditions using green s functions for layered media absorbing boundary conditions are comparatively studied using the green s functions of the vector and scalar potentials for multilayer geometries and general sources since the absorbing boundaries are introduced as additional layers with predefined reflection coefficients into the calculation of the green s functions this approach provides an absolute measure of the effectiveness of different absorbing boundaries the green s functions are calculated using different reflection coefficients corresponding to different absorbing boundaries and compared to those obtained with no absorbing boundary it is observed that the perfectly matched layer pml is by far the best among the other absorbing boundary conditions whose reflection coefficients are available

a fast analysis of scattering from large scale finite periodic microstrip patch arrays arranged on a non orthogonal lattice using sub entire domain basis functions a sub entire domain sed basis function method which was first introduced for modeling large scale finite periodic pec structures in free space has been extended for fast characterization of electromagnetic scattering from an electrically large planar finite periodic microstrip patch array the microstrip array may have a nonrectangular layout and non orthogonal lattice configurations e g hexagons or quadrangles based on the mixed potential integral equation and utilizing the proposed sed basis function algorithm the original large scale finite periodic array of microstrip patches can be efficiently simulated by decomposing it into two problems with matrix equations of small dimensions the first is to construct the sed basis functions for the corresponding microstrip arrays with orthogonal non orthogonal lattices three kinds of the sed basis functions are constructed including those related to the edge patch elements the interior patch elements and the corner patch elements the second is to solve the system equation with significantly reduced problem dimension as compared to the original larger problem based on the obtained sed basis functions the reduced matrix equation of small size can be generated by the galerkin procedure and solved by use of the lu lower upper decomposition based direct solver which results in a fast solution the accuracy and efficiency of the developed algorithms are demonstrated by numerical tests that include the scattering from several large scale finite periodic arrays of microstrip patches with rectangular non orthogonal lattices

interaction of electromagnetic waves with 3 d arbitrarily shaped homogeneous chiral targets in the presence of a lossy half space the interaction of electromagnetic waves with an arbitrarily shaped three dimensional 3 d homogeneous chiral object located above a lossy half space is investigated using the method of moments mom via the coupled mixed potential integral equations mpies based on the surface equivalence principle the equivalent surface electric and magnetic currents are used to replace the homogeneous chiral target in the presence of the half space two coupled mpies are developed for the unknown equivalent surface electric and magnetic currents by utilizing the continuity condition of the tangential total electric and magnetic field components on the chiral body s surface the well known galerkin procedure with rao wilton glisson rwg basis functions is applied to solve this problem the spatial domain half space green s functions are obtained from the corresponding spectral domain green s functions via the discrete complex image method dcim combined with the generalized pencil of function gpof technique the reciprocity theorem is employed to calculate the far zone scattered field numerical results are presented for characterizing electromagnetic scattering by a 3 d arbitrarily shaped homogenous chiral object located above a lossy half space so as to demonstrate the accuracy and efficiency of the proposed technique

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

an accurate derivation of spatial green s function for finite dielectric structures using characteristic green s function perfectly matched layer method a closed form spatial green s function for a truncated dielectric slab is derived by using a combination of the characteristic green s function cgf and perfectly matched layer pml method the original structure is terminated by pml that is backed by perfect electric conductor pec in semi infinite layer at the top and or bottom the eigenmodes of the closed structure by pml construct the continuous spectrum contribution of the original structure efficiently derived green s function is exact for separable finite structure while it is approximate for nonseparable one especially in the corners generalized scattering matrix gsm of truncating surface which contains possible conversions between all modes is computed with mode matching method it is demonstrated that by importing gsm in cgf formulation more exact results for nonseparable structures can be obtained the source and observation points dependence is analytically available in derived expression and allows very efficient computation and storage of the spatial green s function very close to the source where the large number of modes must be considered shank s transform is used to preserve the efficiency of the method the main advantage of the method lies in its accuracy and low dependency of the result to the pml parameters excellent agreements with the rigorous method of moments mom are shown in several examples

spectral gap and decay of correlations in u 1 symmetric lattice systems in dimensions d 2 we consider many body systems with a global u 1 symmetry on a class of lattices with the fractal dimension d 2 and their zero temperature correlations whose observables behave as a vector under the u 1 rotation for a wide class of the models we prove that if there exists a spectral gap above the ground state then the correlation functions have a stretched exponentially decaying upper bound this is an extension of the mcbryan spencer method at finite temperatures to zero temperature the class includes quantum spin and electron models on the lattices and our method also allows finite or infinite quasi degeneracy of the ground state the resulting bounds rule out the possibility of the corresponding magnetic and electric long range orders

radar target recognition based on late time representation closed form expression for criterion in the previous paper we have defined the normalized estimation error and presented the radar target recognition scheme in frequency domain a time domain version of the previous paper is considered and a closed form expression for the defined normalized estimation error in terms of z plane natural frequencies and transient response is derived evaluation of the closed form expression of the normalized estimation error is shown in the numerical results where it is shown that the performance of the radar target recognition scheme improves with an increase of the number of the natural frequencies and with an increase of signal to noise ratio furthermore the mean and the variance of the square of the numerator of the normalized estimation error are obtained and the validity of the statistics is shown using the numerical results

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

taylor expansion based fast multipole method for 3 d helmholtz equations in layered media abstract in this paper we develop a taylor expansion te based fast multipole method fmm for low frequency 3d helmholtz green s function in layered media two forms of taylor expansions with either non symmetric or symmetric derivatives of layered media green s functions are used for the implementations of the proposed te fmm in the implementation with non symmetric derivatives an algorithm based on discrete complex image approximations and recurrence formulas is shown to be very efficient and accurate in computing the high order derivatives meanwhile the implementation based on symmetric derivatives is more robust and pre computed tables for the high order derivatives in translation operators are used numerical tests in layered media have validated the accuracy and o n complexity of the proposed algorithms

a pencil music algorithm for finding two dimensional angles and polarizations using crossed dipoles the authors study the problem of finding two dimensional 2 d angles of wave arrival and wave polarizations using a uniform rectangular array of crossed dipoles the method presented effectively exploits the redundancy in this array via 2 d moving window smoothing to handle coherent sources and to achieve optimum noise sensitivity the method combines the computational advantages of the music and matrix pencil approaches the method is shown in simulation to be nearly optimum compared with the cramer rao bound

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

a technique for extrapolating numerically rigorous solutions of electromagnetic scattering problems to higher frequencies and their scaling properties the possibility of extrapolating the current distribution on two dimensional scatterers to high frequencies from knowledge of the solution at two or more lower frequencies is investigated in this paper a simple extrapolation algorithm is developed in which the current distribution is first calculated at two lower frequencies and then split into propagating or decaying traveling wave components in the lit and shadow regions these components are scaled to higher frequencies by using simple operations such as stretching of the magnitude and linear extrapolation of the phase this technique enables one to solve a class of large body scattering problems well beyond the range of rigorous numerical techniques furthermore the extrapolated solution is rapidly constructed over a very wide range of frequencies typically by utilizing the rigorous solution at only two lower frequencies the application of the extrapolation algorithm is demonstrated for several examples viz an ellipse with a high aspect ratio and wing shaped geometries with rounded and sharp edges the robustness of the technique is illustrated by considering grazing angles of incidence where the asymptotic techniques typically break down

evaluation of efficient closed form green s function in a cylindrically stratified medium an efficient technique is proposed for the removal of the spatial singularity for a z directed current source in a cylindrically layered structure by decomposing the spectral domain green s function into the particular and homogeneous parts the particular part with the singularity is converted into the spatial domain using sommerfeld s identity while the dcim with general pencil of function technique is applied on the spectral domain homogeneous part the use of the ratio form of the reflection transmission matrices the debye approximation and the subsequent envelope extraction for the treatment of the spatial domain singularity is thus avoided in addition a very significant reduction in the number of modes required for convergence is also achieved the technique is applied for evaluating the input impedance of several antennas in the cylindrical multilayer structure together with a coupling configuration for the excitation of the multilayer structure

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

spectral gap and exponential decay of correlations we study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short range interactions on a wide class of lattices we prove that if two observables anticommute with each other at large distance then the nonvanishing spectral gap implies exponential decay of the corresponding correlation when two observables commute with each other at large distance the connected correlation function decays exponentially under the gap assumption if the observables behave as a vector under the u 1 rotation of a global symmetry of the system we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself rather than just the connected correlation function decays exponentially under the gap assumption on a lattice with a certain self similarity in fractal dimensions d 2 in particular if the system is translationally invariant in one of the spatial directions then this self similarity condition is automatically satisfied we also treat systems with long range power law decaying interactions

wave oriented signal processing of dispersive time domain scattering data phase space data processing is receiving increased attention because or its potential for furnishing new discriminants relating to classification and identification of targets and other scattering environments primary emphasis has been on time frequency processing because of its impact on transient especially wideband short pulse excitations here we investigate the windowed fourier transform the wavelet transform and model based superresolution algorithms within the context of a fully quantified and calibrated test problem investigated by us previously two dimensional 2 d short pulse plane wave scattering by a finite periodic array of perfectly conducting coplanar flat strips because the forward problem has been fully calibrated and parametrized some quantitative measures can be assigned with respect to the tradeoffs of these time frequency algorithms yielding tentative performance assessments of the tested processing algorithms

accuracy of singularity expansion method in time and frequency domains to characterize antennas in presence of noise in this paper the accuracy of the singularity expansion method sem used for antenna characterization is investigated a well known limitation of the sem is that pole extraction is very sensitive to noise a comparison between two main methods of pole extraction is presented the matrix pencil mp method and the cauchy s method are used to extract poles from the radiated fields of a dipole antenna and two bowtie antennas results are presented for simulated fields and the robustness to a white gaussian noise is also analyzed we show that the mp method allows working with lower snr than cauchy s method and is more accurate for field reconstruction

closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

direct rational function fitting method for accurate evaluation of sommerfeld integrals in stratified media the current work proposes a direct rational function fitting method employing cylindrical waves alone for the accurate evaluation of sommerfeld integrals for planar multilayered structures three are the key points of the effort 1 until now relative works require the extraction of the quasi static asymptotic terms and branch cut continuous wave contribution explicitly in the current one the explicit treatment of those terms is avoided the proposed methodology is based on the direct fitting of the spectrum of the green s function by rational functions thus it provides the spatial green s function solely in terms of cylindrical waves 2 the effectiveness robustness and accuracy improvement of the rational function fit rely upon the proper sampling of the spectrum this accurate fitting is possible because instead of avoiding large variations of the spectral kernel we introduce proper paths to include more variation and thus more spectrum information before we apply the modified vectfit algorithm 3 furthermore proper weighting of the vectfit is proposed in order to guide the algorithm in providing increased accuracy in specific desired areas of the horizontal distance between the source and observation points armed with the above the direct rational function fitting method provides accurate results both for the near and far field regions various examples among them the correct treatment of a two branch case are given that prove the excellent performance and robustness of the proposed approach

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

a mixed form thin stratified medium fast multipole algorithm for both low and mid frequency problems a mixed form thin stratified medium fast multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid frequencies the newly developed matrix friendly formula of layered medium green s function is applied in this algorithm for well separated interactions the path deformation technique is implemented to achieve a smoother and exponentially convergent integral the two dimensional addition theorem is then incorporated into the integrand to expedite the matrix vector product in our approach multipole expansion low frequency fast multiple algorithm as well as the plane wave expansion mid frequency fast multipole algorithm of the translational addition theorem are combined into a single multilevel tree to capture quasi static physics and wave physics simultaneously the outgoing wave is represented first in terms of multipole expansion at leafy levels and then switched to plane wave expansion automatically at higher levels this seamless connection makes the algorithm applicable in simulations where subwavelength interaction and wave physics both exist

fast and accurate mom analysis of periodic arrays of multilayered stacked rectangular patches with application to the design of reflectarray antennas the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption the solution to the periodic multilayered problem has been traditionally carried out by means of the galerkin s version of the method of moments mom in the spectral domain this approach involves the computation of double infinite summations and whereas some of these summations converge very fast some other converge very slowly in this paper the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation mpie formulation of the mom in the spatial domain this enhanced formulation is based on the interpolation of the multilayered periodic green s functions and on the efficient computation of the four dimensional 4 d integrals leading to the mom matrix entries both the novel hybrid spectral spatial mom code and the standard spectral domain mom code have been used for the design of a contoured beam reflectarray antenna it has been verified that the spectral spatial mom code requires cpu times that are typically 30 times smaller than those required by the pure spectral domain mom code

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

arma based time signature estimator for analyzing resonant structures by the fdtd method we propose an algorithm for estimation of the optimal system parameters of time sequences tss computed by the finite difference time domain fdtd method with the goal of accurate representation of the time signature using low order models the fdtd method requires computation of very long time sequences to accurately characterize the slowly decaying transient behavior of resonant structures therefore it becomes critical to investigate methods of reducing the computational time for such objects several researchers have argued that the fdtd ts can be modeled as the impulse response ir of an autoregressive moving average arma transfer function however it is known that determination of arma parameters by ir matching is a complex nonlinear optimization problem hence many existing methods in em literature tend to use prony based linear predictor type spectrum estimation algorithms which minimize a linearized equation error criterion that approximates the true nonlinear model fitting error criterion as a result significantly high model orders are needed by these methods to achieve good corroboration in the frequency domain especially when a magnitude spectrum has deep nulls or notches we propose to use a deterministic arma approach which minimizes the true nonlinear criterion iteratively and attains significantly improved ir fit over prony s 1795 method using fewer arma model parameters for a given time sequence of an analyzed circuit the issues of model order selection and choice of decimation factor are also addressed systematically the improved performance of the proposed algorithm is demonstrated with transient simulation and signal analysis of microstrip structures which manifest deep nulls in the frequency domain

correlate measurements at different test sites a new method for systematic correlation of measurements in semi anechoic and anechoic chambers is presented a signal measured in a semi anechoic chamber is first processed using the matrix pencil method which is applied sequentially on small frequency intervals on each interval the measured signal is decomposed into its propagating wave components the component corresponding to the wave reflected from the ground is identified and removed to fully retrieve the signal measured in an anechoic chamber three examples using log periodic and vivaldi antennas in different anechoic and semi anechoic chambers for varying frequency ranges illustrate the method the proposed decomposition algorithm can be utilized to characterize measurement test site imperfections

decomposition of one dimensional waveform using iterative gaussian diffusive filtering methods the gaussian smoothing method is shown to have a wide transition zone around the cutoff frequency selected to filter a given dataset we proposed two iterative gaussian smoothing methods to tighten the transition zone one being approximately diffusive and the other being strictly diffusive the first version smoothes repeatedly the remaining high frequency parts and the second version requires an additional step to further smooth the resulting smoothed response in each of the smoothing operation based on the choice of the criterion for accuracy the smoothing factor and the number of iterations are derived for an infinite data length in both methods by contrast for a finite length data string results of the interior points sufficiently away from the two endpoints obtained by both methods can be shown to exhibit an approximate diffusive property the upper bound of the distance affected by the error propagation inward due to the lack of data beyond the two ends is numerically estimated numerical experiments also show that results of employing the iterative gaussian smoothing method are almost the same as those obtained by the strict diffusive version except that the error propagation distance induced by the latter is slightly deeper than that of the former the proposed method has been successfully applied to decompose the wave formation of a number of test cases including two sets of real experimental data

interior green s function solution for a thick and finite dielectric slab an interior green s function solution is presented for a two dimensional thick and finite dielectric slab in the present development the source and the field points are assumed to be inside the dielectric slab the result is composed of two parts the first part which has a discrete spectrum of eigenfunctions includes the surface wave multiple interactions and is obtained by using the generalized scattering matrix and method of moments the second part which is a closed form integral is obtained for a separable dielectric slab that is closely related to the finite slab the closed form integral is evaluated numerically and added to the surface wave solution the solution accounts for the mode conversions at the end caps which occur when surface waves are reflected and diffracted test cases show very good agreement with a finite element solver even when the source is near the end caps

analytical expressions for spatial domain green s functions in layered media accurate and efficient formulas for computing spatial domain green s functions are presented in this paper to apply the formulas we only require a set of sample points of the spectral domain green s function sdgf on an integration path avoiding its singularities and an infinite domain tail path since the sampling is carried out for the integrand excluding the bessel function the number of sample points required is much smaller than the numerical integration method this aspect of the proposed method proves to be very advantageous for evaluating closed form green s functions at large source observer distances it is shown that the proposed formulas provide accurate results for both the near and far field regions as well as a wide range of material parameters such as lossless lossy left handed materials as well as multilayered substrates

pencil back projection method for sar imaging we present a high resolution method for spotlight mode sar imaging that utilizes parametric modeling of projected target reflectivity density function and tomographic reconstruction the method requires no polar to cartesian interpolation in spectral domain utilization of forward backward total least squares bandpass matrix pencil method allows super resolution to be achieved in range for a single imaging angle hence the quality of the image reconstructed by convolution back projection is also improved it is shown that the method is very resistant to noise and can generate images down to very low snr values direct formulation in terms of physical quantities such as electric field and current density is another contribution of this paper

time domain integral equation solver for planar circuits over layered media using finite difference generated green s functions a simple highly accurate and efficient 2d finite difference technique for computing the direct convolution of time domain green s functions tdgfs of layered media with temporal interpolators is presented the proposed tdgfs are incorporated into a recently developed marching on in time mot based time domain integral equation tdie solver based on noncausal high order b spline temporal interpolators without requiring the prediction of future unknowns numerical results demonstrating the applicability of the technique to the analysis of various microwave structures are presented

efficient computation of the off diagonal elements of the vector potential multilayered periodic dyadic green s function the authors focus on the efficient computation of the slowly convergent infinite series that lead to the off diagonal elements of the vector potential multilayered periodic dyadic green s function two different approaches based on kummer s transformation are applied to the evaluation of these series the well known approach that makes use of the generalized pencil of functions gpof and ewald s method is the fastest approach but it does not provide accurate results when the distance between the field point and any of the source points is close to zero to avoid this problem we present a novel approach based on the gpof and the spectral kummer poisson s method with higher order asymptotic extraction this latter approach is slightly slower than the former one but it is accurate in the whole range of distances between the field point and the sources

boundary monomers in the dimer model the correlation functions of an arbitrary number of boundary monomers in the system of close packed dimers on the square lattice are computed exactly in the scaling limit the equivalence of the 2n point correlation functions with those of a complex free fermion is proved thereby reinforcing the description of the monomer dimer model by a conformal free field theory with central charge c 1 comment 15 pages 2 figures

spectral dyadic green s function formulation for planar integrated structures the problem of the complete determination of the dyadic spectral green s function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field the reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral green s function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source furthermore an equivalent circuit representation of the structure allowing a noteworthy simplification in the determination of the total power has been obtained these equivalent circuits and the derived spectral green s function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading such as matched or unmatched loads parasitic and shorting pins

application of the matrix pencil method for estimating the sem singularity expansion method poles of source free transient responses from multiple look directions the matrix pencil method has been utilized for estimating the natural resonances from different transient responses recorded along multiple look directions as a function of time after the incident field has passed the structure the novelty of this article is that a single estimate for all the poles are done utilizing multiple transient waveforms emanating from the structure along multiple look directions the sem poles are independent of the angle at which the transient response is recorded the only difference between the various waveforms are that the residues at the various poles are of different magnitudes some of the residues may even be zero for some of the poles indicating that the contribution from certain sem poles may not be significant along that look direction here all the waveforms are utilized providing a single estimate for the poles without performing an arithmetic mean of the various waveforms

further improvement for fast computation of mixed potential green s functions for cylindrically stratified media a method of fast computation of the mixed potential green s functions mpgfs in spatial domain for cylindrically stratified media has been developed based on the convergence behavior of the mpgfs in spectral domain the discrete complex image method dcim and the extrapolation technique are employed to perform the inverse fourier transform which is different from that of planarly stratified media in order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity the green s functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process for the integral along the deformed sommerfeld integral path with respect to k sub z dcim is used to speed up the computation after the quasistatic components are completely subtracted from the spectral domain green s functions the inverse transform of the remaining parts has an approximated analytical form the proposed method can be used to accurately and efficiently calculate the spatial domain mpgfs which are useful for characterizing conformal patch structures mounted on cylindrically stratified media

green s functions for probe fed arbitrary shaped cylindrical microstrip antennas the efficiency of a method of moments procedure for microstrip antennas is strongly dependent on the convergence of the inverse fourier transformation ift from the spectral to the spatial domain this is especially true when considering cylindrical microstrip antennas cmas in the cylindrical case the calculation of the two dimensional green s functions stays inherently time consuming in the planar case green s function can be reduced to a one dimensional function the problem however becomes a real bottle neck when probe feeding of a cma is considered as the traditional ift used to calculate the excitation in the spatial domain results in a huge ift time in this paper this problem is explicitly treated the asymptotical behavior of the probe related spectral green s functions gfs is rigorously derived subtracted and the corresponding reaction integrals are inverse fourier transformed without the occurrence of any cylindrical functions this results in a much improved calculation efficiency for this type of feeding evident for both thin and thick substrates numerical results for cmas with complex shaped patches are presented applicable to both smaller and larger bandwidths several structures are fabricated and measurements are in good agreement with simulations

locating all the modes of green s function for a three layered medium based on the path tracking algorithm through a mathematical analysis on the relationship between the characteristic equations of the microstrip geometry and a configuration with a three layered medium a method based on the path tracking algorithm is proposed for precisely locating all the modes for a three layered medium with moderate thickness including surface wave modes leaky wave modes and improper real modes with this method the difficulty caused by branch points and cuts in the contour integral method could be avoided this method can be applied not only in the discrete complex image method dcim but also in the steepest descent path sdp method the proposed method can be extended to more complicated configurations