electromagnetic scattering from a buried cylinder in layered media with rough interfaces a solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method ebcm and scattering matrix technique is developed the reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using ebcm and recursive t matrix algorithm respectively the cylinder rough surface interactions are taken into account by applying the generalized scattering matrix technique the scattering matrix technique is used to cascade reflection and transmission matrices from individual systems i e rough surfaces or cylinders in order to obtain the scattering pattern from the overall system bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting floquet modes of the overall system in numerical simulations the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface subsequently the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder

fractals in surface growth with power law noise the authors present a microscopic description of interface growth with power law noise distribution in the form p eta eta 1 approximately 1 mu which exhibits non universal roughening for the mu d 1 case in d 1 dimensions the existence of a fractal pattern in the bulk of the aggregate is explained leading trivially to the proof of the identity alpha z 2 for the roughening and the dynamical scaling exponents alpha and z respectively investigations on the distribution of step sizes of the discretized interface and the saturated growth speed further support the arguments

scaling for the critical percolation backbone we study the backbone connecting two given sites of a two dimensional lattice separated by an arbitrary distance r in a system of size l at the percolation threshold we find a scaling form for the average backbone mass approximately l db g r l where g can be well approximated by a power law for 0 approximately l db psi r psi for the entire range 0 r l we also propose a scaling form for the probability distribution p m b of backbone mass for a given r for r approximately l p mb is peaked around l db whereas for r l p m b decreases as a power law m taub b with taub approximately 1 20 0 03 the exponents psi and taub satisfy the relation psi db taub 1 and psi is the codimension of the backbone psi d db

an investigation of the small slope approximation for scattering from rough surfaces part i theory the small slope approximation ssa of voronovich sov phys jetp 62 65 70 1985 is a promising method for application to scattering from many natural surfaces the theory gives a systematic expansion that can be interpreted as a series in generalized surface slope the ssa series for the t matrix satisfies the appropriate reciprocity condition at each order and reduces to the standard perturbation series for small surface roughness in this paper we examine in detail the derivation of the ssa for surfaces subject to the dirichlet zero field boundary condition a number of points are discussed including the requirements for determining the series terms in addition questions have been raised recently about the ssa it has been argued that 1 an assumption in the derivation contradicts the exact formulation of the problem and 2 there is an arbitrariness in determining the series terms these two points are refuted and the assumptions needed to determine the series terms unambiguously are clarified the meaning of slope orders in the ssa series expansion are examined and the concept of generalized slope is discussed a future companion paper part ii numerical studies will present an investigation of the accuracy of the ssa through comparison with exact results

two dimensional scattering from an inhomogeneous dielectric cylinder embedded in a stratified medium case of tm polarization two dimensional scattering of a tm polarized electromagnetic wave from a transversely inhomogeneous isotropic body buried in a homogeneous layer of an arbitrarily stratified isotropic medium has been considered using the integral equation formulation over the cross section of the body and the moment method the arising system of linear algebraic equations is solved with the aid of the conjugate gradient method and the one dimensional fast fourier transform illustrative numerical results are presented for both an inclusion in a half space and in a layer on a homogeneous substrate

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

fast multipole method for scattering from an arbitrary pec target above or buried in a lossy half space the fast multipole method fmm was originally developed for perfect electric conductors pecs in free space through exploitation of the spectral properties of the free space green s function in the work reported here the fmm is modified for scattering from an arbitrary three dimensional 3 d pec target above or buried in a lossy half space the near terms in the fmm are handled via the original method of moments mom analysis wherein the half space green s function is evaluated efficiently and rigorously through application of the method of complex images the far fmm interactions which employ a clustering of expansion and testing functions utilize an approximation to the green s function dyadic via real image sources and far field reflection dyadics the half space fmm algorithm is validated through comparison with results computed via a rigorous mom analysis further a detailed comparison is performed on the memory and computational requirements of the mom and fmm algorithms for a target in the vicinity of a half space interface

hybrid cluster identification i present a hybrid method for the labelling of clusters in two dimensional lattices which combines the recursive approach with iterative scanning to reduce the stack size required by the pure recursive technique while keeping its benefits single pass and straightforward cluster characterization and percolation detection parallel to the labelling while the capacity to hold the entire lattice in memory is usually regarded as the major constraint for the applicability of the recursive technique the required stack size is the real limiting factor resorting to recursion only for the transverse direction greatly reduces the recursion depth and therefore the required stack it also enhances the overall performance of the recursive technique as is shown by results on a set of uniform random binary lattices and on a set of samples of the ising model i also show how this technique may replace the recursive technique in wolff s cluster algorithm decreasing the risk of stack overflow and increasing its speed and the hoshen kopelman algorithm in the swendsen wang cluster algorithm allowing effortless characterization during generation of the samples and increasing its speed

spreading and shortest paths in systems with sparse long range connections spreading according to simple rules e g of fire or diseases and shortest path distances are studied on d dimensional systems with a small density p per site of long range connections small world lattices the volume v t covered by the spreading quantity on an infinite system is exactly calculated in all dimensions as a function of time t from this the average shortest path distance l r can be calculated as a function of euclidean distance r it is found that l r approximately r for r r c the characteristic length r c which governs the behavior of shortest path lengths diverges logarithmically with l for all p 0

a fast volume integral equation solver for electromagnetic scattering from large inhomogeneous objects in planarly layered media a newly developed iterative method the stabilized biconjugate gradient fast fourier transform bcgs fft method is applied to simulate electromagnetic scattering from large inhomogeneous objects embedded in a planarly layered medium in this fast solver the weak form formulation is applied to obtain a less singular discretization of the volume electric field integral equation several techniques are utilized to speed up the dyadic green s function evaluation to accelerate the operation of the dyadic green s function on an induced current i e the green s operation the green s function is split into convolutional and correlational components so that fft can be applied the cpu time and memory cost of this bcgs fft method is o nlogn and o n respectively where n is the number of unknowns significantly more efficient than the method of moments mom as a result this method is capable of solving large scale electromagnetic scattering problems in a planarly layered background a large scale scattering problem in a layered medium with more than three million unknowns has been solved on a sun ultra 60 workstation with 1 2 gbytes memory

fast algorithm for electromagnetic scattering by buried conducting plates of large size this letter presents a fast algorithm for electromagnetic scattering by buried conducting plates of large size and arbitrary shape using the conjugate gradient cg method combined with the fast fourier transform fft due to the use of fft in handling the cyclic convolutions related to toeplitz matrices the sommerfeld integrals evaluation for the buried scattering problem which is usually time consuming has been reduced to a minimum the memory required for this algorithm is of the order n the number of unknowns and the computational complexity is of order n sub iter nlogn n sub iter is the iteration number n sub iter spl lt n for large problems

guaranteed convergence method of analysis of the scattering by an arbitrarily oriented zero thickness pec disk buried in a lossy half space in this paper a guaranteed convergence method for the accurate and efficient analysis of the electromagnetic scattering by an arbitrarily oriented zero thickness perfectly electrically conducting pec disk buried in a lossy half space is presented an electric field integral equation efie in the vector hankel transform domain is obtained by expanding the unknown surface current density in cylindrical harmonics a convergence of exponential type is achieved by means of galerkin s method with expansion functions reconstructing the expected physical behavior of the bm n th harmonic at the center and the edge of the disk the obtained coefficient matrix can be quickly computed since its elements can be reviewed as the sum of single integrals efficiently evaluable by means of an analytical acceleration technique and double integrals of exponentially decaying functions

on the solutions of a class of dual integral equations occurring in diffraction problems it is shown that there exists a category of two dimensional diffraction problems which can be put into a standard form of dual integral equations these diffraction problems include diffraction of electromagnetic waves by a finite strip a finite slit the diffraction of scalar or vector elastic waves by a rigid strip or crack etc a general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions the sufficient conditions for a given dual integral equations to be solvable in this manner are also determined hence the method forms a complement to the weiner hopf method to illustrate the method solutions are obtained for a bench mark problem the diffraction of light by a finite perfectly conducting strip or equivalently the diffraction of sh waves by a crack comparison with results obtained by others for low intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies both the near field and the far field are obtained the latter is shown to correspond to the fraunhoffer diffraction pattern for high frequency it is also shown that for the equivalent crack problem the stress intensity factor sif fluctuates rapidly with changes in the angle of incidence for high frequencies thus making the sif especially sensitive to angle of incidence at high frequencies

a new high efficient analysis of the scattering by a perfectly conducting rectangular plate the analysis of the scattering by a perfectly conducting rectangular plate by means of galerkin s method in the spectral domain with products of chebyshev polynomials of first and second kind multiplied by their orthogonal weights as basis functions is fast convergent even for scatterers size of some wavelengths but leads to the numerical evaluation of infinite double integrals of oscillating and slowly decaying functions the aim of this paper is the introduction of a new analytical technique that allows to write such integrals as combinations of very quickly converging integrals

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

a numerical method for electromagnetic scattering by 3 d dielectric objects buried under 2 d locally rough surfaces in this work a numerical method is developed to solve a forward scattering problem of three dimensional 3 d objects buried into two half space media with two dimensional 2 d locally rough interface the proposed method exploits the electric field integral equation efie formulation of the scattered field which involves the dyadic green s function of the background medium since the required green s function has no analytical expression in general buried object approach boa is applied to calculate it numerically method of moments mom is then used to solve the efie the presented method is numerically validated by comparing it with finite difference time domain fdtd method furthermore an elaborative numerical analysis of the proposed method is presented to show its feasibility for various roughness profiles and buried objects

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

accurate analysis of two dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique a very efficient and accurate method to characterize two dimensional 2 d electromagnetic scattering from multilayered periodic arrays of parallel circular cylinders is presented using the lattice sums technique the aggregate t matrix algorithm and the generalized reflection and transmission matrices for a layered system the method is quite general and applies to various configurations of 2 d periodic arrays the unit cell of the array can contain two or more cylinders which may be dielectric conductor gyrotropic medium or their mixture with different sizes the periodic spacing of cylinders along each array plane should be the same over all layers but otherwise the cylinders in different layers may be different in material properties and dimensions the numerical examples validate the usefulness and accuracy of the proposed method

tm scattering by perfectly conducting polygonal cross section cylinders a new surface current density expansion retaining up to the second order edge behavior in the analysis of scattering by perfectly conducting cylinders with polygonal cross section by means of surface integral operator formulations fast convergence can be achieved by expanding the surface current density on each side with basis functions factorizing the correct behavior of the fields on the wedges usually the factorized edge behavior is chosen to be coincident with the first order behavior prescribed by meixner s theory however it could not be the correct one and consequently the convergence of the method becomes increasingly slow as the theoretical behavior differs from the real one this phenomenon is particularly notable when one or more of the predicted singularities unexpectedly disappear to overcome this problem in this work the analysis of tm scattering is made by introducing a new expansion devised so that only the first two terms are responsible for the reconstruction of the singularities while the remaining part of the expansion factorizes the second order edge behavior actually the proposed expansion outperforms the one introduced by the authors in a previous work factorizing the first order edge behavior even when this is the correct one

nystrom type method in three dimensional electromagnetic diffraction by a finite pec rotationally symmetric surface time harmonic electromagnetic wave diffraction by a perfectly electrically conducting pec finite rotationally symmetric surface located in free space is investigated the problem is split to independent azimuth orders and reduced to the sets of coupled hypersingular and singular integral equations ies for the surface current components these ies are discretized by the nystrom type method of discrete singularities using the interpolation type quadrature formulas from the solutions of corresponding matrix equations the near and the far field patterns are obtained the presented method has guaranteed convergence for arbitrary not axially symmetric primary field

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

current induced on a conducting strip which resides on the planar interface between two semi infinite half spaces an analysis is described for determining the current induced by a known excitation on a conducting strip which resides on the planar interface between two semi infinite homogeneous half spaces of different electromagnetic properties the perfectly conducting flat strip is of infinite extent and the excitation is transverse magnetic to the strip axis an integral equation for the induced current is formulated and it is shown that its kernel which is in general a sommerfeld type integral can be expressed in closed form when the permeabilities of the two media are the same under this practical condition the integral equation is solved numerically and data are presented for cases of interest for the electrically narrow strip the integral equation is approximated and this approximate equation is solved analytically

scattering by polygonal cross section dielectric cylinders at oblique incidence we analyze the scattering by polygonal cross section lossless dielectric cylinders illuminated by an obliquely incident plane wave the problem is formulated in terms of a system of surface integral equations opportunely devised so as to be valid for objects with edges and incident angles including the total reflection limit angle by means of galerkin s method in the spectral domain with analytically fourier transformable expansion functions factorizing the correct edge behaviors and continuity conditions of the unknowns convergence of exponential type is achieved and the coefficients of the scattering matrix are reduced to single integrals that can be efficiently evaluated numerical results for both near field and far field parameters are presented showing the quick convergence of the method even when applied to composite cylindrical objects

full wave analysis and optimization of a tara like shield assisted paraboloidal reflector antenna using a nystrom type method using the recently developed method based on the rigorous theory of singular and hypersingular integral equations ies and nystrom type discretization a paraboloidal reflector assisted with a conical shield is investigated to decrease the computation time we propose a new method of calculation of the modal green s functions in the quasi optical range the far and near fields of the studied reflector are analyzed in the transmission and reception cases and reveal fine features that escape asymptotic analysis elementary numerical optimization of the shield assisted paraboloidal antenna is performed

conductivity exponent and backbone dimension in 2 d percolation abstract we present high statistics simulations for 2 d percolation clusters in the bus bar geometry at the critical point for site and for bond percolation we measured their backbone sizes and electrical conductivities for all sets of measurements we find large corrections to scaling most of which do not seem to be described by single powers using single power terms for the corrections to scaling of the backbone masses we would obtain fractal dimensions which are different for site and bond percolation while the correct result is d b 1 6432 0 0008 for both for the conductivity the corrections to scaling are strongly non monotonic for bond percolation the exponent t t is measured as 0 9826 0 0008 in disagreement with the alexander orbach and other conjectures

backbone and elastic backbone of percolation clusters obtained by the new method of burning we introduce a method of obtaining information about percolation clusters in which the clusters are burned in different ways this method yields the backbone and the elastic backbone their number of loops shortest path and other quantities it works in any dimension and can be applied also to other clusters we obtain accurate estimates for the backbone exponents in two and three dimensions

current induced on a conducting cylinder located near the planar interface between two semi infinite half spaces an analysis is described for determining the current induced by a known excitation on a conducting cylinder located near the planar interface between two semi infinite homogeneous half spaces of different electromagnetic properties the perfectly conducting cylinder of general cross section is of infinite extent and the excitation is transverse magnetic to the cylinder axis an integral equations for the induced current is derived and a numerical method for solving it is developed the kernel of the integral equation contains a term corresponding to the usual open space green s function plus a term proportional to a sommerfeld type integral in two dimensions various forms of the sommerfeld type integral are given and the choices of form amenable to efficient evaluation are discussed for a flat strip a circular cylinder and a rectangular cylinder data are presented and discussed for selected parameters data are presented for cylinders above and below the interface as well as for a cylinder resting on the interface

precise calculation of the dynamical exponent of two dimensional percolation we report numerical data obtained on the special purpose computer percola for the exponent tilde t of the electrical conductivity of 2d percolation the extrapolation yields tilde t 0 9745 pm 0 0015 and a correction to the scaling exponent 1 2 0 2

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas abstract this work presents accurate numerical method and computational results in the modeling of the axisymmetric radiation of resistive and thin dielectric circular disk on substrate antennas to simulate resistive and thin dielectric disk features we use two side generalized boundary conditions gbc the analysis is based on the singular integral equations ies and the method of analytical regularization mar exploiting a galerkin method gm with judicious basis functions which convert ies into the fredholm second kind infinite matrix equations unlike previously known numerical techniques this guarantees convergence and enables us to compute the solution with controlled accuracy even in sharp resonances numerical results demonstrate the effect of disk losses and transparency on the fundamental radiation phenomena and help improve antenna characteristics such as radiation efficiency

diffraction of electromagnetic plane wave by a rectangular plate and a rectangular hole in the conducting plate the problems of diffraction of an electromagnetic plane wave by a perfectly conducting rectangular plate and its complementary problem diffraction by a rectangular hole in an infinite conducting plate are rigorously solved using the method of the kobayashi 1931 potential the mathematical formulation involves dual integral equations derived from the potential integrals and the boundary condition on the plane where a plate or hole is located the weighting functions in the potential integrals are determined by applying the properties of the weber schafheitlin s integrals and the solution is obtained in the form of a matrix equation illustrative computations are given for the far diffracted field pattern and the current densities induced on the plate the results of the patterns are compared with the results obtained from physical optics po and the physical theory of diffraction ptd the agreement is fairly good particularly with the ptd solutions

a direct electrifying algorithm for backbone identification this paper proposes a new algorithm for identifying backbones in the application of percolation theory this algorithm is based on the current carrying definition of backbone and is carried out on the predetermined spanning cluster it is fairly easy to implement and further parallelize the efficiency is enhanced by the fact that the conductivity of a percolating system can be obtained in the same processing of backbone identification the critical exponents of backbone mass red bonds sites and conductivity obtained by this algorithm are in very good agreement with the existing results

electromagnetic scattering from perfectly conducting rough surfaces a new full wave method a method that does not make use of the telegraphist s equations and takes into account the two dimensional roughness of the surface from the start is developed it is shown that the scattering coefficients obtained agree with those given in earlier work by e bahar 1973 1987 the method is based on reducing the three dimensional scattering problem to a two dimensional problem by expanding each rectangular component of maxwell s equations in terms of local basis functions along the perpendicular direction to the mean surface the transformed two dimensional field equations are solved using fourier transforms the full wave solutions are also compared with the first order perturbation solutions the kirchhoff type solutions and integral equation results

a comparison of forward boundary integral and parabolic wave equation propagation models the parabolic wave equation and its variants have provided the theoretical framework for most practical forward propagation models split step integration generates an easily obtained robust solution for most applications irregular boundaries can be incorporated by using a conformal mapping technique introduced by beilis and tappert 1979 and refined by donohue and kuttler see ibid vol 48 p 260 77 2000 in an earlier paper we demonstrated an alternative method that incorporates a numerical solution to the forward boundary integral equation within each split step cycle this paper compares predictions of forward propagation obtained by these two distinctly different methods the results confirm that the pwe based method is very accurate for smoothly varying surfaces and that it captures the primary forward structure even in the presence of unresolved surface detail the moderate loss of fidelity is often an acceptable trade for increased computational efficiency there are situations however where the details of the surface structure are important furthermore the induced surface currents are unique to the forward boundary integral method we illustrate their use by calculating the bistatic scatter that would he measured from an isolated surface segment we show that the scattered field measured in this way can be normalized to form a bistatic scatter function only when the illuminating beam is tilted slightly toward the surface we interpret this disparity as a breakdown in concept that underlies a local scattering function

scattering by a circular cylinder buried under a slightly rough surface the cylindrical wave approach an analytical numerical technique for the scattering problem of a plane wave by a cylinder buried under a rough surface based on the cylindrical wave approach is presented the rough deviations on the interface are dealt with by means of the small perturbation method reflection and transmission coefficients are evaluated in a first order approximation and fields are the sum of a zeroth order solution relevant to flat surface and first order perturbation fields associated to the surface roughnesses numerical results are obtained through an exact evaluation of the spectral integrals giving results both in near and far field regions for the case of an interface with sinusoidal profile the approach is validated through comparisons with the literature and results showing the effect of geometrical and physical parameters on the scattered field are reported

a note on the jacobian conjecture abstract in this note we show that if the druzkowski mappings f x x ax 3 i e f x x 1 a 11 x 1 a 1 n x n 3 x n a n 1 x 1 a nn x n 3 satisfies trj ax 3 0 then rank a 1 2 n where is the number of diagonal elements of a which are equal to zero furthermore we show the jacobian conjecture is true for the druzkowski mappings in dimension 9 in the case i 1 n a ii 0

some remarks on the jacobian conjecture and druzkowski mappings abstract in this paper we first show that the jacobian conjecture is true for non homogeneous power linear mappings under some conditions secondly we prove an equivalent statement about the jacobian conjecture in dimension r 1 and give some partial results for r 2 finally for a homogeneous power linear keller map f x h of degree d 2 we give the inverse polynomial map under the condition that j h 3 0 we shall show that deg f 1 d k if k 2 and j h k 1 0 but also give an example with d 2 and j h 4 0 such that deg f 1 d 3

generation of percolation cluster perimeters by a random walk a type of self avoiding random walk whish generates the perimeter of two dimensional lattice percolation clusters is given the algorithm has been simulated on a computer yielding the mean perimeter length as a function of occupation probability

spreading and backbone dimensions of 2d percolation the author presents results of high statistics simulations of the spreading of 2d percolation and of backbones of 2d percolation clusters while the algorithm employed for the spreading is more or less standard for identifying backbones the author uses a new and very efficient recursive algorithm the author uses new critical exponents to test previous conjectures

a new algorithm to extract the backbone in a random resistor network the authors present an efficient algorithm to determine the backbone the current carrying part of a lattice in the random resistor network problem it reduces mainly to the determination of the cluster structure on two lattices its efficiency is due to the use of the dual lattice and therefore is specific to the two dimensional case

monte carlo simulation of electromagnetic scattering from two dimensional random rough surfaces the fast multipole method fast fourier transform fmm fft method is developed to compute the scattering of an electromagnetic wave from a two dimensional 2 d rough surface the resulting algorithm computes a matrix vector multiply in o n log n operations this algorithm is shown to be more efficient than another o n log n algorithm the multilevel fast multipole algorithm mlfma for surfaces of small height for surfaces with larger roughness the mlfma is found to be more efficient using the mlfma monte carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2 d random rough surfaces using a workstation for the rougher surface backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient for the smoother surface the monte carlo results compare well with the results of the approximate kirchhoff theory

exponentially converging nystro spl uml m s methods for systems of singular integral equations with applications to open closed strip or slot loaded 2 d structures this paper concerns the fast highly accurate and exponentially convergent solution of three sets of integral equations pertaining to two dimensional generalized microstrip or microslot structures the analysis relies on nystroumlm s method with due regard to all singular integrals and slowly converging series that appear in the kernels the sophisticated treatment and efficient computation of such series and integrals is of paramount importance entailing the use of advanced techniques as a result of our specialized treatment the discretization procedures developed herein a fully account for both the singular nature of the kernels and the singularities of the solution at the edges b obviate the need for taking inner products with testing functions c appear to converge exponentially versus matrix size and d enable expressing all matrix elements via single finite sums detailed numerical examples and case studies illustrate the simplicity flexibility and remarkable efficiency of the algorithms

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

a transformation media based approach for efficient monte carlo analysis of scattering from rough surfaces with objects this paper presents a computational model that utilizes transformation based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two dimensional electromagnetic scattering from objects on or above one dimensional rough sea surfaces monte carlo simulation of the rough surface scattering problem by means of differential equation based finite methods such as finite element or finite difference methods usually places a heavy burden on computational resources because at each realization of the monte carlo technique a mesh must be generated anew for each surface realization the main purpose of the proposed approach in this paper is to create a single mesh without repeating mesh generation at each step by introducing a transformation medium above the rough surface in the computational domain of the finite methods material parameters of the medium are obtained by the coordinate transformation technique which is based on the form invariance property of maxwell s equations at each realization only the material parameters are modified with respect to the geometry of surface without changing the mesh in this manner a great reduction in cpu time is achieved the proposed technique is analyzed and validated via various finite element simulations

te scattering by conducting strips right on the planar interface of a three layered medium combining the fourier transform with powerful singular integral equation methods the authors investigate the scattering properties of a variety of two dimensional three layered planar structures loaded by a strip or a couple of coplanar strips right on an interface the primary excitation is the lowest order incident tm to strip axis surface wave mode or an incident e polarized plane wave in the practical case where the entire space is magnetically homogeneous the kernel of the integral equations is most conveniently decomposed into a singular closed form term added to an exponentially convergent inverse fourier integral an efficient accurate and stable numerical code is obtained and used to determine the strip induced current densities as well as any quantity of practical interest plotted results reveal that by a proper choice of certain geometrical parameters the structures may become very efficient radiators which can be designed to exhibit either very wideband and high directivity or considerable frequency scanning