a highly accurate fgg fg fft for the combined field integral equation in this paper a novel realization of the integral equation in combination with the fast fourier transform for the cfie is established by fitting both the green s function and its gradient onto the nodes of a uniform cartesian grid the new method has been compared with several existing popular fft based methods including the aim the ie fft and the p fft the accuracy of the proposed method is significantly higher than other fft based methods and the method is not sensitive to both the grid spacing and the expansion order the outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions therefore when the higher order basis functions would be adopted in the method of moments only one fitting procedure for the green s function and its gradient on a basis function support is needed to meet all of basis functions defined on this support some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method

an efficient hybrid mlfma fft solver for the volume integral equation in case of sparse 3d inhomogeneous dielectric scatterers electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a method of moments discretization to the volume integral equation for electrically large problems the iterative solution of the resulting linear system is expensive both computationally and in memory use in this paper a hybrid mlfma fft method is presented which combines the fast fourier transform fft method and the high frequency multilevel fast multipole algorithm mlfma in order to reduce the cost of the matrix vector multiplications needed in the iterative solver the method represents the scatterers within a set of possibly disjoint identical cubic subdomains which are meshed using a uniform cubic grid this specific mesh allows for the application of ffts to calculate the near interactions in the mlfma and reduces the memory cost considerably since the aggregation and disaggregation matrices of the mlfma can be reused additional improvements to the general mlfma framework such as an extention of the fft interpolation scheme of sarvas et al from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics are proposed and the choice of the subdomain size is discussed the hybrid method performs better in terms of speed and memory use on large sparse configurations than both the fft method and the hf mlfma separately and it has lower memory requirements on general large problems this is illustrated on a number of representative numerical test cases

electromagnetic analysis of large scale periodic arrays using a two level cbfs method accelerated with fmm fft to realize efficient analysis of large scale planar periodic arrays a two level characteristic basis functions method accelerated with fast multipole method fast fourier transform fmm fft is developed in this paper the characteristic basis functions cbfs for each element are constructed in a two level framework in which the cbfs construction based on plane wave derivation for single element at child level and the cbfs construction based on local interaction between array elements at father level are combined the number of unknowns is reduced significantly by the two level cbfs further fmm fft is applied to expedite the computation of interaction between elements numerical results of large scale planar periodic arrays are given to demonstrate the validity and efficiency of the present method

correction to the application of the conjugate gradient method for the solution of electromagnetic scattering from arbitrarily oriented wire antennas the method of conjugate gradients is applied to the analysis of radiation from thin wire antennas with this iterative technique it is possible to solve electrically large arbitrarily oriented wire structures without storing any matrices as is conventionally done in the method of moments the basic difference between the proposed method and galerkin s method for the same expansion functions is that for the iterative technique we are solving a least squares problem hence as the order of the approximation is increased the proposed technique guarantees a monotonic decrease of the least squared error parallel ai y parallel 2 whereas galerkin s method does not even though the method converges for any initial guess a good one may significantly reduce the time of computation also explicit error formulas are given for the rate of convergence of this method hence any problem can be solved to a prespecified degree of accuracy it is shown that the method has the advantage of a direct solution as the final solution is obtained in a finite number of steps the method is also suitable for solving singular operator equations in which case the method monotonically converges to the least squares solution with minimum norm numerical results are presented for the thin wire antennas and are compared with the solution obtained by the method of moments

cohomology with twisted one dimensional coefficients for congruence subgroups of sl4 z and galois representations abstract we extend the computations in 2 3 4 to find the cohomology in degree five of a congruence subgroup of sl 4 z with coefficients in a field twisted by a nebentype character along with the action of the hecke algebra on the cohomology this is the top cuspidal degree for each hecke eigenclass we find we produce the unique galois representation that appears to be attached to it the computations require serious modifications to our previous algorithms nontrivial coefficients add a layer of complication to our data structures new possibilities must be taken into account in the galois finder the code that finds the galois representations we have improved the galois finder to report when the attached galois representation is uniquely determined by our data

an iterative method for solving electrostatic problems the method of steepest descent is applied to the solution of electrostatic problems the relation between this method and the rayleigh ritz galerkin s and the method of least squares is outlined also explicit error formulas are given for the rate of convergence for this method it is shown that this method is also suitable for solving singular operator equations in that case this method monotonically converges to the solution with minimum norm finally it is shown that the technique yields as a by product the smallest eigenvalue of the operator in the finite dimensional space in which the problem is solved numerical results are presented only for the electrostatic case to illustrate the validity of this procedure which show excellent agreement with other available data

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

symbolic dynamics of fully developed chaos ii random and order 1 markovian two symbol sequences abstract the relations between three different symbolic descriptions of fully developed chaos in iterated one hump maps on the interval are investigated in the case of short memory time

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

accurate analysis of large scale periodic structures using an efficient sub entire domain basis function method an efficient sub entire domain sed basis function method has been proposed to analyze large scale periodic structures with finite sizes accurately the sed basis function is defined on the support of each single cell of the periodic structure after introducing dummy cells with respect to an observation cell the real physics of sed basis function is captured accurately by solving a small size problem further analysis has shown that all kinds of sed basis functions used in the periodic structure can be obtained by solving a single small problem hence the original large scale problem involving n n sub 0 m unknowns is decomposed into two small size problems one of which contains 9m unknowns and the other of which contains only n sub 0 unknowns here n sub 0 is the total cell number in the periodic structure and m is the number of subdomain basis functions in each unit cell several examples are given to test the validity and efficiency of the proposed method numerical results from the new method have excellent agreements with those from the conventional method of moments however the cpu time has been greatly reduced

electromagnetic scattering by finite periodic arrays using the characteristic basis function and adaptive integral methods we introduce a novel technique that combines the aim algorithm with the characteristic basis function method cbfm to solve the problem of electromagnetic scattering by large but finite periodic arrays an important advantage of using the cbfm for this problem is that we only need to analyze a single unit cell to construct the characteristic basis functions cbfs for the entire array the cbfs are generated by illuminating a single unit cell with a plane wave incident from different angles for both the and polarizations the initial set of cbfs generated in the manner described above are then downselected by applying a singular value decomposition svd procedure and retaining only the left singular vectors whose corresponding singular values fall above a threshold next in the conventional cbfm we derive a reduced matrix by applying the galerkin procedure and solve it directly if its size is manageable however when solving an array problem which precludes the direct solve option we can utilize the adaptive integral method aim algorithm detailed below not only to accelerate the solution but to reduce memory requirements as well numerical examples are included in this communication to demonstrate the accuracy and the numerical efficiency of the proposed technique

phase transitions in thermodynamics of a local lyapunov exponent for fully developed chaotic systems fluctuations in the divergence of nearby orbits are studied at a crisis point of chaos a statistical thermodynamic method for the description of the fluctuations is developed by using symbolic dynamics which can explicitly write a relation between a fluctuation and reference orbit the thermodynamics the free energy and entropy is exactly analyzed on a nonhyperbolic attractor of maps conjugate to the map u u a for 0 u a andu 1 u 1 a fora u 1 te free energy has discontinuities in its slope the entropy is directly calculated from the partition function then it becomes clear that the collision of a chaotic attractor with a particular fixed point yields a singular local structure in the distribution of fluctuations the existence of first order phase transitions depends on the asymmetry of a map it is shown that each of the coexisting states at the phase transition points is realized with the same probability in the thermodynamic limit

comparison of semi simplifications of galois representations abstract let be the absolute galois group of a global field let 1 and 2 be two p adic finite dimensional representations of then there exists a finite number of primes q such that if the characteristic polynomials of 1 frob q and 2 frob q are equal then 1 and 2 have isomorphic semi simplifications and so the same l functions we give a method to compute a sufficient list of primes based on the ramification and the dimension of the representations we use then the result to prove a conjecture by b van geemen and j top

investigation of scattering properties of large scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods this paper presents a hybrid approach for efficient analysis of electromagnetic em scattering from large scale aperiodic structures e g aperiodic penrose and danzer tilings which integrates the characteristic basis function method cbfm and the adaptive integral method aim by performing a domain decomposition a series of characteristic basis functions cbfs that are defined on a macro block and comprised of a relatively large number of sub domain basis functions facilitate a substantial reduction in the method of moments mom matrix size enabling the use of a direct solver for large problems the aim is applied to accelerate the calculation of cbfm reduced mom matrices significantly decreasing the cpu time and memory required for solving large scale problems as the size of one block becomes electrically large the original cbfm combined with the aim is employed to generate the initial cbfs by solving a large problem with multiple excitations which results in efficiently constructing the final cbfs afforded by the singular value decomposition svd procedure this methodology produces a two level cbfm aim hybrid algorithm for efficiently characterizing large scale objects the numerical results presented demonstrate the accuracy and efficiency of the proposed hybrid algorithm then the developed solver is applied to investigate em scattering properties of large scale aperiodic tilings the numerical results show that penrose danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts

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

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

a devil s staircase into chaotic scattering abstract we discuss analytically the transition from a regular to a chaotic classical dynamics of a sample scattering model introduced earlier the transition arises as a homoclinic bifurcation of an atypical type in phase space as a discontinuity for the grammatical complexity and as an onset of a devil s staircase for the topological entropy

global bifurcations to strange attractors in a model for skew varicose instability in thermal convection abstract we present a global bifurcation study of a four dimensional system of differential equations proposed by f h busse and coworkers modeling instabilities of convection rolls in the rayleigh benard experiment the rayleigh and prandtl numbers are two natural parameters on which the system depends we focus on a detailed mathematical study combining numerical pathfollowing and bifurcation analysis of chaotic dynamics and transitions to chaotic dynamics numerical continuation makes clear how homoclinic and heteroclinic bifurcations organize the bifurcation diagram in the parameter plane combined with a theoretical bifurcation analysis this explains the development of patterns and the creation of chaotic spatio temporal dynamics in the model the organizing centers such as heteroclinic cycles with resonance conditions among eigenvalues and homoclinic loops with geometric degeneracies inclination flips are identified and their unfoldings are analyzed this ties the creation of strange attractors of various geometric structures to codimension two global bifurcations

analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation the adaptive integral method aim is employed to solve the volume integral equation vie for analyzing the radiation of the antenna with an arbitrarily shaped radome small dipoles are used as exciting sources modeling the radomes by tetrahedron cells the induced volume current is determined by the aim based on vie the application of aim significantly reduces cpu time and computer memory requirement hence the method presented in the paper can be applied to simulate electrically large sized radomes finally the radiation patterns of small dipole arrays in the presence of spherical and conical radomes are calculated

solution of arbitrarily dimensional matrix equation in computational electromagnetics by fast lifting wavelet like transform a new wavelet matrix transform wmt operated by lifting wavelet like transform lwlt is applied to the solution of matrix equations in computational electromagnetics the method can speedup the wmt without allocating auxiliary memory for transform matrices and can be implemented with the absence of the fast fourier transform furthermore to handle the matrix equation of arbitrarily dimension a new in space preprocessing technique based on lwlt is constructed to eliminate the limitation in matrix dimension complexity analysis and numerical simulation show the superiority of the proposed algorithm in saving cpu time numerical simulations for scattering analysis of differently shaped objects are considered to validate the effectiveness of the proposed method in particular due to its generality the proposed preprocessing technique can be extended to other engineering areas and therefore can pave a broad way for the application of the wmt

properties of border states of transient chaos transient chaos with absolutely continuous conditionally invariant measure is studied and a general solution of the frobenius perron equation is presented for complete one dimensional maps in particular properties of borderline situations exhibiting phase transitions within the framework of thermodynamical formalism are investigated

a quasi 3d thin stratified medium fast multipole algorithm for microstrip structures an accurate and efficient full wave simulation method is proposed for general microstrip structures it is called the quasi 3d thin stratified medium fast multipole algorithm tsm fma different from the 2d tsm fma method it is constructed on a vector wave function based dyadic green s function for layered medium dglm instead of the symmetric form dglm this new form of dglm is represented in terms of only two sommerfeld integrals and is suitable for developing fast algorithm in quasi 3d cases similar to the 2d tsm fma the path deformation technique and the multipole based acceleration is used to transform the sommerfeld integral and expedite the matrix vector multiplication the computational time per iteration and the memory requirement is o nlogn in the quasi 3d tsm fma it is suitable to perform a full wave analysis of a large microstrip array with less computational resource

array decomposition method for the accurate analysis of finite arrays presented in this paper is a fast method to accurately model finite arrays of arbitrary three dimensional elements the proposed technique referred to as the array decomposition method adm exploits the repeating features of finite arrays and the free space green s function to assemble a nonsymmetric block toeplitz matrix system the toeplitz property is used to significantly reduce storage requirements and allows the fast fourier transform fft to be applied in accelerating the matrix vector product operations of the iterative solution process each element of the array is modeled using the finite element boundary integral fe bi technique for rigorous analysis consequently we demonstrate that the complete lu decomposition of the matrix system from a single array element can be used as a highly effective block diagonal preconditioner on the larger array matrix system this rigorous method is compared to the standard fe bi technique for several tapered slot antenna tsa arrays and is demonstrated to generate the same accuracy with a fraction of the storage and solution time

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

effects of phase space discretization on the long time behavior of dynamical systems abstract we investigate the effects that roundoff errors have on discrete time dynamical systems computer generated orbits terminate in loops whose lengths scale with the machine precision in a universal way we present arguments to explain this fact

analysis of cylindrical antennas a spectral iteration technique the cylindrical antenna problem has been tackled using the spectral iteration technique an iterative scheme is employed for improving on an initially assumed form of the current distribution use is made of the fast fourier transform fft algorithm and the cumbersome process of matrix inversion is circumvented consequently this method is capable of handling a larger number of unknown coefficients in the expansion of the current distribution furthermore it provides a convenient means of testing for the satisfaction of the boundary conditions on the surface of the antenna convergence criteria for the iteration process have been established and the use of an acceleration procedure is illustrated different types of source models have been investigated and the convergence of both local and nonlocal parameters is also discussed

a fast solver for the helmholtz equation on long thin structures we present a fast solver for the helmholtz equation on long thin structures it operates on an integral equation formulation of the problem in which the solution is represented as a superposition of fields generated by sources on the structure usually on the boundary or boundaries of the structure it uses a standard iterative solver for linear equations in conjunction with a novel method for applying the forward matrix whose computational complexity is o n where n is the number of points on which the integral equation is solved the algorithm is suitable for structures in either two dimensions 2 d or three dimensions it does not depend in any great detail on the specifics of the helmholtz equation and thus is also suitable for similar equations we demonstrate the algorithm by using it to simulate scattering in 2 d from dielectric structures using an integral equation formulation constructed using a combination of single layer and double layer potentials yielding a second kind integral equation numerical results show the algorithm to be efficient and accurate

pruning induced phase transition observed by a scattering method in hyperbolic systems transient chaos is associated with an underlying chaotic saddle in phase space the structure of the chaotic saddle of a class of piecewise linear area preserving two dimensional maps with overall constant lyapunov exponents has been observed by a scattering method the free energy obtained in this way displays a phase transition at 0 in spite of the fact that no phase transition occurs in the free energy dedcued from the spectrum of lyapunov exponents this is possible because pruning introduces a second effective scaling exponent by creating at each level of the approximation particular small pieces in the incomplete cantor set approximating the saddle the second scaling arises for a subset of values of the control parameter that is dense in the parameter interval

noisy one dimensional maps near a crisis ii general uncorrelated weak noise the escape rate for one dimensional noisy maps near a crisis is investigated a previously introduced perturbation theory is extended to very general kinds of weak uncorrelated noise including multiplicative white noise as a special case for single humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law for the rate is derived it predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum of the map is of sufficiently large order a simple heuristic explanation of this effect is given the escape rate is discussed in detail for noise distributions of levy dichotomous and exponential type in the latter case the rate is dominated by an exponentially leading arrhenius factor in the deep precritical regime however the preexponential factor may still depend more strongly than any power law on the noise strength

symbolic dynamics of fully developed chaos i statistics and characteristics of two symbol sequences abstract by discerning levels k of statistical description it is shown that the level k boltzmann entropy h k log possibilities on level k of two symbol sequences equals the information theoretical conditional entropy ks k k 1 s k 1 with s k the average shannon entropy on level k a mixing measure is introduced by means of an appropriate demixing procedure from the properties of the two symbol sequence an expression for a symbolic 2 x 2 correlation matrix is derived

adaptive spectral estimation by the conjugate gradient method this paper proposes an alternative technique for adaptive spectral estimation the new technique applies the method of conjugate gradient which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite hermitian matrix to the adaptive spectral analysis problem computer simulations have been performed to compare the new method to existing ones from the limited examples presented it is seen that the new method is computationally more efficient at the expense of more core storage also this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available the technique performs well for both narrow band and wide band signals

improving the convergence rate of the conjugate gradient fft method using subdomain basis functions a technique to improve the convergence rate of the conjugate gradient fast fourier transform cg fft method is presented the procedure involves the incorporation of subdomain basis functions associated with the current representation of linear and planar radiating elements it is shown that significant improvements are achieved in the convergence of the cg fft when using sinusoidal basis functions numerical results are presented for thin cylindrical dipoles conducting strips and material plates of various sizes in all cases an increase in the rate of convergence by a factor of two or better was observed

a combined full wave cg fft method for rigorous analysis of large microstrip antenna arrays an accurate and efficient technique is presented for the analysis of large microstrip antenna arrays the technique consists of an amalgamation of a spatially discrete scheme consisting of the cg fft method and the complex discrete image cdi technique the unique feature of this approach is the use of the spatially discrete cg fft for analyzing microstrip structures the aliasing and truncation errors are thoroughly eliminated in this approach in addition the grad div operators are transformed from singular green s functions to differentiable expansion and testing functions by using galerkin s procedure thereby improving the accuracy and the rate of convergence to show the accuracy and efficiency of this technique a number of microstrip arrays including a large microstrip reflectarray have been studied it is found that the simulations carried out using this technique are in very good agreement with measurements

an iteration free mom approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems we describe a numerically efficient strategy for solving a linear system of equations arising in the method of moments for solving electromagnetic scattering problems this novel approach termed as the characteristic basis function method cbfm is based on utilizing characteristic basis functions cbfs special functions defined on macro domains blocks that include a relatively large number of conventional sub domains discretized by using triangular or rectangular patches use of these basis functions leads to a significant reduction in the number of unknowns and results in a substantial size reduction of the mom matrix this in turn enables us to handle the reduced matrix by using a direct solver without the need to iterate in addition the paper shows that the cbfs can be generated by using a sparse representation of the impedance matrix resulting in lower computational cost and that in contrast to the iterative techniques multiple excitations can be handled with only a small overhead another important attribute of the cbfm is that it is readily parallelized numerical results that demonstrate the accuracy and time efficiency of the cbfm for several representative scattering problems are included in the paper

properties of fully developed chaos in one dimensional maps we consider single humped symmetric one dimensional maps generating fully developed chaotic iterations specified by the property that on the attractor the mapping is everywhere two to one to calculate the probability distribution function and in turn the lyapunov exponent and the correlation function a perturbation expansion is developed for the invariant measure besides deriving some general results we treat several examples in detail and compare our theoretical results with recent numerical ones furthermore a necessary condition is deduced for the probability distribution function to be symmetric and an effective functional iteration method for the measure is introduced for numerical purposes

chaotic scattering modelled by an inclined billiard abstract chaotic scattering as observed in satellite encounters and in other problems is modelled by a simple billiard a point particle bounces on two disks and in addition is subjected to a constant acceleration in an appropriate limit this problem reduces to a piecewise linear mapping we consider a one parameter family of orbits obtained by starting the particle at rest from a constant height we find that this family exhibits chaotic scattering it has an infinite number of discontinuities forming a self similar cantor set with the help of symbolic dynamics the structure of the family can be completely elucidated

a vector dual primal finite element tearing and interconnecting method for solving 3 d large scale electromagnetic problems a lagrange multiplier based non overlapping domain decomposition method referred to as the dual primal finite element tearing and interconnecting feti dp is formulated for the finite element simulation of large three dimensional 3 d electromagnetic problems this formulation extends the feti dp for solving the scalar helmholtz equation to the solution of the vector curl curl wave equation using edge based finite elements it enforces the field continuity explicitly along the edges shared by more than two subdomains and implicitly at the interfaces between two subdomains through the use of lagrange multipliers with the aid of a direct sparse solver for each subdomain system the large global problem is reduced to a much smaller interface problem from which a neumann boundary condition is obtained at the interfaces between all the subdomains this neumann boundary condition is then used to calculate the field within each subdomain it is shown that the resulting feti dpem method is scalable with respect to the size of finite elements and the number of subdomains it is also scalable with respect to the size of the subdomains when the subdomains with its surfaces enclosed by perfect magnetic conductors cannot support any resonant modes the feti dpem method is applied to the electromagnetic simulation of array type structures where the geometrical redundancy is fully exploited to speedup the simulation and reduce the memory requirement numerical results for the simulation of finite antenna arrays and photonic bandgap devices are presented to demonstrate the application accuracy efficiency and capability of the feti dpem method

application of a conjugate gradient fft method to scattering from thin planar material plates the backscatter cross section is calculated for thin material plates with finite electric permittivity conductivity and magnetic permeability illuminated by a plane wave the plates are assumed to be planar with an arbitrary perimeter the integral equations are formed and solved by a combined conjugate gradient fast fourier transform cg fft method the cg fft method was tested for several geometrics and materials measured and computed backscatter results are compared for a perfectly conducting equilateral triangle plate a square dielectric and magnetic plate and a circular dielectric plate the agreement between measured and computed data is generally good except toward edge on incidence where several factors cause discrepancies accurate approximations to the geometry and far field integrals become critical near edge on incidence and it is postulated that as the incidence angle approaches edge on the sampling interval and tolerance should be decreased

onset of homoclinic chaos due to degeneracy in the spectrum of the saddle abstract the emergence of complex regimes of behaviour is considered in a dynamical system with a one dimensional unstable manifold of the saddle point it is shown that if both components of the unstable manifold return to the saddle point from opposite sides complex dynamics arises after a sequence of bifurcations including a cascade of period doubling bifurcations the problem is considered near a point of degeneracy of the saddle point spectrum this giving the possibility of constructing a model return map

a combined finite element boundary integral formulation for solution of two dimensional scattering problems via cgfft a novel technique is presented for computing the scattering by two dimensional structures of arbitrary inhomogeneity the proposed approach combines the usual finite element fe method with the boundary integral equation to formulate a discrete system this is subsequently solved via the conjugate gradient cg algorithm a particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer several of the resulting boundary integrals are then convolutions and can be evaluated via the fast fourier transform fft in the implementation of the cg algorithm the solution approach presented here offers the principal advantage of having o n memory demand and employs a one dimensional fft as against the two dimensional fft required in a traditional implementation of the proposed cg fft algorithm the speed of the proposed solution method is compared with that of the traditional cg fft algorithm results are presented for several rectangular composite cylinders and one perfectly conducting cylinder these are shown to be in excellent agreement with the moment method

error and convergence in numerical implementations of the conjugate gradient method em problems the conjugate gradient method has previously been applied in electromagnetics in two ways to moment method matrices and directly to continuous operator equations numerical implementations of these two methods are shown here to be equivalent it is concluded that the advantage of the conjugate gradient method is therefore its potential computational efficiency as a solution procedure not its ability to achieve a more exact solution than the moment method

properties of maps related to flows around a saddle point abstract general properties of maps associated with systems in which trajectories of the flow get close to a hyperbolic fixed point with a two dimensional stable and a one dimensional unstable manifold are examined in the chaotic region exponents characterizing power law singular behaviour of the jacobian of the shape of and of the stationary probability distribution on the chaotic attractor are expressed in terms of the ratios of the eigenvalues of the linearized flow at the hyperbolic point emphasis is laid on the study of the limiting case of strong dissipation leading to a simple one dimensional attractor but to a dynamics with interesting features

numerical analysis of large scale finite periodic arrays using a macro block characteristic basis function method numerical analysis of a large scale finite periodic array is accurate but quite costly when the array is analyzed as a finite array the computational cost for the numerical analysis can be reduced greatly when the array is approximated as an infinite periodic structure however the edge effect that strongly affects the active impedance or current distribution of the array elements near the edge is neglected in this paper a macro block characteristic basis function method mb cbfm for numerical analysis of a large scale finite periodic array with a uniform amplitude and linear phased excitation is proposed the mb cbfm utilizes blocks and macro blocks to group the elements in order to reduce its computational cost without degrading accuracy numerical simulations demonstrate that the cpu time and computer memory of the mb cbfm are o n when the size of array is sufficiently large

scattering from planar structures containing small features using the adaptive integral method aim fast integral equation algorithms such as the adaptive integral method aim have been demonstrated to reduce memory and execution time associated with moment method solutions for arbitrarily shaped three dimensional 3 d geometries in this paper we examine the efficiency of aim in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns aim with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries in the latter part of the paper we demonstrate the application of aim in connection with a finite element boundary integral formulation for cavity backed antennas

on the images of modular and geometric three dimensional galois representations we study compatible families of three dimensional galois representations constructed in the etale cohomology of a smooth projective variety we prove a theorem asserting that the residual images will be generically large if certain easy to check conditions are satisfied we only consider representations with coefficients in an imaginary quadratic field for primes inert in this field the residual representations when irreducible are unitary we apply our result to an example constructed by van geemen and top obtaining a family of special linear groups and one of special unitary groups as galois groups over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we also consider the case of cohomological modular forms for a congruence subgroup of sl inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i assuming clozel s conjecture stating that a geometric family of three dimensional galois representations can be attached to them we verify for three examples the conditions guaranteeing generically large images and explicitly bound the finite set of primes with non maximal image we also discuss what intrinsic conditions a modular form should verify to guarantee that the images of the attached galois representations will be generically large

te scattering by a two dimensional groove in a ground plane using higher order boundary conditions an application of a third order generalized boundary condition to scattering by a filled rectangular groove is presented deficiencies of such higher order boundary conditions are addressed and a correction for the present case is proposed as part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition

correlations and spectra of periodic chaos generated by the logistic parabola we consider the one parameter family of mappingsfa x 4ax 1 x a x e 0 1 and define an infinite countable set of parameter values a for which the solutions show observable chaos their properties are investigated by means of correlation functions and spectra which can be interpreted and approximated by separating periodic and chaotic components in the solutions and introducing two simple assumptions on the statistics of the chaotic component

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

frequency locking near the gluing bifurcation spin torque oscillator under periodic modulation of current abstract we consider entrainment by periodic force of limit cycles which are close to the homoclinic bifurcation taking as a physical example the nanoscale spin torque oscillator in the lc circuit we develop the general description of the situation in which the frequency of the stable periodic orbit in the autonomous system is highly sensitive to minor variations of the parameter and derive explicit expressions for the strongly deformed borders of the resonance regions arnold tongues in the parameter space of the problem it turns out that proximity to homoclinic bifurcations hinders synchronization of spin torque oscillators

suppression of deterministic diffusion by noise a one dimensional discrete time dynamics near the onset of deterministic diffusion additively coupled to weak gaussian white noise is studied the diffusion coefficient is related to the escape rate out of an interval and a method for the calculation of this rate is introduced which unlike previous investigations fully takes into account all relevant escape paths it is found that the diffusion coefficient of the deterministic dynamics may be considerably reduced by the noise in agreement with numerical simulations it is shown that certain fundamental problems in the concept of deterministic diffusion without noise do not affect the validity of our result

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

a scheme to analyze conducting plates of resonant size using the conjugate gradient method and the fast fourier transform a scheme for analyzing electrodynamic problems involving conducting plates of resonant size using the conjugate gradient cg method and the fast fourier transform fft is presented in detail the problems are analyzed by solving their corresponding electric field integral equation the procedure is made easy and systematic by using a sampling process with rooftop functions to represent the induced current and pulses to average the fields these functions have been widely used in moment method mm applications the scheme is an efficient numerical tool benefiting from the good convergence and low memory requirements of the cg and the low cpu time consumed in performing convolutions with the fft in comparison with the mm the scheme avoids the storage of large matrices and reduces the computer time by an order of magnitude several results are presented and compared with analytical numerical or measured values that appear in the literature