surface integral equation method for the analysis of an obliquely stratified half space the radiation of a source in the presence of an obliquely stratified half space is studied using the surface integral equation method a generalized extinction theorem for the obliquely stratified half space problem is derived which gives eight surface integral equations for the fields the green s functions for the stratified media are found by a semianalytical method these surface integral equations can be used to solve the rather complicated two dimensional problem by the one dimensional finite element method fem which saves computer memory and computation time compared to the conventional two dimensional fem for some special cases the results obtained by this method are compared with those obtained by the numerical mode matching method and the fourier integral technique excellent agreement has been observed between them this method is general for any obliquely stratified half space with arbitrarily many layers in each region

stable evaluation of green s functions in cylindrically stratified regions with uniaxial anisotropic layers we present a robust algorithm for the computation of electromagnetic fields radiated by point sources hertzian dipoles in cylindrically stratified media where each layer may exhibit material properties permittivity permeability and conductivity with uniaxial anisotropy analytical expressions are obtained based on the spectral representation of the tensor green s function based on cylindrical bessel and hankel eigenfunctions and extended for layered uniaxial media due to the poor scaling of these eigenfunctions for extreme arguments and or orders direct numerical evaluation of such expressions can produce numerical instability i e underflow overflow and or round off errors under finite precision arithmetic to circumvent these problems we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain to yield a robust algorithm for all parameter ranges numerical results are presented to illustrate the robustness of the formulation including cases of practical interest

3 d numerical mode matching nmm method for resistivity well logging tools a three dimensional 3 d numerical mode matching nmm method is presented for poisson s equation in general inhomogeneons media it reduces the original 3 d problem into a series of two dimensional 2 d eigenvalue problems plus a one dimensional 1 d layered medium problem which can be modeled efficiently by a recursion procedure the algorithm is tested for several 3 d inhomogeneous media and an excellent agreement between the nmm and analytical solutions is obtained for all test cases we demonstrate some typical applications of the 3 d nmm algorithm in resistivity well logging including invasion zones of noncircular shape vertical and horizontal fractures and horizontal wells the solution procedure proposed is directly applicable to wave propagation in 3 d inhomogeneous media

an efficient approach for extracting poles of green s functions in general multilayered media a fast approach of closed form green s functions for mixed potential integral equation analysis of both near field and far field in planar multilayered media is presented in this paper since all components of the green s functions in spectral domain are restructured concisely by four elementary functions the surface wave pole extraction is very effective in terms of a function related to the generalized reflection coefficients meanwhile the number of required two level discrete complex image method dcim with high order sommerfeld identities is also minimized under this scheme the numerical results show that this approach is more efficient and accurate for the electromagnetic scattering by and radiation in the presence of electrically large three dimensional 3 d objects in multilayered media although lossless examples are considered in the numerical examples the method presented here works also for the lossy materials where the poles move away from the real axis in the complex plane

exact static solutions of a generalized discrete φ 4 model including short periodic solutions we carry out a comprehensive analysis of a generalized discrete 4 model of which virtually all 4 models discussed in the literature are particular cases for this model we construct the exact solutions in the form of the basic jacobi elliptic hyperbolic and sine functions and also give a list of short periodic and even aperiodic solutions some of those solutions coincide with the known ones others generalize the existing solutions and the rest of them are new we then discuss the relation between the models supporting exact static solutions and the two point maps in particular we show that some of the short periodic and sine solutions can be found from factorized difference equations and even from a set of two difference equations one of the first and another of the second order particular attention is paid to the discussion of the exceptional discrete ed models defined as models supporting the translationally invariant ti static solutions that can be placed arbitrarily with respect to the lattice we show that some of the derived short periodic solutions are ti ones while the others are not for the ti static solutions we demonstrate the existence of the translational goldstone mode for any location of the solution with respect to the lattice we then analyze numerically the stability and other properties of the ti kink solutions in conclusion we divide the ed models into two classes the ed i models support a two parameter set of ti static solutions while the ed ii models support only a one parameter set of such solutions

three dimensional induction logging problems part i an integral equation solution and model comparisons a 3 d frequency domain solution based on a volume integral equation approach has been implemented to simulate induction log responses in our treatment of the problem we assume that the electrical properties of the bedding as well as the borehole and invasion zones can exhibit transverse anisotropy the solution process uses a krylov subspace iteration to solve the scattering equation which is based on the modified iterative dissipative method internal consistency checks and comparisons with mode matching and finite difference solutions for vertical borehole models demonstrate the accuracy of the solution there are no known analytical solutions for induction log responses arising from deviated boreholes intersecting horizontal bed boundaries to simulate such responses requires the numerical solution of maxwell s equations in three dimensions along with independent tests to validate the solution approach and its accuracy in this paper we compare two independent 3 d frequency domain solutions for the

closed form solutions for analysis of cylindrically conformal microstrip antennas with arbitrary radii an efficient and accurate closed form solution based on the spectral domain method of moments mom is presented to analyze the characteristics of cylindrically conformal microstrip antennas with arbitrary radii first an algorithm that combines the recursive and the uniform asymptotic expansion method in different regions is developed to calculate the spectral domain green s functions for arbitrary dielectric coated cylinders accurately next the integrands of the spectral integrals involved in mom equation are partitioned into two parts i e the fast oscillatory slowly convergent part and the well behaved part consequently all of the integrals in mom analysis can be categorized into two types through the sommerfeld identity and its extension these integrals are cast into closed forms by using the nonlinear approximation method generalized pencil of function method in this method any time consuming numerical integration procedure is eliminated which improves the computational efficiency drastically compared with the results from published references the validity and accuracy of the method are demonstrated

paraxial space domain formulation for surface fields on a large dielectric coated circular cylinder a new method to evaluate the surface fields excited within the paraxial nearly axial region of an electrically large dielectric coated circular cylinder is presented this representation is obtained by performing the watson s transformation in the standard eigenfunction solution and using the fact that the circumferentially propagating series representation of the appropriate green s function is periodic in one of its two variables therefore it can be approximated by a fourier series where the two leading terms of the expansion yield engineering accuracy in most cases this work can be used in conjunction with a method of moments solution for the design analysis of conformal microstrip antennas and arrays numerical results are presented and compared with a standard eigenfunction expansion

moment method analysis of a conformal curl antenna printed within layered dielectric cylindrical media a curl antenna printed within a grounded cylindrical dielectric substrate is analyzed efficiently using the method of moments mom the antenna consists of a single archimedean spiral arm printed on the cylindrical surface which is fed through the substrate using a radial probe and a rigorous model is developed for this feeding probe the cylindrical media is modeled using dyadic green s functions dgf where a novel asymptotic extraction approach and the generalized pencil of functions gpof method are employed to expedite the analysis computations are compared with those of antennas in equivalent planar structures as well as with the results of commercial software and good agreement is achieved in all cases

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

asymptotic extraction approach for antennas in a multilayered spherical media an efficient algorithm is introduced to enhance the convergence of dyadic green s functions dgf in a layered spherical media where asymptotic expressions have been developed the formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media green s function using the addition theorem of spherical hankel functions substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original dgf the subtracted components are then added to the solution using the homogenous media green s function format

dispersion of waves guided along a cylindrical substrate superstrate layered medium the effects of curvature and of the electrical parameters of thin dielectric layers deposited as superstrates on a perfectly conducting circular cylinder on the modal dispersion of waves guided tangentially along the outer superstrate layer of a two layer geometry are examined to chart the propagation characteristics of the layer guided modes relevant to the three dimensional dipole excited green s function for this geometry it is necessary to solve the radial eigenvalue problem for the complex azimuthal propagation constants nu sub p beta p 1 2 which also identify poles of the nu dependent spectral integrand of the green s function here beta is the spectral variable along the axial direction with the green s function synthesized as a double spectral integral over nu and beta the pole locations are obtained numerically by solving the dispersion equation using davidenko s method and are parameterized in terms of layer radius dielectric constant and thickness the dispersion relation and hence the propagation constants are shown to reduce correctly to the corresponding results for the planar geometry in the limit where the superstrate outer radius approaches infinity

exact static solutions for discrete ϕ 4 models free of the peierls nabarro barrier discretized first integral approach we propose a generalization of the discrete klein gordon models free of the peierls nabarro barrier derived in spreight nonlinearity 12 1373 1999 and barashenkov et al phys rev e 72 035602 r 2005 such that they support not only kinks but a one parameter set of exact static solutions these solutions can be obtained iteratively from a two point nonlinear map whose role is played by the discretized first integral of the static klein gordon field as suggested by dmitriev et al j phys a 38 7617 2005 we then discuss some discrete ensuremath phi 4 models free of the peierls nabarro barrier and identify for them the full space of available static solutions including those derived recently by cooper et al phys rev e 72 036605 2005 but not limited to them these findings are also relevant to standing wave solutions of discrete nonlinear schr odinger models we also study stability of the obtained solutions as an interesting aside we derive the list of solutions to the continuum ensuremath phi 4 equation that fill the entire two dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models

a generalized asymptotic extraction solution for antennas in multilayered spherical media an efficient model is developed to accelerate the convergence of the dyadic green s function s dgf infinite summation when the source and observation points are placed in different layers of a dielectric sphere thereby expediting computational analysis the proposed procedure is based on asymptotic extraction principles in which the quasi static images are extracted from the spectral domain dgf the effectiveness of the approach is demonstrated in a method of moment model where a microstrip antenna as well as a conformal dipole array have been studied

diffraction of axisymmetric waves in a borehole by bed boundary discontinuities this paper presents the calculation of the diffraction of axisymmetric borehole waves by bed boundary discontinuities the bed boundary is assumed to be horizontal and the inhomogeneities to be axially symmetric in such a geometry an axially symmetric source will produce only axially symmetric waves since the borehole is an open structure the mode spectrum consists of a discrete part as well as a continuum the scattering of a continuum of waves by bed boundaries is difficult to treat the approach used in the past in treating this class of problem has been approximate in nature or highly numerical such as the finite element method we present here a systematic way to approximate the continuum of modes by discrete modes after discretization the scattering problem can be treated simply since the approach is systematic it allows derivation of the solution to any desired degree of accuracy in theory but in practice it is limited by the computational resources available we also show that our appr

efficient analysis of printed structures of arbitrary shape on coated cylinders via spatial domain mixed potential green s function we present an approach for the method of moments mom analysis of antennas of arbitrary shape printed on a cylindrical substrate we propose several key components of a code to perform this analysis with the explicit goal of adapting mom codes devised for planar stratified structures for that purpose the background medium green s function is expressed in the mixed potential mp format to allow for efficient numerical integration the spectral dyadic green s function is first recast in the spectral counterpart of the spatial mixed potential form the convergence of the spectral to spatial transform is accelerated by extraction of spectral asymptotic functions and exploitation of the azimuthal periodicity several important issues of implementation numerical stability and accuracy are addressed with a view to incorporate the spatial mp green s function into the mom analysis of printed structures of arbitrary shape using rwg basis functions the numerical results are in good agreement with those obtained by other methods and with measured data

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

exact static solutions to a translationally invariant discrete phi4 model for a discrete translationally invariant 4 model introduced by barashenkov et al 2005 phys rev e 72 35602r we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a jacobi elliptic function jef solution the first integral can be written in the form of a nonlinear map from which the static solution supported by the model can be constructed a set of jef solutions including the staggered ones is derived we also report on the stability analysis for the static bounded solutions and exemplify the dynamical behaviour of the unstable solutions this work provides a road map through this illustrative example on how to fully analyse translationally invariant models in terms of their static problem its first integral their full set of static solutions and associated conservation laws

riemannian manifold learning recently manifold learning has been widely exploited in pattern recognition data analysis and machine learning this paper presents a novel framework called riemannian manifold learning rml based on the assumption that the input high dimensional data lie on an intrinsically low dimensional riemannian manifold the main idea is to formulate the dimensionality reduction problem as a classical problem in riemannian geometry that is how to construct coordinate charts for a given riemannian manifold we implement the riemannian normal coordinate chart which has been the most widely used in riemannian geometry for a set of unorganized data points first two input parameters the neighborhood size k and the intrinsic dimension d are estimated based on an efficient simplicial reconstruction of the underlying manifold then the normal coordinates are computed to map the input high dimensional data into a low dimensional space experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data preserve radial geodesic distances and yield regular embeddings

response of a source on top of a vertically stratified half space the solution of the response of a source on top of a horizontally stratified half space is well known however when the half space is vertically stratified the problem can only be solved with numerical methods like the finite element method here a semi analytic approach to solve such a problem is presented the three dimensional variation of the problem is reduced to two dimensional variation by fourier transform in one coordinate variable the remaining two dimensional problem is solved by finding the eigensolution in each of the half spaces the eigensolutions of each region are found from the partial differential equation directly using the same basis set of expansion functions this makes the calculation of the reflection and transmission operators very efficient the reflection and transmission operators account for the mode conversion reflection and transmission of the waves with the reflection and transmission operators the field everywhere can be calculated the solution reduces to that of the sommerfeld s half space problem when the two half spaces are homogeneous

analysis of printed antennas mounted on a coated circular cylinder of arbitrary size an efficient numerical algorithm for the analysis of printed antennas on a dielectric coated circular cylinder is presented the formulation employs the spectral domain approach green s function is evaluated via olver s uniform asymptotic expansions the fourier summation is transformed into integration and the asymptotic part of the integral is evaluated in closed form the whole procedure results in a numerical algorithm that is at least as accurate and efficient as the respective one for the planar structure the present approach can be applied for any source receiver position and any cylinder radius

the singularities of a fourier type integral in a multicylindrical layer problem the singularities of the integrand of a fourier type integral obtained in solving the multicylindrical layer boundary value problem are discussed the integrand is a function of the radial wavenumber k ip of all the cylindrical layers and the radial wavenumber in the ith layer is related to the axial wavenumber by k ip sqrt k i 2 k 2 where k i is the wavenumber of the i th layer and k z is the axial wavenumber of all the layers which have to be the same by phase matching on the complex k z plane there seemingly are branch points of logarithmic type and algebraic type for k z k i for all the layers however by invoking uniqueness principle in the solution of this boundary value problem one can show that the only singularities on the complex k z plane are the branch point singularity associated with the outermost medium which extends radially to infinity and pole singularities which correspond to discrete guided modes in the multicylindrical medium

dynamical transitions between equilibria in a dissipative klein gordon lattice abstract we consider the energy landscape of a dissipative klein gordon lattice with a 4 on site potential our analysis is based on suitable energy arguments combined with a discrete version of the ojasiewicz inequality in order to justify the convergence to a single nontrivial equilibrium for all initial configurations of the lattice then global bifurcation theory is explored to illustrate that in the discrete regime all linear states lead to nonlinear generalizations of equilibrium states direct numerical simulations reveal the rich structure of the equilibrium set consisting of non trivial topological kink shaped interpolations between the adjacent minima of the on site potential and the wealth of dynamical convergence possibilities these dynamical evolution results also provide insight on the potential stability of the equilibrium branches and glimpses of the emerging global bifurcation structure elucidating the role of the interplay between discreteness nonlinearity and dissipation

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

a spectral lanczos decomposition method for solving 3 d low frequency electromagnetic diffusion by the finite element method a very efficient three dimensional 3 d solver for the diffusion of the electromagnetic fields in an inhomogeneous medium is described the proposed method employs either the node based or the edge based finite element method fem to discretize maxwell s equations the resultant matrix equation is solved by the spectral lanczos decomposition method sldm which is based on the krylov subspace lanczos approximation of the solution in the frequency domain by analyzing some practical geophysical problems it is shown that the sldm is extremely fast and furthermore the electromagnetic fields at many frequencies can be evaluated by performing the sldm iteration only at the lowest frequency

intrinsic dimension estimation the paper reviews state of the art of the methods of intrinsic dimension id estimation the paper defines the properties that an ideal id estimator should have the paper reviews under the above mentioned framework the major id estimation methods underlining their advances and the open problems dimensionality reduction methods are preprocessing techniques used for coping with high dimensionality they have the aim of projecting the original data set of dimensionality n without information loss onto a lower m dimensional submanifold since the value of m is unknown techniques that allow knowing in advance the value of m called intrinsic dimension id are quite useful the aim of the paper is to review state of the art of the methods of id estimation underlining the recent advances and the open problems

exact stationary solutions for the translationally invariant discrete nonlinear schrodinger equations from a wide class of translationally invariant discrete nonlinear schrodinger dnls equations we extract a two parameter subclass corresponding to kerr nonlinearity for which any stationary solution can be derived recurrently from a quadratic equation this subclass which incorporates the integrable ablowitz ladik lattice as a special case admits exact stationary solutions that are derived in terms of the jacobi elliptic functions exact moving solutions for the discrete equations are also obtained in the continuum limit the constructed stationary solutions reduce to the exact moving solutions to the continuum nls equation with kerr nonlinearity numerical results are also presented for the special case of localized solutions including sech pulse or bright soliton tanh kink or dark soliton and 1 tanh called here inverted kink profiles for these solutions we discuss their linearization spectra and their mobility particularly we demonstrate that discrete dark solitons are dynamically stable for a wide range of lattice spacings contrary to what is the case for their standard dnls counterparts furthermore the bright and dark solitons in the non integrable translationally invariant lattices can propagate at slow speed without any noticeable radiation

an error embedded method based on generalized chebyshev polynomials in this paper we develop an error embedded method based on generalized chebyshev polynomials for solving stiff initial value problems the solution and the error at each integration step are calculated by generalized chebyshev polynomials of two consecutive degrees having overlapping zeros which enables us to minimize overall computational costs further the errors at each integration step are embedded in the algorithm itself in terms of concrete convergence and stability analysis the constructed algorithm turns out to have the 6th order convergence and an almost l stability we assess the proposed method with several numerical results showing that it uses larger time step sizes and is numerically more efficient

translationally invariant discrete kinks from one dimensional maps for most discretizations of the phi4 theory the stationary kink can only be centered either on a lattice site or midway between two adjacent sites we search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites we show that this translational invariance of the kink implies the existence of an underlying one dimensional map phi n 1 f phi n a simple algorithm based on this observation generates three families of exceptional discretizations

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

nonlinear dimensionality reduction by topologically constrained isometric embedding many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space the embedding process usually relies on distances between neighboring features mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non convexity distortions resulting from using long geodesics indiscriminately lead to a known limitation of the isomap algorithm when used to map non convex manifolds presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries the resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold thus avoiding an inherent limitation of the isomap algorithm since the proposed algorithm matches non local structures it is robust to strong noise we show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques both global and local in nature

high speed kinks in a generalized discrete phi 4 model we consider a generalized discrete ensuremath phi 4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity the constructed exact moving solutions are dependent on the specific value of the propagation velocity we demonstrate that in this class of models given a specific velocity the problem of finding the exact moving solution is integrable namely this problem originally expressed as a three point map can be reduced to a two point map from which the exact moving solutions can be derived iteratively it was also found that these high speed kinks can be stable and robust against perturbations introduced in the initial conditions

exact static solutions of a two dimensional discrete ϕ4 model for a two dimensional scalar discrete 4 model we obtain several exact static solutions in the form of the jacobi elliptic functions jef with arbitrary shift along the lattice the quispel roberts thompson type quadratic maps are identified for the considered two dimensional model by using a jef solution we also show that many of the static solutions can be constructed iteratively from these quadratic maps by starting from an admissible initial value the kink solution having the form of tanh is numerically demonstrated to be generically stable

frequency domain and time domain finite element solution of maxwell s equations using spectral lanczos decomposition method an efficient solver is described for the solution of the electromagnetic fields in both time and frequency domains the proposed method employs the node based and the edge based finite element method fem to discretize maxwell s equations the resultant matrix equation is solved by the spectral lanczos decomposition method sldm which is based on the krylov subspace lanczos approximation of the solution first a new explicit axisymmetric solver for the diffusion of electromagnetic fields in an inhomogeneous medium is introduced the procedure is then extended to treat the three dimensional problems in the low frequency regime finally maxwell s equations in their general form are solved in frequency and time domains depending on the application our method requires the implementation of the lanczos process only at the largest or smallest time or frequency of interest consequently a multiple time and frequency domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time the efficiency and effectiveness of this new technique are illustrated by using various practical numerical examples

efficient computation of surface fields excited on a dielectric coated circular cylinder an efficient method to evaluate the surface fields excited on an electrically large dielectric coated circular cylinder is presented the efficiency of the method results from the circumferentially propagating representation of the green s function as well as its efficient numerical evaluation along a steepest descent path the circumferentially propagating series representation of the appropriate green s function is obtained from its radially propagating counterpart via watson s transformation and then the path of integration is deformed to the steepest descent path on which the integrand decays most rapidly numerical results are presented that indicate that the representations obtained here are very efficient and valid even for arbitrary small separations of the source and field points this work is especially useful in the moment method analysis of conformal microstrip antennas where the mutual coupling effects are important

exceptional discretizations of the sine gordon equation the method of one dimensional maps was recently introduced as a means of generating exceptional discretizations of the phi 4 theory i e discrete phi 4 models which support kinks centered at a continuous range of positions relative to the lattice in this paper we employ this method to obtain exceptional discretizations of the sine gordon equation i e exceptional frenkel kontorova chains we also use one dimensional maps to construct a discrete sine gordon equation supporting kinks which move with arbitrary velocities without emitting radiation

standard nearest neighbour discretizations of klein gordon models cannot preserve both energy and linear momentum we consider nonlinear klein gordon wave equations and illustrate that standard discretizations thereof involving nearest neighbours may preserve either standardly defined linear momentum or standardly defined total energy but not both this has a variety of intriguing implications for the non potential discretizations that preserve only the linear momentum such as the self accelerating or self decelerating motion of coherent structures such as discrete kinks in these nonlinear lattices

stable pseudoanalytical computation of electromagnetic fields from arbitrarily oriented dipoles in cylindrically stratified media computation of electromagnetic fields due to point sources hertzian dipoles in cylindrically stratified media is a classical problem for which analytical expressions of the associated tensor green s function have been long known however under finite precision arithmetic direct numerical computations based on the application of such analytical canonical expressions invariably lead to underflow and overflow problems related to the poor scaling of the eigenfunctions cylindrical bessel and hankel functions for extreme arguments and or high order as well as convergence problems related to the numerical integration over the spectral wavenumber and to the truncation of the infinite series over the azimuth mode number these problems are exacerbated when a disparate range of values is to be considered for the layers thicknesses and material properties resistivities permittivities and permeabilities the transverse and longitudinal distances between source and observation points as well as the source frequency to overcome these challenges in a systematic fashion we introduce herein different sets of range conditioned modified cylindrical functions in lieu of standard cylindrical eigenfunctions each associated with nonoverlapped subdomains of numerical evaluation to allow for stable computations under any range of physical parameters in addition adaptively chosen integration contours are employed in the complex spectral wavenumber plane to ensure convergent numerical integration in all cases we illustrate the application of the algorithm to problems of geophysical interest involving layer resistivities ranging from 1000 wm to 10 8 wm frequencies of operation ranging from 10 mhz down to the low magnetotelluric range of 0 01 hz and for various combinations of layer thicknesses

complex plane generalization of scalar levin transforms a robust rapidly convergent method to compute potentials and fields in multi layered media abstract we propose the complex plane generalization of a powerful algebraic sequence acceleration algorithm the method of weighted averages mwa to guarantee exponential cum algebraic convergence of fourier and fourier hankel f h integral transforms this complex plane mwa effected via a linear path detour in the complex plane results in rapid absolute convergence of field and potential solutions in multi layered environments regardless of the source observer geometry and anisotropy loss of the media present in this work we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra subsequently we 1 exhibit the foundational relations behind the complex plane extension to a general levin type sequence convergence accelerator 2 specialize this analysis to one member of the levin transform family the mwa 3 address and circumvent restrictions arising for two dimensional integrals associated with wave dynamics problems through minimal complex plane detour restrictions and a novel partition of the integration domain 4 develop and compare two formulations based on standard real axis mwa variants and 5 present validation results and convergence characteristics for one of these two formulations

normal form for travelling kinks in discrete klein gordon lattices abstract we study travelling kinks in the spatial discretizations of the nonlinear klein gordon equation which include the discrete 4 lattice and the discrete sine gordon lattice the differential advance delay equation for travelling kinks is reduced to the normal form a scalar fourth order differential equation near the quadruple zero eigenvalue we show numerically the non existence of monotonic kinks heteroclinic orbits between adjacent equilibrium points in the fourth order equation making generic assumptions on the reduced fourth order equation we prove the persistence of bounded solutions heteroclinic connections between periodic solutions near adjacent equilibrium points in the full differential advance delay equation with the technique of centre manifold reduction existence of multiple kinks in the discrete sine gordon equation is discussed in connection to recent numerical results of aigner et al a a aigner a r champneys v m rothos a new barrier to the existence of moving kinks in frenkel kontorova lattices physica d 186 2003 148 170 and results of our normal form analysis

modeling of borehole resistivity measurements using infinite electrical grids an infinite electrical resistive grid generated by a finite difference approximation to poisson s equation in cylindrical coordinates with no azimuthal variation has been used to model borehole resistivity measurements the medium surrounding the borehole is infinite in extent and its resistivity varies only in the radial direction as a result the branch resistance values of the infinite grid also vary only in the radial direction a continued fraction of laurent operators determines the node voltages along the borehole s surface use of an operational calculus based upon the finite fourier transformation converts the continued fraction into a readily computed form this yields new formulas for apparent resistivity given various resistivity measuring arrays and a resistivity profile in the radial direction in contrast to classical methods the need to match boundary conditions at the interface of a cylindrically layered earth is eliminated so that the procedure is just as easily applied to a continuo

analysis of nearly cylindrical antennas and scattering problems using a spectrum of two dimensional solutions this paper presents a powerful method for analysing antennas which can be considered principally two dimensional 2 d or cylindrical except for some three dimensional 3 d physical or equivalent sources e g dipoles or slots it is shown by fourier transform techniques that such antennas can be analyzed as 2 d problems with harmonic longitudinal field variation the radiation pattern can often be determined directly from a finite set of such 2 d solutions each one obtained by any method e g the moment method the mutual interaction between the cylindrical scatterer and the sources must be calculated to determine the exact current distribution on the sources and their impedances or admittances this is facilitated by performing an inverse fourier transform of an infinite spectrum of the numerical 2 d solutions followed by a moment method solution in the spatial domain to satisfy the boundary conditions on the 3 d equivalent sources themselves the inverse fourier transform is simplified by the use of asymptote extraction the method is in itself a hybrid technique as one method is used to solve the harmonic 2 d problem and the other to solve for the source currents

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

fast simulation of triaxial borehole induction measurements acquired in axially symmetrical and transversely isotropic media we introduce and successfully test an efficient method to simulate triaxial borehole electromagnetic em induction measurements acquired in axially symmetrical and transversely isotropic ti media the method uses a fourier series expansion to express the azimuthal dependence of em fields and the source term whereby the essentially 3d problem collapses to a series of independent 2d problems each 2d problem is solved with a semianalytic method that uses normalized bessel functions and normalized hankel functions to express the radial dependence of em fields thereby improving numerical stability in addition use is made of amplitude and slope basis functions to describe the longitudinal dependence of em fields to avoid grid refinement in the vicinity of horizontal formation boundaries for validation we compare the new simulation method to two 1d analytic methods in horizontally and radially layered formations and to one 3d finite difference method 3dfd in multilayered formations that include borehole and invasion zones numerical results indicate that the method is accurate in formations with high conductivity contrasts compared to 1d methods and is more than ten times more efficient than the 3dfd method in multilayer formations

finite element analysis of controlled source electromagnetic induction using coulomb gauged potentials a 3 d finite element solution has been used to solve controlled source electromagnetic em induction problems in heterogeneous electrically conducting media the solution is based on a weak formulation of the governing maxwell equations using coulomb gauged em potentials the resulting sparse system of linear algebraic equations is solved efficiently using the quasi minimal residual method with simple jacobi scaling as a preconditioner the main aspects of this work include the implementation of a 3 d cylindrical mesh generator with high quality local mesh refinement and a formulation in terms of secondary em potentials that eliminates singularities introduced by the source these new aspects provide quantitative induction log interpretation for petroleum exploration applications examples are given for 1 d 2 d and 3 d problems and favorable comparisons are presented against other previously published multidimensional em induction codes the method is general and can also be adapted for controlled so

two dimensional induction log modeling using a coupled mode multiple reflection series method in induction logging both vertical and radial conductivity variations exist in the logged medium elementary separation of variables cannot be applied directly to the partial differential equation describing the electromagnetic field in such a medium a modal expansion method of solution can be designed using modes defined with respect to the vertical coordinate this method breaks the original two dimensional 2 d problem into a set of independent one dimensional 1 d problems the receiver signal is decomposed into a direct signal traveling within the borehole and a reflection signal bearing information about the conductivity distribution outside the borehole the solution is obtained as a coupled mode multiple reflection series accounting for repeated mode reflections at the vertical boundaries in the medium each term in the series represents the next higher order reflection in a sequence of multiple reflections results show two terms are sufficient to reach accuracy acceptable for log modeling

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

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

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

numerical mode matching method for the multiregion vertically stratified media em wave propagation the response of a source in the presence of an n region vertically stratified media is solved using the numerical mode matching method by treating the fields propagating in the direction parallel to the subboundaries of the stratified media in terms of the propagators and by introducing the concepts of reflection operators transmission operators and generalized reflection operators the two dimensional problem is reduced to several one dimensional problems which are solved by the one dimensional finite element method fem the one dimensional method saves computer storage and computation time compared to the two dimensional version a formulation valid for a general n region vertically stratified medium is derived when there are only three regions the results compare well with those in the literature some typical numerical results for n 3 are also shown

computation of potentials from current electrodes in cylindrically stratified media we present an efficient and robust semi analytical formulation to compute the electric potential due to arbitrary located point electrodes in three dimensional cylindrically stratified media where the radial thickness and the medium resistivity of each cylindrical layer can vary by many orders of magnitude a basic roadblock for robust potential computations in such scenarios is the poor scaling of modified bessel functions used for computation of the semi analytical solution for extreme arguments and or orders to accommodate this we construct a set of rescaled versions of modified bessel functions which avoids underflows and overflows in finite precision arithmetic and minimizes round off errors in addition several extrapolation methods are applied and compared to expedite the numerical evaluation of the otherwise slowly convergent associated sommerfeld type integrals the proposed algorithm is verified in a number of scenarios relevant to geophysical exploration but the general formulation presented is also applicable to other problems governed by poisson equation such as newtonian gravity heat flow and potential flow in fluid mechanics involving cylindrically stratified environments

a generalized haskell matrix method for borehole electromagnetics theory and applications in borehole electromagnetics both cylindrical and planar interfaces are present leading to nonseparable field equations the problem is two dimensional 2 d and the finite element method is usually employed for solution in this paper the generalized haskell matrix layer eigenstate propagator method is introduced to this class of problems in the method the solution problem is decomposed into a set of one dimensional 1 d problems and then the 1 d solutions are combined to form the final solution the method employs no approximation other than discretization of a continuous system as in all computer methods induction logs are calculated for the 6ff40 tool and a number of models results agree well with those of the finite element method an important case in induction log interpretation is studied namely a three layer formation traversed by a borehole the center layer being an oil bearing resistive layer sandwiched between two conductive shoulder layers simulation shows that conventional c

jacobian elliptic function solutions of the discrete cubic quintic nonlinear schrodinger equation the study of solitary wave solutions is of prime significance for the nonlinear schrodinger equation with higher order dispersion and or higher degree nonlinearities in nonlinear physical systems we derive the discrete cubic quintic nonlinear schrodinger equation from a hamiltonian using different poisson brackets by using the extended jacobian elliptic function approach we investigate the abundant exact stationary solitons and periodic waves solution of this equation these solutions include jacobian periodic solutions alternating phase jacobi periodic solution kink and bubble soliton solutions alternating phase kink soliton solution and alternating phase bubble soliton solution provided that coefficients are bound by special relation and then with the aid of symbolic computation we present in explicit form these solutions the stability of bubble and kink soliton as well as alternating kink and alternating bubble soliton are also investigated

three dimensional induction logging problems part 2 a finite difference solution a 3 d finite difference solution is implemented for simulating induction log responses in the quasi static limit that include the wellbore and bedding that exhibits transverse anisotropy the finite difference code uses a staggered grid to approximate a vector equation for the electric field the resulting linear system of equations is solved to a predetermined error level using iterative krylov subspace methods to accelerate the solution at low induction numbers lins a new preconditioner is developed this new preconditioner splits the electric field into curl free and divergence free projections which allows for the construction of an approximate inverse operator test examples show up to an order of magnitude increase in speed compared to a simple jacobi preconditioner comparisons with analytical and mode matching solutions demonstrate the accuracy of the algorithm

efficient simplicial reconstructions of manifolds from their samples an algorithm for manifold learning is presented given only samples of a finite dimensional differentiable manifold and no a priori knowledge of the manifold s geometry or topology except for its dimension the goal is to find a description of the manifold the learned manifold must approximate the true manifold well both geometrically and topologically when the sampling density is sufficiently high the proposed algorithm constructs a simplicial complex based on approximations to the tangent bundle of the manifold an important property of the algorithm is that its complexity depends on the dimension of the manifold rather than that of the embedding space successful examples are presented in the cases of learning curves in the plane curves in space and surfaces in space in addition a case when the algorithm fails is analyzed

fast 2d inversion of large borehole em induction data sets with an efficient frechet derivative approximation in addition to reliability and stability the efficiency and expediencyofinversionmethodshavelongbeenastrongconcernfor their routine applications by well log interpreters we have developedandsuccessfullyvalidatedanewinversionmethodtoestimate2dparametricspatialdistributionsofelectricalresistivity from array induction measurements acquired in a vertical well the central component of the method is an efficient approximation to frechet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion to further enhance the overall efficiency of the inversion we combined the new approximation with both the improved numerical mode matching method and domain decomposition examples of application with synthetic data sets show that the new method iscomputerefficientandcapableofretrievingoriginalmodelresistivities even in the presence of noise performing equally well in both high and low contrasts of formation resistivity in thin resistive beds the new inversion method estimates more accurate resistivities than standard commercial deconvolution software we also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately 40 minutes of cpu time on a desktop computer in addition to 2d parametric spatial distributions of electrical resistivity the new inversion methodprovidesaqualitativeindicatoroftheuncertaintyofestimated parameters based on the estimator s covariance matrix the uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfitlieswithinthemeasurementerrornoise

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

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

efficient computation of electromagnetic waves in anisotropic orthogonal plano cylindrically layered media using the improved numerical mode matching nmm method an orthogonal plano cylindrically layered opcl medium consists of materials stratified planarly and layered concentrically in the orthogonal directions the numerical mode matching nmm method has previously been shown to be a fast and robust semianalytical solver to investigate the propagation of electromagnetic em waves in such a complex but isotropic or transversely isotropic medium in this paper several important improvements have been made to extend applications of this efficient solver to the anisotropic ocpl medium the formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application the perfectly matched layer pml is incorporated along the radial direction as an absorbing boundary condition abc to make the nmm method more accurate and efficient for unbounded low conductivity media and applicable to lossless media we manipulate the weak form of maxwell s equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem finally we also offer formulas for computing em fields excited by a magnetic dipole located at any position with an arbitrary orientation numerical results have demonstrated the efficiency and accuracy of this method

an efficient rescaled formulation for tensor green s function computation in cylindrical multilayered media a robust formulation is presented to eliminate overflow underflow and convergence problems that arise the computation of tensor green s functions in cylindrical multilayered media under finite precision arithmetic this is done by first introducing a set of rescaled functions associated to the canonical cylindrical bessel and hankel functions representing standing waves and outgoing waves along the radial direction the rescaled cylindrical functions are designed to avoid the poor scaling inherent to the canonical cylindrical functions for very small or very large arguments in addition a parabolic sommerfeld integration path is constructed in the spectral complex plane to yield a numerical integration with good convergence properties for a wide range of parameter values

efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders an efficient and accurate hybrid method based on the combination of the method of moments mom with a special green s function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders the efficiency and accuracy of the method depend strongly on the computation of the green s function which is the kernel of the integral equation that is solved via mom for the unknown equivalent currents representing only the antenna elements three types of space domain green s function representations are used each accurate and computationally efficient in a given region of space consequently a computationally optimized analysis tool for conformal microstrip antennas is obtained input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method

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

novel and stable formulations for the response of horizontal coil eccentric antennas in a cylindrically multilayered medium in this paper we present a set of novel and stable formulations to calculate the response of logging tools with horizontal coil antennas in an eccentric borehole straddling cylindrically multilayered formations it can be applied in fast forward computation and the inverse problem for electromagnetic em well logging in deviated and horizontal wells where eccentric scenarios are often encountered our formulations are different from previous ones in following aspects first the tool mandrel can be cylindrically multilayered and the electrical parameters of each layer are arbitrary namely it is not limited to being perfectly metallic second the em propagation in inhomogeneous medium is considered by the generalized reflection and transmission method in place of the transfer matrices the associated generalized reflection and transmission coefficients are expressed by the ratios of bessel or hankel functions that obviate the notorious overflow problem for numerical computation finally a set of linear matrix functions are constructed to solve for the em waves in a borehole based on the concept of the generalized reflection rather than that of the fictitious boundary numerical results in comparison with those from other approaches have demonstrated the validity and stability of our new formulations

discrete klein gordon models with static kinks free of the peierls nabarro potential for the nonlinear klein gordon type models we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice these discrete models are therefore free of the peierls nabarro potential previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method a relevant physical consequence of our findings is the existence of a wide class of discrete klein gordon models where slow kinks practically do not experience the action of the peierls nabarro potential such kinks are not trapped by the lattice and they can be accelerated by even weak external fields