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

the fast multipole method fmm for electromagnetic scattering problems the fast multipole method fmm developed by v rokhlin 1990 to efficiently solve acoustic scattering problems is modified and adapted to the second kind integral equation formulation of electromagnetic scattering problems in two dimensions the present implementation treats the exterior dirichlet problem for two dimensional closed conducting objects of arbitrary geometry the fmm reduces the operation count for solving the second kind integral equation from o n sup 3 for gaussian elimination to o n sup 4 3 per conjugate gradient iteration where n is the number of sample points on the boundary of the scatterer a sample technique for accelerating convergence of the iterative method termed complexifying k the wavenumber is also presented this has the effect of bounding the condition number of the discrete system consequently the operation count of the entire fmm all iterations becomes o n sup 4 3 computational results for moderate values of ka where a is the characteristic size of the scatterer are given

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

asymptotic behavior of solutions of second order differential equations with integrable coefficients the differential equation x a t f x 0 t 0 is considered under the condition that lim x fl a s ds exists and is finite and necessary and or sufficient conditions are given for this equation to have solutions which behave asymptotically like nontrivial linear functions cl c2t

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

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

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

characterization of subwavelength elastic cylinders with the decomposition of the time reversal operator theory and experiment the decomposition of the time reversal operator provides information on the scattering medium it has been shown chambers and gautesen j acoust soc am 109 2616 2624 2001 that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time reversal operator in this paper the 2d problem of scattering by an elastic cylinder imbedded in water measured by a linear array of transducers is considered in this case the array response matrix has three nonzero singular values experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength it is shown how the singular value distribution and the singular vectors depend on the elastic velocities cl ct the density of each wire and on the density 0 and velocity c0 of the surrounding fluid these results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array proce

homoclinic orbits for second order self adjoint difference equations abstract in this paper we discuss how to use variational methods to study the existence of nontrivial homoclinic orbits of the following nonlinear difference equations p t u t 1 q t u t f t u t t z without any periodicity assumptions on p t q t and f providing that f t x grows superlinearly both at origin and at infinity or is an odd function with respect to x r and satisfies some additional assumptions

dependence on parameters for a discrete emden fowler equation abstract we investigate the dependence on parameters for the discrete boundary value problem connected with the emden fowler equation a variational method is used in order to obtain a general scheme allowing for investigating the dependence on parameters of discrete boundary value problems

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

scattering from multiple objects buried beneath two dimensional random rough surface using the steepest descent fast multipole method generalized formulations are presented to analyze the electric field scattered from multiple penetrable shallow objects buried beneath two dimensional random rough surfaces these objects could have different materials shapes or orientations in addition their separation distance may range from a fraction of a wavelength to several wavelengths the fast algorithm steepest descent fast multipole method sdfmm is used to compute the unknown electric and magnetic surface currents on the rough ground surface and on the buried objects parametric investigations are presented to study the effect of the objects proximity orientations materials shapes the incident waves polarization and the ground roughness on the scattered fields a significant interference is observed between the objects when they are separated by less than one free space wavelength even when the clutter due to the rough ground is removed the return from the second object can be dominating causing a possible false alarm in detecting the target the results show that the distortion in target signature significantly increases with the increase of both the proximity to a clutter item and the ground roughness

nontrivial solutions of boundary value problems of second order difference equations we employ the critical point theory to establish the existence of nontrivial solutions for some boundary value problems of second order difference equations

existence and multiple solutions for a second order difference boundary value problem via critical point theory in this paper the critical point theory is employed to establish existence and multiple solutions for a second order difference boundary value problem

a note on the multiplicity of solutions for a second order difference equation with a parameter abstract we undertake the question of the multiplicity of solutions to the discrete emden fowler bvp by correcting some results contained in 2

existence of multiple solutions for a second order difference equation with a parameter applying the critical point theorem we establish existence and multiple solutions for a second order difference boundary value problem and show the explicit intervals of l such that the equation has at least 2n distinct solutions

existence and multiplicity of solutions for nonlinear second order difference boundary value problems in the present paper the following nonlinear second order difference boundary value problems d p n 1 du n 1 q n u n f n u n 0 n z 1 n u 0 u n p 0 du 0 p n du n are studied by using the critical theory and three new multiple results of solutions are obtained where z 1 n 1 2 n f z 1 n xr r is a continuous function in the second variable p q z 0 n r and p n 0

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

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

multiple scattering between two elastic cylinders and invariants of the time reversal operator theory and experiment the decomposition of the time reversal operator method is an ultrasonic method based on the analysis of the array response matrix used for detection and characterization the eigenvalues and the eigenvectors of the time reversal operator equivalent to the singular values and the singular vectors of the array response matrix provide information on the localization and nature of scatterers in the insonified medium here the eigenmodes of the time reversal operator are studied for two elastic cylinders the effects of multiple scattering and anisotropic scattering are considered analytical expressions for the singular values are established within the isotropic scattering approximation then the comparison with a complete model is presented putting in evidence the importance of the anisotropy of the scattering experiments carried out at central frequency 1 5mhz on 0 25mm diameter nylon and copper cylinders embedded in water confirm the theory in particular the small cylinder limit and the effect o

positive solutions for nonlinear discrete second order boundary value problems with parameter dependence in this paper we consider the nonlinear discrete boundary value problem p t 1 u t 1 q t u t f t u t t z 1 t u 0 u t p 0 u 0 p t u t where is a positive parameter by using the fixed point index theory the criteria of the existence multiplicity and nonexistence of positive solutions are established in terms of different values of