direct singular integral equation methods in scattering and propagation in strip or slot loaded structures problems of three dimensional 3 d scattering hybrid wave propagation for strip or slot loaded structures are often formulated in terms of systems of singular integral integrodifferential equations sie side of the first kind proper handling of the singular part of the kernels constitutes a major difficulty in carrying out method of moments mom three powerful techniques explored in the present paper provide efficient solutions by direct recourse to the theory of singular integral equations in contrast to low frequency methods wherein similar concepts are utilized for electrically narrow strips slots the proposed procedures are applicable uniformly to the whole range of widths from very narrow to very wide scatterers with remarkable accuracy numerical results are presented to validate and compare to one another the various numerical codes

exact image theory for the calculation of fields transmitted through a planar interface of two media exact image theory recently developed for the calculation of fields reflected from a planar interface between two homogenous media is extended for transmitted field calculation the image of a point source is found to be a line source located in complex space for proper convergence unlike for the reflection image the transmission image line is seen to be curved in complex space for efficient computation expressions are derived for the transmission image of the most general three dimensional electric and magnetic sources and for media with both epsilon and mu discontinuous across the interface the new theory is verified with several asymptotic tests and properties of the transmission image function are discussed as an application radiation from a resonant horizontal loop antenna into the ground is calculated and results are seen to agree with those given in the literature

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

numerical mode matching for sound propagation in silencers with granular material abstract this work presents an efficient numerical approach based on the combination of the mode matching technique and the finite element method fem to model the sound propagation in silencers containing granular material and to evaluate their acoustic performance through the computation of transmission loss tl the methodology takes into account the presence of three dimensional 3d waves and the corresponding higher order modes while reducing the computational expenditure of a full 3d fem calculation first the wavenumbers and transversal pressure modes associated with the silencer cross section are obtained by means of a two dimensional fem eigenvalue problem which allows the consideration of arbitrary transversal geometries and material heterogeneities the numerical approach considers the possibility of using different filling levels of granular material giving rise to cross sections with abrupt changes of properties located not only in the usual central perforated passage but also in the transition between air and material that involves a significant change in porosity after solving the eigenvalue problem the acoustic fields acoustic pressure and axial velocity are coupled at geometric discontinuities between ducts through the compatibility conditions to obtain the complete solution of the wave equation and the acoustic performance tl the granular material is analysed as a potential alternative to the traditional dissipative silencers incorporating fibrous absorbent materials sound propagation in granular materials can be modelled through acoustic equivalent properties such as complex and frequency dependent density and speed of sound tl results computed by means of the numerical approach proposed here show good agreement with full 3d fem calculations and experimental measurements as expected the numerical mode matching outperforms the computational expenditure of the full 3d fem approach different configurations have been studied to determine the influence on the tl of several parameters such as the size of the material grains the filling level of the chamber the granular material porosity and the geometry of the silencer cross section

general solutions of the narrow strip and slot integral equations analytic solutions of the integral equations for the current induced on a narrow conducting strip are obtained by two methods one method follows from an expansion of the strip current in a series of chebyshev polynomials while the other is based on a special power series expansion in the former fourier type coefficients depending on integrals of the excitation are derived while in the latter the coefficients depend upon derivatives of the excitation from knowledge of the strip current simple expressions for the far zone scattered field are derived explicit results are given for plane wave excitation the solution methods apply to the equations for the narrow slot in a planar conducting screen

the transfer matrix for a dissipative silencer of arbitrary cross section in this work the acoustic transfer matrix for a cylindrical dissipative silencer of arbitrary cross section and bulk reacting lining is derived for the case of negligible mean flow the derivation is performed in a two step procedure first the corresponding infinite lined duct is analyzed by separating the longitudinal dependence and using collocation for the entailing eigenvalue problem then using the resulting eigenmodes the acoustic field in the silencer is expanded and adjusted to the boundary conditions at the in outlet by mode matching to illustrate the applicability and numerical efficiency of the proposed technique a practical example is given

cluster synchronization in directed networks of partial state coupled linear systems under pinning control this paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure for the case with fixed topology it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters the couplings within the each cluster are sufficiently strong an extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies such a balanced condition can be removed via the use of dwell time technique for all the cases the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified finally some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings

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

cluster synchronization of complex networks via event triggered strategy under stochastic sampling abstract this paper is concerned with the issue of mean square cluster synchronization of non identical nodes connected by a directed network suppose that the nodes possess nonlinear dynamics and split into several clusters then an event triggered control scheme is proposed for synchronization based on the information from stochastic sampling meanwhile an equilibrium is considered to be the synchronization state or the virtual leader for each cluster which can apply pinning control to the following nodes assume that a spanning tree exists in the subgraph consisting of the nodes belonging to the same cluster and the corresponding virtual leader and the instants for updating controllers are determined by the given event triggered strategy then some sufficient conditions for cluster synchronization are presented according to the lyapunov stability theory and linear matrix inequality technique finally a specific numerical example is shown to demonstrate the effectiveness of the theoretical results

computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths the acoustic modelling of automotive exhaust devices such as catalytic converters cc and diesel particulate filters dpf usually requires the use of multidimensional analytical and numerical techniques the presence of higher order modes and three dimensional waves in the expansion and contraction subdomains as well as sound propagation within the monolith capillary ducts can be considered through the finite element method fem although this approach is traditionally thought to be very time consuming with a view to overcome this limitation and to reduce the computational effort of the fem alternative modelling techniques are presented in the current work to speed up transmission loss calculations in exhaust devices incorporating monoliths these approaches are based on the point collocation technique and the mode matching method as shown in earlier studies the sound attenuation of an exhaust device incorporating a monolith can be properly predicted if the latter is replaced by a plane wave four pole transfer matrix providing a relationship between the acoustic fields at both sides of the monolithic region therefore this work combines the presence of multidimensional higher order modes in the expansion and contraction regions with one dimensional wave propagation within the capillary ducts of the central monolith the point collocation technique and the mode matching method are applied to the compatibility conditions of the acoustic fields at all the subdomain interfaces to couple the solutions of the wave equation in the corresponding exhaust device subcomponents for the particular case of rigid circular ducts bessel functions are considered as transversal pressure modes the computational efficiency and accuracy of the results associated with the two analytical modelling techniques presented here are assessed including the effect of the number of modes and collocation points as well as their location all the analytical approaches proposed in this work provide accurate predictions of the device attenuation performance and outperform the computational expenditure of a fe computation some differences are found however among the various analytical schemes in terms of computational speed and solution accuracy from the results presented here the mode matching method is the most efficient technique for the particular configurations under study mainly due to the possibility of exploiting the orthogonality properties of the transverse pressure modes analytical techniques are proposed to speed up tl calculations in exhaust devices with monoliths multidimensional sound propagation in the ducts is combined with plane waves in the capillaries the computational effort and accuracy of the analytical approaches is compared

a point collocation approach to modelling large dissipative silencers a numerical matching technique known as point collocation is used to model mathematically large dissipative splitter silencers of a type commonly found in hvac ducts transmission loss predictions obtained using point collocation are compared with exact analytic mode matching predictions in the absence of mean flow over the frequency range in which analytic mode matching predictions are available excellent agreement with point collocation transmission loss predictions is observed for a range of large splitter silencers the validity of using point collocation to tackle large dissipative silencers is established as is the computational efficiency of the method and its suitability for tackling dissipative silencers of arbitrary but axially uniform cross sections

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

cluster synchronization in directed networks of non identical systems with noises via random pinning control abstract this paper is concerned with the issue of mean square cluster synchronization in directed networks which consist of non identical nodes infected by communication noises the pinning control method is employed in designing controllers for guaranteeing cluster synchronization meanwhile all the controllers are supposed to occur with different probabilities by introducing the bernoulli stochastic variables based on the lyapunov stability theory and the stochastic theory the sufficient synchronization conditions are derived and proved theoretically which are mainly for the controllers to be designed and the noise intensities finally some numerical examples are presented to demonstrate the effectiveness of the results

a fast multipole method for layered media based on the application of perfectly matched layers the 2 d case an efficient fast multipole method fmm formalism to model scattering from two dimensional 2 d microstrip structures is presented the technique relies on a mixed potential integral equation mpie formulation and a series expression for the green functions based on the use of perfectly matched layers pml in this way a new fmm algorithm is developed to evaluate matrix vector multiplications arising in the iterative solution of the scattering problem novel iteration schemes have been implemented and a computational complexity of order o n is achieved the theory is validated by means of several illustrative numerical examples this paper aims at elucidating the pml fmm mpie concept and can be seen as a first step toward a pml based multilevel fast multipole algorithm mlfma for 3 d microstrip structures embedded in layered media

scattering of h polarized waves from conducting strips in the presence of an electrically uniaxial half space a singular integrodifferential equation approach electromagnetic scattering from perfectly conducting infinitely long strips in the presence of an electrically uniaxial half space is treated analytically a uniform h polarized plane wave is incident from the isotropic region as a prerequisite to this approach the h mode scalar green s function of the structure is developed its use in connection with the reciprocity theorem leads to a singular integrodifferential equation for the current density induced on the scatterer surface the equation is solved for strips parallel or perpendicular to the interface located above or embedded in the anisotropic region following a special technique based on the theory of singular integral equations that has been developed in connection with strips and slots and e or h polarized incident waves numerical results for the induced current density and for the scattered far field in a variety of cases are presented in graphical form whenever possible they are compared with existing results based on purely numerical procedures

the point matching method on dissipative silencers of arbitrary cross section a most straightforward and simple numerical technique known as point matching or collocation is used to obtain the wavenumbers and eigenmodes of an infinite cylindrical dissipative silencer of arbitrary cross section in the case of negligible mean flow this technique provides an alternative both to the different numerical variational formulations used in the literature so far as well as to possible analytical techniques such as for instance the null field approach in principle the point matching method does not suffer from any severe restrictions upon the cross sectional shape of the silencer even though the rate of convergence is strongly related to the geometry the grid used in the collocation is also found to be critical for the rate of convergence especially in the case of the points in the collocation separated by equal polar angles the results are poor to handle this complication a simple technique for choosing the grid is proposed to show the applicability of the point matching method a commercial dissipative silencer is analyzed and comparisons with measurements are made

point collocation scheme in silencers with temperature gradient and mean flow this work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow three dimensional wave propagation is considered in silencer geometries with arbitrary but axially uniform cross section to reduce the computational requirements of a full multidimensional finite element calculation a method is developed combining axial and transversal solutions of the wave equation first the finite element method is employed in a two dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section mean flow as well as transversal temperature gradients and the corresponding thermal induced material heterogeneities are included in the model in addition an axially uniform temperature field is taken into account its value being the inlet outlet average a point collocation technique is then used to match the acoustic fields pressure and axial acoustic velocity at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes transmission loss predictions are compared favorably with a general three dimensional finite element approach offering a reduction in the computational effort sound attenuation in perforated dissipative silencers including temperature gradients and mean flow is computed a two dimensional finite element eigenvalue problem is solved for a silencer cross section with transversal thermal variations a point collocation scheme is presented to match the acoustic pressure and axial velocity at the silencer geometrical discontinuities a significant reduction in the computational requirements is obtained compared to a full three dimensional finite element approach

surface electric fields and impedance matrix elements of stratified media for the various geometrical configurations of waves in stratified media we consider the important case when both source and field points are located on the same interface separating two different dielectric media we denote this configuration as surface electric field case in this paper the electric fields are calculated numerically without using potentials for the surface electric field case the integrand of the electric field grows with k sub spl rho sup 3 2 for large spl kappa sub spl rho making the sommerfeld integral singular to calculate the surface electric fields in the spatial domain we previously applied a technique of higher order asymptotic extraction in the higher order asymptotic extraction the higher order asymptotic parts were calculated analytically the remainder which has an integrand decays as spl kappa sub spl rho sup 3 2 was calculated numerically along the sommerfeld contour path of integration in this paper we use a different extraction technique the half space extraction after the half space extraction the integrand of the sommerfeld integral of stratified media decays exponentially and the integral is calculated along the sommerfeld integration path the half space extraction part is calculated by numerical integration along the vertical branch cuts the surface electric fields for stratified media using half space extraction and higher order asymptotic extraction are in good agreement to validate the accuracy of the solution we also compute the impedance matrix elements using surface electric fields testing and basis functions all in the spatial domain the results are then compared with the results of the spectral domain method the comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2

experiments on node to node pinning control of chua s circuits abstract in this paper we study the global intermittent pinning controllability of networks of coupled chaotic oscillators we explore the feasibility of the recently presented node to node pinning control strategy through experiments on chua s circuits we focus on the case of two peer to peer coupled chua s circuits and we build a novel test bed platform comprised of three inductorless chua s oscillators we investigate the effect of a variety of design parameters on synchronization performance including the coupling strength between the oscillators the control gains and the switching frequency of node to node pinning control experimental results demonstrate the effectiveness of this novel pinning control strategy in rapidly taming chaotic oscillator dynamics onto desired reference trajectories while minimizing the overall control effort and the number of pinned network sites from an analytical standpoint we present sufficient conditions for global node to node pinning controllability and we estimate the maximum switching period for network controllability by adapting and integrating available results on lyapunov stability theory and partial averaging techniques

scattering of arbitrarily polarized plane waves obliquely incident on infinite slots or strips in a planar stratified medium an exact analysis of three dimensional scattering by a slot or by a strip right on an interface between two adjacent layers of a planar stratified isotropic medium is presented the most general case of arbitrarily polarized obliquely incident plane waves is considered the formulation is based on systems of singular integral integrodifferential equations sie side these systems are discretized with the help of two independent algorithms developed by tsalamengas see ibid vol 46 p 1560 70 1998 filling up the matrix elements involves rapidly convergent spectral integrals the expression of the far radiated field is derived and numerical results are presented for several cases

self triggered output feedback control of linear plants in the presence of unknown disturbances this note addresses the control of linear time invariant plants in the presence of unknown bounded disturbances when the output of the plant is only measured at sampling instants determined by a self triggered strategy in a self triggered scenario the controller is allowed to choose when the next sampling time should occur and does so based on available measurements and on a priori knowledge about the plant the proposed solution is a cascade interconnection of a state observer and a self triggered state feedback controller we focus our attention on state observers that are only updated at sampling times and that are input to state stable iss with respect to disturbances due to the cascade structure of the closed loop system and the fact that self triggered control strategies presented in the literature are iss with respect to observation errors and exogenous disturbances we conclude that the closed loop is rendered iss with respect to exogenous disturbances

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