second order pml the n th order pmls based on the unsplit field formulations and the z transform methods are proposed to truncate the finite difference time domain fdtd domains which will be validated through numerical simulations whether the higher order pml with more than two poles such as n 3 will hold better absorption performance as compared with the conventional complex frequency shifted cfs second order perfectly matched layer pmls the advantages and disadvantages of different pmls are demonstrated it has shown that the higher order pmls have the advantages of both the conventional and the cfs pmls in terms of absorption performance since the conventional pml is ineffective at absorbing the evanescent waves and the cfs pml is incapable of absorbing low frequency propagating waves it is clearly shown that the second order pml is overall the optimal choice for truncating arbitrary fdtd domains since it not only requires less computational time and memory but holds almost the same absorption performance as compared with the third order pml three numerical simulations have been carried out in three dimensional 3d problems to confirm the analysis

a generalized recursive convolution method for time domain propagation in porous media an efficient numerical method referred to as the auxiliary differential equation ade method is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media for this purpose the relaxation functions are approximated in the frequency domain by rational functions the time variation of the convolution is thus governed by first order differential equations which can be straightforwardly solved the accuracy of the method is first investigated and compared to that of recursive convolution methods it is shown that while recursive convolution methods are first or second order accurate in time the ade method does not introduce any additional error the ade method is then applied for outdoor sound propagation using the equations proposed by wilson et al in the ground 2007 appl acoust 68 173 200 a first one dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications finally the ade method is used to compute sound propagation in a three dimensional geometry over an absorbing ground results obtained with wilson s equations are compared to those obtained with zwikker and kosten s equations and with an impedance surface for different flow resistivities

a finite difference method for dispersive linear waves with applications to simulating microwave pulses in water the epdmethod a finite difference method for highly dispersive linear wave equations is introduced and analyzed motivated by the problem of simulating the propagation of microwave pulses through water the method attempts to relieve the computational burden of resolving fast processes such as dipole relaxation or oscillation occurring in a material with dynamic structure this method based on a novel differencing scheme for the time step is considered primarily for problems in one spatial dimension with constant coefficients it is defined in terms of the solution of an initial value problem for a system of ordinary differential equations that in an implementation of the method need be solved only once in a preprocessing step for certain wave equations of interest nondispersive systems the telegrapher s equation and the debye model for dielectric media explicit formulas for the method are presented the dispersion relation of the method exhibits a high degree of low wavenumber asymptotic agreement with the dispersion relation of the model to which it is applied comparisons with a finite difference time domain approach and an approach based on strang splitting demonstrate the potential of the method to substantially reduce the cost of simulating linear waves in dispersive materials a generalization of the epdmethod for problems with variable coefficients appears to retain many of the advantages seen for constant coefficients

finite difference and pseudospectral time domain methods applied to backward wave metamaterials backward wave bw materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions these materials were predicted to have many unusual electromagnetic properties among them amplification of the near field of a point source which could lead to the perfect reconstruction of the source field in an image j pendry phys rev lett vol 85 pp 3966 2000 often systems containing bw materials are simulated using the finite difference time domain technique we show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving bw materials problematic the pseudospectral time domain technique on the other hand uses a collocated grid and is free of this artifact it is also shown that when modeling the dispersive bw material the linear frequency approximation method introduces error that affects the frequency of vanishing reflection while the auxiliary differential equation the z transform and the bilinear frequency approximation method produce vanishing reflection at the correct frequency the case of vanishing reflection is of particular interest for field reconstruction in imaging applications

debye function expansions of complex permittivity using a hybrid particle swarm least squares optimization approach with appropriate modifications the finite difference time domain fdtd method can be used to analyze propagation through linear isotropic dispersive media although materials characterized by the debye permittivity model can be analyzed accurately and efficiently using well established methods the treatment of other types of frequency dependence is more difficult this paper proposes the use of a weighted sum of debye functions to approximate more general complex permittivity functions a combination of the particle swarm optimization method and linear least squares optimization is used to find the relaxation frequencies and weights in the expansion which can then be accommodated in the fdtd method using one of the established methods two key advantages of the proposed approach are that the relaxation frequencies are bandlimited and the weights are always positive these two characteristics help to maintain the accuracy and stability of the fdtd solution it is also shown that the correlation between the imaginary parts of two debye functions is the same as that between the real parts

time domain numerical simulation of a flow impedance tube an efficient method has been developed for the application of the surface acoustic impedance condition in time domain solutions of aeroacoustic problems such as the broadband frequency simulation of a flow impedance tube the basis for this method is the standard impedance condition stated in the frequency domain as the particle displacement continuity equation the development of the time domain impedance condition follows the relations among the frequency z and discrete time domains and a rational function representation of the impedance in thez domain the resultant impedance condition consists of finite infinite impulse response type digital filter operations in the time domain which is very suitable to computational aeroacoustics algorithms this paper describes the present approach and discusses the time domain numerical simulations of the nasa langley flow impedance tube with a constant depth ceramic tubular liner both single and broadband frequency simulations are performed excellent agreement is shown with experimental data at various frequencies and flow conditions

fdtd algorithm in curvilinear coordinates em scattering the finite difference time domain fdtd algorithm for the solution of electromagnetic scattering problems is formulated in generalized coordinates in two dimensions and implemented in a code with the lowest order bayliss turkel radiation boundary condition expressed in cylindrical coordinates it is shown that for a perfect conductor such a formulation leads to a stable well posed algorithm and that in regions where the curvature of the coordinate lines is not great the dispersion and anisotropy effects are negligible such effects become more pronounced in regions of high curvature leading to unphysical phase shifts the magnitude of such shifts and the amount of wavefront distortion is studied via numerical experiments using a cylindrical mesh near field results are given for two canonical shapes for each polarization the circular cylinder and cylinders of square and rectangular cross sections these results are compared with those obtained by exact eigenfunction expansion techniques with method of moments mm solutions and with solutions obtained from an alternate fdtd approach in each case agreement is excellent the propagation of a plane wave through a polar space in the absence of a scatterer is also examined and it is shown that the fdtd algorithm is capable of tracking the incident wave closely

integral based exponential time differencing algorithms for general dispersive media and the cfs pml two efficient integral based exponential time differencing etd algorithms for general dispersive media in the finite difference time domain fdtd are introduced the first employs a linear approximation for the field over an integral time step in the integrand denoted algorithm i and the second employs a taylor series for approximating the field over the integral time step denoted algorithm ii compared with the auxiliary differential equation ade method and the piecewise linear recursive convolution plrc method the proposed algorithms have the same second order accuracy but can lead to a substantial saving in both the memory space and cpu time consumption to complete the scheme for the open region problems a novel integral based etd implementation of the complex frequency shifted perfectly matched layer cfs pml is proposed compared with the well known recursive convolution implementation of the cfs pml cpml this new implementation can lead to a substantial saving in the cpu time and a significant improvement of around 20 db in the absorbing performance and through the integral based etd algorithm a much simpler interpretation of the cpml is presented

transient analysis of dispersive periodic structures for oblique plane wave incidence using laguerre marching on in degree mod transient analysis of dispersive periodic structures in the case of obliquely incident plane wave is presented in this work the laguerre marching on in degree mod is used for the development of an unconditionally stable algorithm due to the unconditional stability courant freidrich levy cfl temporal discretization limit can be circumvented resulting in less simulation time compared to the conventional dispersive finite difference time domain fdtd this is particularly advantageous for multiscale dispersive structures the uniaxial perfectly matched layer upml is implemented in the laguerre domain by virtue of the laguerre decomposition the presented method can simulate general dispersive media compared to conventional dispersive fdtd which can simulate only standard dispersion models such as debye lorentz and drude the formulations are validated by estimating the transmission spectra of an infinite double pole debye slab and comparing the results with analytical results further confirmation is obtained by estimating the transmission spectra of zeroth order floquet mode of a 1d periodic array of dispersive square cylinders and comparing the results with periodic method of moments solution

fdtd analysis of periodic structures with arbitrary skewed grid an efficient finite difference time domain fdtd algorithm with a simple periodic boundary condition pbc is developed to analyze general periodic structures with arbitrary skewed grids the algorithm is easy to implement and efficient in both memory usage and computation time the stability criterion of the algorithm is angle independent and therefore it is suitable for implementing incidence with angle close to grazing as well as normal incidence the validity of this algorithm is verified through several numerical examples such as dipole and jerusalem cross frequency selective surfaces fss with various skew angles

spectral hirzebruch milnor classes of singular hypersurfaces we introduce spectral hirzebruch milnor classes for singular hypersurfaces these can be identified with steenbrink spectra in the isolated singularity case and may be viewed as their global analogues in general their definition uses vanishing cycles of mixed hodge modules and the todd class transformation these are compatible with the pushforward by proper morphisms and the classes can be calculated by using resolutions of singularities formulas for hirzebruch milnor classes of projective hypersurfaces in terms of these classes are given in the case where the multiplicity of a generic hyperplane section is not 1 these formulas using hyperplane sections instead of hypersurface ones are easier to calculate in certain cases here we use the thom sebastiani theorem for the underlying filtered d modules of vanishing cycles from which we can deduce the thom sebastiani type theorem for spectral hirzebruch milnor classes for the chern classes after specializing to y 1 we can give a relatively simple formula for the localized milnor classes which implies a new formula for the euler numbers of projective hypersurfaces using iterated hyperplane sections applications to log canonical thresholds and du bois singularities are also explained for instance the latter can be detected by using hirzebruch milnor classes in the projective hypersurface case

flatness based control of a nonlinear chemical reactor model the nonlinear model of a continuous stirred tank reactor is shown to be flat the flatness permits the design of suitable trajectories on the basis of the explicit stationary solution and the tracking of these trajectories asymptotically using quasi static state feedback linearization a nonlinear local observer with a time varying gain is designed allowing the realisation of the state feedback in the case of partial measurement of the state simulation results illustrate the tracking behavior of the closed loop with the observer

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

the poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface abstract for a simple complete ideal of a local ring at a closed point on a smooth complex algebraic surface we introduce an algebraic object named poincare series p that gathers in a unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to this paper is devoted to prove that p is a rational function giving an explicit expression for it

on the accuracy and stability of several widely used fdtd approaches for modeling lorentz dielectrics a rigorous and comparative study on the approximation accuracy and stability limits of several widely used finite difference time domain fdtd approaches namely the auxiliary differential equation ade approach the bilinear transform bt approach the z transform approach zt and the piecewise linear recursive convolution plrc approach for modeling dispersive lorentz dielectrics is presented following the given updating equations between the electric flux density and the electric field intensity we find the zt approach with modified material parameters is much more accurate than the original zt approach and the other three approaches for modeling lorentz dielectrics the stability limits of the ade zt and plrc approaches in simulating lorentz dielectrics are also shown to be a bit more stringent than that of bt approach which preserves the courant stability limit as previously reported

the analysis of periodic structures with 2 d staggered grid by fdtd algorithm according to the characteristics of the periodic structures with 2 d staggered grids two new effective construction methods dealing with periodic boundaries based on the finite difference time domain fdtd algorithm are developed in this work the two proposed staggered periodic boundary conditions pbc arrangement methods can be implemented combining the existing boundary data mapping techniques applying these arrangements coordinate change and additional ladder boundary grids can be avoided during the modeling process so that the simulation accuracy of the fdtd algorithm can be maintained the performance and the applicable conditions of the two staggered pbc arrangement methods are discussed and compared with the common nonstaggered pbc arrangement method the validity of the two staggered pbc arrangement methods is verified through the numerical examples of an infinite dielectric slab and jerusalem cross frequency selective surface with 2 d staggered girds

propagation in linear dispersive media finite difference time domain methodologies finite difference time domain fdtd methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media an nth order lorentz and an mth order debye medium the temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first order differential equations from this the final equations are temporally advanced using the classical leapfrog method one dimensional scattering from a dielectric slab is chosen for a test case provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space as shown in the error analysis the agreement between the computed and exact solutions will be excellent the attached data which are associated with the four pole lorentz dielectric and the five pole debye medium verify this assertion

generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

on b function spectrum and rational singularity by duality 18 because r tr ccy 0 for i 0 by 6 31 this follows also from 13 21 23 where rc is assumed projective here coy denotes the dualizing sheaf i e the dualizing complex 18 shifted by the dimension to the right the trace morphism 0 2 is injective and its image is independent of the choice of resolution because 0 2 is an isomorphism if y is smooth we will denote by csy the image of 0 2 see 2 4 8 below now assume y is a reduced divisor d on a complex manifold x of dimension n let f be a reduced defining equation of d on a neighborhood of a c d the b function i e bernstein polynomial of f is a monic polynomial bf s in s with rational coefficients and is a generator of the ideal whose element b s satisfies the relation

an analysis of new and existing fdtd methods for isotropic cold plasma and a method for improving their accuracy over the past few years a number of different finite difference time domain fdtd methods for modeling electromagnetic propagation in an isotropic cold plasma have been published we have analyzed the accuracy and stability of these methods to determine which method provides the greatest accuracy for a given computation time for completeness two new fdtd methods for cold plasma one of which is based on the concept of exponential fitting are introduced and evaluated along with the existing methods we also introduce the concept of cutoff modification which can be easily applied to most of the fdtd methods and which we show can improve the accuracy of these methods with no additional computational cost von neumann s stability analysis is used to evaluate the stability of the various methods and their accuracy is determined from a straightforward time and space harmonic analysis of the dispersion and dissipation errors results of numerical experiments to verify the accuracy analysis are presented it is found that for low loss plasma the piecewise linear recursive convolution method plrc method is the most accurate but the method of young see radio sci vol 29 p 1513 22 1994 can use less memory and is nearly as accurate in this low loss plasma regime cutoff modification can significantly reduce the error near cutoff at the expense of slightly greater error at lower frequencies for strongly collisional plasmas the plrc method also provides the most accurate solution

a novel td vie based on mot scheme for analysis of dispersive objects a novel time domain volume integral equation td vie is proposed to analyze the transient electromagnetic scattering from inhomogeneous dispersive objects in this td vie method the higher order nystrom method is applied in spatial domain namely the curvilinear tetrahedron elements are utilized to discretize dielectric objects and resulting unknowns are volume electric current density the lagrange interpolation polynomials are used to represent spatial basis functions in temporal domain the marching on in time mot scheme is applied and the shifted lagrange interpolation functions are used to represent temporal basis functions moreover the point matching method is applied both in spatial and temporal domain compared with the traditional spatial schaubert wilton glisson basis based on td vie this novel td vie method is more efficient several numerical examples have demonstrated that the proposed method is accurate stable and also more efficient than the traditional td vie

control of flat systems by quasi static feedback of generalized states generalized states the state representations of which depend on time derivatives of the input are naturally used in the control design for flat systems quasi static feedback of these generalized states which involves time derivatives of the closedloop input is shown to allow control of all flat systems by feedback linearization of the tracking error dynamics this is then used in a method proposed for the analysis and design by subsystems of certain flat series connections the results are illustrated on a gantry crane example

a pml using a convolutional curl operator and a numerical reflection coefficient for general linear media a general time domain representation of the chew and weedon 1994 stretched coordinate perfectly matched layer pml absorbing boundary condition is described this new approach mathematically operates on the spatial field derivatives and allows the pml update equations to be trivially derived from any set of general linear medium update equations a method for calculating the frequency dependent reflection coefficient for this form of the pml is derived for general linear media two and three dimensional numerical test results which validate the calculation of the reflection coefficient are presented the range of numerical tests include the pml matching of free space a magnetoplasma and a free space waveguide improving the reflection coefficient is examined

flatness based control of nonlinear delay systems a chemical reactor example a trajectory tracking control method for a class of non linear systems with time delays is proposed for this the new concept of delta flatness is introduced which is an extension of the notions of flatness for non linear systems and delta freeness for linear delay systems a two step design procedure is derived it splits into trajectory design which directly provides an open loop tracking controller and stabilization around the reference trajectory this feedback stabilization is based on a state prediction leading to a discrete time controller

efficient fdtd pml simulation of gain medium based on exponential time differencing algorithm an exponential time differencing etd algorithm is introduced to incorporate the homogeneously broadened lorentzian oscillator of gain medium in a four level atomic system into the finite difference time domain fdtd compared with the well known auxiliary differential equation ade method the proposed algorithm shows the same accuracy but can save one third of the additional memory space for treating the lorentzian oscillators and has simpler formulations the etd implementation of the stretched coordinates perfectly matched layer sc pml with the complex frequency shifted cfs stretching variable is applied to truncate computational domain with gain media simulations involving both te and tm waves indicate that compared with the modified conventional pmls and the convolution pml cpml the proposed absorbing boundary formulations can lead to a significant improvement of the absorbing performance with a similar memory requirement compared with the application of the material dependent pmls to the gain media in previous studies the proposed absorbing boundary condition has simpler formulas and can be applied to complex computational domains much more straightforwardly

flatness based control by quasi static feedback illustrated on a cascade of two chemical reactors flat non linear systems are linearizable by quasi static feedback of generalized states as a consequence stable tracking of reference trajectories can be achieved with controllers which do not introduce extra dynamics into the loop if moreover the system has a series structure this may be exploited for simplifying the flatness based analysis and design the resulting method is illustrated on a series connection of two chemical reactors flatness based analysis of the stationary solution and using these results the design of reference trajectories which account for constraints are discussed in detail quasi static feedback controllers are designed and some simulations are reported

corrected impulse invariance method in z transform theory for frequency dependent fdtd methods the classical impulse invariance method in z transform theory is found to be incorrect and inaccurate when the impulse response is discontinuous at initial time t 0 such inaccuracy results in higher numerical errors if it is used to develop the update equations for frequency dependent finite difference time domain fdtd methods in this paper thorough discussions of corrected impulse invariance method in the realm of z transform theory for dispersive media are presented the correction is shown to be necessary for dispersive media which exhibit discontinuity at t 0 in the time domain susceptibility function a corrected z transform table is provided to facilitate the conversion from frequency to z domain with the aid of the table various formulations of frequency dependent fdtd update equations using both corrected and classical impulse invariance methods are carried out conveniently detailed performance measures such as numerical permittivity leading error term dispersion relation normalized phase and attenuation errors as well as memory storage requirements are included along with some extensive numerical comparisons

observer design for nonlinear systems under unknown time varying delays the design of observers for nonlinear systems with unknown time varying bounded delays on both state and input still constitutes an open problem in this technical note we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a lyapunov krasovskii functional suitable choice sufficient conditions are provided to prove the practical stability of the observer it is shown that the observation error is bounded and depends on the size of two parameters the known upper bound delay of the unknown time varying function delay and the instantaneous state dynamic variation furthermore for the particular case of constant known time delay the convergence of the proposed observer becomes exponential the feasibility of the proposed strategy is illustrated by a numerical example

high order accurate fdtd schemes for dispersive maxwell s equations in second order form using recursive convolutions abstract we propose a novel finite difference time domain fdtd scheme for the solution of maxwell s equations in which linear dispersive effects are present the method uses high order accurate approximations in space and time for the dispersive maxwell s equations written as a second order vector wave equation with a time history convolution term the modified equation approach is combined with the recursive convolution rc method to develop high order approximations accurate to any desired order in space and time high order accurate centered approximations of the physical maxwell interface conditions are derived for the dispersive setting in order to fully restore accuracy at discontinuous material interfaces second and fourth order accurate versions of the scheme are presented and implemented in two spatial dimensions for the case of the drude linear dispersion model the stability of these schemes is analyzed finally our approach is also amenable to curvilinear numerical grids if used with an appropriate generalized laplace operator

inner jumping numbers of non degenerate polynomials the inner jumping numbers were introduced by budur to relate two different measures of the complexity of the singularities of an effective divisor d on a nonsingular complex variety x the jumping numbers of a pair x d and the hodge spectrum at a singular point of d we give an elementary proof for an effective and combinatorial description of inner jumping numbers 1 of non degenerate polynomials

implementation of the periodic boundary condition in the finite difference time domain algorithm for fss structures a method for implementing the general floquet boundary condition in the finite difference time domain algorithm fdtd is presented the floquet type of phase shift boundary condition is incorporated into the time domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step with this approach the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence theoretical results are compared for various planar frequency selective surfaces fss and for one with a three dimensional element e g a thick double concentric square loop

an efficient realization of frequency dependent boundary conditions in an acoustic finite difference time domain model abstract the finite difference time domain fdtd method provides a simple and accurate way of solving initial boundary value problems however most acoustic problems involve frequency dependent boundary conditions and it is not easy to include such boundary conditions in an fdtd model although solutions to this problem exist most of them have high computational costs and stability cannot always be ensured in this work a solution is proposed based on mixing modelling strategies this involves separating the fdtd mesh and the boundary conditions a digital filter representation of the impedance and combining them into a global solution this solution is based on an interaction model that involves wave digital filters the proposed method is validated with several test cases

continuous time non linear flatness based predictive control an exact feedforward linearisation setting with an induction drive example a general flatness based framework for non linear continuous time predictive control is presented it extends the results of fliess and marquez 2000 to the non linear case the mathematical setting which is valid for multivariable systems is provided by the theory of flatness based exact feedforward linearisation introduced by the authors hagenmeyer and delaleau 2003b thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints but allows to use simple linear feedback parts in a two degree of freedom control structure moreover this formalism permits one to handle non minimum phase systems and furthermore to deal with parameter uncertainties and exogenous perturbations respective robustness analysis tools are available finally an induction drive example is discussed in detail and experimental results for this fast electro mechanical system are presented

poincare series of multiplier ideals in two dimensional local rings with rational singularities abstract we study the multiplicity of the jumping numbers of an m primary ideal a in a two dimensional local ring with a rational singularity the formula we provide for the multiplicities leads to a very simple and efficient method to detect whether a given rational number is a jumping number we also give an explicit description of the poincare series of multiplier ideals associated to a proving in particular that it is a rational function

fdtd for nth order dispersive media previously a method for applying the finite difference time domain fdtd method to dispersive media with complex permittivity described by a function with a single first order pole was presented this method involved the recursive evaluation of a discrete convolution and was therefore relatively efficient in this work the recursive convolution approach is extended to media with dispersions described by multiple second order poles the significant change from the first order implementation is that the single backstore variable for each second order pole is complex the approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second order poles and excellent agreement is obtained with the exact solution

memory optimized shift operator alternating direction implicit finite difference time domain method for plasma abstract through introducing the alternating direction implicit adi technique and the memory optimized algorithm to the shift operator so finite difference time domain fdtd method the memory optimized so adi fdtd for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced in order to further the computational efficiency the iteration method rather than gauss elimination method is employed to solve the equation set in the derivation of the formulae complicated transformations and convolutions are avoided in the proposed method compared with the z transforms zt adi fdtd method and the piecewise linear je recursive convolution pljerc adi fdtd method the numerical dispersion of the so adi fdtd method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given the accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet the testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory the reflection coefficient of a perfect electric conductor pec sheet covered by multilayer plasma and the rcs of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed

a novel piecewise linear recursive convolution approach for dispersive media using the finite difference time domain method two novel methods for implementing recursively the convolution between the electric field and a time dependent electric susceptibility function in the finite difference time domain fdtd method are presented both resulting algorithms are straightforward to implement and employ an inclusive susceptibility function which holds as special cases the lorentz debye and drude media relaxations the accuracy of the new proposed algorithms is found to be systematically improved when compared to existing standard piecewise linear recursive convolution plrc approaches it is conjectured that the reason for this improvement is that the new proposed algorithms do not make any assumptions about the time variation of the polarization density in each time interval no finite difference or semi implicit schemes are used for the calculation of the polarization density the only assumption that these two new methods make is that the first time derivative of the electric field is constant within each fdtd time interval

a general approach for the stability analysis of the time domain finite element method for electromagnetic simulations this paper presents a general approach for the stability analysis of the time domain finite element method tdfem for electromagnetic simulations derived from the discrete system analysis the approach determines the stability by analyzing the root locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix the approach is applicable to the tdfem simulation involving dispersive media and to various temporal discretization schemes such as the central difference forward difference backward difference and newmark methods it is shown that the stability of the tdfem is determined by the material property and by the temporal and spatial discretization schemes the proposed approach is applied to a variety of tdfem schemes which include 1 time domain finite element modeling of dispersive media 2 time domain finite element boundary integral method 3 higher order tdfem and 4 orthogonal tdfem numerical results demonstrate the validity of the proposed approach for stability analysis

full wave parallel dispersive finite difference time domain modeling of three dimensional electromagnetic cloaking structures a parallel dispersive finite difference time domain fdtd method for the modeling of three dimensional 3 d electromagnetic cloaking structures is presented in this paper the permittivity and permeability of the cloak are mapped to the drude dispersion model and taken into account in fdtd simulations using an auxiliary differential equation ade method it is shown that the correction of numerical material parameters and the slow switching on of source are necessary to ensure stable and convergent single frequency simulations numerical results from wideband simulations demonstrate that waves passing through a three dimensional cloak experience considerable delay comparing with the free space propagations as well as pulse broadening and blue shift effects

z transform theory and the fdtd method in implementing the finite difference time domain fdtd method on materials which are dispersive or nonlinear the relationship between the flux density and the electric field can be the most complicated part of the problem because the fdtd method is a sampled time domain method this relationship can be can be looked upon as a digital filtering problem the z transform is typically used in digital filtering and signal processing problems the paper illustrates the use of the z transform in implementing the fdtd method where complicated dispersive or nonlinear materials are involved

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

introduction of oblique incidence plane wave to stratified lossy dispersive media for fdtd analysis in the application of finite difference time domain fdtd method to the wideband plane wave scattering analysis of objects embedded in stratified lossy dispersive media it is a challenge to solve the obliquely incident wave in this work a novel configuration of auxiliary one dimensional 1 d fdtd grids is proposed to provide the obliquely incident plane wave at the total field scattered field tfsf boundary in stratified lossy dispersive media thus a closed tfsf boundary is formed where the incident waves are directly obtained from the auxiliary simulations without any interpolation the formulations of the auxiliary simulations are presented by the modified 1 d maxwell s equations given the dispersion characteristic perfectly matched layer pml is implemented to the 1 d simulations examples demonstrate the effectiveness of the proposed technique of obliquely incident wave introduction

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

a general three dimensional tensor fdtd formulation for electrically inhomogeneous lossy media using the z transform a general three dimensional tensor finite difference time domain tfdtd formulation is derived to model electrically inhomogeneous lossy media of arbitrary shapes the time domain representation of electric losses is achieved using z transforms the regular cubical grid structure is maintained everywhere in the calculation domain by defining a 3 d face fraction based 3 x 3 permittivity tensor on the interfaces that describes the relationship between the known average flux density vector and the unknown local electric field vector for electrically lossy media this tensor is complex in the frequency domain however it can be modified for use with the z transform only this modified real form is inverted then transformed from the frequency into the z domain and finally into the time domain furthermore a local interface matrix is used to describe the relationship between the local electric field in the grid node and its counterpart on the other side of the interface this matrix is complex in the frequency domain for lossy media by applying the z transform this matrix can also be transformed into the time domain using only real modified matrix elements the accuracy of the method is confirmed by comparisons with analytical solutions

application of aim and mbpe techniques to accelerate modeling of 3 d doubly periodic structures with nonorthogonal lattices composed of bianisotropic media an efficient methodology is introduced for rapid analysis and design of three dimensional 3 d doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral febi methods the 3 d doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily shaped metallic patches based on floquet theory and periodic boundary conditions the original stated problem that involves infinite periodic structures can be converted into a single unit cell using the equivalence principle the derived bi equation formulation is applied to the top and bottom surfaces of the unit cell which results in a perfectly reflectionless boundary condition for the fe based approach then the unit cell was meshed using triangular prismatic volume elements which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction the adaptive integral method aim was employed to accelerate the calculation of the matrix vector product for the bi portion within the iterative solver furthermore a model based parameter estimation mbpe technique was proposed for the wide band interpolation of the required impedance matrix elements in the bi part for near field components that were used in the aim procedure the accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results e g in comparison with analytical solutions several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily shaped metallic patches bianisotropic materials and nonorthogonal lattice configurations

modelling of wave propagation in wire media using spatially dispersive finite difference time domain method numerical aspects the finite difference time domain fdtd method is applied for modelling of wire media as artificial dielectrics both frequency dispersion and spatial dispersion effects in wire media are taken into account using the auxiliary differential equation method according to the authors knowledge this is the first time when the spatial dispersion effect is considered in the fdtd modelling the stability of developed spatially dispersive fdtd formulations is analyzed through the use of von neumann method combined with the routh hurwitz criterion the results show that the conventional stability courant limit is preserved using standard discretization scheme for wire media modelling flat sub wavelength lenses formed by wire media are chosen for validation of proposed spatially dispersive fdtd formulation results of the simulations demonstrate excellent sub wavelength imaging capability of the wire medium slabs the size of the simulation domain is significantly reduced using the modified perfectly matched layer mpml which can be placed in close vicinity of the wire medium it is demonstrated that the reflections from the mpml wire medium interface are less than 70 db that lead to dramatic improvement of convergence compared to conventional simulations

modeling dispersive dielectric media in fdtd a systematic approach two popular and distinct methods to model dispersive dielectric media in finite difference time domain are the piecewise linear recursive convolution approach and the auxiliary differential equation approach as they are used to model the same phenomenon and address the same equations it is reasonable to think there is a close connection between the two as a result of exploring this connection we propose a new approach that can be seen as an extension of the two methods and thus to some extent serves to unify the two in addition the new approach has the advantages of being 1 more systematic allowing the treatment of different types of dispersive dielectric media in the same manner and 2 less ad hoc the so called recursive accumulators can be identified naturally and automatically

efficient implementation of tam and auriault s time domain impedance boundary condition a new and efficient time domain implementation is proposed for the impedance model originally introduced by tam and auriault tam c k w and auriault l time domain impedance boundary conditions for computational aeroacoustics aiaa journal vol 34 no 5 may 1996 pp 917 923 in the frequency domain the pressure can be calculated from the product of the impedance with the normal velocity in the time domain a convolution is needed which may become a costly operation present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency domain models to time domain formulations involving time derivatives the former approach is very costly in terms of memory and cpu time the latter makes the implementation discretization specific and vulnerable to stability issues a new formulation based on recursive convolution results in an efficient implementation that stores only one accumulator which can be updated at each time step with minimal addition and multiplication it allows for the exact representation of the impedance at a given frequency the formulation is validated by a comparison with the measurement data from the nasa langley grazing flow impedance tube the simulations are performed by introducing a plane wave at a single frequency in the tube and this is done for six frequencies and five different mean flow speeds

an fdtd algorithm with perfectly matched layers for general dispersive media a three dimensional 3 d finite difference time domain fdtd algorithm with perfectly matched layer pml absorbing boundary condition abc is presented for general inhomogeneous dispersive conductive media the modified time domain maxwell s equations for dispersive media are expressed in terms of coordinate stretching variables we extend the recursive convolution rc and piecewise linear recursive convolution plrc approaches to arbitrary dispersive media in a more general form the algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media i e lorentz medium unmagnetized plasma and debye medium excellent agreement between the fdtd results and analytical solutions is obtained for all testing cases with both rc and plrc approaches we demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine like objects cylinders and spheres buried in a dispersive half space and the mapping of a curved interface because of their generality the algorithm and computer program can be used to model biological materials artificial dielectrics optical materials and other dispersive media

analysis of transient em scattering from penetrable objects by time domain nonconformal vie a marching on in time mot based nonconformal volume integral equation vie is proposed to analyze the transient electromagnetic scattering from the inhomogeneous penetrable objects the gradient gradient operator is acted on the green s function to realize the nonconformal tetrahedral meshes discretization half schaubert wilton glisson swg basis functions are chosen for the trail and test spatial functions meanwhile the piecewise polynomial lagrange interpolation functions are applied for temporal expansion in addition the quasi explicit scheme is introduced to accelerate the calculation of conventional implicit mot system numerical results are given to demonstrate the flexibility and validity of the proposed scheme

dispersive periodic boundary conditions for finite difference time domain method a dispersive periodic boundary condition dpbc is developed for the finite difference time domain method to analyze periodic structures with dispersive media on the boundaries of a unit cell the formulation is based on the auxiliary differential equation ade method with a two term debye model and the constant horizontal wavenumber approach the developed formulation is easy to implement and is efficient in both memory usage and computational time the validity of this formulation is verified through several numerical examples such as infinite dispersive slab and sandwiched composite frequency selective surface fss structure

on the fdtd formulations for modeling wideband lorentzian media several popular numerical approaches for modeling the dispersion characteristics of complex media are applied to simulate the wave propagation in the wideband lorentzian wbl media under the second order or fourth order accurate finite difference time domain fdtd formulation their implementing algorithms and work performance for this type of dispersive materials are studied and compared to each other the coefficients of a general second order discrete numerical model pertaining to each of these approaches are derived respectively and a unified set of fdtd updating equations for implementing them is presented in light of the analytical results calculated from the given numerical dispersion equations that determines the effective permittivity and permeability of a corresponding artificial wbl medium and the simulation results from the practical fdtd simulations for an exemplified wbl medium the modeling accuracy and stability limits of these approaches are presented by evaluating the absolute errors of both the propagation and transmission functions of a plane electromagnetic pulse wave propagating in the wbl material and transmitting through an interface between the vacuum and the wbl medium under the second order or fourth order fdtd formulation combined with each of the discussed approaches

an fdtd formulation for dispersive media using a current density a novel finite difference time domain fdtd formulation for dispersive media called the je convolution jec method is derived using the convolution relationship between the current density j and the electric field e the high accuracy of the jec method is confirmed by computing the reflection and transmission coefficients for a nonmagnetized plasma slab in one dimension it is found that the new method has an accuracy comparable to the auxiliary differential equation ade while having the same computational efficiency as the less accurate recursive convolution rc method numerical simulations also show that the jec method exhibits significantly higher accuracy than the rc method in modeling wave attenuation inside the plasma

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

a high order accurate scheme for maxwell s equations with a generalized dispersive material model abstract a high order accurate scheme for solving the time domain maxwell s equations with a generalized dispersive material model is described the equations for the electric field are solved in second order form and a general dispersion model is treated with the addition of one or more polarization vectors which obey a set of auxiliary differential equations ade numerical methods are developed for both second order and fourth order accuracy in space and time the equations are discretized using finite differences and advanced in time with a single stage three level space time scheme which remains stable up to the usual explicit cfl restriction as proven using mode analysis because the equations are treated in their second order form there is no need for grid staggering and instead a collocated grid is used composite overlapping grids are used to treat complex geometries with boundary conforming grids and a high order upwind dissipation is added to ensure robust and stable approximations on overlapping grids numerical results in two and three space dimensions confirm the accuracy and stability of the new schemes

flatness and quasi static state feedback in non linear delay systems two notions from the theory of non linear systems without time delays are generalized to non linear delay systems flatness and quasi static state feedback depending on the generality of the relations considered flatness properties of increasing generality are obtained flatness flatness flatness and difference differential flatness it is then shown that difference differentially flat delay systems are linearizable by a certain class of predictive quasi static state feedback i e that they are equivalent by such feedback to a linear controllable system the mathematical framework is difference differential algebra

on hodge spectrum and multiplier ideals we describe a relation between two invariants which measure the complexity of a hypersurface singularity one is the hodge spectrum which is related to the monodromy and the hodge filtration on the cohomology of the milnor fiber the other is the multiplier ideal having to do with log resolutions

spectral fdtd a novel technique for the analysis of oblique incident plane wave on periodic structures this paper introduces a new technique which calculates the reflection coefficient for the plane wave incident on planar periodic structures the method referred to as spectral finite difference time domain sfdtd replaces the conventional single angle incident wave with a constant transverse wavenumber ctw wave because the transverse wavenumbers are constant the fields have no delay in the transverse plane x y plane and pbc periodic boundary condition can be directly implemented in the time domain for both oblique and normal incident waves the stability criterion for this new fdtd technique is angle independent and therefore this method works well for incident angles close to grazing spl theta 90 spl deg as well as normal incident spl theta 0 spl deg this shows the efficiency of the method compared to other available fdtd techniques for the same purpose that force a more restricted stability criterion as angles turns to grazing the validity of this method is verified by comparing the reflection coefficient calculated by this method with the analytical results of a grounded slab the results of this technique are also compared with method of moments for a periodic array of metallic patches and a good agreement is observed a periodic array of metallic patches above a pec plate is analyzed and the reflection coefficient is calculated over a wide frequency band for angles varying from 0 spl deg to close to 90 spl deg

accessibility of nonlinear time delay systems a full characterization of accessibility is provided for nonlinear time delay systems it generalizes the rank condition which is known for weak controllability of linear time delay systems as well as the celebrated geometric approach for delay free nonlinear systems and the characterization of their accessibility besides fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time delay systems they are shown to impact preconceived ideas about canonical forms for nonlinear time delay systems

scaling factors of id fdtd scheme for dispersive media based on the auxiliary differential equation ade method the isotropic dispersion finite difference time domain id fdtd scheme is modified for a dispersive medium the proposed id fdtd scheme is based on the ade method in this correspondence three typical dispersive media are considered debye drude and lorentz media for which scaling factors are formulated the dispersion property is then examined and the accuracy of the proposed scheme is verified by consideration of two scattering problems

jumping coefficients and spectrum of a hyperplane arrangement in an earlier version of this paper written by the second named author we showed that the jumping coefficients of a hyperplane arrangement depend only on the combinatorial data of the arrangement as conjectured by musta for this we proved a similar assertion on the spectrum after this first proof was written the first named author found a more conceptual proof using the hirzebruch riemann roch theorem where the assertion on the jumping numbers was proved without reducing to that for the spectrum in this paper we improve these methods and show that the jumping numbers and the spectrum are calculable in low dimensions without using a computer in the reduced case we show that these depend only on fewer combinatorial data and give completely explicit combinatorial formulas for the jumping coefficients and part of the spectrum in the case the ambient dimension is 3 or 4 we also give an analogue of musta s formula for the spectrum

finite element time domain solution of the vector wave equation in doubly dispersive media using mobius transformation technique several finite element time domain fetd formulations to model inhomogeneous and electrically magnetically doubly dispersive materials based on the second order vector wave equation discretized by the newmark scheme are developed in contrast to the existing formulations which employ recursive convolution rc approaches we use a mobius transformation method to derive our new formulations hence the obtained equations are not only simpler in form and easier to derive and implement but also do not suffer from the intrinsic limitations of the rc methods in modeling arbitrary high order media to obtain the formulations we first demonstrate that the update equation for the electric field strength e in the mixed crank nicolson cn fetd formulation which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first order differential equations using crank nicolson scheme in time is equivalent to the unconditionally stable us second order vector wave equation for the same variable e discretized by the newmark method with 1 4 in addition we show that the update equation for the magnetic flux density b in cn fetd is the same as the second order vector wave equation for b on the dual grid discretized again by a similar newmark method subsequently thanks to the mixed fetd formulation properties we derive update equations for the constitutive relations using a mobius transformation method separately in addition we use the shown equivalence to derive formulations based on the vector wave equation finally several numerical examples are solved to validate the developed formulations

computing interior eigenvalues of nonsymmetric matrices application to three dimensional metamaterial composites we propose a numerical method to calculate interior eigenvalues and corresponding eigenvectors for nonsymmetric matrices based on the subspace projection technique onto expanded ritz subspace it becomes possible to obtain eigenvalues and eigenvectors with sufficiently high precision this method overcomes the difficulties of the traditional nonsymmetric lanczos algorithm and improves the accuracy of the obtained interior eigenvalues and eigenvectors using this algorithm we investigate three dimensional metamaterial composites consisting of positive and negative refractive index materials and it is demonstrated that the finite difference frequency domain algorithm is applicable to analyze these metamaterial composites

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

locally implicit discontinuous galerkin time domain method for electromagnetic wave propagation in dispersive media applied to numerical dosimetry in biological tissues we are concerned here with the numerical simulation of electromagnetic wave propagation in biological media because of their water content these media are dispersive i e their electromagnetic material characteristics depend of the frequency in the time domain this translates in a time dependency of these parameters that can be taken into account through and additional auxiliary differential equation for e g the electric polarization which is coupled to the system of maxwell s equations from the application point of view the problems at hand most often involve irregularly shaped structures corresponding to biological tissues modeling realistically the interfaces between tissues is particularly important if one is interested in evaluating accurately the impact of field discontinuities at these interfaces in this paper we propose and study a locally implicit discon tinuous galerkin time domain method formulated on an unstructured tetrahedral mesh for solving the resulting system of differential equations in the case of debye type media three dimensional numerical simulations are presented concerning the exposure of head tissues to a localized source radiation 1 introduction this article is concerned with the numerical simulation of electromagnetic wave propagation in dispersive media these are materials in which either or both of the electromagnetic material parameters e and are functions of frequency note that the conductivity may also be a function of frequency but its effect can be rolled into the complex permittivity in reality all materials have frequency dependent e and but many materials can be approximated as frequency independent over a frequency band of interest simplifying their analysis and simulation here we will focus on the much more common case of frequency dependent permittivity a lot of practical electromagnetic wave propagation problems involve such propagation media such as those involving the interaction of an electromagnetic wave with biological tissues the numerical modeling of the propagation of electromagnetic waves through human tissues is at the heart of many biomedical applications such as the microwave imaging of cancer tumors or the treatment of the latter by hy perthermia for example microwave imaging for breast cancer detection is expected to be safe for the patient and has the potential to detect very small cancerous tumors in the breast 3 14 24 beside the definition of microwave based hyperthermia as an immunotherapy strategy for cancer can also be cited 2 11 the electroporation technique can also be an application which consists of applying nanopulses to the tissues enabling only intracellular membranes to be affected and then opening the route to therapeutic strategies such as electrochemotherapy or gene transfer 21 30 25 26 28 because for all these biomedical applications experimental modeling is almost impossible computer simulation is the approach of choice for understanding the underlying

a fast time domain integral equation based scheme for analyzing scattering from dispersive objects a fast integral equation based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented a time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle i e by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field the proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux to reduce the computational cost and memory requirement of the resulting marching on in time scheme it is augmented with the plane wave time domain algorithm numerical results that validate the proposed approach and demonstrate its accuracy are presented

a general framework for the finite difference time domain simulation of real metals we present an efficient framework for the finite difference time domain simulation of real metals the complex permittivity function of a metal is fitted to experimental data in the frequency domain using a non linear least squares algorithm a memory efficient finite difference time domain fdtd scheme is presented for the simulation of the dispersive behavior of a metal in the frequency domain the stability limit for the proposed scheme is determined and compared to the courant limit excellent agreement between our fdtd formulation and the analytical solution for reflections from a thin metal sheet is found

on the robust flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations the accurate simulation of compressible flows requires the appropriate modeling of the reflection of acoustic waves at the boundaries in the present study we discuss time domain impedance boundary conditions tdibc the formulation proposed allows to impose a desired reflection coefficient at the inflow and outflow boundaries our formulation is an extension of the well known navier stokes characteristic boundary conditions the frequency dependent reflections at the boundaries are implemented with a state space model in the time domain we provide a comprehensive discussion on how such state space models can be constructed and interpreted this discussion shows that the state space description allows a robust and flexible implementation it allows to consider complex reflection coefficients and account for non constant cfd time steps in a straight forward manner furthermore we prove analytically and demonstrate numerically that the formulation proposed is consistent i e the formulation ensures that the flow simulation exhibits the reflection coefficient imposed accurately as long as the waves impinging on the boundary are plane and it prohibits drift of the mean flow variables finally the boundary conditions are tested successfully for laminar and turbulent flows

fractional calculus based fdtd algorithm for ultrawideband electromagnetic characterization of arbitrary dispersive dielectric materials a novel finite difference time domain algorithm for modeling ultrawideband electromagnetic pulse propagation in arbitrary multirelaxed dispersive media is presented the proposed scheme is based on a general yet computationally efficient series representation of the fractional derivative operators associated with the permittivity functions describing the frequency dispersion properties of a given dielectric material dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time marching scheme moreover a total field scattered field formulation is adopted in order to analyze the material response under plane wave excitation compared with alternative numerical methodologies available in the scientific literature the proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems involving higher order dispersive dielectrics such as the ones typically encountered in geoscience and bioengineering applications

finite difference time domain study of guided modes in nano plasmonic waveguides a conformal dispersive finite difference time domain fdtd method is developed for the study of one dimensional 1 d plasmonic waveguides formed by an array of periodic infinite long silver cylinders at optical frequencies the curved surfaces of circular and elliptical inclusions are modelled in orthogonal fdtd grid using effective permittivities eps and the material frequency dispersion is taken into account using an auxiliary differential equation ade method the proposed fdtd method does not introduce numerical instability but it requires a fourth order discretisation procedure to the authors knowledge it is the first time that the modelling of curved structures using a conformal scheme is combined with the dispersive fdtd method the dispersion diagrams obtained using eps and staircase approximations are compared with those from the frequency domain embedding method it is shown that the dispersion diagram can be modified by adding additional elements or changing geometry of inclusions numerical simulations of plasmonic waveguides formed by seven elements show that row s of silver nanoscale cylinders can guide the propagation of light due to the coupling of surface plasmons

optimized 2 4 stencil runge kutta ade adi fdtd with application to plasma this paper discusses the improvement of the numerical dispersion characteristics of alternating direction implicit adi finite difference time domain fdtd aimed at acquiring more accurate electromagnetic information of plasma through adding the optimization method which is based on the optimization of spatial derivative to the 2 4 stencil adi fdtd the optimized 2 4 stencil adi fdtd is proposed and its unconditional stability is proved theoretically the phase velocity error of the optimized 2 4 stencil adi fdtd versus propagation angle and grid density is investigated in addition the runge kutta auxiliary differential equation rkade scheme for tackling the constitutive relation equation of plasma is deduced which is without additional storage occupation and computational burden compared with ade scheme its numerical conductivity error is analyzed under different incident frequencies and electron collision frequencies through incorporating the rkade scheme into the optimized 2 4 stencil adi fdtd the optimized 2 4 stencil rkade adi fdtd is presented the accuracy and relatively wideband capability of the proposed method is validated by two numerical experiments

on steenbrink s conjecture let f x c be a holomorphic function on a complex manifold using the monodromy and mixed hodge structure on the cohomology of milnor fiber we can associate the spectrum sp f x of f at x e xo f 1 0 it is a fractional laurent polynomial n t with n z this notion is first introduced by steenbrink 15 cteq in the isolated singularity case cf also 19 and 16 in general if f has isolated singularity n are nonnegative and 0 n 0 counted with multiplicity are called the exponents or spectra 19 of f assume f has one dimensional singular locus and consider a deformation of the form f g where g is a linear form i e a function such that g x 0 and dg 0 at x then f g has isolated singularity if g is generic let zk be a local irreducible component of singf at x and mk its multiplicity along z zk x f is viewed as constant deformation of isolated singularity let k j be its exponents which are constant on z 20 we can also define ilk j e 0 1 in a compatible way with k j so that exp 2ni 3k j are the eigenvalues of the monodromy along z then steenbrink conjectured

new predictive scheme for the control of lti systems with input delay and unknown disturbances a new predictive scheme is proposed for the control of linear time invariant lti systems with a constant and known delay in the input and unknown disturbances it has been achieved to include disturbances effect in the prediction even though there are completely unknown the artstein reduction is then revisited thanks to the computation of this new prediction an extensive comparison with the standard scheme is presented throughout the article it is proved that the new scheme leads to feedback controllers that are able to reject perfectly constant disturbances for time varying ones a better attenuation is achieved for a wide range of perturbations and for both linear and nonlinear controllers a criterion is given to characterize this class of perturbations finally some simulations illustrate the results

poles of the complex zeta function of a plane curve abstract we study the poles and residues of the complex zeta function f s of a plane curve we prove that most non rupture divisors do not contribute to poles of f s or roots of the bernstein sato polynomial b f s of f for plane branches we give an optimal set of candidates for the poles of f s from the rupture divisors and the characteristic sequence of f we prove that for generic plane branches f g e n all the candidates are poles of f g e n s as a consequence we prove yano s conjecture for any number of characteristic exponents if the eigenvalues of the monodromy of f are different

novel and efficient fdtd implementation of higher order perfectly matched layer based on ade method based on the stretched coordinate perfectly matched layer sc pml formulations and the auxiliary differential equation ade method an efficient and unsplit field implementation of the higher order pml scheme with more than one pole is proposed to truncate the finite difference time domain fdtd lattices the higher order pml has the advantages of both the conventional pml and the complex frequency shifted pml cfs pml in terms of absorbing performances the proposed algorithm is validated through two numerical tests carried out in three dimensional and two dimensional domains it is shown in the numerical simulations that the proposed pml formulations with the higher order scheme are efficient in terms of attenuating both the low frequency propagating waves and evanescent waves and reducing late time reflections and also hold much better absorbing performances than the conventional sc pml and the convolutional pml cpml with the cfs scheme

a stable and efficient direct time integration of the vector wave equation in the finite element time domain method for dispersive media the finite element time domain fetd solution of the vector wave equation vwe is directly extended to doubly dispersive media using the bilinear transform approach the proposed formulation is quite general and flexible in the sense of material dispersion model in contrast to limitations of existing convolutional based approaches in addition it can be implemented in a very straightforward and efficient manner a stability analysis is performed that demonstrates the unconditional stability of the original formulation is preserved in the dispersive case however in order to avoid the well known late time instabilities that arise in this formulation an alternative formulation is considered and extended to the dispersive case with the same approach several numerical examples are simulated to verify the validity and accuracy of the proposed formulations the late time stability of the alternative formulation is tested through a numerical example with 20 million time steps the solution is completely free from late time growth

an improved new implementation of complex frequency shifted pml for the fdtd method a new implementation of the perfectly matched layer absorbing boundary for finite difference time domain grids is presented the approach which is based on the complex co ordinate stretching perfectly matched layer pml formulation uses the complex frequency shifted stretching function and is based on the simple concept of the recursive evaluation of an integral avoiding the calculation of time derivatives this recursive integration pml is simple to implement efficient and exhibits a modest gain in performance over the convolutional pml without requiring any extra computational resources or an increase in the algorithmic complexity of the pml implementation