This paper introduces a computational approach for transient analysis of extensive scattering problems. This novel method is based on the combination of physical optics (PO) and the fast inverse Laplace transform (FILT). PO is a technique for analyzing electromagnetic scattering from large-scale objects. We modify PO for application in the complex frequency domain, where the scattered fields are evaluated. The complex frequency function is efficiently transformed into the time domain using FILT. The effectiveness of this combination is demonstrated through large-scale analysis and transient response for a short pulse incidence. The accuracy is investigated and validated by comparison with reference solutions.

In this study, a computational method is proposed for acoustic field analysis tasks that require lengthy observation times. The acoustic fields at a given observation time are obtained using a fast inverse Laplace transform with a finite-difference complex-frequency-domain. The transient acoustic field can be evaluated at arbitrary sampling intervals by obtaining the instantaneous acoustic field at the desired observation time using the proposed method.

At present, the application of different types of memristors in electronics is being deeply studied. Given the nonlinearity characterizing memristors, a circuit with memristors cannot be treated by classical circuit analysis. In this paper, memristor is equivalent to a nonlinear dynamic system composed of linear dynamic system and nonlinear static system by Volterra series. The nonlinear transfer function of memristor is derived. In the complex frequency domain, the n-order complex frequency response of memristor is established by multiple Laplace transform, and the response of MLC parallel circuit is taken as an example to verify. Theoretical analysis shows that the complex frequency domain analysis method of memristor transforms the problem of solving nonlinear circuit in time domain into n times complex frequency domain analysis of linear circuit, which provides an idea for nonlinear dynamic system analysis.

Numerical inverse Laplace transform (NILT) methods are potential methods for time domain simulations, for instance the analysis of the transient phenomena in systems with lumped and/or distributed parameters. This paper proposes a numerical inverse Laplace transform method based originally on hyperbolic relations. The method is further enhanced by properly adapting several convergence acceleration techniques, namely, the epsilon algorithm of Wynn, the quotient-difference algorithm of Rutishauser and the Euler transform. The resulting accelerated models are compared as for their accuracy and computational efficiency. Moreover, an expansion to two dimensions is presented for the first time in the context of the accelerated hyperbolic NILT method, followed by the error analysis. The expansion is done by repeated application of one-dimensional partial numerical inverse Laplace transforms. A detailed static error analysis of the resulting 2D NILT is performed to prove the effectivness of the method. The work is followed by a practical application of the 2D NILT method to simulate voltage/current distributions along a transmission line. The method and application are programmed using the Matlab language.

A novel computational method based on a combination of the method of moments in the complex frequency domain and the fast inverse Laplace transform is proposed for solving time-domain electromagnetic problems. Using our proposed method, it is easy to estimate and control the computational error, and the observation time can be selected independently. We investigate canonical scattering problems and verify these advantages.

In the paper, a technique of the numerical inversion of multidimensional Laplace transforms (nD NILT), based on a complex Fourier series approximation is elaborated in light of a possible ralative error achievable. The detailed error analysis shows a relationship between the numerical integration of a multifold Bromwich integral and a complex Fourier series approximation, and leads to a novel formula relating the limiting relative error to the nD NILT technique parameters.

A novel computational method is proposed to investigate electromagnetic scattering problems. It is error controllable and reliable simulation in time domain can be performed. We apply the proposed method to analysis of transient scattering from open-ended structures and discuss scattering mechanisms.

Formulae required for accurate approximate calculation of transition probabilities of embedded Markov chain for single-server queues of the GI/ M/1,GI/M/1/K,M/G/1,M/G/1/K type with heavy-tail lognormal distribution of inter-arrival or service time are given.

Transient scattering from parallel plate waveguide cavities is studied by using the combination of a point matching technique and numerical inversion of Laplace transform. We thoroughly investigate the scattering mechanism for a half-sine pulse and modulated-sine pulse incidence. The advantages and disadvantages on the target recognition are clarified in terms of the internal objects, incident waveforms, and polarizations.

The potential attenuation process of charged human body (HB) is analyzed. A two-dimensional circuit model is presented for predicting the potential attenuation characteristics of the HB charged on the floor. The theoretical equation for the HB potential is derived in the closed form in the Laplacian transformation domain, and the numerical inverse Laplace transform is used to compute it. The half-life or relaxation time of the HB potential for decay is numerically examined with respect to the electrical parameters of shoes. The experiment is also conducted for verifying the validity of the computed result.

This letter deals with the reliability function in the case of periodic preventive replacement of items in order to increase MTBF, that is, two replacement policies; strictly periodic replacement (SPR) and randomly periodic replacement (RPR). We stress on simple introduction of the reliability theory under preventive replacement policies using the Laplace transform and obtain the theoretical results of SPR and RPR. Then these results are applied to the Weibull distribution and finally in order to show useful information of preventive replacement, the numerical results of SPR are provided.

The transient scattering of a half sine pulse wave by a conducting rectangular cylinder with an open sidewall is rigorously analyzed by using the point matching method (taking into account the edge condition exactly) combined with the fast inversion of Laplace transform. Numerical results are presented for back scattered and forward scattered responses of the far fields when a half sine pulse is incident on the open side and the closed side of the cylinder. The physical meaning of the transient responses is discussed in detail. The comparison of the responses with those by a perfect conducting rectangular cylinder is presented.

In the present paper we present a mathematical theory for the transient analysis of probabilistic models relevant to communication networks. First we review the z-transform method, the matrix method, and the Laplace transform, as applied to a class of birth-and-death process model that is relevant to characterize network traffic sources. We then show how to develop transient solutions in terms of the eigenvalues and spectral expansions. In the latter half the paper we develop a general theory to solve dynamic behavior of statistical multiplexer for multiple types of traffic sources, which will arise in the B-ISDN environment. We transform the partial differential equation that governs the system into a concise form by using the theory of linear operator. We present a closed form expression (in the Laplace transform domain) for transient solutions of the joint probability distribution of the number of on sources and buffer content for an arbitrary initial condition. Both finite and infinite buffer capacity cases are solved exactly. The essence of this general result is based on the unique determination of unknown boundary conditions of the probability distributions. Other possible applications of this general theory are discussed, and several problems for future investigations are identified.

We studied transient fields on a perfectly conducting sphere excited by a half sine pulse wave and examined the Poynting vectors, the energy densities and the energy velocities of the creeping waves. We used FILT (Fast Inversion of Laplace Transform) method for transient analysis. We compared the amplitudes of the creeping wave with that of steady state high frequency approximation obtained by the Watson transformation. The main results are: (1) We confirmed in the transient response that the pulse propagates clockwise and counterclockwise along the geodesic circumference. (2) In the transient electromagnetic field observed in the E-plane we can recognize creeping waves clearly. (3) The existence of creeping waves is not clear in the H-plane. (4) The pulse wave propagation on the sphere is seen more clearly from the Poynting vectors and the energy densities than the field components. (5) The energy velocity of the wave front is equal to the light velocity as should be. The energy velocity of the wave body becomes smaller with the passage of time. (6) The amplitude of the creeping wave for a beat pulse and the amplitude obtained by the Watson transform for mono spectrum agree in the order of relative error below 25%.