Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method

The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable and $s$-stage $s$-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method of $s$-stage $2s$-order has been proposed by using undetermined coefficients method and Padéapproximations. The numerical results show that the proposed differential quadrature method is more precise than the traditional differential quadrature method.     

结构动力分析的时域配点DQ半解析法

直接从控制微分方程出发,以梁为对象提出了本计算方法。该方法在空间域采用DQ法(DiferentialQuadratureMethod),在时间域取级数,采用时域配点的方式得到求位移场全部待定参数的可解方程组,求解一次线性方程组即可求得全域的响应位移场。     

求解声辐射问题的微分求积法与微分求积单元法

基于无限域中的Helmholtz波动方程,将微分求积法与微分求积单元法应用于二维及三维声辐射问题的求解,对最外层节点施加不同阶数的人工边界条件,区域内使用均匀及非均匀的节点分布方式,分析了节点分布方式及人工边界条件对计算结果的影响,比较了两种数值方法的计算精度。研究结果表明:微分求积法与微分求积单元法,前者精度更高,而后者耗时更少,在频率较低时,具备较高的效费比。人工边界条件对计算结果的影响主要体现在低频段,而节点分布方式的影响主要体现在高频段。非均匀的节点分布方式在不同频段都具备更好的计算精度。      

求解结构动力响应的卷积型DQ半解析法

通过卷积将原始控制方程构造成包含初始条件的新的具有完整初值问题特征的控制方程.该方程既与Gurtin变分原理一样有合理的数学内涵,又避免了卷积型Gurtin变分原理泛函和计算的繁复.对新的控制方程在时间域取解析函数,在空间域采用离散的DQ法,经对梁的动力响应问题的计算表明,该方法是一种精度好效率高的求解动力响应问题的计算方法.     

Performance Comparison of Long-Haul Direct Detection Optical Transmission Systems Adopting Dispersion Management with Pre-Compensation

Abstract

This article reports a numerical investigation on the performance of return-to-zero intensity-modulated direct detection, return-to-zero differential phase shifting key, and return-to-zero differential quadrature phase shifting key systems operating in G.652 links adopting dispersion management. Also illustrated are the role and benefits of pre-compensation. For such an aim, the influence of the non-linear Kerr impairments on the in-phase and quadrature components of the signal are studied, along with the consequent degradations in terms of the Q-factor for the different modulation formats. Such an investigation is applied to evaluate the maximum propagation distances for 40- and 80-Gb/s capacities.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.     

Differential Quadrature Analysis of Moving Load Problems

The differential quadrature method (DQM) has been successfully used in a variety of fields. Similar to the conventional point discrete methods such as the collocation method and finite difference method, however, the DQM has some difficulty in dealing with singular functions like the Dirac-delta function. In this paper, two modifications are introduced to overcome the difficulty encountered in solving differential equations with Dirac-delta functions by using the DQM. The moving point load is work-equivalent to loads applied at all grid points and the governing equation is numerically integrated before it is discretized in terms of the differential quadrature. With these modifications, static behavior and forced vibration of beams under a stationary or a moving point load are successfully analyzed by directly using the DQM. It is demonstrated that the modified DQM can yield very accurate solutions. The compactness and computational efficiency of the DQM are retained in solving the partial differential equations with a time dependent Dirac-delta function.     

时域自适应精细算法求解对流热传导问题

应用时域自适应精细算法求解对流传热问题.通过展开技术,可更准确地描述变量随时间的变化,同时将时空耦合的初边值问题转化为一系列的空间边值问题,并采用有限元方法递推求解.自适应技术可弥补时间步长不同时可能造成的计算精度损失.并进行了数值检验.     

Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

光频域喇曼反射光纤温度传感器的频域参量设计

研究了功率调制型光频域反射技术空间采样函数的基本特征,得到了频域测量参量对测量距离和空间分辨率的基本限制;用数值计算模拟了功率调制型光频域光纤温度传感器的测量过程,通过比较模拟测量得到的喇曼反射强度空间分布因子对实际喇曼反射强度空间分布因子的再现程度,研究了调制频率范围、频率采样间隔以及起始调制频率对测量结果的影响,得出技术可行的最佳频域测量方案.     

OPTIMAL CONTROL METHOD WITH TIME DELAY IN CONTROL

Optimal control method for active vibration control of linear time-delay systems is investigated in this paper. In terms of two cases that time delay is integer and non-integer times of sampling period, motion equation with time delay is transformed as standard discrete forms which contain no time delay by using zero order holder respectively. Discrete quadratic function is used as objective function in design of controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Because the controller is deduced directly from time-delay differential equation, system stability can be guaranteed easily, thus this method is generally applicable to ordinary control systems. The performance of the control method proposed and system stability when using this method are all demonstrated by numerical simulation results. Simulation results demonstrate that the presented method is a viable and attractive control strategy for applications to active vibration control. Instability in responses occurs possibly if the systems with time delay are controlled using controller designed in case of no time delay.     

An investigation of time-dependent domain wall pinning effects in Tb/Fe multilayer thin films

Reverse domain nucleation time measurements have been performed on two Tb/Fe multilayer magneto-optic films exhibiting different degrees of domain wall pinning. A linear relationship between ln (reverse domain nucleation time) and the applied field has been predicted and observed for a sample exhibiting weak domain wall pinning. This is in agreement with theoretical work presented which addresses time dependence in systems possessing weak domain wall pinning. A non-linear relationship applicable over a restricted field range has been derived for a sample exhibiting strong domain wall pinning. Experimental results have indicated that this relationship is also valid.     

Sampling of the NMR time domain along concentric rings

We present a novel approach to sampling the NMR time domain, whereby the sampling points are aligned on concentric rings, which we term concentric ring sampling (CRS). Radial sampling constitutes a special case of CRS where each ring has the same number of points and the same relative orientation. We derive theoretically that the most efficient CRS approach is to place progressively more points on rings of larger radius, with the number of points growing linearly with the radius, a method that we call linearly increasing CRS (LCRS). For cases of significant undersampling to reduce measurement time, a randomized LCRS (RLCRS) is also described. A theoretical treatment of these approaches is provided, including an assessment of artifacts and sensitivity. The analytical treatment of sensitivity also addresses the sensitivity of radially sampled data processed by Fourier transform. Optimized CRS approaches are found to produce artifact-free spectra of the same resolution as Cartesian sampling, for the same measurement time. Additionally, optimized approaches consistently yield fewer and smaller artifacts than radial sampling, and have a sensitivity equal to Cartesian and better than radial sampling. We demonstrate the method using numerical simulations, as well as a 3D HNCO experiment on protein G B1 domain.     

Time-resolved entanglement and photon number correlation of twin beams: Application to quantum key distribution scheme

Quantum entanglement and intensity correlations in continuous variable (CV) regimes have investigated in the time domain in addition to many analogous investigations performed in the frequency domain. The specific signatures of time-resolved CV quadrature entanglement and intensity difference squeezing have been analyzed for periodically-pulsed optical parametric oscillator (OPO). An application to quantum key distribution scheme based on intensity correlation of twin beams has also been considered. The text was submitted by the author in English.     

Vibration analysis of a circular arch with variable cross-section using differential transformation and generalized differential quadrature

Vibration analysis of circular arches is an important subject in mechanics due to its various applications. In particular, circular arches with variable cross-section have been widely used to satisfy modern architectural and structural requirements. Recently, the generalized differential quadrature method (GDQM) and differential transformation method (DTM) were proposed by Shu and Zhou, respectively. In this study, GDQM and DTM are applied to vibration analysis of circular arches with variable cross-section. The governing equation of motion is derived and the non-dimensional natural frequencies are obtained for various boundary conditions. The concepts of differential transformation and generalized differential quadrature are briefly introduced. The results obtained by these methods are compared with previously published works. GDQM and DTM showed fast convergence, accuracy and validity in solving the vibration problem for circular arches with variable cross-sections.     

Conditional quadrature method of moments for kinetic equations

Kinetic equations arise in a wide variety of physical systems and efficient numerical methods are needed for their solution. Moment methods are an important class of approximate models derived from kinetic equations, but require closure to truncate the moment set. In quadrature-based moment methods (QBMM), closure is achieved by inverting a finite set of moments to reconstruct a point distribution from which all unclosed moments (e.g. spatial fluxes) can be related to the finite moment set. In this work, a novel moment-inversion algorithm, based on 1-D adaptive quadrature of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative quadrature weights). This conditional quadrature method of moments (CQMOM) can be used to compute exact N-point quadratures for multi-valued solutions (also known as the multi-variate truncated moment problem), and provides optimal approximations of continuous distributions. In order to control numerical errors arising in volume averaging and spatial transport, an adaptive 1-D quadrature algorithm is formulated for use with CQMOM. The use of adaptive CQMOM in the context of QBMM for the solution of kinetic equations is illustrated by applying it to problems involving particle trajectory crossing (i.e. collision-less systems), elastic and inelastic particle–particle collisions, and external forces (i.e. fluid drag).     

A fluctuation problem in particle transport theory II

A balance equation is formulated for the probability that a particle injected into an infinite, amorphous medium will have suffered N collisions and have given rise to n new particles in a given energy range at time t. The method of regeneration points has been employed and this leads, in the case of two particle production, to a non-linear, integro-differential equation for the probability generating function. This equation is solved for the case of foreign particles slowing down, in which case it becomes linear and results are obtained which include the effects of electronic stopping and absorption, thus generalizing the work in part I. In the cascade problem, a single particle gives rise to two new particles in every collision and it is shown, for a simple hard-sphere model with 1/v scattering and absorption, how the non-linear equation may be solved. The probability for the number of particles and the number of collisions suffered to absorption is obtained in the case of zero absorption, the probability law is shown to obey a Furry distribution. The limitations of the method described in part I for dealing with cascades are highlighted.     

TIME INTEGRATION OF NON-LINEAR DYNAMIC EQUATIONS BY MEANS OF A DIRECT VARIATIONAL METHOD

Non-linear dynamic problems governed by ordinary (ODE) or partial differential equations (PDE) are herein approached by means of an alternative methodology. A generalized solution named WEM by the authors and previously developed for boundary value problems, is applied to linear and non-linear equations. A simple transformation after selecting an arbitrary interval of interest T allows using WEM in initial conditions problems and others with both initial and boundary conditions. When dealing with the time variable, the methodology may be seen as a time integration scheme. The application of WEM leads to arbitrary precision results. It is shown that it lacks neither numerical damping nor chaos which were found to be present with the application of some of the time integration schemes most commonly used in standard finite element codes (e.g., methods of central difference, Newmark, Wilson-θ, and so on). Illustrations include the solution of two non-linear ODEs which govern the dynamics of a single-degree-of-freedom (s.d.o.f.) system of a mass and a spring with two different non-linear laws (cubic and hyperbolic tangent respectively). The third example is the application of WEM to the dynamic problem of a beam with non-linear springs at its ends and subjected to a dynamic load varying both in space and time, even with discontinuities, governed by a PDE. To handle systems of non-linear equations iterative algorithms are employed. The convergence of the iteration is achieved by takingn partitions of T. However, the values of T/n are, in general, several times larger than the usual Δt in other time integration techniques. The maximum error (measured as a percentage of the energy) is calculated for the first example and it is shown that WEM yields an acceptable level of errors even when rather large time steps are used.