Exponential Time Differencing Algorithm for Debye Medium in FDTD

The exponential time differencing (ETD) formultion is proposed for Debye medium using finite-difference time-domain (FDTD) method. The schemes of the auxiliary differential equation (ADE) and ETD algorithms are presented. The algorithms are validated by comparing the simulation results with analytical values. The ETD method costs the same memory as the ADE method, and the numerical results indicate that the ETD technique is more accurate than the ADE method. This work is supported by the foundation under Grant No. Zl 0502.     

Shift operator method and Runge-Kutta exponential time differencing method for plasma

In this paper, the shift operator finite difference time domain (SO-FDTD) method and Runge-Kutta exponential time differencing (RKETD) method are introduced. The high accuracy and efficiency of the two methods are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collisional plasma slab. A comparison of computational efficiency of the two methods is presented by simulating the electromagnetic wave propagation in homogeneous non-magnetized plasma. The numerical results indicate that the calculation time using SO-FDTD method is less than that using RKETD method with almost the same accuracy.     

Analysis of backscattering RCS of targets coated with parabolic distribution and time-varying plasma media

The backscattering radar cross section (RCS) of targets coated with parabolic distribution and time-varying unmagnetized plasma is analyzed by the finite-difference time-domain (FDTD) method based on the Runge–Kutta exponential time differencing (RKETD) technique. The two-dimensional RKETD-FDTD formulations are derived. The effects of the plasma parameters on the RCS are investigated. The numerical results illustrate that plasma cloaking system can successfully reduce the backscattering RCS, the plasma stealth is effective, and reasonable selection of different parameters of plasma can enhance its effectiveness.     

An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell

Over the last decade there has been renewed interest in applying exponential time differencing (ETD) time stepping schemes to the solution of stiff systems. In this paper, we present an implementation of such a scheme to the fully spectral solution of the incompressible magnetohydrodynamic equations in a spherical shell. One problem associated with ETD schemes is the accurate calculation of the necessary matrices; we implement and discuss in detail a variety of different methods including direct computation, contour integration, spectral expansions and recurrence relations. We compare the accuracy of six different second-order methods in determining the evolution of a three-dimensional magnetic field under the action of a prescribed time-dependent flow of electrically conducting fluid, and find that for the timestep restriction imposed by the nonlinear terms, ETD methods are no more accurate than linearly implicit methods which have the significant advantage of being easier to implement. However, ETD methods are more readily extendable than those which are linearly implicit and will become much more advantageous at higher order.     

任意阶隐式指数时程差分多步法及其在非线性系统中的应用

对非线性系统提出了任意阶隐式指数时程差分多步法，实现了任意阶次指数时程差分预测 校正算法.发展完善了指数时程差分法.将新算法应用于非线性系统，取得了较好的效果.数值结果表明隐式指数时程差分多步法很好地修正了显式指数时程差分多步法，隐式指数时程差分多步法是一种高精度、高效率的方法. 关键词： 非线性系统 任意阶隐式指数时程差分多步法 混沌     

New Predictor-Corrector Methods Based on Exponential Time Differencing for Systems of Nonlinear Differential Equations

We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams-Bashforth-Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.     

Analysis of the Karmarkar-Karp differencing algorithm

The Karmarkar-Karp differencing algorithm is the best known polynomial time heuristic for the number partitioning problem, fundamental in both theoretical computer science and statistical physics. We analyze the performance of the differencing algorithm on random instances by mapping it to a nonlinear rate equation. Our analysis reveals strong finite size effects that explain why the precise asymptotics of the differencing solution is hard to establish by simulations. The asymptotic series emerging from the rate equation satisfies all known bounds on the Karmarkar-Karp algorithm and projects a scaling n ^{−c ln n} , where c = 1/(2 ln 2) = 0.7213 .... Our calculations reveal subtle relations between the algorithm and Fibonacci-like sequences, and we establish an explicit identity to that effect.     

选择性双向顺序压缩感知重建动态磁共振成像

压缩感知是一种新兴技术,该技术能够用远低于奈奎斯特采样频率采集的信号恢复出原始信号. 压缩感知成像方法大大提高了心脏磁共振成像的采集速度,已有的方法主要利用动态图像时间相关及心脏的周期性运动特征,如采用在时间维做傅立叶变换或求解每帧数据跟参考帧数据的差异获取稀疏数据,满足压缩感知重建的要求. 该文提出了选择性双向顺序压缩感知重建算法,利用相邻帧的差异更小的特点,获取更加稀疏的差异数据,同时利用动态图像的周期性,以目标函数积分为判据,在时间顺序和时间逆序两个方向选择效果更好的方向进行数据重建,降低图像伪影和噪声. 该选择算法,可以在不增加重建时间的情况下,选择双向顺序重建中最佳的结果. 该文对心脏磁共振图像数据进行了数据处理实验,并且跟传统压缩感知算法、参考帧差异方法及匙孔成像方法进行了比较. 结果表明：该方法无论从视觉效果还是从统计结果上,都有很大的改善.     

Time dependent Schrödinger equation on arbitrary structured grids: Application to photoionization

A systematic technique for conservatively discretizing the time dependent Schrödinger equation on an arbitrary structured grid is given. Spatial differencing is carried out by finite volumes, and temporal differencing is carried out semi-implicitly. It is shown that the resulting algorithm conserves probability to within a round-off error regardless of the grid geometry. The algorithm is efficient for both serial and parallel computation. The conservative nature of the algorithm, and its phase accuracy, are demonstrated for a bound state, and for a free state in an electromagnetic field. The ionization rate for a hydrogen atom in a strong electromagnetic field is computed, and compared with the rate from tunneling theory. The regime of validity of tunneling theory is clarified.     

空间差分格式对有限体积法数值散射的影响

数值散射是辐射传递方程近似算法中最常见的离散误差。本文主要讨论空间差分格式对有限体积法数值散射的影响。构造激光平行及倾斜入射的物理模型,验证和比较阶梯格式、中心差分格式及指数格式下温度场的计算精度及数值散射特性。计算结果表明,在激光平行入射与倾斜入射两种情况下,阶梯格式引起的的数值散射比菱形格式及指数格式要多,但其计算精度高于菱形及指数格式。不同激光入射条件下,各种差分格式表现出的数值散射分布有明显的差异。     

Computational modeling of MR flow imaging by the lattice Boltzmann method and Bloch equation

In this work, a computational model of magnetic resonance (MR) flow imaging is proposed. The first model component provides fluid dynamics maps by applying the lattice Boltzmann method. The second one uses the flow maps and couples MR imaging (MRI) modeling with a new magnetization transport algorithm based on the Eulerian coordinate approach. MRI modeling is based on the discrete time solution of the Bloch equation by analytical local magnetization transformations (exponential scaling and rotations).     

Investigation of the Influence of Overvoltage,Auxiliary Glow Current and Relaxation Time on the Electrical Breakdown Time Delay Distributions in Neon

Results of the statistical analysis of the electrical breakdown time delay for neon‐filled tube at 13.3 mbar are presented in this paper. Experimental distributions of the breakdown time delay were established on the basis of 200 successive and independent measurements, for different overvoltages, relaxation times and auxiliary glows. Obtained experimental distributions deviate from usual exponential distribution. Breakdown time delay distributions are numerically generated, usingMonte‐Carlo method, as the compositions of the two independent random variables with an exponential and a Gaussian distribution. Theoretical breakdown time delay distribution is obtained from the convolution of the exponential and Gaussian distribution. Performed analysis shows that the crucial parameter that determines the complex structure of time delay is the overvoltage and if it is of the order of few percentage, then distribution of time delay must be treated as an convolution of two random variables. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wavepacket Propagation Algorithm with Wavefunction Splitting:Application to Calculate Harmonic Emission of Atom in Intense Laser Pulse

1.IntroductionInrecentyears,intenselaserphysicshasbecomeanactivefield[1'2].WiththelaserintensityincreasingmanynewPerformanceshaveemerged,suchasabovethresholdion-ization(ATI)[3J,high-orderopticalharmonicemission[4~6Jandstabilizationofatomsinintenselaserfield[7~9J.Uptodate,thelaserint6nsityoflO"W/cm'hasbeenobtained.ItismuchgreaterthantheIimitationoflO"W/cm'forwhichthePerturbativetheoryisva1id.Therefore,nonperturbativemethodshavebeenemployedtodealwiththeintensefieldphysicalproblems.Generall…     

光子晶体传输特性的时域精细积分法分析

将精细积分法应用于时域有限差分法中,提出了一种求解光子晶体传输特性的时域精细积分法,并对其计算精度及稳定性进行了分析.从一阶麦克斯韦方程出发,在空间上采用Yee元胞进行差分离散,结合吸收边界条件及激励源表达式将方程整理为标准的一阶常微分方程组形式.通过时间步长的精细划分和指数矩阵的加法定理,在时间上利用精细积分法对齐次微分方程进行积分求解,并结合激励向量的特解得到空间离散的场分量,最终通过傅里叶变换求得方程的解.利用时域精细积分法对光子晶体进行了实例计算,并将其结果分别与时域有限差分法和四阶龙格库塔法在精度、稳定性等方面进行了比较,结果表明时域精细积分法具有更高的计算精度,并且克服了时域有限差分法以及四阶龙格库塔法在计算稳定性上对时间步长的限制.提出的方法具有精确、稳定的特点,为光子晶体传输特性的研究提供了一种新的有效的分析方法.     

A new differencing scheme for the discrete-ordinates method in complex geometries

This paper is an assessment of a new discrete-ordinates algorithm recently developed by the authors for the numerical treatment of radiative participating media in both two- and three-dimensional enclosures. The algorithm is based on the utilization of general characteristic relations instead of the traditional differencing schemes for the spatial marching procedure. It is ideally suited for the treatment of complex geometries, the grid being formed from triangles (2D) or tetrahedra (3D). The method is exempt of any numerical oscillation and may be readily interfaced with the finite-element method for the solution of problems involving other modes of heat transfer. The mathematical derivation is detailed in the text and several examples are given for complex enclosures. The method proves to be very accurate and of good flexibility.     

稀疏贝叶斯学习远近场混合源定位方法

针对远、近场混合源定位,提出一种基于稀疏重构理论框架的远、近场混合源分离和定位算法。该算法充分考虑平面波导向矢量和球面波导向矢量的相关特性,利用远、近场声源在阵列上的响应机理的差异,针对远、近场区域分别构造过完备字典,采用多测量矢量模型下的稀疏贝叶斯学习算法重构远近场混合源的空间谱,同时完成远近场混合源的分离和定位。本文算法可以在半波长间距布放的线列阵下对混合源进行定位,适用于高斯和非高斯信号,且无需信源数和噪声功率等先验信息,并具有较高的分辨力和定位精度·计算机仿真结果验证了算法的有效性。      

Efficient gradient estimation using finite differencing and likelihood ratios for kinetic Monte Carlo simulations

While many optimization and control methods for stochastic processes require gradient information from the process of interest, obtaining gradient information from experiments is prohibitively expensive and time-consuming. As a result, such information is often obtained from stochastic process simulations. Computing gradients efficiently and accurately from stochastic simulations is challenging, especially for simulations involving computationally expensive models with significant inherent noise. In this work, we analyze and characterize the applicability of two gradient estimation methods for kinetic Monte Carlo simulations: finite differencing and likelihood ratio. We developed a systematic method for choosing an optimal perturbation size for finite differencing and discuss, for both methods, important implementation issues such as scaling with respect to the number of elements in the gradient vector. Through a series of numerical experiments, the methods were compared across different time and size regimes to characterize the precision and accuracy associated with each method. We determined that the likelihood ratio method is appropriate for estimating gradients at short (transient) times or for systems with small population sizes, whereas finite differencing is better-suited for gradient estimation at long times (steady state) or for systems with large population sizes.     

Application of trilinear SLICING to analyse a single relaxation curve

Determining the time constants and amplitudes of exponential decays from relaxation data is a common task in LF-NMR. In this communication, we present an application of the SLICING algorithm to evaluate its possibilities for solving this problem. The method, originally introduced to compare different samples, is applied here to analyse a single relaxation curve, using the embedding technique. To test this procedure, we acquired data sets from samples of liquids properly separated, and characterized by different relaxation times. The results show a good estimation of parameters, comparable with those obtained applying Marquardt's algorithm, when the components have sufficiently different relaxation times.     

High order conservative differencing for viscous terms and the application to vortex-induced vibration flows

A new set of conservative 4th-order central finite differencing schemes for all the viscous terms of compressible Navier–Stokes equations are proposed and proved in this paper. These schemes are used with a 5th-order WENO scheme for inviscid flux and the stencil width of the central differencing scheme is designed to be within that of the WENO scheme. The central differencing schemes achieve the maximum order of accuracy in the stencil. This feature is important to keep the compactness of the overall discretization schemes and facilitate the boundary condition treatment. The algorithm is used to simulate the vortex-induced oscillations of an elastically mounted circular cylinder. The numerical results agree favorably with the experiment.     

Role of coherence in adiabatic search algorithms

We systematically investigate the role of coherence in adiabatic search algorithms by using the relative entropy measure of coherence. Both in the ideal case (adiabatic evolution) and the non-ideal case (nonadiabatic evolution), the success probability increases with the decreases of coherence. In addition, the coherence depletion in global adiabatic search algorithm, local adiabatic search algorithm and an adiabatic search algorithm with constant evolution time was discussed. The results show that the coherence decreases faster in more efficient algorithm and an exponential decaying of coherence is necessary to achieve fast search (constant evolution time) in the adiabatic search algorithm. More importantly, we demonstrate that the efficiency of adiabatic search algorithm can be improved by utilizing appropriate method to speed up the coherence depletion.