Nonlinear suboptimal filtration of pseudorandom sequences

The critical importance of studies of alternative methods of representation and processing of signals constructed from pseudorandom sequences of maximal period is demonstrated. For the first time, it is proposed that a multidimensional nonlinear finite-difference representation of an arbitrary pseudorandom sequence be employed. A suboptimal algorithm for nonlinear discrete Kalman filtration of a pseudorandom sequence is obtained. A numerical example of filtration of a sequence formed on the basis of a given recurrence rule is considered and its efficiency is demonstrated.     

基于波动方程的聚焦点控制照明叠前深度偏移

 基于波动方程的聚焦点控制照明叠前深度偏移技术借助于差分计算，把速度、密度等介质参数的影响体现在差分计算的矩阵方程中，能够自动适应速度场的任意变化，快速傅里叶变换的使用也加速了波场延拓的计算速度。因此此法兼具有限差分偏移方法和傅里叶偏移方法的优点，既可适应速度场的剧烈变化，又可保证对陡倾地层的成像效果，是目前针对复杂构造最有效的成像方法之一。对于单个聚焦点及其周围的成像步骤为：①采用矩形网格情况下绕射走时的有限差分计算方法生成合成算子；②应用合成算子来合成面炮震源和面波记录；③对合成的面炮震源和面波记录做傅里叶有限差分法波动方程叠前深度偏移，得到该聚焦点及其附近区域的成像结果。按照上述成像步骤，将震源波场和炮集记录依据相应的外推公式进行延拓，最终应用成像条件求取成像值。在地质目标处选取多个聚焦点，可以得到面向目标的控制照明偏移成像，在多个层位上选取多个聚焦点进行控制照明叠前深度偏移，可以得到整块区域的成像。通过对Marmousi模型的试算，取得了较好的效果。     

两种群食饵-捕食者模型参数估计的数值微分法

给出了一种基于数值微分的两种群食饵-捕食模型参数估计的两阶段方法。该方法将参数的非线性最小二乘估计,转化为一个数值微分和一个线性最小二乘估计问题,具有计算简单快速的特点。数值算例详细分析了三种常见有限差分数值微分法及非线性最小二乘估计对参数估计精度的影响,结果表明提出的方法是可行的。     

Numerical modeling of high-temperature corrosion processes

Numerical modeling of the diffusional transport associated with high-temperature corrosion processes is reviewed. These corrosion processes include external scale formation and internal subscale formation during oxidation, coating degradation by oxidation and substrate interdiffusion, carburization, sulfidation and nitridation. The studies that are reviewed cover such complexities as concentration-dependent diffusivities, cross-term effects in ternary alloys, and internal precipitation where several compounds of the same element may form (e.g., carbides of Cr) or several compounds exist simultaneously (e.g., carbides containing varying amounts of Ni, Cr, Fe or Mo). In addition, the studies involve a variety of boundary conditions that vary with time and temperature. Finite-difference (F-D) techniques have been applied almost exclusively to model either the solute or corrodant transport in each of these studies. Hence, the paper first reviews the use of F-D techniques to develop solutions to the diffusion equations with various boundary conditions appropriate to high-temperature corrosion processes. The bulk of the paper then reviews various F-D modeling studies of diffusional transport associated with high-temperature corrosion.     

高阶旋转体时域有限差分法

旋转体时域有限差分法(BOR FDTD)是模拟电磁波与旋转对称目标体相互作用的一种高效算法,但目前的BOR FDTD对时间和空间的差分精度均只有二阶.通过把电磁场各分量作泰勒展开,并结合麦克斯韦方程,提出了BOR FDTD的三种高阶算法.相对于目前的BOR FDTD,三种高阶算法均不增加存储量.通过模拟简谐波与介质球的相互作用并和理论值作比较,证实了高阶算法在提高计算精度方面的有效性.此外还分析了三种高阶算法的优、缺点,给出了关于高阶算法应用的建议.     

黑磷纳米盘-层等离激元系统中的各向异性可调多阶强耦合

黑磷支持各向异性的表面等离激元,可用于设计具备更多功能的原理性器件。用时域有限差分法数值模拟了中红外到远红外波段基于黑磷的层-盘-层系统中不同等离激元模式之间的杂交行为。通过动态调节黑磷中的载流子浓度,可以实现两个晶格方向上强耦合现象的产生与控制。对不同模式间的耦合进行分析并计算,得到吸收光谱中的拉比分裂能最高可达42.9 meV。此外,还计算了偏振角度对各向异性强耦合的影响,其最高可以实现6个吸收频带。该模型可为构建未来在中远红外波段工作的基于二维材料紧凑型各向异性等离激元器件提供基础。     

Unconditionally stable C1-cubic spline collocation method for solving parabolic equations

This article aims to present a new approach based on C¹-cubic splines introduced by Sallam and Naim Anwar [Sallam, S. and Naim Anwar, M. (2000). Stabilized cubic C¹-spline collocation method for solving first-order ordinary initial value problems, Int. J. Comput. Math., 74, 87–96.], which is A-stable, for the time integration of parabolic equations (diffusion or heat equation). The introduced method is an example of the so-called method of lines (the solution is thought to consist of space discretization and time integration), which is an extension of the 1/3-Simpson's finite-difference scheme. Our main objective is to prove the unconditional stability of the proposed method as well as to show that the method is convergent and is of order O (h ²)?+?O (k ⁴) i.e. it is a fourth-order in time and second-order in space. Computational results also show that the method is relevant for long time interval problems.     

起伏地表条件下坐标变换的瑞雷波场正演模拟

利用高精度交错网格有限差分技术模拟起伏地表条件下的瑞雷波全波场正演,通过坐标变换的方式实现起伏地表自由边界条件。与一个已知模型结果对比,验证该算法的可行性与正确性,并通过在一个地表起伏的均匀介质中瑞雷波的模拟,结果说明了该方法的适应性。两个模型的模拟结果均表明,即使是地下室均一的介质,但由于地表起伏的存在不可避免地会产生波型的转换与能量的再分配,瑞雷波波场必然受到一定的影响。     

普适化坐标系下的FDTD算法及实现

时域有限差分(FDTD)算法在光子晶体理论研究中获得了较为广泛的应用,但它在处理一些非均匀、非正交问题时,计算耗时量大,计算效率低.研究了普适化坐标下的光子晶体理论研究方法,对常用的基于笛卡尔坐标系的FDTD算法作了扩展,并设计了一个可以计算一维到三维光子晶体的能带结构和态密度的软件.主要介绍了普适化坐标系下FDTD算法的程序实现,并简要描述了GCFE软件的设计思路.给出了利用该软件计算得到的立方和六角结构的光子晶体光纤的能带结构和光子态密度的结果,与其他研究者报道的结果相吻合.     

新型光子晶体四通道滤波器研究与设计

基于光子晶体环形腔缺陷与线缺陷波导之间的共振耦合原理,设计了 一种由新型环形腔和主波导组成的四通道二维三角晶格光子晶体滤波器.运用平面波展开法和时域有限差分法分析了光波在整合结构中的传输特性,并进一步讨论环形滤波器内的内部介质柱半径大小对滤波器传输特性的影响.结果表明:新改进环形的滤波器传输效率达到80％左右.通过实验...