基于蒙特卡罗方法的海洋环境不确定性仿真

海洋中的声速是研究声波在海洋中传播以及水声战的基本物理量之一.由于海洋环境的复杂性,使得声速梯度存在一定的不确定性,进而导致声场计算的不确定性以及声纳作用距离预报的不确定性.采用蒙特卡洛方法捕捉海洋中声速梯度的不确定性,模拟真实海洋环境中的声速梯度,并将模拟得到的声速梯度输入波束位移射线简正波(BDRM)声场预报模型中,得到声传播损失,再对结果进行统计分析,得到声传播损失的概率分布图,并提出用传播损失期望值作为预报值,提高了声场预报的精度.最后,利用声纳优质因子(FOM)导出声纳作用距离概率分布图,为声纳作用距离的预报提供了概率的依据.     

基于跳频和同步捕获技术的水下无线通信技术研究

本文所阐述的水下无线技术即基于跳频技术和同步捕获技术的水声通信,由于声波在海水中的传播特性显著优越于电磁波和可见光,使得水声技术成为海洋高技术的主要研究领域之一 ,在国防领域也具有十分重要的研究意义.本文主要论述了水声通信中跳频技术和同步捕获技术的原理、具体算法的实现方案以及部分硬件设施的使用简述,并通过展示实验结果验证算法的可行性.     

相关性算法在超声波形分析中的应用

相关的概念是为研究随机信号的统计特性而引入的,相关性可以用来描述为两组信号的相似程度,超声在介质中传播会产生多次反射波,通过计算各次波的相关系数,可以获得超声在介质中的传输时间,从而得到介质的厚度.     

油管声波色散特性仿真

在油井监测系统中,以油管管壁作为信道的声波通信方法可以降低成本和提高可靠性。声波在油管这种周期性结构中传播时表现出色散特性,即发生畸变失真,这是影响声波数据传输方法的一个主要障碍。根据油管中声波频率和波数的关系,该文详细分析了具体的求解过程,给出了一种适合于计算机仿真的方法,并且提供了使用Madab语言实现的主要源代码。仿真结果显示：在油管这种声波信道中,通带和阻带交替出现;油管可以视为一种梳状滤波器,而且随着频率的增加,通带越来越窄,阻带越来越宽,色散越严重。该文对于从事相关研究的人员有一定的参考价值。     

文字作品互联网传播模型的研究与应用

通过分析文字作品在互联网中的传播过程与规律,建立文字作品的网络传播模型,通过仿真实验将采集的真实数据与模型的理论值作对比分析,结果表明该模型可以用来描述互联网中文字作品的传播趋势.进而将所提出的模型与一个网络监测系统相结合,在监测网站数目有限的情况下能对整个网络中的转载网站数目做出估计,为有效遏制文字作品的网络非法转载提供了理论依据.     

体外超声碎石机声场仿真

体外冲击波碎石机(Extracorporeal shock wave lithotripter,ESWL)是治疗结石的主要手段,现阶段对其微观工作机理、动态声场分布等问题的研究尚处于起步阶段.通过对ESWL声场的建模及仿真可以对上述性能的研究带来很大的帮助.应用非线性传播方程建立了ESWL声场的数学模型,并通过有限差分算法结合MATLAB软件的图形模块进行了数值仿真.模型不仅考虑了非线性的影响,还引入了衍射、和热粘性吸收对声波的作用,最大限度地与实际声场所受到的各种影响保持一致.仿真很好地反映出ESWL产生的高强度超声波传播的非线性及一些与线性声波传播显著不同的特性.对形象地了解ESWL声波的传播过程和ESWL反射罩优化设计有很好的参考价值.     

一个异常传播分析工具的设计与实现

异常处理是一种用来检测异常并对其进行处理的技术,异常传播改变程序原来的执行路线,从而可能改变程序中的数据流、控制流和各种成分的依赖关系.在进行程序分析时,如果不考虑异常传播对其造成的影响,则得到的信息将是不准确的.本文设计并实现了一个分析C 程序中异常传播分析工具CETool.该工具可以有效地分析C 程序的异常传播,它既可以获得异常处理结构的局部信息,也可以获得异常处理结构的全局信息,这对于有效地分析异常的传播,分析异常传播路径,以及改进异常处理结构都有很大的帮助.     

二维三角陀螺声子晶体的波调控研究

本文研究了一种二维三角陀螺声子晶体,采用拉格朗日方程对结构进行建模,推导出动力学方程.通过调节陀螺转速,可以控制结构的色散关系,并获得较大的带隙,从而可以将其用来进行振动控制和噪声抑制.从色散曲面等频截线发现波在结构中的传播方向会随频率变化,在低频时各向同等传播,高频时则出现六个集中的传播方向.通过数值计算验证了理论获得的带隙的准确性.     

腹足纲土壤动物在监测和评价重金属污染中的应用研究进展

重金属污染正日益受到人们的关注.利用指示生物监测和评价重金属污染是一种简单可行的方法,但是却能提供具有重要价值的信息,特别是在反映生态系统功能变化方面具有独特的优势.在指示生物和生物监测研究领域,软体动物可以被用来获取陆地、海洋和淡水生态系统的环境质量信息.本文综述了腹足纲土壤动物应用于重金属污染监测和评价中的研究进展.     

利用声波探测材料失效位置的数学模型

通过运用声波对探测定位裂纹的形成和增长的研究，给出了一个关于声波探测的数学模型以及计算机实现的原理，并且提供了利用这个计算机程序的实验及其结果。该算法采用FORTRAN语言实现，比较计算和试验结果，误差存在于合理的范围内。实验中采用PACAEDSP-32／16数据采集系统来获得声波探测信号，采用连续信号收集方法用来判断和搜集有效信号。     

Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for <Emphasis Type="Italic">k</Emphasis>-Means Clustering

In this paper, we propose an implicit gradient descent algorithm for the classic k-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch gradient in every iteration. It is the average of the fixed-point trajectory that is carried over to the next gradient step. We draw connections between the proposed stochastic backward Euler and the recent entropy stochastic gradient descent for improving the training of deep neural networks. Numerical experiments on various synthetic and real datasets show that the proposed algorithm provides better clustering results compared to k-means algorithms in the sense that it decreased the objective function (the cluster) and is much more robust to initialization.     

On a system of first-order quasi-variational inequalities connected with the optimal switching problem

In this paper we prove the existence of the maximum bounded Lipschitz continuous solution to a system of first-order quasi-variational inequalities. The method is to discretize by an Euler scheme the characteristic lines of the differential operator appearing in the system and to solve by iteration the corresponding approximate problem. The solution is interpreted as the value function of a deterministic optimal switching problem.     

基于Euler操作的四边形网格细分算法设计与实现

通过分析细分曲面在Euler规则下的性质,提出了适用于四边形网格细分的基本Euler操作方法.在这些方法中,任意一种操作都是不可分割原子操作,而每一次细分迭代实际上就是这些基本操作顺序有效的组合.在Euler操作的基础上,选择halfedge数据结构,四边形网格的初始细分和对偶细分得以成功实现.     

Physical-bound-preserving finite volume methods for the Nagumo equation on distorted meshes

In this paper, we present a boundedness preserving finite volume scheme for the Nagumo equation. In this method, we use the implicit Euler method for the time discretization, and construct a maximum-principle-preserving discrete normal flux for the diffusion term. For the nonlinear reaction term, we design a type of Picard iteration to ensure that at each iterative step it keeps physical boundedness. Moreover we prove that the numerical solution of the resulting scheme can preserve the bound of the solution for the Nagumo equation on distorted meshes. Some numerical results are presented to verify the theoretical analysis.     

Parallel single grid and multigrid solution of industrial compressible flow problems

The Euler and Navier-Stokes equations with a k-ε turbulence model are solved numerically in parallel on a distributed memory machine IBM SP2, a shared memory machine SGI Power Challenge, and a cluster of SGI workstations. The grid is partitioned into blocks and the steady state solution is computed using single grid and multigrid iteration. The multigrid algorithm is analyzed leading to an estimate of the elapsed time per iteration. Based on this analysis, a heuristic algorithm is devised for distributing and splitting the blocks for a good static load balance. Speed-up results are presented for a wing, a complete aircraft and an air inlet.     

On the performance of SPAI and ADI-like preconditioners for core collapse supernova simulations in one spatial dimension

The simulation of core collapse supernovæ calls for the time accurate solution of the (Euler) equations for inviscid hydrodynamics coupled with the equations for neutrino transport. The time evolution is carried out by evolving the Euler equations explicitly and the neutrino transport equations implicitly. Neutrino transport is modeled by the multi-group Boltzmann transport (MGBT) and the multi-group flux limited diffusion (MGFLD) equations. An implicit time stepping scheme for the MGBT and MGFLD equations yields Jacobian systems that necessitate scaling and preconditioning. Two types of preconditioners, namely, a sparse approximate inverse (SPAI) preconditioner and a preconditioner based on the alternating direction implicit iteration (ADI-like) have been found to be effective for the MGFLD and MGBT formulations. This paper compares these two preconditioners. The ADI-like preconditioner performs well with both MGBT and MGFLD systems. For the MGBT system tested, the SPAI preconditioner did not give competitive results. However, since the MGBT system in our experiments had a high condition number before scaling and since we used a sequential platform, care must be taken in evaluating these results.     

神经网络BP学习算法动力学分析

研究神经网络BP学习算法与微分动力系统的关系.指出BP学习算法的迭代式与相 应的微分动力系统数值解Euler方法在一定条件下等价,且二者在解的渐近性方面是一致的. 给出了神经网络BP学习算法与相应的微分动力系统解的存在性、唯一性定理和微分动力系统 的零解稳定性定理.从理论上证明了神经网络的学习在一定条件下与微分动力系统的数值方法 所得的数值解在渐近意义下是等价的,从而借助于微分动力系统的数值方法可以解决神经网络 的学习问题.最后给出了用改进Euler方法训练BP网的例子.     

Gauss–Newton Multilevel Methods for Least-Squares Finite Element Computations of Variably Saturated Subsurface Flow

We apply the least-squares mixed finite element framework to the nonlinear elliptic problems arising in each time-step of an implicit Euler discretization for variably saturated flow. This approach allows the combination of standard piecewise linear H ¹-conforming finite elements for the hydraulic potential with the H(div)-conforming Raviart–Thomas spaces for the flux. It also provides an a posteriori error estimator which may be used in an adaptive mesh refinement strategy. The resulting nonlinear algebraic least-squares problems are solved by an inexact Gauss–Newton method using a stopping criterion for the inner iteration which is based on the change of the linearized least-squares functional relative to the nonlinear least-squares functional. The inner iteration is carried out using an adaptive multilevel method with a block Gauss–Seidel smoothing iteration. For a realistic water table recharge problem, the results of computational experiments are presented. Received January 4, 1999; revised July 19, 1999     

A general framework of piecewise-polynomial Mumford–Shah model for image segmentation

A new general framework of piecewise-polynomial Mumford–Shah model is proposed. In terms of the fidelity term, we use piecewise polynomials to approximate the inner and outer regions of the contour of the objective image. For more accurate approximation of the image, the proposed model has no constraint on the regularization term for polynomials. Moreover, we apply the anisotropic control to drive the initial contour to the desirable position. The proposed model generalizes the well-known Chan–Vese model and improves Vese's model, which is almost the simplest framework to apply piecewise polynomials to approximate the original Mumford–Shah model. Instead of solving the Euler–Lagrange equation by evolution implementation, we utilize the split Bregman iteration, which is shown to be a fast algorithm. Experimental results demonstrate that the proposed model has more desirable performance in terms of segmentation accuracy, efficiency and robustness, compared with several other variational models in addressing some challenging segmentation scenarios.     

NURBS曲面上积分曲率线的B样条表示

对NURBS曲面的曲率线的积分进行了系统的公式推导,并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算,加速了Euler法迭代求解曲率线微分方程的过程;在求得曲率线上的离散点集以后,应用奇异混合插值技术,在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线．文中的思想与算法有助于曲率线技术在计算机辅助几何设计及曲面造型中的使用与推广．