Periodic surface modeling for computer aided nano design

Current solid and surface modeling methods based on Euclidean geometry in traditional computer aided design are not efficient in constructing a large number of atoms and particles. In this paper, we propose a periodic surface model for computer aided nano design such that geometry of atoms and molecules can be constructed parametrically. At the molecular scale, periodicity of the model allows thousands of particles to be built efficiently. At the meso scale, inherent porosity of the model represents natural morphology of polymer and macromolecule. Surface and volume operations are defined to support crystal and molecular model creation with loci and foci periodic surfaces. The ultimate goal is to enable computer assisted material and system design at atomic, molecular, and meso scales.     

Adaptive output-feedback stabilization of non-local hyperbolic PDEs

We address the problem of adaptive output-feedback stabilization of general first-order hyperbolic partial integro-differential equations (PIDE). Such systems are also referred to as PDEs with non-local (in space) terms. We apply control at one boundary, take measurements on the other boundary, and allow the system’s functional coefficients to be unknown. To deal with the absence of both full-state measurement and parameter knowledge, we introduce a pre-transformation (which happens to be based on backstepping) of the system into an observer canonical form. In that form, the problem of adaptive observer design becomes tractable. Both the parameter estimator and the control law employ only the input and output signals (and their histories over one unit of time). Prior to presenting the adaptive design, we present the non-adaptive/baseline controller, which is novel in its own right and facilitates the understanding of the more complex, adaptive system. The parameter estimator is of the gradient type, based on a parametric model in the form of an integral equation relating delayed values of the input and output. For the closed-loop system we establish boundedness of all signals, pointwise in space and time, and convergence of the PDE state to zero pointwise in space. We illustrate our result with a simulation.     

Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.     

基于梯度的受限空间安全定位方法

现有的无线传感器网络定位技术消耗了大量的计算和处理资源,并且受到了环境因素以及对手攻击等干扰,在受限空间中定位精度较低,无法满足定位需求。为了提高受限空间中的定位精度,提出了一种基于梯度的安全定位算法,算法在双曲线定位模型基础上,引入梯度的概念,降低了算法的计算复杂度,使算法能够适应受限空间的环境要求,实现高效高精度的定位;为了提高算法的安全性,增加了对不一致性测量的选择性剪枝过程,增强了算法对恶意攻击的抵抗能力。最后,以室内走廊为实验环境进行了仿真验证,通过主频计时策略,提高了算法的定位精度。分析结果表明,在室内受限空间中,提出的算法在定位精度、能量消耗和抗干扰能力上优于现有算法。     

S变换时变滤波在去噪处理中的应用研究

针对常用的滤波去噪方法都受到使用条件的限制,实际资料的滤波去噪不能达到良好效果,S变换时变滤波克服了传统滤波去噪方法滤波因子不能随时间、频率变化而变化的缺陷.将地震资料用S变换方法变换到时频域,对不同时间内不同频率的噪声部分充零,再将去噪后的地震数据利用S反变换到时间域,以获得所需要的有效信号.通过理论计算分析和实例计算表明,S变换时变滤波能够有效去除不同时段、不同频率的噪声.该方法具有一定的可行性.     

S变换时频分析在隧道岩溶地震勘探解释中的应用

介绍了短时傅立叶变换、小波变换和S变换的优缺点及其彼此间的相互关系。详述了S变换的概念及性质,认为S变换方法具有良好的自适应性和时频分辨率,能提供高质量的时频谱信息。将S变换时频分析用于宜万铁路隧道地震映像法数据解释。结果表明,S变换时频剖面上的溶洞异常显示比时间剖面更为清晰,在推断岩溶的分布位置、大小、埋藏深度等方面具有良好效果。S变换方法有助于提高地震数据解释的精度和准确性。     

采用多分辨率广义S变换的电能质量扰动识别

为提高电能质量复合扰动识别能力,提出一种采用多分辨率广义S变换(multiresolution generalized S-transform,GST)的扰动识别方法.首先,将信号频谱分为低频、中频、高频3个频域,分别设定窗宽调整因子,使其在各个频域具有不同的时-频分辨率,满足不同扰动信号识别要求.并针对高频振荡识别问题,设计基于基频傅里叶谱特征的自适应窗宽调整方法.在此基础上,提取6种特征用于构建决策树.最后,提出最小分类损失原则,确定决策树节点分类阈值,设计扰动分类器.仿真与实测信号实验证明,新方法能够准确识别含5种复合扰动在内的13种扰动.相较于S变换、广义S变换和Hyperbolic S变换,新方法具有更好的特征表现能力,分类效果好,抗噪声干扰能力强.     

Fault tolerance in cellular automata at high fault rates

A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the case we treat in this paper. We are concerned with the degree (the number of neighboring cells on which the state transition function depends) needed to achieve fault tolerance when the fault rate is high (nearly 1/2). We consider both the traditional transient fault model (where faults occur independently in time and space) and a recently introduced combined fault model which also includes manufacturing faults (which occur independently in space, but which affect cells for all time). We also consider both a purely probabilistic fault model (in which the states of cells are perturbed at exactly the fault rate) and an adversarial model (in which the occurrence of a fault gives control of the state to an omniscient adversary). We show that there are cellular automata that can tolerate a fault rate 1/2−ξ (with ξ>0) with degree O((1/ξ²)log(1/ξ)), even with adversarial combined faults. The simplest such automata are based on infinite regular trees, but our results also apply to other structures (such as hyperbolic tessellations) that contain infinite regular trees. We also obtain a lower bound of Ω(1/ξ²), even with only purely probabilistic transient faults.     

A Numerical Study of Diagonally Split Runge–Kutta Methods for PDEs with Discontinuities

Diagonally split Runge–Kutta (DSRK) time discretization methods are a class of implicit time-stepping schemes which offer both high-order convergence and a form of nonlinear stability known as unconditional contractivity. This combination is not possible within the classes of Runge–Kutta or linear multistep methods and therefore appears promising for the strong stability preserving (SSP) time-stepping community which is generally concerned with computing oscillation-free numerical solutions of PDEs. Using a variety of numerical test problems, we show that although second- and third-order unconditionally contractive DSRK methods do preserve the strong stability property for all time step-sizes, they suffer from order reduction at large step-sizes. Indeed, for time-steps larger than those typically chosen for explicit methods, these DSRK methods behave like first-order implicit methods. This is unfortunate, because it is precisely to allow a large time-step that we choose to use implicit methods. These results suggest that unconditionally contractive DSRK methods are limited in usefulness as they are unable to compete with either the first-order backward Euler method for large step-sizes or with Crank–Nicolson or high-order explicit SSP Runge–Kutta methods for smaller step-sizes. We also present stage order conditions for DSRK methods and show that the observed order reduction is associated with the necessarily low stage order of the unconditionally contractive DSRK methods. The work of C.B. Macdonald was partially supported by an NSERC Canada PGS-D scholarship, a grant from NSERC Canada, and a scholarship from the Pacific Institute for the Mathematical Sciences (PIMS). The work of S. Gottlieb was supported by AFOSR grant number FA9550-06-1-0255. The work of S.J. Ruuth was partially supported by a grant from NSERC Canada.