Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

PDE4B专一性抑制剂选择性的起源

采用分子动力学模拟和结合自由能计算研究了PDE4B抑制剂选择性的起源.首先,探索了模拟时间、溶质介电常数、配体的电荷方案和结合自由能的计算方法对结合自由能预测值准确度的影响,确定最佳模拟条件为:模拟时间40~50 ns,溶质介电常数ε=2,采用MM/GBSA方法以及RESP配体电荷计算方案.接着,通过能量分解分析了抑制剂A33与PDE4B/PDE4D的相互作用,发现PDE4B酶上的Ile410、Gln443、Phe446和Phe506对抑制剂的选择性识别贡献较大.最后,通过位点突变方法探索了PDE4B的CR3螺旋上的Leu502残基对A33选择性所起的作用.当前的工作为设计高活性、高选择性的PDE4B抑制剂提供了有价值的结构与活性关系信息.

变分分数阶PDE的自适应图像保边缘去噪方法

为了优化图像去噪过程中的边缘保真问题,本文以ROF模型及其改进模型为基础,以分数阶变分偏微分方程方法为工具,通过构造自适应的边缘检测函数,提出了一种能更好地保护图像的边缘特征,有利于纹理细节保持和“阶梯效应”抑制的基于自适应分数阶变分PDE的图像去噪模型,并以标准图像测试了新模型的去噪效果。实验结果表明:与同类方法相比,新方法可以更加有效地提高图像的信噪比;从去噪前后的图像差可以看出,新方法在去噪的同时更好地保护了图像的边缘特征及纹理细节信息。文中提出的方法可以用于遥感成像、医学图像处理及地震图像处理等领域。

ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE FOURTH-ORDER NONLINEAR SCHR?DINGER EQUATION WITH LARGE INITIAL DATA

We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5.

Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties

This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4th-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4th-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures.

基于Matlab PDE工具箱的土体冻结温度场模拟研究

分析并运用Matlab PDE tool模拟模型槽土体冻结的温度场并验证模拟值的准确性。首先,通过合理的边界假设,使三维的模型槽土体冻结热传导问题转化为二维空间;然后,运用Matlab PDE tool进行模拟并对比测温点的模拟温度和实测温度。结果表明:土体冻结中温度场导热可以通过Matlab PDE tool模拟,且操作简单易于掌握;测温点模拟值的准确性与测温点距边界距离和冻结时间有关。

PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution

This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2).

PDES策略在冷连轧动态系统仿真中的应用研究

并行离散事件仿真(PDES)策略是当今仿真界研究的热点,它是解决复杂系统问题以及分布式仿真交互管理的有效工具之一。冷连轧动态仿真是由多台计算机组成的分布式协同仿真系统,该论文在处理其中的离散事件管理以及系统运行的逻辑管理上不仅使用到并行离散事件仿真策略,而且在某些应用上改进或调整了PDES仿真算法,取得了预期的控制效果。

利用PDES／STEP实现CAD／CAM信息集成

本文介绍了新一代基于产品数据的数据交换标准ＰＤＥＳ／ＳＴＥＰ的结构和特点，并提出了将基于特征的造型系统所建立的产品信息模型运用ＰＤＥＳ／ＳＴＥＰ来表示，从而实现ＣＡＤ／ＣＡＭ信息集成系统中数据交换和共享的方法。

产生和求解PDEs对称确定方程组的微分特征列集算法理论及其应用

基于作者给出的吴－微分特征列集算法理论〔１，６〕，给出了计算微分方程（组）对称的关键一步产生和求解确定方程组的特征列集算法．利用计算机代数系统Ｍａｔｈｅｍａｔｉｃａ１．２ｆｏｒＤｏｓ〔９〕具体实现了本文提出的算法．

一维泊松方程的结构优化及对PDEs的精确解

关于PDEs的精确解问题,在实际求解中较为困难。本文以一维泊松方程为例,结合Lie对称方法和Wu方法分析方程的古典对称,计算单参数的无穷小向量,并设计方程的最优结构,通过两个定义得出一维泊松方程的最优换位和伴随算子,由此优化方程结构。以此为基础计算一维泊松方程最优结构单个元素对PDEs的精确解,在两种古典对称情况下,分别求出对PDEs的两个新解。此结果对PDEs精确解问题是一次有新意的尝试。

基于PDEs的二维条形码图像预处理方法

目前二维条形码在各领域得到了广泛地应用,但实际环境中受图像采集设备的限制,译码图像中通常混有较大的噪声,导致经常出现误码。为了进一步提高二维码译码的可靠性,必须对图像进行有效地预处理。本文根据条形码边界具有方向性的特点,将基于偏微分方程的Perona&Malik模型应用到二维条形码的图像预处理中,并对Perona&Malik模型的缺点进行了算法改进,通过合理地设计和选择参数,能很好地适应所有二维条码的图像特征,实际计算结果表明该方法对二维条形码图像的处理能得到令人满意的效果。

基于四阶PDEs和对比度增强的荧光显微图像去噪

提出一种用于荧光显微图像去噪扩散模型的算法。该算法针对二阶偏微分方程去噪模型易引起的"块效应"和伪边缘等问题,采用正则化方法,利用四阶偏微分方程,同时融合对比度增强技术设计去噪模型。与二阶偏微分方程扩散模型相比,该算法不仅使去噪图像看起来更加自然清晰,而且在峰值信噪比和结构相似度等客观评价方法下也取得了更加满意的结果。

基于PDES乐观时间管理的周期时间桶算法研究

时间管理是影响并行离散事件仿真PDES系统高效运行的重要因素之一。文章首先分析了离散事件仿真的原理,以及PDES所面临的时间管理方面的挑战;然后阐述了乐观时间管理机制,重点提出了周期时间桶算法的设计与实现,并对其性能作了大体上的评估。

PDES中乐观时间同步的时空损耗研究

并行离散事件仿真对复杂大规模动态系统的研究以及探索其长远的应用提供了便利,近年来日益成为研究的热点。然而时间同步管理是影响并行离散事件仿真系统高效运行的重要因素之一。乐观的同步是采用检测和回退机制,允许逻辑进程积极的处理本地事件,一旦出现同步错误则利用回退机制从错误中恢复到较早状态,然后再恢复执行。这一切都是通过基于检查点状态保存重建机制来实现的,因而状态保存及状态重建必然伴随着时间和空间的损耗。该文深入研究了在乐观同步机制下,仿真执行时间和内存空间的损耗与检查点间隔之间的关系,并通过推理计算给出了检查点间隔的最优取值范围。

Domain-based noise removal method using fourth-order partial differential equation

Due to the fact that the fourth-order partial differential equation （PDE） for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the second-order PDE, a domain-based fourth-order PDE method for noise removal is proposed. First, the proposed method segments the image domain into two domains, a speckle domain and a non-speckle domain, based on the statistical properties of isolated speckles in the Laplacian domain. Then, depending on the domain type, different conductance coefficients in the proposed fourth-order PDE are adopted. Moreover, the frequency approach is used to determine the optimum iteration stopping time. Compared with the existing fourth-order PDEs, the proposed fourth-order PDE can remove isolated speckles and keeps the edges from being blurred. Experimental results show the effectiveness of the proposed method.

PDES时间推进中保守算法的研究与实现

介绍了PDES时间推进中的保守算法,给出了保守策略,分析了死锁的产生原因,并给出了解决死锁的方法,最后对算法进行了实现。