Control of 1-D parabolic PDEs with Volterra nonlinearities, Part I: Design

Boundary control of nonlinear parabolic PDEs is an open problem with applications that include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present stabilizing control designs for a broad class of nonlinear parabolic PDEs in 1-D. Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and employs spatial Volterra series nonlinear operators both in the transformation to a stable linear PDE and in the feedback law. The control law design consists of solving a recursive sequence of linear hyperbolic PDEs for the gain kernels of the spatial Volterra nonlinear control operator. These PDEs evolve on domains T_n of increasing dimensions n+1 and with a domain shape in the form of a “hyper-pyramid”, 0≤ξ_n≤ξ_n−1?≤ξ₁≤x≤1. We illustrate our design method with several examples. One of the examples is analytical, while in the remaining two examples the controller is numerically approximated. For all the examples we include simulations, showing blow up in open loop, and stabilization for large initial conditions in closed loop. In a companion paper we give a theoretical study of the properties of the transformation, showing global convergence of the transformation and of the control law nonlinear Volterra operators, and explicitly constructing the inverse of the feedback linearizing Volterra transformation; this, in turn, allows us to prove L² and H¹ local exponential stability (with an estimate of the region of attraction where possible) and explicitly construct the exponentially decaying closed loop solutions.     

The anti-reflective algebra: structural and computational analysis with application to image deblurring and denoising

Anti-reflective (AR) boundary conditions (BC) have been introduced recently in connection with fast deblurring algorithms, both in the case of signals and images. Here we extend such BCs to d dimensions (d ≥ 1) and we study in detail the algebra induced by the AR-BCs, with strongly symmetric point spread functions (PSF), both from a structural and computational point of view. The use of the re-blurring idea and the computational features of the AR-algebra allow us to apply Tikhonov-like techniques within O(n ^d log(n)) arithmetic operations, where n ^d is the number of pixels of the reconstructed object. Extensive numerical experimentation concerning 2D images and strongly symmetric PSFs confirms the effectiveness of our proposal.      

回转体头部压力分布规律及其对转捩点的影响

以圆头回转体为研究对象,头部线型采用双参数椭圆曲线,利用面元法求解绕流势流流场,利用F.W.Scholkemeier的积分方法,确定该压力分布下的层流边界层,利用P.S.Granville方法求解边界层转捩点.通过变换头部线型参数,以最小压力系数绝对值的下降方向为搜索方向,研究不同头型压力分布的变化规律及其对转捩点的影响.结果表明:最小压力系数绝对值越小的头型其最小压力点离头部驻点的距离越近;不同头型的转捩点不光与其压力分布有关,而且还与其头部长径比有关.     

一种三维刚架—桁架静力分析有限元程序

介绍了三维刚架计算原理以及作者所编制的一种应用于ＰＣ微机的有限元程序．本程序用＂ＦＯＲＴＲＡＮ＂语言编写,采用半动态一维存储．引入了单元整体形函数矩阵,简化了单元非结点载荷与结点载荷的转换过程．可用于计算三维及二维刚架或桁架在多种载荷条件下的位移及杆端内力并可绘出结构的有限元模型、支承、受载及变形状况．通过一系列算例验证了程序的正确性．     

基于衍射色散原理的光谱共焦位移测量技术综述

位移检测技术是几何量精密测量的基础,在当代精密制造领域应用广泛。光谱共焦位移测量技术具有对环境杂散光、被测物倾斜、材料类型不敏感,测量频率高以及分辨率高等优点,可以检测位移量、表面粗糙度、三维形貌以及单层或多层透明材料的厚度,在精密位移测量领域中占据重要地位。近年来,利用衍射光学元件提高光学系统性能的光谱共焦测量技术被广泛研究。文章综述了基于衍射色散原理的光谱共焦位移测量技术的研究进展。首先,介绍了光谱共焦位移测量原理和衍射光学元件的色散特性;其次,阐述了基于衍射色散原理的光谱共焦位移测量技术的发展历史及研究进展;最后展望了该技术的发展趋势。     

新工科理念下思政元素与电子实践教学的融合探索

为了落实建设新工科和大思政教育模式的育人理念,结合专业发展,本文以工程训练中的电子创新实践课程为例,研究思政元素如何融入实践教学的各个环节,具体探讨在设定教学目标、教学内容、优化教学方法、教学考核设置及课后总结交流等环节中,将思政元素与专业课程相互贯通融合的教学设计理念与方法。     

Digital at the edge – antecedents and performance effects of boundary resource deployment

With business ecosystems digitalizing by the force of digital innovation, the deployment of boundary resources (such as application programming interfaces: APIs) becomes a strategic option across contexts. We distinguish between boundary resources that provide access openness and those that provide resource openness, and theorize the antecedents and consequences of their deployment. Employing panel data regressions to a longitudinal cross-industry dataset, we find that the digital knowledge base of the focal firm and the existence of potential digital complementors drive boundary resource deployment. Such deployment benefits firm performance depending on the firm’s market power. From our empirical analysis, we reveal a differentiated perspective on the quality of the confined openness provided by boundary resources as well as the embeddedness of their deployment in the rationales and motivations of the associated actors in digital business ecosystems. We complement the existent theoretical framework on boundary resources and provide valuable insights to managers reflecting about deploying boundary resources in a beneficial way.     

Isogeometric analysis of fluid‐saturated porous media including flow in the cracks

An isogeometric model is developed for the analysis of fluid transport in pre‐existing faults or cracks that are embedded in a fluid‐saturated deformable porous medium. Flow of the interstitial fluid in the porous medium and fluid transport in the discontinuities are accounted for and are coupled. The modelling of a fluid‐saturated porous medium in general requires the interpolation of the displacements of the solid to be one order higher than that of the pressure of the interstitial fluid. Using order elevation and Bézier projection, a consistent procedure has been developed to accomplish this in an isogeometric framework. Particular attention has also been given to the spatial integration along the isogeometric interface element in order to suppress traction oscillations that can arise for certain integration rules when a relatively high dummy stiffness is used in a poromechanical model. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

A framework to validate and generate curved nodal high‐order meshes on Computer‐Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin‐shell and 3D finite element analysis with unstructured high‐order methods. First, we define a distortion (quality) measure for high‐order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high‐order), and handles with low‐quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high‐order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process. Copyright © 2015 John Wiley & Sons, Ltd.     

锌铜钛合金的研究进展与应用

简述了锌资源概况、锌合金的研究历程和以锌代铜的可行性,主要介绍了锌基抗蠕变合金——锌铜钛合金的使用状况及优点,特别是锌铜钛板材的情况。综述了国内外锌铜钛合金的研究和应用进展,论述了铜、钛及各合金元素在锌基合金中的作用,并阐明成分优化、形变热处理对其组织演变和性能方面的影响,最后对锌铜钛合金的应用和前景进行了探讨和展望。