fKenzo: A user interface for computations in Algebraic Topology

fKenzo (=friendly Kenzo) is a graphical user interface providing a user-friendly front-end for the Kenzo system, a Common Lisp program devoted to Algebraic Topology. The fKenzo system provides the user interface itself, an XML intermediary generator-translator and, finally the Kenzo kernel. We describe in this paper the main points of fKenzo, and we explain also the advantages and limitations of fKenzo with respect to Kenzo itself. The text is separated into two parts, trying to cover both the user and the developer perspectives.     

Analytical benchmarks for topological optimization IV: square-shaped line support

Michell’s problem of optimizing truss topology for stress or compliance constraints under a single load condition is solved analytically for plane trusses having a square-shaped line support. Geometrical characteristics of the Hencky nets giving the truss layout are expressed in terms of Lommel functions. Analytically derived truss volumes for the above problem are compared with those of trusses supported along circles of equivalent area. Some general implications of the results are also discussed.     

Angular MST‐Based Topology Control for Multi‐hop Wireless Ad Hoc Networks

This letter presents an angular minimum spanning tree (AMST) algorithm for topology control in multi‐hop wireless ad hoc networks. The AMST algorithm builds up an MST for every angular sector of a given degree around each node to determine optimal transmission power for connecting to its neighbors. We demonstrate that AMST preserves both local and network‐wide connectivity. It also improves robustness to link failure and mitigates transmission power waste.     

Relay sensor placement in wireless sensor networks

This paper addresses the following relay sensor placement problem: given the set of duty sensors in the plane and the upper bound of the transmission range, compute the minimum number of relay sensors such that the induced topology by all sensors is globally connected. This problem is motivated by practically considering the tradeoff among performance, lifetime, and cost when designing sensor networks. In our study, this problem is modelled by a NP-hard network optimization problem named Steiner Minimum Tree with Minimum number of Steiner Points and bounded edge length (SMT-MSP). In this paper, we propose two approximate algorithms, and conduct detailed performance analysis. The first algorithm has a performance ratio of 3 and the second has a performance ratio of 2.5. Xiuzhen Cheng is an Assistant Professor in the Department of Computer Science at the George Washington University. She received her MS and PhD degrees in Computer Science from the University of Minnesota - Twin Cities in 2000 and 2002, respectively. Her current research interests include Wireless and Mobile Computing, Sensor Networks, Wireless Security, Statistical Pattern Recognition, Approximation Algorithm Design and Analysis, and Computational Medicine. She is an editor for the International Journal on Ad Hoc and Ubiquitous Computing and the International Journal of Sensor Networks. Dr. Cheng is a member of IEEE and ACM. She received the National Science Foundation CAREER Award in 2004. Ding-Zhu Du received his M.S. degree in 1982 from Institute of Applied Mathematics, Chinese Academy of Sciences, and his Ph.D. degree in 1985 from the University of California at Santa Barbara. He worked at Mathematical Sciences Research Institutea, Berkeley in 1985-86, at MIT in 1986-87, and at Princeton University in 1990-91. He was an associate-professor/professor at Department of Computer Science and Engineering, University of Minnesota in 1991-2005, a professor at City University of Hong Kong in 1998-1999, a research professor at Institute of Applied Mathematics, Chinese Academy of Sciences in 1987-2002, and a Program Director at National Science Foundation of USA in 2002-2005. Currently, he is a professor at Department of Computer Science, University of Texas at Dallas and the Dean of Science at Xi’an Jiaotong University. His research interests include design and analysis of algorithms for combinatorial optimization problems in communication networks and bioinformatics. He has published more than 140 journal papers and 10 written books. He is the editor-in-chief of Journal of Combinatorial Optimization and book series on Network Theory and Applications. He is also in editorial boards of more than 15 journals. Lusheng Wang received his PhD degree from McMaster University in 1995. He is an associate professor at City University of Hong Kong. His research interests include networks, algorithms and Bioinformatics. He is a member of IEEE and IEEE Computer Society. Baogang Xu received his PhD degree from Shandong University in 1997. He is a professor at Nanjing Normal University. His research interests include graph theory and algorithms on graphs.     

一种城域网物理拓扑快速自动发现实现方法

根据城域网网管软件开发过程中的设计经验,本文阐述了一种基于路由接口地址空间和SNMP异步扫描的网络物理拓扑快速发现的方法,并在具体项目中予以实现和应用,解决了拓扑发现过程中面临的设备搜索的完整性、拓扑发现的速度和拓扑判定的准确性三个主要问题,并取得了良好的效果。     

机械系统拓扑结构的通用表达模型设计

提出了一种适用于机械系统的通用拓扑模型——环基树拓扑结构模型 ,研究了环基树的性质及自动生成算法 ,介绍了运动和力的拓扑表等概念 ,给出了两个基于环基树结构的通用自由度计算公式。研究结果为机械系统的计算机表达、管理、维护和加工提供了统一机制 ,构成了机械系统计算机辅助装配和性能分析统一建模的重要基础     

Shape morphing of laminated composite structures with photostrictive actuators via topology optimization

In this paper, a new design method is presented for achieving remote wireless shape morphing of laminated composite structures using topology optimization methods. A recently emerging family of smart materials, photostrictive materials, is introduced as the actuation discipline to implement the active control of optical structures by utilizing the photostriction mechanism, which arises from the superposition of photovoltaic effect and converse piezoelectric effect when exposed to the illumination of near ultraviolet light. In terms of the Mindlin plate theory of first-order shear deformation, a finite element formulation including multiphysics effects of photovoltaic, pyroelectric and thermal expansion is developed to model composite structures of ferroelectric materials polarized in 0–1 and 0–3 directions, respectively. The design is formulated as a multi-constrained optimization problem with a least square objective function to minimize structural shape errors. The topology optimization method is used as a systematic design approach to seek the optimal topologies of material layouts for both the photostrictive and host layers as well as the actuator light distribution. In terms of design sensitivity analysis, many gradient-based optimization algorithms can be applied to solve the problem effectively. Numerical examples are presented to demonstrate the effectiveness of this method in the field of active photonic control of laminated composite structures.     

岩体质量的可拓学评价方法在边坡工程中的应用

可拓工程评价方法是在解决矛盾问题的过程中，既可利用物元的可拓性确定定性因素，又可利用可拓集合论，通过关联函数可取负值这一特点进行定量计算，使评价方法能较全面地分析对象属于集合的程度，较好地解决了岩体质量评价中定性与定量因素综合评价的问题。     

基于人工制造约束的三维拓扑优化设计方法

为了更好地解决三维拓扑优化工程实用化的问题,提出了基于人工制造约束的拓扑优化设计方法。该方法在拓扑优化过程中实时地监控拓扑优化结果,并借助设计人员的工程经验,实时地加入符合制造工艺成型的约束条件辅助计算进行机拓扑优化设计。钢结构拱桥算例中以有限元软件ANSYS为平台进行二次开发、以双向渐进结构优化法为核心算法通过人为干预实现了在拓扑优化过程中钢结构拱桥斜支撑向竖直支撑的转变。通过对比发现该方法的优化结果与实际拱桥模型结构相似,表明了该方法是有效的和可行的。     

结构动力学设计优化方法的新进展

阐述结构动力学优化设计的研究背景和意义。根据实践,扼要介绍近十年作者在结构动力学设计研究方面取得的若干新近展,内容包括,随机激励下以均方响应为约束的设计方法、结构动力学形状优化、结构动力学拓扑优化、动力学设计约束的性质和解的存在性以及结构／控制一体化优化设计,并对进一步的研究工作做简要展望。