《数学实验》课程建设的认识与实践

我们认为 :数学实验 ,就是对数学进行折腾 .我们提出一些饶有趣味而又有深刻背景的问题 ,让学生尝试自己去解决 ,借助于计算机 ,自己动手去折腾 ,在折腾过程中学习 ,观察现象和结果 ,猜测和验证规律 ,尝试和体验数学的探索、发现和应用     

Piezoelectricity of ordered (ScxGa1-xN) alloys from first principles

First-principles calculations are performed to compute the e₃₃ piezoelectric coefficients of GaN, ScN and (Sc_xGa_1-xN) alloys exhibiting an alternation of hexagonal GaN, with hexagonal ScN along the c-axis. For Sc compositions larger than 50%, each atom has nearly five nearest neighbors (i.e., the ground state exhibits a phase that is five-fold coordinated). On the other hand, Sc-deficient (Sc, Ga) N alloys adopt a ground-state that is four-fold coordinated). The magnitude of e₃₃ in the Sc-deficient ideally ordered (Sc_0.25Ga_0.75N) is found to be larger than the magnitude of the corresponding e₃₃ coefficients resulting from the compositional weighted average over the hexagonal (h-ScN) and the wurtzite (w-GaN) parent compounds. On the other hand, the e₃₃ coefficients of the Sc-rich ordered (Sc_0.75Ga_0.25N) is found to be negligibly small. In addition, e₃₃ piezoelectric coefficients in ordered (Sc_0.5Ga_0.5N) exhibit quite large magnitudes, due to the nonpolar to polar transition occurs at Sc composition x = 0.5, and thus can bridge the corresponding coefficients of (Ga, In) N and ferroelectric alloys. The microscopic origins for this huge enhancement in the piezoelectric behavior in Sc-low and Sc-intermediate alloys and the role of each atom are revealed and discussed.     

复合结构剪切板的屈曲与后屈曲研究

基于Ｒｅｉｓｓｎｅｒ剪切板理论，本文将现有理论模型推进了一步，导出了控制复合材料和构造矩形板平衡的广义Ｋａｒｍａｎ大挠度方程。此外，运用摄动技术，构造了一个单向压缩简支剪切矩形板的后屈曲渐近解，适用于面板和夹心材料都具正交各向异性的夹层板以及计及横向剪切变形对称铺设的层合板。文中给出了典型算例，并将当前结果与其它理论或数值解作了比较，显示出相当好的一致性。     

架设阶段悬索桥静力问题的随机有限元分析

架设阶段的悬索桥不仅具有显著的几何非线性行为，而且存在材料特性的变异。本文建立了以增量形式表达的非线性摄动法随机有限元列式，并编制了悬索桥静力分析程序ＳＮＡＰ。针对一座国内在建的悬索桥，计算了该桥在某一施工阶段考虑缆索弹性模量随机性时主梁跨中点位移的变化。结果表明，材料随机性的影响十分明显。     

认可机制下实验室人员培训工作的组织与开展

针对部分实验室在人员培训工作中存在的培训模式不清、培训机制不健全、培训质量较低的问题,系统地分析了计量实验室人员培训所涉及的主要类别、内容及要求等。对培训工作的流程逐个进行详尽地描述,分内部培训和外部培训两个方面对培训中应注意的问题进行重点说明,为广大计量实验室管理人员开展人员培训工作提供借鉴。     

地方高校省级物理示范实验室建设的探索与实践

提出了示范实验室建设的思路与目标,阐述分层次模块化的实验教学体系,介绍了多样化的实验教学手段。经过3年的探索与实践,示范实验室建设成效显著、特色明显,取得了较为显著的成绩,有一定示范性和辐射作用。     

国际地下实验室发展综述

地下实验室是开展粒子物理学、天体物理学及宇宙学等领域一些重大基础性前沿课题的重要研究场所和良好的低本底环境,建设和发展地下实验室对于一个国家的基础科学研究具有重要科学意义.目前,国际上许多国家都已经建立起地下实验室,而中国一直没有很好的地下实验室,特别是极深地下实验室.2009年,清华大学与二滩水电开发有限责任公司开展战略合作,利用锦屏山隧道建立中国首个世界最深的地下实验室--中国锦屏地下实验室(China Jinping Underground Laboratory,CJPL),并于2010年12月12日正式启用.中国锦屏地下实验室的建成,标志着中国已经具备开展物理学重大基础前沿科学研究的自主地下实验平台,对于推动我国相关领域的重大基础前沿课题的自主研究意义重大.文章对国际上一些重要地下实验室的情况进行了介绍,并对中国锦屏地下实验室的基本情况进行了介绍.     

Clifford algebra method for network expression,computation, and algorithm construction

Clifford algebra is introduced as a theoretical foundation for network topology expression and algorithm construction. Network nodes are coded with basis vectors in a vector space , and the edges and k‐walk routes can be expressed by 2‐blades and k‐blades, respectively, in the Clifford algebra Cl(n,0). The topologies among nodes, edges, and routes of networks can be directly calculated, and the network routes can be extended and traversed with oriented join products. The network algorithm construction processes based on Clifford algebra are instantiated by the single source shortest path algorithm. The experimental results on different scale random networks suggest that Clifford algebra is suited for network expression and relation computation. The Clifford algebra‐based shortest path algorithm is vivid and clear in geometric meaning and has great advantage on temporal and spatial complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

Approximation algorithms for constructing some required structures in digraphs

We consider a new problem of constructing some required structures in digraphs, where all arcs installed in such required structures are supposed to be cut from some pieces of a specific material of length L. Formally, we consider the model: a digraph D = (V, A; w), a structure S and a specific material of length L, where w: A → R⁺, we are asked to construct a subdigraph D′ from D, having the structure S, such that each arc in D′ is constructed by a part of a piece or/and some whole pieces of such a specific material, the objective is to minimize the number of pieces of such a specific material to construct all arcs in D′.