拓扑流体力学及其新近发展

拓扑流体力学是理性力学的一个重要研究方向,在理论上具有重要价值,在实践中日益显出独特的作用.本文试对该方向进行综述性介绍,目的是吸引更多的国内科研工作者进入这一重要领域.本文的重点放在流体螺度(Helicity)的拓扑内涵方面.除了列出螺度与数学纽结场论的关系(即与互缠绕、自缠绕数以及作者近年来发展出来的流体纽结多项式拓扑不变量之间的关系),还介绍了国际上在流体纽结复杂系综的能量-结构复杂性关系方面的研究.最后,通过超流涡旋纽结/链环重联的具体实例,展示了这一领域当中典型的数值计算方法.我们希望通过这种理论推导与数值计算同时呈现的方式,使读者对这一国际前沿交叉领域的核心问题、研究方法以及科研中可能面对的技术困难获得一个整体的了解和把握.     

2020年细胞力学热点回眸

 概述了2020年细胞力学研究的热点和进展，探讨了细胞膜表面张力、细胞粘附力、细胞弹性模量、细胞与纳米颗粒相对刚度等对细胞生物学行为的影响及其在疾病诊疗中的应用。     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality – i.e. without making any assumptions about the system׳s dynamics or the nature of the interactions between its components – that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another – again fully general – theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor (such as ergodicity or typicality), the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.     

Multiplicity in Everett׳s interpretation of quantum mechanics

Everett׳s interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This notion of multiplicity has been understood in different ways by proponents of Everett׳s theory. In fact the spectrum of opinions on various ontological questions raised by Everett׳s approach is rather large, as we attempt to document in this critical review. We conclude that much remains to be done to clarify and specify Everett׳s approach.     

球直坐标转换误差分析及对卡尔曼滤波的制约

将观测器 (如雷达 )在球坐标系的测量值转换到三维直角坐标系后 ,其误差分布规律将发生变化。通过分析 ,证明了理论模型不能直接应用于卡尔曼滤波 ,得到了适用于卡尔曼滤波的直角坐标系的工作模型 ,并对转换后的误差的理论模型和工程模型进行数值比较 ,两者的数字特征非常接近。     

气体吸附理论的研究

应用统计力学研究实际气体吸附,导出了吸附方程式的普遍形式,并给出气体分子在Ｋｅｅｓｏｍ势和Ｌ－Ｊ势作用下的具体形式,应用自动吸附仪测定微孔和中孔活性炭吸附Ｎ２的实验等温线,微孔炭的实验等温线和理论等温线吻合程度令人满意。     

撞击损伤过程的有限元分析

运用连续介质损伤力学理论．在接触-冲击问题中引入由Lemaitre提出的一个各向同性韧性损伤模型,通过有限元法来计算、反映接触-冲击过程中材料性能的劣化程度和进程,并以有限单元间的分离来模拟诸如“穿甲”等一类包含材料破碎的接触-冲击过程．为在接触-冲击问题中考虑损伤的影响,提供了一般的方法．     

纺织材料力学性能研究有限元方法应用综述

综述至今为止有限元方法在纤雄、纱线和织物结构力学方面所有代表性研究工作,并对纺织材料结构力学的发展方向作了展望。     

两板条理想粘结问题的应力场

采用复变函数解法,解出了两不同材质无限大板沿ｘ轴（ｘ－ａ）和（－ｘ－ａ）处理想粘结,并在无限远处作用剪力和压力时的应力场．采用与本文完全类似的方法,还可以解出应力全场解及位移全场解．