在非线性系统中的微观粒子的特性和非线性量子力学理论(上)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

在非线性系统中的微观粒子的特性和非线性量子力学理论(下)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

信息融合非线性控制理论初探

将信息融合思想引入控制领域，提出信息融合非线性控制理论．基于信息融合最优估计理论，研究非线性离散控制系统的最优控制问题．信息融合控制是把对控制系统的所有性能要求以及系统动力学转化为可融合信息，然后从信息融合估计的角度，使原问题转化为求控制量的“融合估计”问题．首先，给出了非线性信息融合估计定理；然后，推导了非线性系统信息融合控制的算法；最后，通过对机械手的转移控制问题的仿真研究说明了信息融合非线性控制算法的有效性．     

一类飞行器姿态动力学特征建模研究

本文研究飞行器姿态动力学的特征建模问题.针对飞行器姿态动力学所具有的三角形式的仿射非线性系统,通过引入非线性系统的时间尺度和一类与系统状态有关的压缩函数,给出了将动力学压缩到特征模型参数中的一般方法,并且给出了特征模型的参数范围及其极限.从所给出的参数范围可以看出,特征模型参数的界与采样周期、建模误差、系统阶数、系统变化率有关.所建立的特征模型的建模误差可以按照控制精度的要求任意小,表明了特征建模和一般模型降阶方法是不同的,该方法并不丢失系统信息.在此基础上建立了挠性卫星姿态特征模型,并给出了参数的界和极限,为基于特征模型的飞行器控制设计奠定了理论基础.     

考虑结构非线性的铁路弹性车轮动态特性研究

为研究结构非线性(包括弹性车轮橡胶材料非线性和接触边界非线性)对弹性车轮力学行为的影响,设计静动态试验获得弹性车轮中橡胶材料非线性本构关系并探讨了橡胶黏弹性特性;推导弹性车轮系统中橡胶弹性模量与刚度的转换关系,并确定黏弹性橡胶材料的刚度特性;基于橡胶Yeoh本构模型,建立整体车轮、线弹性车轮、考虑材料非线性特性的弹性车轮(以下简称:非线性弹性车轮)以及同时考虑材料与接触非线性特性的弹性车轮(以下简称:接触弹性车轮)等四个动力学模型,研究四种车轮模型在轮轨垂向力激扰下车轮的动态规律,并探明橡胶材料参数对弹性车轮动态特性的影响.研究表明:弹性车轮能有效降低车轮垂向振动;线弹性车轮的端点和中点较之非线性弹性车轮分别最大增加10%和13%的变形量,且橡胶中点变形量小于端点变形量;线弹性车轮较之整体车轮最大能降低17%的垂向振动,非线性弹性车轮较整体车轮最大能降低22%的垂向振动,同时考虑橡胶材料非线性和接触非线性对弹性车轮的动态特性影响不显著;四种车轮振动主频均为3～5, 10以及22 Hz;弹性车轮的振动和变形量随材料硬度增加而增加.     

大展弦比飞机几何非线性气动弹性稳定性的线性化方法

基于动力学小扰动假设建立了具有大展弦比机翼柔性飞机的全机几何非线性气动弹性稳定性分析的线性化方法和工程求解流程,并通过复杂算例验证了该方法的工程适用性.对某高空长航时无人机,计算了飞机在平飞设计载荷以及阵风载荷作用下的非线性静变形,在对应的非线性平衡态下对全机进行动力学线性化,计算了考虑静态大变形因素的全机固有振动特性,采用偶极子格网法计算了非定常气动力,进一步分析了全机的气动弹性稳定性,并与传统线性计算结果进行了对比研究.计算结果表明,由于结构大变形引起的几何非线性会引起机翼面内弯曲和扭转的运动耦合,改变相应模态的频率和振型,从而影响气动弹性耦合关系,降低颤振临界速度.传统的线性方法不但不能得到准确的颤振临界速度,而且有可能给出错误的稳定性结论.因此,对于具有大展弦比机翼的高空长航时无人机,以及类似的大柔性飞行器,必须在其设计过程中进行几何非线性气动弹性稳定性分析.     

一类非线性奇异Hamilton系统的H_∞控制

文中研究了一类非线性奇异Hamilton系统的稳定性和H_∞控制问题.基于该系统的结构特征,首先应用严格系统等价理论将该系统等价地转化为非线性耗散Hamilton微分代数系统,接着在此耗散形式下,研究非线性奇异Hamilton系统的稳定性问题并设计它的H_∞控制器,最后给出一个非线性电路系统的仿真实例.     

群时延和放大器非线性对TDRSS系统误码性能的影响

为研究群时延失真和行波管放大器(TWTA)非线性两者对TDRS系统误码性能影响的关系,首先介绍了群时延和TWTA非线性的概念以及对应的数学推导;然后使用MATLAB/SIMULINK仿真软件包搭建基于TDRS系统的群时延失真和TWTA非线性特性的联合仿真模型;通过对QPSK调制信号在该模型下的仿真分析,得出了群时延失真和TWTA非线性特性对TDRS系统误码性能的影响是不相关的关系。     

非线性随机动力学与控制研究进展及展望

随机动力学系用概率与统计方法研究自然界、工程及社会中各种随机动力学过程与现象。经一个世纪的发展，非线性随机动力学与控制已有相当的理论方法，主要是扩散过程理论方法。本文概述该理论方法，特别是作者提出与发展的非线性随机动力学与控制的Hamilton理论体系框架。最后建议各领域随机动力学与控制研究者进行跨学科的合作研究。     

并联机床的非线性特性及其在插补精度分析中的应用

应用微分几何的观点研究了并联机床关节空间输入向量与工作空间输出向量之间的运动学非线性特性. 提出了应用并联机构正解解轨迹的曲率, 对解轨迹的弯曲和等间距输入映射到解轨迹上的不等间距输出的非线性程度进行度量的方法. 通过对并联机构非线性引起的插补误差的分析, 给出了这种非线性曲率度量方法在涉及并联机构非线性的分析中的应用实例. 以并联机床VAMT1Y为例进行了分析计算, 并与正解数值算法得出的结论进行了比较研究.     

Pluralism and anarchism in quantum physics: Paul Feyerabend's writings on quantum physics in relation to his general philosophy of science

This paper aims to show that the development of Feyerabend's philosophical ideas in the 1950s and 1960s largely took place in the context of debates on quantum mechanics.In particular, he developed his influential arguments for pluralism in science in discussions with the quantum physicist David Bohm, who had developed an alternative approach to quantum physics which (in Feyerabend's perception) was met with a dogmatic dismissal by some of the leading quantum physicists. I argue that Feyerabend's arguments for theoretical pluralism and for challenging established theories were connected to his objections to the dogmatism and conservatism he observed in quantum physics.However, as Feyerabend gained insight into the physical details and historical complexities which led to the development of quantum mechanics, he gradually became more modest in his criticisms. His writings on quantum mechanics especially engaged with Niels Bohr; initially, he was critical of Bohr's work in quantum mechanics, but in the late 1960s, he completely withdrew his criticism and even praised Bohr as a model scientist. He became convinced that however puzzling quantum mechanics seemed, it was methodologically unobjectionable – and this was crucial for his move towards ‘anarchism’ in philosophy of science.     

Does time-symmetry imply retrocausality? How the quantum world says “Maybe”?

It has often been suggested that retrocausality offers a solution to some of the puzzles of quantum mechanics: e.g., that it allows a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum nonlocality, without action-at-a-distance. Some writers have argued that time-symmetry counts in favour of such a view, in the sense that retrocausality would be a natural consequence of a truly time-symmetric theory of the quantum world. Critics object that there is complete time-symmetry in classical physics, and yet no apparent retrocausality. Why should the quantum world be any different?This note throws some new light on these matters. I call attention to a respect in which quantum mechanics is different, under some assumptions about quantum ontology. Under these assumptions, the combination of time-symmetry without retrocausality is unavailable in quantum mechanics, for reasons intimately connected with the differences between classical and quantum physics (especially the role of discreteness in the latter). Not all interpretations of quantum mechanics share these assumptions, however, and in those that do not, time-symmetry does not entail retrocausality.     

Holism, physical theories and quantum mechanics

Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.     

A note on the prehistory of indistinguishable particles

In modern terms, quantum statistics differs from classical statistics for the indistinguishability of its elementary entities. An historical investigation of the emergence of Bose–Einstein statistics, however, shows that quantum statistics was initially interpreted as a statistics of non-independence, for it extended to gas particles the statistical correlation that was a long-recognized characteristic of light quanta. At the same time, the development of a quantum–statistical theory of the ideal gas was riddled with the question of the statistical significance of the exchange symmetry of a system of equal particles. Indistinguishability combines exchange symmetry and statistical correlation, and relates them to the loss of identity of particles in quantum mechanics. It is instructive, however, not to conflate these properties when analysing the historical emergence of quantum statistics. The statistical correlation of light quanta and the exchange symmetry of gas molecules remained two separate problems even though quantum gas theory and Bose–Einstein statistics were born from gas-radiation analogies in statistical theory.     

Some philosophical aspects of particle physics

The paper is concerned with explaining some of the principal theoretical developments in elementary particle physics and discussing the associated methodological problems both in respect of heuristics and appraisal. Particular reference is made to relativistic quantum field theory, renormalization, Feynman diagram techniques, the analytic S-matrix and the Chew — Frautschi bootstrap.     

Is the classical limit “singular”?

We argue against claims that the classical ? → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ? → 0 limit. We then use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics.     

Whence chemistry?

Along with exploring some of the necessary conditions for the chemistry of our world given what we know about quantum mechanics, I will also discuss a different reductionist challenge than is usually considered in debates on the relationship of chemistry to physics. Contrary to popular belief, classical physics does not have a reductive relationship to quantum mechanics and some of the reasons why reduction fails between classical and quantum physics are the same as for why reduction fails between chemistry and quantum physics. However, a neoreductionist can accept that classical physics has some amount of autonomy from quantum mechanics, but still try to maintain that classical+quantum physics taken as a whole reduces chemistry to physics. I will explore some of the obstacles lying in the neoreductionist's path with respect to quantum chemistry and thereby hope to shed more light on the conditions necessary for the chemistry of our world.     

A Bayesian reconstruction of the methodology of scientific research programmes

The paper is concerned with explaining some of the principal theoretical developments in elementary particle physics and discussing the associated methodological problems both in respect of heuristics and appraisal. Particular reference is made to relativistic quantum field theory, renormalization, Feynman diagram techniques, the analytic S-matrix and the Chew — Frautschi bootstrap.