On the history of the isomorphism problem of dynamical systems with special regard to von Neumann’s contribution

This article reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory (ergodic theory). In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this article clarifies von Neumann’s contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the article is that von Neumann’s argument described in his letter to Ulam is the very first proof that spatial isomorphism and spectral isomorphism are not equivalent because spectral isomorphism is weaker than spatial isomorphism: von Neumann shows that spectrally isomorphic ergodic dynamical systems with mixed spectra need not be spatially isomorphic.     

Compensation for time-delayed feedback bang-bang control of quasi-integrable Hamiltonian systems

The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced.Then,two time delay compensation methods,namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT),are proposed.The conditions applicable to each compensation method are discussed.Finally,an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation ...     

The ergodic hierarchy, randomness and Hamiltonian chaos

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’ (EH), which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems.     

Dynamics of vehicle-pavement coupled system based on a revised flexible roller contact tire model

A revised flexible roller contact tire model (RFRC tire model) is proposed,which considers not only the geometric and flexible filtering effect,but also tire damping and pavement displacement.A vehicle-pavement coupled system is modeled as a two DOF oscillator moving along a simply supported beam on a linear viscoelastic foundation.By using the Galerkin's and Direct Integral method,dynamical responses of the vehicle-pavement coupled system are obtained based on the RFRC tire model and the traditional single...     

基于系统动力学的价格振荡系统收敛条件

从离散动力系统的角度建立动态价格振荡系统模型。描述了中间产品价格振荡的动态过程,利用系统动力学中不动点的稳定性理论,给出了价格振荡系统收敛的一般性条件。并结合具体例子对最优产量反应函数为线性和非线性的情况进行分析,验证了振荡过程的收敛性,得出在一定条件下供应链能通过价格振荡过程达到均衡,并实现供应链总体利益最大。     

汽车爆胎报警及控制系统的研究现状及发展趋势

本文分析了汽车爆胎发生的原因及爆胎后车辆的运动特征,综述了防爆胎报警系统和爆胎控制系统的研究现状。在总结上述两种系统优缺点的基础上,对兼有爆胎报警和控制功能的系统的发展趋势进行了展望。     

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。     

On miracles and spacetime

What have recently been dubbed two ‘miracles’ of general relativity—(1) that all non-gravitational interactions are locally governed by Poincaré invariant dynamical laws; and (2) that, in the regime of experimental practice in which curvature effects may be ignored, the local Poincaré symmetries of the dynamical laws governing matter fields coincide with the local Poincaré symmetries of the dynamical metric field—remain unaccounted for in that theory. In this paper, I demonstrate that these two ‘miracles’ admit of a natural explanation in one particular successor theory to general relativity—namely, perturbative string theory. I argue that this point has important implications when considering both the ‘chronogeometricity’ (that is, the object in question being surveyed by rods and clocks built from matter fields) and spatiotemporal status of the dynamical metric field in both general relativity and perturbative string theory.     

Large-Eddy Simulations of turbulent flows with lattice Boltzmann dynamics and dynamical system sub-grid models

In this paper,two sub-grid scale (SGS) models are introduced into the Lattice Boltzmann Method (LBM),i.e.,the dynamics SGS model and the dynamical system SGS model,and applied to numerically solving three-dimensional high Re turbulent cavity flows.Results are compared with those obtained from the Smagorinsky model and direct numerical simulation for the same cases.It is shown that the method with LBM dynamics SGS model has advantages of fast computation speed,suitable to simulate high Re turbulent flows.In ...     

具有双控制输入通道高阶不确定非线性系统控制设计

本文研究了一类高阶不确定非线性系统的全局渐近稳定控制设计问题.不同于现有结果,本文所研究的高阶非线性系统具有两个控制输入通道,即控制输入直接作用于两个一维子系统.这导致已有的控制设计方法不能或难以用来解决该类控制设计问题,因此,寻求新的控制设计方法,用以解决多控制输入通道高阶非线性系统的控制设计问题,是一个很有意义的研究课题.本文首先引入一个有效的反馈变换,从而在非线性系统满足适当假设条件下,成功地将该类系统的控制设计问题转化为规范的单控制输入通道情况下的控制设计问题.进而借助于已有结果,特别是增加幂次积分方法,给出所研究非线性系统的全局渐近稳定控制器的设计方法.尽管本文所研究的系统是具有多控制输入通道高阶非线性系统的特殊情况,所得结果具有一定的局限性,但对更一般情况具有借鉴和指导作用.最后,仿真算例验证了本文理论结果的有效性.     

Decomposition of almost Poisson structure of non-self-adjoint dynamical systems

Non-self-adjoint dynamical systems,e.g.,nonholonomic systems,can admit an almost Poisson structure,which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity.A general theory of the almost Poisson structure is investigated based on a decomposition of the bracket into a sum of a Poisson one and an almost Poisson one.The corresponding relation between Poisson structure and symplectic structure is proved,making use of Jacobiizer and symplecticizer.Based on a...     

基于计算机仿真的心肌动脉血管网流固耦合仿真分析

针对运动员运动时易出现动脉、毛细血管损伤等现象,基于流体动力学、固体力学、计算机仿真技术和超弹性材料模型,利用有限元分析方法,建立了心肌动脉血管网流固耦合模型,并分析了心肌动脉及其支血管网内血液流动的速度场、压力分布以及由血液流动引起的血管受力变形等力学特征。基于心肌动脉血管网流固耦合模型,利用PID控制算法控制心肌动脉入口压力成功实现了血管内待测点血液流速的自动控制,并且此PID控制系统对血液流速的变化有很好的响应灵敏度。     

复杂软件系统的成长性构造与适应性演化

随着信息网络技术的渗透性发展,复杂软件系统正在成为一种泛在的新型软件形态.此类软件系统通常由相当数量的局部自治的软件系统相互耦合关联而成,具有"系统之系统"、"信息—物理"融合系统和"社会—技术"交融系统的特点,表现出成员异质、边界开放、行为涌现、持续演化等一系列新的性质.这些特征打破了传统基于"还原论"思想的软件工程理论和技术所基于的基本假设,使其难以适用于复杂软件系统的构建.本文分析复杂软件系统的内涵、形成特征和基本性质,深入讨论复杂软件系统在构造和演化环节所面临的挑战,借鉴互联网以及生命系统、社会系统和经济系统等复杂系统的形成和演进模式,提出复杂软件系统的"成长性构造"和"适应性演化"法则,阐述这两条法则所涉及的主要科学问题和关键支撑技术.本文试图为复杂软件系统的构建和发展提供新的方法学和架构层面的支持.     

The non-relativistic limits of the Maxwell and Dirac equations: the role of Galilean and gauge invariance

The aim of this paper is to illustrate four properties of the non-relativistic limits of relativistic theories: (a) that a massless relativistic field may have a meaningful non-relativistic limit, (b) that a relativistic field may have more than one non-relativistic limit, (c) that coupled relativistic systems may be “more relativistic” than their uncoupled counterparts, and (d) that the properties of the non-relativistic limit of a dynamical equation may differ from those obtained when the limiting equation is based directly on exact Galilean kinematics. These properties are demonstrated through an examination of the non-relativistic limit of the familiar equations of first-quantized QED, i.e., the Dirac and Maxwell equations. The conditions under which each set of equations admits non-relativistic limits are given, particular attention being given to a gauge-invariant formulation of the limiting process especially as it applies to the electromagnetic potentials. The difference between the properties of a limiting theory and an exactly Galilean covariant theory based on the same dynamical equation is demonstrated by examination of the Pauli equation.     

Bursting of Morris-Lecar neuronal model with current-feedback control

The Morris-Lecar (ML) neuronal model with current-feedback control is considered as a typical fast-slow dynamical system to study the combined influences of the reversal potential VCa of Ca2+ and the feedback current I on the generation and transition of different bursting oscillations.Two-parameter bifurcation analysis of the fast subsystem is performed in the parameter (I,VCa)-plane at first.Three important codimension-2 bifurcation points and some codimension-1 bifurcation curves are obtained which enabl...     

具有通信受限的网络控制系统量化反馈控制

针对一类通信受限的网络控制系统,研究量化反馈控制器及动态调度策略的联合设计问题.考虑到介质访问约束和信号量化误差的影响,将网络控制系统建模为等价的离散时间切换系统;通过Lyapunov稳定理论推导出保证系统鲁棒稳定的模式及量化依赖型充分条件,并给出了量化反馈控制器的设计方法;在此基础上,设计了基于实时状态的动态通信调度策略,实现了网络控制系统的镇定控制.最后通过仿真示例验证了所提出方法的有效性.     

Bifurcation and chaos of the bladed overhang rotor system with squeeze film dampers

To study the nonlinear dynamic behavior of the bladed overhang rotor system with squeeze film damper (SFD),a blade-overhang rotor-SFD model is formulated using the lumped mass method and the Lagrange approach.The cavitated short bearing model is employed to describe the nonlinear oil force of the SFD.To reduce the scale of the nonlinear coupling system,a set of orthogonal transformations is employed to decouple the one nodal diameter equations of blades,which are coupled with the dynamical equations of the ...     

基于Watch—dog的嵌入式煤层注水多级保护系统设计

针对现有煤层注水自动控制系统因抗干扰能力有限,无法在部分条件恶劣的采区长时间稳定工作的实际情况,设计了采用多级看门狗组成的嵌入式保护系统。本系统提供了四个级别的保护措施,根据故障严重程度,保护级别逐步升级,在控制系统出现软硬件故障后,包括出现电磁干扰或死锁现象后,不同看门狗启动不同保护措施,使系统恢复正常。在保护系统电路设计中充分考虑了看门狗定时器的独立性、故障安全性和作用实时性三方面因素,各级看门狗用最少的软件及硬件实现,降低了系统冗余。本设计在多个注水自动控制系统的改造实践中应用,有效地提高了原系统的稳定性、可靠性,具有很强的应用和推广价值。     

面向网络的操作系统——现状和挑战

操作系统是计算机系统中最为关键的一层系统软件．长期以来,操作系统发展的主线是面向单机,追求更好地发挥计算机硬件的计算能力,同时为上层应用和用户提供更友好易用的接口．随着网络技术的发展,如何更好地支持网络构成了操作系统发展的一个重要辅线．近年来,由于互联网的迅速普及,面向网络的操作系统得到了广泛的关注,并逐渐成为操作系统发展的新主线．为了更好地管理互联网上的分布海量资源,同时为互联网时代的新型应用和服务提供支持,操作系统技术正在产生许多重要的变革．本文简要回顾了操作系统的发展历史,分析了在互联网时代操作系统面临的主要挑战．在总结现有面向网络的操作系统的研究进展的基础上,讨论了其主要特点和未来发展趋势．最后,也介绍了我们在此领域针对网构软件的研发尝试．     

Celestial chaos: The new logics of theory-testing in orbital dynamics

I explore how the nature, scope, and limits of the knowledge obtained in orbital dynamics has changed in recent years. Innovations in the design of spacecraft trajectories, as well as in astronomy, have led to new logics of theory-testing—that is, new research methodologies—in orbital dynamics. These methodologies—which combine resonance overlap theories, numerical experiments, and the implementation of space missions—were developed in response to the discovery of chaotic dynamical systems in our solar system. In the past few decades, they have replaced the methodology that dominated orbital research in the centuries following Newton's Principia. As a result, the kind of knowledge achieved by orbital research has changed: we can know how orbiting bodies in chaotic systems behave, but only over sufficiently short time scales; and we can reliably measure those temporal limitations, using Lyapunov time.