Isochoric specific heat of sulfur hexafluoride at the critical point: Laboratory results and outline of a spacelab experiment for the d1-mission in 1985

The specific heat at constant volume c_v shows a weak singularity at the critical point. Renormalization group techniques have been applied, predicting a universal critical behavior which has to be experimentally confirmed for different systems. In this paper an experiment is presented to measure the specific heat of SF₆ along the critical isochore (_c=0.737 g·cm^–3), applying a continuous heating method. The results cover a temperature span of –1.5×10^–2< <1.70×10^–2 [=(T–T _c)/T _c] and were strongly affected by gravity effects that emerge in the sample of 1-mm hydrostatic height near the critical point. Using regression analysis, data were fitted with functions of the form c _v/R=A × ¦¦^– + B for the one-phase state and c _v/R=A × ¦¦^– + B for the twophase state. Within their error bounds the critical values (==0.098, A/A=1.83) represent the measurements for the temperature span 3.5×10^{–5< ¦¦<2.0×10 –3}, in good agreement with theoretical predictions. In order to exclude density profiles in the specimen, which are unavoidable in terrestrial experiments due to the high compressibility of fluids at the critical point and the gravity force, a space-qualified scanning ratio calorimeter has been constructed, which will permit long-term c_v measurements under microgravity (-g) conditions. The experiment will be part of the German Spacelab mission in October 1985. The significant features of the apparatus are briefly sketched.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Switching contact task control in hydraulic actuators: Stability analysis and experimental evaluation

A switching contact task control for hydraulic actuators is proposed. The controller is built upon three individually designed control laws for three phases of motion: (1) position regulation in free space, (2) impact suppression and stable transition from free to constrained motion and (3) force regulation in sustained‐contact motion. The position and force control schemes are capable of asymptotic set‐point regulation in the presence of actuator friction and without the complexity of sliding mode or adaptive control techniques. The intermediate impact control scheme is included for the first time to dampen the undesirable impacts and dissipate the impact energy that could potentially drive the whole system unstable. The solution concept and the stability of the complete switching control system are analyzed rigorously using the Filippov's solution concept and the concept of Lyapunov exponents. Both computer simulations and experiments are carried out to demonstrate the efficacy of the designed switching control law. Copyright © 2009 John Wiley & Sons, Ltd.     

Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

Abstact The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field ( = 1/2 in the immediate vicinity of the critical point to Ising-like (= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.Invited paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder. Colorado, U.S.A.     

Influence of ions on the critical behavior of a binary mixture near the consolute point

The lower critical point of stratification of a 3-methylpyridine (MP)+heavy water (D₂O) mixture in the presence of Na⁺ and CI^– ions has been studied by the Toepler shadow method. Addition of 0.3% ions lowered the critical temperature and reduced the equilibration time and the gradient of the refractive index (compressibillity). The analysis of the form of the near-critical isotherm demonstrated the ionic mixture to be described by the index = 3.05 ± 0.15. which corresponds to the classical mean-field theory. The results obtained provide evidence that even small admixtures of charged particles result in a substantial suppression of fluctuations near the critical point by the long-range Coulomb interaction.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Lyapunov指数混沌特性判定研究

探讨了Lyapunov指数混沌特性判据原理，分析了时间序列Lyapunov指数的计算过程，通过计算我国上证综合指数收益率时间序列的Lyapunov指数谱系，分析了我国资本市场的混沌特性。     

基于RBF网络的动力系统Lyapunov指数的计算方法

提出一种基于径向基函数(RBF)神经网络的动力系统Lyapunov指数计算方法，设计了一个RBF网络结构，推导了基于RBF网络的Lyapunov指数计算公式．仿真实验表明，与其它现有方法相比，此方法计算精度较高，收敛速度较快，而且只需要较少的样本数据量．本方法能更准确、更快速地计算动力系统的Lyapunov指数．     

一个新自治混沌系统的动力学分析

为产生复杂的混沌信号用于混沌保密通讯,构造了一个不同于经典的Lorenz系统、Chen系统和L系统的三维连续自治混沌系统,该系统含有二个参数,二个非线性项.利用理论分析和数值仿真、Lyapunov指数谱、分岔图、相图、时间响应和功率谱等非线性动力学分析方法,研究了新混沌系统的一些基本动力学特性.分析结果表明,该混沌系统具有丰富的动力学行为,并能通过一个常数控制器控制到稳定的周期轨道.     

双频调制的单环铒光纤激光器的混沌产生和同步

首先通过对单环掺铒光纤激光器的损耗进行双频调制研究其混沌的产生,数值结果表明:通过适当地调节双频正弦信号的幅值和频率,该系统可以进入混沌状态,给出了进入混沌状态的途径和混沌态的参数区间.然后利用混沌信号驱动法研究了双频调制的单环铒光纤激光器的混沌同步,结果表明,无论两个双频调制的单环铒光纤激光器被驱动前处于混沌状态还是周期状态,只要在适当的驱动强度下使最大条件李指数为负,就能实现这两个单环铒光纤激光器的混沌同步.     

基于纳米压痕的氧化镓不同晶面的蠕变特性

使用Berkovich压头,采用恒载荷法对氧化镓的(100)及(010)晶面进行纳米压痕试验,通过数据拟合获得氧化镓晶体的蠕变应力指数.单晶氧化镓(100)晶面的蠕变应力指数范围在15.5～27.8,(010)晶面的蠕变应力指数范围在46.1～63.4.纳米压痕法能够有效测量氧化镓的蠕变变形量;氧化镓的2个晶面均呈现了...     

Stability analysis via the concept of Lyapunov exponents: a case study in optimal controlled biped standing

Balancing control is important for biped standing. In spite of large efforts, it is very difficult to design balancing control strategies satisfying three requirements simultaneously: maintaining postural stability, improving energy efficiency and satisfying the constraints between the biped feet and the ground. In this article, a proportional-derivative (PD) controller is proposed for a standing biped, which is simplified as a two-link inverted pendulum with one additional rigid foot-link. The genetic algorithm (GA) is used to search for the control gain meeting all three requirements. The stability analysis of such a deterministic biped control system is carried out using the concept of Lyapunov exponents (LEs), based on which, the system stability, where the disturbance comes from the initial states, and the structural stability, where the disturbance comes from the PD gains, are examined quantitively in terms of stability region. This article contributes to the biped balancing control, more significantly, the method shown in the studied case of biped provides a general framework of systematic stability analysis for certain deterministic nonlinear dynamical systems.