CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART II: ELEMENTARY STRUCTURE-PRESERVING TRANSFORMATIONS

It has been shown in a previous paper that there is a real-valued transformation from the generalN -degree-of-freedom second order system to a second order system characterized by diagonal matrices. An immediate extension of this fact is that for any second order system, there is a set of real-valued transformations (thestructure-preserving transformations) which transform this system to a different second order system having identical characteristic behaviour. There are several possible reasons why it may be very useful to achieve a particular structure in the transformed system. It is obvious that a diagonal structure is extremely useful and a method has been devised for determining the diagonalizing transformation from the solution of the usual (complex) eigenvalue-eigenvector problem.This paper begins by outlining the usefulness of some other structures. Then it defines a class of elementary structure-preserving co-ordinate transformations that transform from one N -degree-of-freedom second order system to another. The termelementary is applied because any one of these transformations is the minimum-rank modification of the identity transformation. The changes occurring in the system matrices as a result of the application of one such elementary transformation transpire to be very simple in form, they are low rank, and they can be computed very efficiently.This paper provides the fundamental tools to enable the design of structure-preserving co-ordinate transformations which transform a second order system originally characterized by three general matrices in stages into a mathematically similar second order system characterized by three diagonal matrices. The procedure by which the individual elementary transformations are obtained is still under development and it is not discussed in this paper. However, an illustration is given of a five-degree-of-freedom self-adjoint system being transformed into tridiagonal form.     

Monitoring microstructural material changes in paper through microscopic speckle correlation rate measurements

A system for real-time digital speckle correlation rate measurements is developed and applied on printing paper in the micro-scale. The system consists of a continuous laser and a CCD camera connected to a PC. To measure on objects in the micro-scale the system is connected to a stereomicroscope where one of the channels is used for imaging and the other channel is used for illumination of the object surface. The system is evaluated through measurements on printing paper over an area of 1 mm² and with a spatial resolution of 30 μm on the object. The results show that the system is able to monitor the dynamics in paper during both wetting and drying in real-time over a time scale ranging from one-tenth of a second to several hours.     

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion.Equations of a dynamical system of relative motion in phase space are given.Poisson theory of the system is established.The Jacobi last multiplier of the system is defined,and the relation between the Jacobi last multiplier and the first integrals of the system is studied.Our research shows that for a dynamical system of relative motion,whose configuration is determined by n generalized coordinates,the solution of the system can be found by using the Jacobi last multiplier if (2n 1) first integrals of the system are known.At the end of the paper,an example is given to illustrate the application of the results.     

El-Nabulsi动力学模型下非Chetaev型非完整系统的精确不变量与绝热不变量

研究El-Nabulsi动力学模型下非Chetaev型非完整系统精确不变量与绝热不变量问题. 首先, 导出El-Nabulsi-d'Alembert-Lagrange原理并建立系统的运动微分方程. 其次, 建立El-Nabulsi模型下未受扰动的非Chetaev 型非完整系统的Noether对称性与Noether对称性导致的精确不变量之间的关系; 再次, 引入力学系统的绝热不变量概念, 研究受小扰动作用下非Chetaev型非完整系统Noether对称性的摄动导致绝热不变量问题, 给出了绝热不变量存在的条件及其形式. 作为特例, 本文讨论了El-Nabulsi模型下Chetaev型非完整系统的精确不变量与绝热不变量问题. 最后分别给出非Chetaev型和Chetaev型两种约束下的算例以说明结果的应用.     

Introduction to Multi-Conjugate Adaptive Optics systems

The paper describes the basic concepts underlying the design of Multi-Conjugate Adaptive Optics systems. The paper takes into account mainly three papers. The first paper, published in 1988, is due to J. Beckers and it introduces the currently used multi-conjugation concept and quantifies the increase in FoV achieved applying this concept with respect to the single conjugate adaptive system. The second paper considered is due to M. Tallon and R. Foy. This paper, published in 1990, provides a quantitative method to estimate the 3D map of the atmospheric phase perturbation. This is the needed information to properly control the multi-conjugate system introduced by J. Beckers. Finally a third paper, published in 2000 and due to R. Ragazzoni et al. is considered, where the Layer Oriented scheme is described opening the multi-conjugate adaptive system field to natural guide stars. These three papers stimulated a lot of other contributions from several people and some of them are briefly discussed in the paper. To cite this article: S. Esposito, C. R. Physique 6 (2005).     

一个三维四翼自治混沌系统的拓扑马蹄分析

基于拓扑马蹄映射理论,验证了一个三维四翼自治的混沌系统的拓扑马蹄的存在.由于该混沌系统是连续系统,首先选取了一个Poincaré截面,并在该截面下定义了该混沌系统的一个一次回归Poincaré映射.通过利用计算机辅助证明方法,得出了该映射与一个2移位映射拓扑半共扼,说明该三维四翼自治系统的拓扑熵大于或等于ln2,进而证明了该系统的混沌行为. 关键词： 四翼混沌系统 拓扑马蹄 Poincaré映射 拓扑熵     

Development of electrostatic paper separation and feed mechanism

A new paper separation and feed mechanism is proposed to realize a highly reliable paper handling system for printers and copiers. The paper-separation system consisted of a pair of parallel electrodes and a paper pile between the electrodes. Electrostatic separation of a piece of paper was possible from the top of the pile when the applied voltage exceeded the threshold needed to generate an electrostatic force larger than the weight of the paper. The threshold voltage was on the order of several kilovolts, and it agreed with the numerical value calculated using the finite element method (FEM) for the electrostatic field. Based on these basic investigations, a prototype mechanism for paper separation and feeding was constructed. It consisted of a roller-type separation electrode coated with an insulating film, a biased charger roller in contact with the separation roller to charge the insulating film on the separation roller, a ground electrode, and a paper pile situated between the electrodes. When an electrostatic field was applied between the biased charger roller and the ground electrode on which the paper pile was mounted, only the top sheet of paper separated, adhering electrostatically to the roller. The sheet was then fed rotating the separation roller. Using this system, reliable paper separation and feed was realized and a feed speed over 600 mm/s was demonstrated.     

负值量子条件熵与双量子系统一类混合态纠缠量度

运用负值量子条件熵研究了双量子系统一类混合态的纠缠量度.给出了负值量子条件作为条件熵纠缠度的定义，证明了条件熵纠缠满足作为2×2系统一类混合纠缠态量度的四个基本条件.当双量子系统处于纯态时，条件熵纠缠度即为部分熵纠缠度.应用条件熵纠缠度研究了真空腔场中两全同二能级原子之间纯态和一类混合态纠缠的时间演化，比较了相同条件下两全同原子系统concurrence纠缠度的时间演化.结果表明，两纠缠度演化规律完全一致，验证了负值量子条件熵可以作为双量子系统纯态和一类混合态的纠缠量度. 关键词： 双量子系统 负值量子条件熵 条件熵纠缠度 混合态纠缠度     

Design of partially optically stable reflector systems and prisms

The characteristics and design method of the total optically stable (TOS) reflector systems/prisms were introduced in an early paper (Tsai and Lin in Appl. Opt. 47:4158–4163, 2008), where only two types of TOS reflector system exist, namely preservation or retroreflection. In this paper, we introduce the partially optically stable (POS) reflector system, which is only optically stable about a specific directional vector; nevertheless, the exiting light ray is not restricted to preservation or retroreflection. The proposed paper also presents an analytic method for the design of POS reflector systems comprised of multiple reflectors. Furthermore, it is shown that a POS prism can be obtained by adding two refracting flat boundary surfaces with specific conditions at the entrance and exit positions of the light ray in an optical system with multiple reflectors.     

Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities

This paper proposes a eight-term 3-D polynomial chaotic system with three quadratic nonlinearities and describes its properties. The maximal Lyapunov exponent (MLE) of the proposed 3-D chaotic system is obtained as L ₁ = 6.5294. Next, new results are derived for the global chaos synchronization of the identical eight-term 3-D chaotic systems with unknown system parameters using adaptive control. Lyapunov stability theory has been applied for establishing the adaptive synchronization results. Numerical simulations are shown using MATLAB to describe the main results derived in this paper.     

Symmetry Reduction for a System of Nonlinear Evolution Equations

Abstract

In this paper we obtain the maximal Lie symmetry algebra of a system of PDEs. We reduce this system to a system of ODEs, using some rank three subalgebras of the finite-dimensional part of the symmetry algebra. The corresponding invariant solutions of the PDEs are obtained.     

The decoupling of damped linear systems in free or forced vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the “classical decoupling problem.” Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.     

Stochastic dynamics of parametrically excited two d.o.f. systems with symmetry

In this paper we investigate the non-linear dynamics of a two-degree-of-freedom system with symmetries subject to random parametric excitation. The study of this non-linear near-Hamiltonian system is simplified by using the symmetry and separation of scales present in the problem. To this end, we study the equations as a random perturbation of a four-dimensional weakly dissipative Hamiltonian system. We achieve the model-reduction through stochastic averaging and the reduced process is simply a Markov process on a line. Examination of the reduced Markov process on the line yields many important results, namely, probability density functions, and stochastic bifurcations. The steady state dynamics is computed explicitly. Phenomenological and dynamical bifurcations are investigated. The approach adopted in this paper can in principle, be applied to any four-dimensional integrable system.     

On Some Annihilating and Coalescing Systems

In the present paper we continue the investigation of the so-called coalescing ideal gas in one dimension, initiated by Ermakov. The model consists of point-like particles moving with velocities ±1 which coalesce and choose a fresh velocity with the same distribution when colliding. In the previous paper various identities in law were derived for the infinitely extended system. In the present paper we consider the scaling limit of the model in its various guises. The main result is the derivation of the scaling limit (invariance principle) for the joint law of an arbitrary finite number of individual particle trajectories in this system. We also obtain the scaling limit of the density profile of the system, which strongly resembles earlier results of Belitsky and Ferrari.     

基于CCD的新型尿液分析仪设计

尿液分析仪是用来检测人体尿液中某些成分含量的分析仪器,是诊断泌尿系统疾病的常用设备。目前尿液分析仪普遍采用光电二极管或光电三极管作为光检测传感器,造成测量速度慢。介绍了CCD图像传感器在尿液分析中的测试原理,设计并实现了基于CCD的新型尿液分析仪的原形系统,该系统采用了触摸屏和重新设计的试剂带传送装置。结果表明,新研制的尿液分析仪功能齐备,其测试速度及操作性能都有了很大的提高。     

Ultrasonic system for accurate distance measurement in the air

This paper presents a system that accurately measures the distance travelled by ultrasound waves through the air. The simple design of the system and its obtained accuracy provide a tool for non-contact distance measurements required in the laser’s optical system that investigates the surface of the eyeball.     

A LabVIEW-based real-time measurement system for polarization detection and calibration

A rapid real-time polarization measurement system was designed and implemented in this paper. The system is centered round a computer running application developed for the purpose. The paper illustrates how to build such an excellent application with National Instruments’ graphical programming language LabVIEW, a synchronized high speed multi-channels data acquisition card and some photoelectric conversion module in detail. With simple and friendly user interface, the experimental result shows that the measurement system has high computational efficiency, high precision calibration matrix, which can be efficiently utilized in experiments relating to the measurement of polarization.     

A Class of Counterexamples to Jeans' Theorem for the Vlasov–Einstein System

The Vlasov–Poisson and Vlasov–Einstein systems model the motion of a self gravitating system such as a galaxy. The Vlasov–Poisson system is nonrelativistic. Jeans' theorem states that every spherically symmetric solution of the Vlasov–Poisson system that is independent of time may be expressed as a function of the two invariants, energy and angular momentum. This paper shows this is not the case for the Vlasov–Einstein system. Received: 2 November 1998 / Accepted: 24 December 1998     

Data detection for the P-SLAM optical data storage system

This paper presents an intersymbol interference (ISI) and system noise analysis of the P-SLAM (parallel-sub-lambda) optical data storage system. Data are stored in sub-wavelength features accessed by transmitting light through the structure and collecting optical power measurements in the near-field. The non-linear ISI caused by the interactions of light between these features is characterized using finite-difference time-domain (FDTD) simulations. A system noise analysis is also presented that quantifies the effects of imperfections in fabrication and material properties. Previously, the authors proposed a detection scheme that dealt with the non-linear ISI by physically reducing it with air gaps. In this paper a signal processing method, the Viterbi algorithm, is proposed to overcome ISI. A modification is proposed to the Viterbi algorithm that is designed to deal with both the non-linear ISI and system noise. System simulations are used to show the uncoded bit error rate of the system is similar to current technologies. Conservative predictions estimate a data density of 5 Gbits/cm² for the system which exceeds densities achievable by current optical technologies.     

A unified quantum theory of mechanics and thermodynamics. Part IIa. Available energy

Part II of this three-part paper presents some of the most important theorems that can be deduced from the four postulates of the unified theory discussed in Part I. In Part IIa, it is shown that the maximum energy that can be extracted adiabatically from any system in any state is solely a function of the density operator associated with the state. Moreover, it is shown that for any state of a system, nonequilibrium, equilibrium or stable equilibrium, a unique propertyS exists which is proportional to the total energy of the system minus the maximum energy that can be extracted adiabatically from the system in combination with a reservoir. For statistically independent systems, propertyS is extensive, it is invariant during all reversible processes, and it increases during all irreversible processes.Part I of this paper appeared inFound. Phys. 6(1) (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part I.