On recovering the parameters and velocity state of the Duffing's oscillator

In this Letter, we propose a simple method to recover the unknown parameters and the velocity state from a known suitable output which is the position of the Duffing mechanical oscillator. We show that the system is constructible. Hence, it allows us to obtain an integral output parametrization of the remaining state. Based on this integral parametrization, we construct an iterative integral equation of the output. This method is numerically feasible and easy to implement by means of integrators, avoiding the necessity to evaluate the derivatives of the output.     

On the algebraic reconstruction of the Duffing's mechanical system

The identification of the unknown parameters of the Duffing's mechanical system, based on an algebraic approach, is presented. This approach is fast, accurate, and simple to numerically implement. Also, the method, combined with a suitable invariant filter, can became robust against high frequency output measurement noises. Our method uses the availability of one measurable output and produces an exact formula for the unknown parameters, which may be realized in terms of iterated convolutions. First, we show that the Duffing's system parameters are linearly identifiable with respect to the position variable, then we obtain a linear system where the unknowns are the unavailable parameters. Suitable algebraic operations on the output differential equations makes the identification schema independent of the unavailable initial conditions of the underlying nonlinear dynamical system.     

Construct order parameters from the reduced density matrix spectra

In this paper, we try to establish a connection between a quantum information concept, i.e., the mutual information, and the conventional order parameter in condensed matter physics. We show that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system. By analyzing the spectra of the reduced density matrices that are used to calculate the mutual information, we show how to derive the local order operators that identify various ordered phases in condensed matter physics.     

Randomly transitional phenomena in the system governed by Duffing's equation

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.     

Systematic derivation of order parameters through reduced density matrices

A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the degenerate ground states without the aid of empirical knowledge, and thus opens a way to explore unknown exotic orders. The applicability of this method is demonstrated numerically or rigorously in models that are considered to exhibit dimer, scalar chiral, and topological orders.     

Parameter identification of chaos system based on unknown parameter observer

Parameter identification of chaos system based on unknown parameter observer is discussed generally. Based on the work of Guan et al. [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26], the design of unknown parameter observer is improved. The application of the improved approach is extended greatly. The works in some literatures [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26; J.H. Lü, S.C. Zhang, Phys. Lett. A 286 (2001) 148; X.Q. Wu, J.A. Lu, Chaos Solitons Fractals 18 (2003) 721; J. Liu, S.H. Chen, J. Xie, Chaos Solitons Fractals 19 (2004) 533] are only the special cases of our Corollaries 1 and 2. Some observers for Lü system and a new chaos system are designed to test our improved method, and simulations results demonstrate the effectiveness and feasibility of the improved approach.     

Measuring Stokes parameters by means of a polarization grating

Ordinary gratings act on the amplitude and (or) the phase of a wave front. Polarization gratings produce instead a periodic modulation of the state of polarization. A simple grating of the latter type is constituted by a linear polarizer whose orientation varies periodically along a line. It is shown that, for a generic polarization state of the incident field, such a grating gives rise to first-order diffracted beams with counterrotating circular polarizations. It is also shown that such a grating can be used for measuring the Stokes parameters of a light beam in an achromatic manner. Several extensions are briefly discussed.     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.     

On the equivalence of different order parameters for Ising ferromagnets

In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter _{i j k} are the same as those of the magnetization _i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT _c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ _e independent of the way in which the odd interactionsJ _o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.     

On a weakly forced third order weakly non-linear system

The behaviour of a weakly non-linear third order system under a weak forcing function is considered. By the method of multiple time scales, it is found that the amplitude of the forced oscillation increases with the amplitude of the forcing function until a critical value is reached. Beyond this value, stable oscillations exist whose amplitude decreases with the amplitude of the forcing function but which are superimposed on a constant of increasing magnitude.     

不确定混沌系统的反同步与参数辨识

针对一类混沌系统,提出了一种系统的混沌反同步设计方案,基于该方案,设计一种自适应控制方法,实现了参数不确定系统的混沌反同步和未知参数的辨识.数值模拟结果表明了提出方法的有效性.     

利用高阶统计识别二维FIR系统的参数

本文利用二维FIR系统输出的四阶统计累积(cumulant),识别出系统的冲激响应函数。我们的方法允许测量噪声是有色高斯的,以及二维FIR系统是非最小相位的,非可分的。     

Determination of reduced thicknesses by means of the variable take-off angle technique

Reduced thicknesses can be determined by means of substrate, layer and ratio methods. All these methods require the determination of two unknown quantities — the reduced thickness and a proportional factor which is specific for the method applied. Experimental results can be evaluated by regression, employing equations derived for plane, smooth, homogeneous layers. The aim of this paper is to show how the measured data are influenced by surface roughness, by the energy-dependence of the mean free path of the photoelectrons, and by measurement errors. Moreover, a method is presented for applying the equations derived for ideal layers to results obtained from real structures, taking these influences into account. This evaluation procedure is demonstrated by two examples.     

Using wavelet multi-resolution nature to accelerate the identification of fractional order system

Because of the fractional order derivatives, the identification of the fractional order system(FOS) is more complex than that of an integral order system(IOS). In order to avoid high time consumption in the system identification, the leastsquares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.     

InSe electrical characterization by means of transport parameters

SCLC measurements in single crystals of the layered semiconductor n-type InSe are reported. The measurements were carried out at various temperatures and on samples grown with indium added in excess (from 5 to 10%). The experimental results suggest that the trapping levels location and the charge transport are dependent on the indium excess. Only the samples grown with an indium excess of about 5% show the features typical of intrinsic semiconductors. The anomalous behaviour of samples grown with indium excess between 6 and 10 is explained by means of scattering mechanisms between charge carriers and ionized impurity centers.     

On a leveraging effect of weak azimuthal inhomogeneities explaining the nonuniqueness of critical Maier-Saupe order parameters

The Maier--Saupe theory of liquid crystals predicts a unique critical order parameter for the transition point of isotropic--nematic phase transitions. Experimental studies have shown that critical order parameters are shifted away from that unique value. We show that micro-defects and weak azimuthal inhomogeneities can result due to a leveraging effect in the experimentally observed macro-shifts of the critical order parameter. We demonstrate the leveraging effect by computing the corresponding micro-shifts of the order parameter in the isotropic phase with the help of an effective order parameter. Our approach accounts for critical order parameters observed in experimental studies which is explicitly demonstrated for methyl-deuterated para-azoxyanisole (PAA-d₆), 4-n-pentyl-4′-cyanobiphenyl (5CB), N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Finally, in line with the effective order parameter approach and the dynamical mean field approaches by Hess, Doi, and Edwards, predictions are derived that provide novel testbeds for experimental studies.     

Force identification by means of in-operation modal models

In-operation modal analysis has become a valid alternative for structures where a classic forced-vibration test would be difficult if not impossible to conduct. The modelling of output-only data obtained from naturally excited structures is particularly interesting because the test structure remains in its normal in-operation condition during the test. One of the drawbacks of in-operation analysis is that part of the modal parameters can no longer be estimated. Consequently, the applicability of in-operation modal models remains somewhat restricted. For some in-operation applications, interest lies in the identification of the forces that gave rise to the measured response signals. In order to solve this ill-conditioned problem, a complete modal model of the structure is required. Recently, a sensitivity-based method was proposed for the normalization of operational mode shape estimates on the basis of in-operation modal models only. This method allows the reconstruction of complete modal models from output-only data. In this paper, the possibility of using such re-completed in-operation modal models for the identification of localized forces is explored.     

On the actual measurability of the density matrix of a decaying system by means of measurements on the decay products

The density matrix ρ describing a decaying system can be expressed in terms of correlations among observables belonging to the subsystems. Due to this structure and to the difficulties in measuring higher rank tensors of decay products for a single decay event, it is found that the mean value of ρ cannot be determined, in general, from measurements on the decay products. We also discuss the consequences of this conclusion as far as tests of quantum mechanics are concerned.