An expansion of system with time delayed feedback control into spatio-temporal state space

Time delayed feedback control is well known as an effective continuous control method for stabilizing the unstable periodic orbit embedded in chaotic attractors. As for the system with time delay, the solution is in a function space and shows characteristics governed by an infinite dimension. Therefore it is difficult to understand the system behavior analytically. In this paper, it is shown that, when the state space for the system with time delay is expanded into the spatio-temporal state space, the solution propagates in the space as a wave theoretically and numerically. The dynamic behavior experimentally obtained in the sinusoidally excited magneto-elastic beam system under time delayed feedback control is also discussed by the transformation into the expanded spatio-temporal state space. (c) 1999 American Institute of Physics.     

Anomalous spatio-temporal chaos in a two-dimensional system of nonlocally coupled oscillators

A two-dimensional system of nonlocally coupled complex Ginzburg-Landau oscillators is investigated numerically for the first time. As previously shown for the one-dimensional case, this two-dimensional system exhibits anomalous spatio-temporal chaos characterized by power-law spatial correlations. In this chaotic regime, the amplitude difference between neighboring elements displays temporal noisy on-off intermittency. The system is also spatially intermittent in this regime, as revealed by multiscaling analysis: The amplitude field is multiaffine and the difference field is multifractal. Correspondingly, the probability distribution function of the measure defined for each field is strongly non-Gaussian, exhibiting scale-dependent deviations in the tail due to intermittency. (c) 1999 American Institute of Physics.     

振转耦合振子实验研究

介绍一个非常有趣的物理演示实验——振转耦合振子实验.弹簧振子实际上是一个具有两个振动模式的振动系统,两振动模式之间存在着耦合,振动能量将从一种模式向另一模式转移.在共振条件下可以实现能量在两模式之间的来回完全转移.     

Phase transition of superparamagnetic system in spontaneous coherent state

In the system of magnetic particles in superparamagnetic that interacted with resonance radiation field, phase transition in the spontaneous coherent state takes place. There are brought critical value for temperature and density of the system. Direct magnetic dipole-dipole interactions take into account in the molecular field approximation and it influence on the conditions of the phase transition is investigated.     

First order phase transition in the system of two coupled fields with different transition temperatures

It is shown that for the case of a strong field coupling in the system of two fields the low temperature phase may be stable in the fluctuation region of the high temperature phase.     

Synchronization of indirectly coupled Lorenz oscillators: An experimental study

The dynamics of indirectly coupled Lorenz circuits is investigated experimentally. The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev. E 81, 046216 (2010) is verified by physical experiments with electronic circuits. Two chaotic systems coupled through a common dynamic environment shows the verity of synchronization behaviours such as anti-phase synchronization, in-phase synchronization, identical synchronization, anti-synchronization, etc.     

耦合激光列阵的连续模型及其时空特性的研究

继对整体耦合激光列阵的讨论,本文介绍作者最近对局部耦合激光列阵的研究结果.文中采用连续的近似方法,推导出描述耦合激光列阵的连续模型.正如数字计算结果所表明,耦合激光系统是另外一个很典型的“光学流体”系统.本文还对如何设计耦合激光系统,使之具有高功率、单模输出并保持良好的光束特性,进行了定性的讨论.对波导式耦合的本征不稳定性,运用孤子理论进行了初步的分析,进而讨论了耦合激光列阵中的孤子波现象及其应用.     

Space-time renormalization at the onset of spatio-temporal chaos in coupled maps

The transition regime to spatio-temporal chaos via the quasiperiodic route as well as the period-doubling route is examined for coupled-map lattices. Space-time renormalization-group analysis is carried out and the scaling exponents for the coherence length, the Lyapunov exponent, and the size of the phase fluctuations are determined. Universality classes for the different types of coupling at various routes to chaos are identified.     

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.     

The first experimental evidence of a field-induced magnetic phase transition in an S = 1 singlet ground state system

A magnetic phase transition to a long range ordered state is observed in Ni(C₅H₅NO)₆(ClO₄)₂ in external fields 26.4 kOe< H < 71.0 kOe applied parallel to the threefold axis and below temperatures of 0.80 K.     

An experimental determination of the critical exponents at the metal-insulator transition

This work deals with a determination of the magnitude of the critical exponents and their ratio from an analysis of the temperature dependence of the conductivity and magnetoresistivity of doped Ge 〈 As 〉 with an impurity concentration making it an insulator near the metal-insulator transition. The values found are $\text{?? = 0.60 ± 0.04}$, ξ = 1.38 ± 0.07, $\text{ξ}\text{??}\text{= 2.3 ± 0.2}$; neither the critical exponents nor their ratio depend on compensation within 0 < k < 60%.     

Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Two numerical techniques are proposed to construct a polynomial chaos (PC) representation of an arbitrary second-order random vector. In the first approach, a PC representation is constructed by matching a target joint probability density function (pdf) based on sequential conditioning (a sequence of conditional probability relations) in conjunction with the Rosenblatt transformation. In the second approach, the PC representation is obtained by having recourse to the Rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target Spearman’s rank correlation coefficient (SRCC) matrix. Both techniques are applied to model an experimental spatio-temporal data set, exhibiting strong non-stationary and non-Gaussian features. The data consists of a set of oceanographic temperature records obtained from a shallow-water acoustics transmission experiment [1]. The measurement data, observed over a finite denumerable subset of the indexing set of the random process, is treated as a collection of observed samples of a second-order random vector that can be treated as a finite-dimensional approximation of the original random field. A set of properly ordered conditional pdfs, that uniquely characterizes the target joint pdf, in the first approach and a set of target marginal pdfs and a target SRCC matrix, in the second approach, are estimated from available experimental data. Digital realizations sampled from the constructed PC representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy. The relative advantages and disadvantages of the two proposed techniques are also highlighted.     

Dynamics of spatio-temporal defects in the Taylor-Dean system

The dynamics of defects in a pattern of traveling inclined rolls has been investigated. Two regimes were identified in the neighborhood of defects: a diffusive regime, with a negative phase diffusion coefficient, and a coalescence regime in which the phase gradient diverges in time following a power law behavior. The observed periodic nucleation of defects is related to the frequency inhomogeneity induced by the disymmetry of the wave amplitude. Amplitude holes have been observed in the secondary modulated pattern. Received 23 February 1999 and Received in final form 26 May 1999     

Phase transition in anisotropic coupled random walk

We have studied the continous limit of a coupled random walk including scattering anisotropy. We found a phase transition in the behaviour of the probability distribution around the isotropic critical point. We show the transient behaviour of the variance, and the power spectrum of the random forces.     

Simplified models and experimental verification for coupled transmission tower-line system to seismic excitations

The simplified computational models of high-voltage transmission tower-line system under out-of-plane and in-plane vibrations are presented due to seismic excitations in this paper. The equations of motion are derived and the computer program is compiled to obtain the earthquake responses of the coupled system. To verify the rationality of the proposed approaches, the shaking-table experiments of the coupled system of transmission lines and their supporting towers are carried out and the results indicate that the errors of theoretical and testing results of systemic seismic responses are within the acceptable arrange in engineering area. Based on these studies, a simplified analysis method is proposed to make the seismic response calculation of coupled tower-conductor system faster and more effective.     

Finite-size-induced transition in ensemble of globally coupled oscillators

The collective behavior of overdamped nonlinear noise-driven oscillators coupled via mean field is investigated numerically. When a coupling constant is increased, a transition in the dynamics of the mean field is observed. This transition scales with the number of oscillators and disappears when this number tends to infinity. Analytical arguments explaining the observed scaling are presented.