Synchronization in Coupled Oscillators with Two Coexisting Attractors

Dynamics in coupled Dufling oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dufl~ng oscillators coupled linearly, the transition to the synchronization generally consists of two steps： Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.     

Analytical Approach for Piecewise Linear Coupled Map Lattices

A simple construction is presented which generalizes piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. In particular, the spin Hamiltonian which is generated by the symbolic dynamics is accessible. As an example, a formal relation between a globally coupled system and an Ising mean-field model is established. The phase transition in the limit of infinite system size is analyzed and analytical results are compared with numerical simulations.     

Stochastic Huge-Resonance Caused by Coupling for a Globally Coupled Linear System

In the paper, we investigate a globally coupled linear system with finite subunits subject to temporal periodic force and with multiplicative dichotomous noise. It is shown that, the global coupling among the subunits can hugely enhance the phenomenon of SR for the amplitude of the average mean field as the functions of the transition rate of the noise and that as the function of the frequency of the signal respectively.     

Linear Response Theory for Thermally Driven Quantum Open Systems

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes in thermally driven quantum open systems. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [V. Jakšić Y. Ogata and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.].     

四涡卷超混沌吸引子的DSP实现

提出了基于数字信号处理(DSP)实现四涡卷超混沌吸引子的方法.利用四阶龙格库塔法对连续四维超混沌系统进行离散化处理,用C语言编写源程序,并在CCS编译器上编译、调试和仿真成功后,下载固化到DSP芯片内,实现四涡卷超混沌吸引子,硬件实验与软件仿真结果完全一致.     

Fluctuation Relation beyond Linear Response Theory

The Fluctuation Relation (FR) is an asymptotic result onthe distribution of certain observables averaged over timeintervals τ as τ → ∞ and it is a generalization of thefluctuation–dissipation theorem to far from equilibrium systemsin a steady state, which reduces to the usual Green–Kubo (GK)relation in the limit of small external non-conservative forces.FR is a theorem for smooth uniformly hyperbolic systems, and it isassumed to be true in all dissipative ‘chaotic enough’ systemsin a steady state. In this paper, we develop a theory of finitetime corrections to FR, needed to compare the asymptoticprediction of FR with numerical observations, which necessarilyinvolve fluctuations of observables averaged over finite timeintervals τ. We perform a numerical test of FR in two cases inwhich non-Gaussian fluctuations are observable, while GK does notapply and we get a non-trivial verification of FR that is independent of and different from linear response theory.Our results are compatible with the theory of finite timecorrections to FR, while FR would be observably violated,well within the precision of our experiments, if such correctionswere neglected.     

Prime Number Decomposition, the Hyperbolic Function and Multi-Path Michelson Interferometers

The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect.     

Linear Full Decoupling,Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations

We propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correction, which can completely decouple all variables in the model. Meanwhile, the schemes are not only linear and only need to solve a series of linear partial differential equations with constant coefficients at each time step, but also the standard velocity correction algorithm can produce the Neumann boundary condition for the pressure field, but the rotational velocity correction algorithm can produce the consistent boundary which improve the accuracy of the pressure field. Thus, improving our computational efficiency. Then, we give the energy stability of the algorithms and give a detailed proofs. The key idea to establish the stability results of the rotation velocity correction algorithm is to transform the rotation term into a telescopic symmetric form by means of the Gauge–Uzawa formula. Finally, numerical experiments show that the rotation velocity correction projection algorithm is efficient to solve the thermally coupled magneto-hydrodynamic equations.     

Novel Bandpass Filter Configuration Using Coupled Linear Tapered Line Resonators

A novel tapped bandpass filter composed of twocoupled linear taperedline resonators (LTLRs) is proposed. Multistepped resonators are applied to analyzing LTLRs, which are difficult to analyze directly. Through this analysis method, fundamental characteristics of LTLRs and their filter design parameters can be easily derived. This new filter has insertion loss less than 0.6dB at 1.9 GHz, the return loss less than 18dB in the range 1.81.93GHz and 12.3% 3dB bandwidth. Experimental results of fabricated filter are in good agreement with the design results.     

Nonequilibrium Linear Response for Markov Dynamics,II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.     

加偏置电场的双曲线量子阱中线性与三阶非线性光学吸收系数的计算

利用紧致密度矩阵近似方法,研究了加偏置电场双曲线量子阱中的线性与三阶非线性光学吸收系数. 得到了该系统中的线性与三阶非线性光学吸收系数的解析表达式.分析了势阱的形状、外加电场的大小以及入射光场的强度对吸收系数的影响规律. 文章以典型的AlxGa1－xAs/ GaAs双曲线量子阱为例作了数值计算.结果表明：随着势阱宽度的增加,系统的吸收系数将减小;随着外加电场的增加,系统的非对称性增加,系统的吸收系数将增加;随着外加光场强度的增加,系统的吸收系数将减小,并且当光强增加到一定值时会出现明显的饱和吸收现象,这一结论为进一步的实验研究提供了相应的理论依据.     

Applications of Extended Hyperbolic Function Method for Quintic Discrete Nonlinear Schr(o)dinger Equation

By using the extended hyperbolic function method,we have studied a quintic discrete nonlinear Schr(o)dinger equation and obtained new exact localized solutions,including the discrete bright soliton solution,dark soliton solution,bright and dark soliton solution,alternating phase bright soliton solution,alternating phase dark soliton solution,and alternating phase bright and dark soliton solution,if a special relation is bound on the coefficients of the equation.     

Soliton Solutions of Discrete Complex Ginzburg-Landau Equation via Extended Hyperbolic Function Approach

In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple,we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.     

Nuclear Spin Transverse Response Function

The spin transverse response functions for ⁴⁰Ca and ¹²C in different approximations have been calculated.By using the coupled RPA equations for polarization propagator including the delta degree of freedom,the influence of the delta on the response function has been investigated.The results show that they are reduced explicitly.Introducing the energy dependent effective nucleon mass,which embodies the manybody ef ects,the satisfactory results are obtained.     

关联实验数据线性函数拟合情况下无偏χ2估计量的构造

针对线性函数拟合的情况构造了一种无偏的因子化形式的χ²估计量, 用以处理关联数据的极小化. 详细比较并说明了有偏性与无偏性χ²拟合的区别. 利用简化的R值测量数据对相关的结论进行了定量的检验.     

基于径向基函数神经网络的线性衰减系数的重建算法

层析γ扫描(TGS)技术是非破坏性分析(NDA)中的一项重要技术.在TGS透射测量中,线性衰减系数值的图像重建问题是TGS的难点和核心问题.在文[1]的基础上,提出了将神经网络方法应用于TGS重建线性衰减系数图像的算法.计算机上的仿真模拟结果表明,在一定范围内,径向基函数(RBF)神经网络方法重建的线性衰减系数值与实际值的相对误差小于4%,且具有快速、高精度等优点,表明了此方法的有效性.     

关联实验数据线性函数拟合情况下无偏x~2估计量的构造(英文)

针对线性函数拟合的情况构造了一种无偏的因子化形式的x~2估计量,用以处理关联数据的极小化.详细比较并说明了有偏性与无偏性x~2拟合的区别.利用简化的R值测量数据对相关的结论进行了定量的检验.