Extension of SEA model to subsystems with non-uniform modal energy distribution

In order to widen the application of statistical energy analysis (SEA), a reformulation is proposed. Contrary to classical SEA, the model described here, statistical modal energy distribution analysis (SmEdA), does not assume equipartition of modal energies.Theoretical derivations are based on dual modal formulation described in Maxit and Guyader (Journal of Sound and Vibration 239 (2001) 907) and Maxit (Ph.D. Thesis, Institut National des Sciences Appliquées de Lyon, France 2000) for the general case of coupled continuous elastic systems. Basic SEA relations describing the power flow exchanged between two oscillators are used to obtain modal energy equations. They permit modal energies of coupled subsystems to be determined from the knowledge of modes of uncoupled subsystems. The link between SEA and SmEdA is established and make it possible to mix the two approaches: SmEdA for subsystems where equipartition is not verified and SEA for other subsystems.Three typical configurations of structural couplings are described for which SmEdA improves energy prediction compared to SEA: (a) coupling of subsystems with low modal overlap, (b) coupling of heterogeneous subsystems, and (c) case of localized excitations.The application of the proposed method is not limited to theoretical structures, but could easily be applied to complex structures by using a finite element method (FEM). In this case, FEM are used to calculate the modes of each uncoupled subsystems; these data are then used in a second step to determine the modal coupling factors necessary for SmEdA to model the coupling.     

关联函数的长时间渐近行为——波对弛豫过程的影响

本文从非平衡态统计的一般理论出发,系统地讨论了宏观体系中波对弛豫过程的影响,特别是关联函数的非指数型渐近行为。由于表象选择对处理耗散过程的重要性,我们必须从元激发表象出发(而不是自由粒子表象)计算关联函数或输运系数(久保公式)。为此,应用了C代数的基本概念,发展了一套算子展开的方法,用之将流算子在元激发二次量子化表象中一般地表示出来。我们从刘维算子的预解式出发,对元激发间的剩余相互作用作微扰,应用了投影算子方法后,可以比较简单地得到关联函数非指数衰减部分的一般表达式。根据对元激发处理过程的分析,我们将元激 关键词：     

Factorizing coupled quantum systems and damped nonlinear Schrödinger equations

We show that the wave function of a coupled quantum system may factorize for certain coupling operators, resulting in wave functions and effective nonlinear Hamiltonians for the subsystems. Systems of coupled harmonic oscillators with discrete or continuous spectra are considered, where all degrees of freedom move in time-dependent coherent Glauber states.We present the general formalism and study two examples in detail. The problem of radiation damping results under drastic assumptions in exponentially damped harmonic motion, obeying a nonlinear Schrödinger equation. In the second example, a different type of coupling is studied which yields inverse power law damping.     

Response variance prediction in the statistical energy analysis of built-up systems

In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Perturbation-induced radiative decay of solitons

New results concerning emission of radiation (quasi-linear waves) from kinks described by various versions of a perturbed sine-Gordon equation are presented. Considered physical problems pertain to condensed matter physics and nonlinear optics. In perticular, intensities of Swihart wave emission from a fluxon in a long dc driven Josephson junction, and of spin wave emission from a domain wall in a weak ferromagnet driven by external constant magnetic field are calculated. A general estimate for an exponentially small intensity of emission from a kink oscillating near a bottom of an effective potential wall is obtained. A system of coupled double sine-Gordon equations describing a double DNA helix is briefly investigated. It is demonstrated that a collision of a bi-kink (a bound state of two 2Π-kinks belonging to different subsystems) with a 4Π-kink belonging to either subsystem may result in excitation of large-amplitude internal oscillations of both the colliding solitons, and the rate of radiative damping of those oscillations is found. At last, radiative effects accompanying motion of a stimulated-Raman-scattering soliton in a dissipative medium are studied.     

三层弱循环耦合可激发介质中螺旋波动力学

采用Bär模型研究了具有循环反馈耦合的三层可激发介质中的螺旋波动力学行为,数值模拟结果显示: 在耦合强度较小时, 在各子系统中可观察到螺旋波漂移或漫游; 当耦合强度稍大时, 相互作用既可以使螺旋波漫游或漂移出系统边界而使子系统回到静息态,还可以使子系统的螺旋波态转变为靶波或湍流态, 并观察到子系统的渐近态依赖初值现象; 继续增大耦合强度, 三个子系统的螺旋波可达到近似广义同步; 当耦合强度更大时, 螺旋波演化为湍流态.     

Nonequilibrium thermofield dynamics

The dissipative effects in nonequilibrium thermodfield dynamics are the gauge fields of theSU(1, 1) symmetry of the free bosonic thermal theory [SU(2) for the fermionic one]. In two dimensions some nonequilibrium systems are equivalent to equilibrium systems. An interesting relation exists between the equivalence principle of general relativity and the assumption, in statistical mechanics, of the existence of local subsystems in equilibrium.     

Qubit movement-assisted entanglement swapping

We propose a scheme to generate entanglement between two distant qubits(two-level atom) which are separately trapped in their own(in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement.It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement(Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.     

A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures

Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures. High frequency techniques, such as statistical energy analysis (SEA), often miss important information such as dominant resonance behavior due to stiff or small scale parts of the structure. Hybrid methods circumvent this problem by coupling FEM/BEM and SEA models in a given built-up structure. In the approach adopted here, the whole system is split into a number of subsystems that are treated by either FEM or SEA depending on the local wavelength. Subsystems with relative long wavelengths are modeled using FEM. Making a diffuse field assumption for the wave fields in the short wave length components, the coupling between subsystems can be reduced to a weighted random field correlation function. The approach presented results in an SEA-like set of linear equations that can be solved for the mean energies in the short wavelength subsystems.     

指数型径向阻抗变换器功率传输效率的优化设计

 利用解析方法和电路模拟方法研究了阻抗变换器功率传输效率的优化设计。电路计算中,采用了脉冲上升沿等效的正半周正弦波作为输入波形的假设,并忽略了水介质能量损失的影响。首先对比了线性、饱和型变化和陡变型变化3种典型阻抗的功率和能量传输效率,分析讨论了影响指数型阻抗变换器功率传输效率的关键影响因素,并得到了功率传输效率最大化的中间参数和符合系数的参数范围。讨论了实际设计中应注意的绝缘安全系数的结构设计、杂散参数对阻抗计算的影响、水介质能量损失等问题。     

基于高级统计能量分析的周期加筋板振动特性研究

统计能量分析(statistical energy analysis, SEA)是复杂耦合系统中、高频动力学特性计算的有力工具. 本文以波传播理论和SEA的基本原理为基础, 研究周期加筋板中弯曲波传播特性. 分析了周期结构的频率带隙特性和加强筋对板上弯曲波的滤波特性对SEA计算结果的影响规律, 发现经典SEA由于忽视了加筋板中物理上不相邻子系统间存在的能量隧穿效应, 而导致响应预测结果产生最高近 40 dB的误差. 为了解决这一问题, 本文应用高级统计能量分析(advanced statistical energy analysis, ASEA)方法, 考虑能量在不相邻子系统间的传递、转移和转化的物理过程, 从而大幅提高子系统响应的预测精度, 将误差在大部分频段降低至小于5 dB. 设计了模拟简支边界条件的加筋板振动测试实验装置, 实验测试结果与有限元结果符合较好, 对理论模型进行了验证.     

On radiation modes in the time-dependent coupled power theory for optical waveguides

A derivation in terms of a statistical theory of power coupling is performed in order to estimate the effects of the radiation modes of an optical waveguide. Earlier, the loss term introduced in this theory was always of heuristic origin. In this paper, we derive an identical term from first principles. Accordingly, we find that coupling from radiation to guided modes along the waveguide can be neglected.     

Atomic Bell states generation in an open driven cavity QED system

We show that two uncorrelated two-level atoms can become maximally entangled if they are both off-resonantly coupled to a dissipative cavity mode, initially in the vacuum state, and strongly driven by a resonant coherent field. For moderate atom-field detuning we find that the quantum correlations in the tripartite system can alternatively concentrate either in the atom-atom subsystem or in the two atom-field subsystems. In the first case Bell states as well as their superpositions are generated for low enough cavity decay rates. In a dispersive coupling regime the atomic entanglement grows up monotonically to the maximum value where it remains nearly stationary without being affected by cavity dissipation.     

Nuclear clusters in dissipative medium

An exact solution of channel coupling equations describing the relative motion of two heavy clusters was analyzed without additional (commonly used) simplifications concerning a restricted number of the channels and low excitation energy in comparison with the total energy. It was found that excitation of even very simple quantum system with only one degree of freedom may reveal the dissipative features at slow collisions if the spectra of this system is sufficiently random. An excitation of such a system at sub-barrier tunnelling increases significantly (by several orders) the transmission probability, in spite of the large dissipation of relative motion kinetic energy occurs. At deep sub-barrier energies the soft degrees of freedom are excited with the most probability. Dynamics of wave packet in dissipative environment was also analyzed and a new effect of wave packet sticking to a potential wall due to its tangling and time delay inside the inelastic channels was found.     

Dissipative soliton in an amplifier with a Bragg grating

A dissipative soliton in an amplifier with a Bragg grating is numerically investigated by direct simulation of Maxwell-Bloch equations. The result of the simulation indicates that a solitary wave can exist in such a medium. However, the pulse shape of the dissipative soliton is asymmetrical because of the gain saturation effect. This gain saturation effect results from the high power of the ultrashort dissipative soliton. The influence of amplifier gain on the solitary wave is also investigated.     

Vibration of L-shaped plates under a deterministic force or moment excitation: a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary.     

双层非线性耦合反应扩散系统中复杂Turing斑图

采用双层耦合的Brusselator模型, 研究了两个子系统非线性耦合时Turing 模对斑图的影响, 发现两子系统Turing 模的波数比和耦合系数的大小对斑图的形成起着重要作用. 模拟结果表明: 斑图类型随波数比值的增加, 从简单斑图发展到复杂斑图; 非线性耦合项系数在0–0.1时, 系统1中短波模在系统2失稳模的影响下不仅可形成简单六边形、四边形和条纹斑图, 两模共振耦合还可以形成蜂窝六边形、超六边形和复杂的黑眼斑图等超点阵图形, 首次在一定范围内调整控制参量观察到由简单正四边形向超六边形斑图的转化过程; 耦合系数在0.1–1时, 系统1中短波模与系统2失稳模未发生共振耦合仅观察到与系统2相同形状的简单六边形、四边形和条纹斑图. 关键词： Brusselator模型 非线性耦合 Turing模     

Kink dynamics in one-dimensional nonlinear systems

A certain class of nonlinear evolution equations of one space dimension which permits kink type solutions and includes one-dimensional time-dependent Ginzburg-Landau (TDGL) equations and certain nonlinear wave equations is studied in some strong coupling approximation where the problem can be reduced to the study of kink dynamics. A detailed study is presented for the case of TDGL equation with possible applications to the late stage kinetics of order-disorer phase transitions and spinodal decompositions. A special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics. A new conservation law for dissipative systems is found which corresponds to the momentum conservation law for wave equations.