Correlation of fluctuations of the quadrature amplitudes of interacting modes in the instability region of intracavity third-harmonic generation

Correlation of fluctuations of quadrature amplitudes of interacting modes is studied for the process of intracavity third-harmonic generation in the region of instability. It is shown that this correlation strongly depends on the value of the nonlinear mode coupling coefficient. For small values of the coupling coefficient, correlation of fluctuations of quadrature amplitudes is small. With increasing coupling coefficient, the correlation increases (states of the subsystems become entangled). Then, starting from a certain value of the coupling coefficient, it starts decreasing gradually, tending to zero (entanglement of states of the subsystems decreases). Correlation of fluctuations of quadrature amplitudes decreases also when the amplitude of the fundamental mode perturbing field is decreased.     

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models.     

Extension of the statistical modal energy distribution analysis for estimating energy density in coupled subsystems

The present article deals with an extension of the Statistical modal Energy distribution Analysis (SmEdA) method to estimate kinetic and potential energy density in coupled subsystems. The SmEdA method uses the modal bases of uncoupled subsystems and focuses on the modal energies rather than the global energies of subsystems such as SEA (Statistical Energy Analysis). This method permits extending SEA to subsystems with low modal overlap or to localized excitations as it does not assume the existence of modal energy equipartition. We demonstrate that by using the modal energies of subsystems computed by SmEdA, it is possible to estimate energy distribution in subsystems. This approach has the same advantages of standard SEA, as it uses very short calculations to analyze damping effects. The estimation of energy distribution from SmEdA is applied to an academic case and an industrial example.     

Numerical and experimental validation of a hybrid finite element-statistical energy analysis method

The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.     

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.     

Coexisting chaotic attractors,their basin of attractions and synchronization of chaos in two coupled Duffing oscillators

Two coupled Duffing oscillators equations with several coexisting chaotic attractors are considered. Six coexisting chaotic attractors are observed for the range of initial conditions considered in our study. For two attractors the basin of attraction is a simple disconnected straight line, while for the rest of the attractors it appears to be very complex. Phase portraits of (two) subsystems are found to be distinct for two attractors while identical for the other four attractors. Among these four attractors, state variables of the subsystems are perfectly synchronized for two attractors and asynchronized for the other two attractors. Synchronization of subsystems is studied by employing a continuous feedback method.     

Ordering of interacting subsystems. Molecular dynamics

The molecular dynamics method is used to examine the ordering of interacting subsystems in a two-component, two-dimensional Coulomb gas, consisting of equal amounts of positively and negatively charged particles, which simulates the behavior of a system of interacting vortices. In particular, it is found that when the system temperature is lowered from the Kosterlitz-Thouless transition point, additional ordering of the vortex chains may take place. It is noted that this process may stimulate the development of vortex chains observed in real superfluid, magnetic, and superconducting systems. Possible applications of the molecular dynamics method to phase separation and the ordering of adiabatically slowly moving subsystems in the collective field of a fast subsystem are considered. Fiz. Tverd. Tela (St. Petersburg) 40, 1701–1704 (September 1998)     

耦合电路中的复杂振荡行为分析

讨论了两个非线性电路适当连接后的耦合系统随耦合强度变化的演化过程.给出了两子系统各自的分岔行为及通向混沌的过程,指出原子系统均为周期运动时,耦合系统依然会由倍周期分岔进入混沌,同时在混沌区域中存在有周期急剧增加及周期增加分岔等现象.而当周期运动和混沌振荡相互作用时,在弱耦合条件下,受混沌子系统的影响,原周期子系统会在其原先的轨道邻域内作微幅振荡,其振荡幅值随耦合强度的增加而增大,混沌的特征越加明显,相反,周期子系统不仅可以导致混沌子系统的失稳,也会引起混沌吸引子结构的变化. 关键词： 非线性电路 耦合强度 分岔 混沌     

Specific features of the propagation of a shear elastic wave in an acoustic superlattice of the magnet-ideal diamagnet type: Localization conditions

The influence of gyrotropy on the conditions for propagation and localization of a shear elastic wave in a semi-infinite magnetic superlattice composed of ferromagnetic and superconducting layers is investigated by the effective-medium method. This method correctly takes into account the dynamic interaction between the spin and elastic subsystems.     

Self-sustained spatiotemporal oscillations induced by membrane-bulk coupling

We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality. Specifically, we show that coupling a passive diffusive bulk of dimension d with an excitable membrane of dimension d-1 produces a self-sustained oscillatory behavior. An analytical explanation of the phenomenon is provided for d=1. Moreover, in-phase and antiphase synchronization of oscillations are found numerically in one and two dimensions. This novel dynamic instability could be used by biological systems such as cells, where the dynamics on the cellular membrane is necessarily different from that of the cytoplasmic bulk.     

A hybrid formulation for mid-frequency analysis of assembled structures

A new formulation able to predict the behaviour of structures in the mid-frequency range is presented in this paper. The mid-frequency field is a hybrid domain for which assembled structures exhibit simultaneously low- and high-frequency behaviours, depending on the material and geometrical properties of different subsystems. Thus, dealing with the mid-frequency field requires simulation methods which are able to account the differences in behaviour of different subsystems. The hybrid formulation is based on the coupling of two different formulations, the finite elements for the low-frequency behaving subparts and a probabilistic formulation, the smooth integral formulation, applied to the high-frequency subsystems. The hybrid method enables to correctly predict the deterministic response of the low-frequency parts which is not affected by randomness, and the smooth trend of the contributions of the high-frequency parts. The paper is concluded with several numerical examples computed for coupled one- and two-dimensional structures.     

Perturbation evolution at a metal-metal interface subjected to an oblique shock wave: Supersonic velocity of the point of contact

The perturbation evolution at the interface between identical metals (metal plates) that is exposed to high-speed oblique shock waves is observed experimentally for the first time (the waves are attached to the point of contact, so that a cumulative jet cannot form). The experiments are numerically simulated by the two-dimensional Lagrange method. An elastoplastic model where the dynamic yield strength is a function of material state parameters is employed. An analytical technique to treat instability development under given loading conditions is suggested. High strains produce a high-temperature zone near the interface (thermal softening zone). A short-lived shear flow with a high velocity gradient depending on the angle and velocity of plate collision is observed. In this zone, the shear modulus and the yield strength are appreciably lower than under normal conditions, which favors instability development.     

Orientational Instability and Hysteresis Phenomena in a Ferronematic Liquid Crystal in a Magnetic Field

A magnetic-field-induced orientational structure in a ferronematic (FN) liquid crystal (LC) layer is studied within the continuum theory. The rotation angles of the director and the magnetization and the concentration of magnetic impurity corresponding to a supertwisted orientational structure of the suspension are calculated. It is shown that the deviation angle of the director from the direction of the external field has the hysteresis region in which the orientational structure of the FN changes stepwise from a state with a positive twist of the director to a state with a negative twist. A value of the magnetic field strength is found above which orientational bistability regions arise. It is shown that orientational instability under the rotation of the field most clearly manifests itself in FNs with strong anchoring of particles to the LC matrix. It is established that the effect of magnetic segregation responsible for the redistribution of magnetic particles in the layer leads to the expansion of the hysteresis region and to a decrease in the field at which orientational instability arises. It is shown that, in FNs with soft anchoring between magnetic and LC subsystems, there exist several response modes to a quasistatic rotation of the magnetic field.     

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.     

Mutual influence of the spectral components of perturbations on the modulation instability frequency interval in a cubic nonlinear medium

The influence of the shape of a Gaussian pulse propagating in a cubic nonlinear medium on the development of its modulation instability is analyzed, taking into account the time dispersion of the nonlinear response as well. Analytical dependences of the frequency interval of the perturbation development on the dispersion of the nonlinear response, the pulse duration, and the number of simultaneously acting perturbations, which affect each other due to the inhomogeneous pulse shape, are obtained. It is shown that, with increasing dispersion of nonlinear response, the frequency interval of the instability development initially narrows and then expands. Qualitative agreement between the analytical dependences and the results of computer simulation is demonstrated. The frequency interval of the modulation instability development in a medium without the nonlinear response dispersion that was previously determined by different authors under the assumption of “long” pulses is found to coincide with that obtained in this study for the Gaussian pulse under the assumption of the simultaneous action of a large number of perturbations.     

A joint relaxation technique for the receptance solution of structural vibration problems

A well-established technique for the analysis of a complex vibrating system is to cut it into a convenient number of simpler subsystems. An alternative approach, suggested by recent studies of displacement excitation, is to convert the system into a set of independent subsystems by clamping it at a sufficient number of co-ordinates. Exact solutions for free and forced vibration are then obtained by considering the relaxation of the clamps. Data in the Vibration Analysis Tables [1] are used for the numerical solution of framed structures by this method. This displacement approach is in some cases simpler than the standard methods and leads to smaller frequency determinants.     

激波加载初始非均匀气体流场界面不稳定性数值模拟

流体力学界面不稳定性及其后期的界面混合现象,是一种十分复杂的多尺度非线性物理问题,在惯性约束聚变、天体物理以及水中爆炸等领域有着广泛的应用前景,对该问题的研究不仅具有很高的学术价值,而且对促进相关领域的发展具有重要意义.中国工程物理研究院流体物理研究所基于Euler有限体积方法,发展了适用于可压缩多介质黏性流动具有多亚格子尺度模型的大涡模拟程序MVFT,并评估分析了不同亚格子尺度模型对界面不稳定性及界面混合的模拟能力;提出了流场非均匀性对R-M不稳定性影响的问题,并在激波驱动轻重气体双模扰动R-M界面不稳定性实验中成功应用并解读了新的实验现象和规律,在此基础上进而开展了反射激波作用下两种初始非均匀流场界面不稳定性引起的界面混合数值模拟研究,探讨了流场非均匀性对激波反射后强非线性阶段界面不稳定性发展、演化规律的影响,近期还对非均匀流场R-M不稳定性的演化规律、初始流场非均匀性和初始扰动效应及其影响的物理机制进行了分析和研究.      

Modulation instability of wave packets in the presence of linear and nonlinear mode coupling

Conditions for modulation instability of a wave packet consisting of two codirected linearly coupled waves propagating in a light guide with Kerr-type nonlinearity are formulated. The development of the instability with regard to light guide parameters, linear and nonlinear mode coupling, and input power is analyzed for symmetric and antisymmetric light guide excitations. Unlike in single-mode light guides, here modulation instability may arise in the frequency ranges of normal material dispersion and at the zero perturbation frequency.     

可压缩Kelvin-Helmholtz不稳定性低耗散锐界面方法直接模拟

采用低耗散WENO(weighted essential non-oscillatory)格式及锐界面方法模拟可压缩Kelvin-Helmholtz不稳定性问题.由于物质界面被描述成一种接触间断, 该方法可精确求解切向速度间断.基于优化模板对原始光滑指标进行正规化后, 得到一种低耗散WENO格式.修正后的方法显著降低了普通流动区域的过衰减问题, 保持了良好的激波捕捉性能, 并可获得与混合格式相当的求解精度.不同于以往求解单一流体或易混界面时, 通过初始设定有限宽度的剪切层或快速数值耗散以抑制高波数模态, 该方法允许高波数扰动的发展.计算结果表明, 高波数扰动展现出与以往理想Kelvin-Helmholtz不稳定性问题数值模拟或线化理论结果不同的特征, 但与有限厚度的剪切层结果相符.      

Interaction of dislocations with nanoprecipitates of the metastable phase and dispersion strengthening of the Fe-Cu alloy

The interaction of dislocations with copper-enriched precipitates in the matrix of body-centered cubic iron has been investigated by the molecular dynamics method. It has been shown that dislocations stimulate the development of a phase instability of body-centered cubic copper precipitates in a specific range of their sizes. This process is accompanied by the pinning of dislocations by precipitates and makes a significant contribution to strengthening. The results obtained provide an adequate explanation for the observed dependence of the strengthening in the Fe-Cu system on the precipitate size.