Generalized reduced-order synchronization of chaotic system based on fast slide mode

A new kind of generalized reduced-order synchronization of different chaotic systems is proposed in this paper. It is shown that dynamical evolution of third-order oscillator can be synchronized with the canonical projection of a fourth-order chaotic system generated through nonsingular states transformation from a cell neural net chaotic system. In this sense, it is said that generalized synchronization is achieved in reduced-order. The synchronization discussed here expands the scope of reduced-order synchronization studied in relevant literatures. In this way, we can achieve generalized reduced-order synchronization between many famous chaotic systems such as the second-order D\"{u}ffing system and the third-order Lorenz system by designing a fast slide mode controller. Simulation results are provided to verify the operation of the designed synchronization.     

Reduced-order model for redox kinetics of oxygen carrier in chemical looping combustion

A reduced-order model was developed to calculate the redox kinetics of oxygen carrier in chemical looping combustion. The reduced-order model can describe the major physical/chemical features of the redox steps of oxygen carrier, such as gas diffusion around and inside the particle, surface reaction, product growth, product layer diffusion, pore structure change etc. It is an analytical model simplified using the Thiele modulus method and thus is much easier for computational fluid dynamics modeling and reactor design. The accuracy of variations of redox conversion under different temperatures and gas concentrations predicted by the reduced-order model is verified by comparison with both the detailed one-dimensional model and the experimental data. The results indicate that the reduced-order model can reproduce the prediction accuracy of the detailed one-dimensional model and agrees well with the experimental data. The well observed two-stage behavior of a fast initial stage followed by a second slower stage was discussed in detail. Further, the reduced-order model was used to analyze the effect of particle structural parameters on the kinetics. The relative importance of each controlling step in the kinetics of oxygen carrier predicted by the reduced-order model was compared.     

Karhunen–Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments

The Karhunen–Loeve (K–L) decomposition method has become a popular technique to create low-dimensional, reduced-order models of dynamical systems. In this paper this technique is applied to a multi-degree-of-freedom chain of linear coupled oscillators with a strongly nonlinear (nonlinearizable), lightweight end attachment. By performing K–L decomposition we show that the lightweight nonlinear attachment (possessing 0.5% of the total mass of the chain) can affect the global dynamics of the linear chain, exhibiting nonlinear energy-pumping phenomena; that is, irreversible passive targeted energy transfers from the linear chain to the nonlinear end attachment, where this energy is locally confined and dissipated without ‘spreading back’ to the primary system. It is shown that the occurrence of energy pumping can be identified by studying the dominant K–L modes of the dynamics, as well as, the energy distribution among them. Moreover, by comparing the action of the strongly nonlinear attachment to the classical linear vibration absorber, we show robustness of passive nonlinear energy absorption over wide parameter ranges. On the other hand, the case-sensitive nature of K–L-based reduced-order models has always been a constraint for K–L decomposition, since one cannot quantify a priori the error bound of such low-dimensional reduced-order models when different initial conditions are applied to the system. To alleviate this constraint, the paper proposes a multiple correlation coefficient (MCC) as a quantitative measure to effectively assess the applicability of a K–L-based reduced-order model derived for a specific set of initial conditions to a small neighborhood of initial conditions containing that initial state. The derived reduced-order models are validated through reconstruction of the system responses and comparisons to direct numerical integrations.     

Detection of diffusion and distribution of oxygen by fast-scan EPR imaging

The diffusion and distribution of oxygen in models of biological systems have been followed by a fast-scan 2D EPR imaging apparatus. The EPR imager is based on the use of two sets of gradient coils with computer control to select projections. Currently the time per projection (six seconds) is sufficient to follow oxygen diffusion in the model systems. Typically 18–20 projections are obtained to generate an image. Using physical rotation of x/y coils, this apparatus can be used for three-dimensional EPR imaging.     

Projection operator approach to transport in complex single-particle quantum systems

We discuss the time-convolutionless (TCL) projection operator approach to transport in closed quantum systems. The projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. In particular, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in “modular” quantum systems corresponding to quasi one-dimensional structures which consist of identical or similar many-level subunits. Such modular quantum systems are demonstrated to represent many physical situations and several examples of complex single-particle models are analyzed in detail. For these quantum systems lowest order TCL is shown to represent an efficient tool which also allows to investigate the dependence of transport on the considered length scale. To estimate the range of validity of the obtained equations of motion we extend the standard projection to include additional degrees of freedom which model non-Markovian effects of higher orders.     

Modeling vibratory damage with reduced-order models and the generalized finite element method

This paper investigates a coupled computational analysis framework that uses reduced-order models and the generalized finite element method to model vibratory induced stress near local defects. The application area of interest is the life prediction of thin gauge structural components exhibiting nonlinear, path-dependent dynamic response. Full-order finite element models of these structural components can require prohibitively large amounts of processor time. Recent developments in nonlinear reduced-order models have demonstrated efficient computation of the dynamic response. These models are relatively insensitive to small imperfections. Conversely, the generalized finite element method provides the ability to model local defects without geometric dependency on the mesh. A more robust version of the method, with numerically built enrichment functions, provides a multiple-scale modeling capability through direct coupling of global and local finite element models. Replacing the component finite element model with a reduced-order model allows for efficient computation of dynamic response while providing the necessary information to drive local, solid analyses which can zoom in on regions containing stress risers or cracks. This paper describes the coupling of these approaches to enable fatigue and crack propagation predictions. Numerical/experimental examples are provided.     

Two-level discretizations of nonlinear closure models for proper orthogonal decomposition

Proper orthogonal decomposition has been successfully used in the reduced-order modeling of complex systems. Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed. Since modern closure models for turbulent flows are generally nonlinear, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This paper proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear closure models for proper orthogonal decomposition reduced-order models. The two-level method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter ν = 10^?3, the two-dimensional flow past a cylinder at Reynolds number Re = 200, and the three-dimensional flow past a cylinder at Reynolds number Re = 1000.     

Assessment of reduced models for the detection of modal interaction through rotor stator contacts

Interactions through direct contact between blade-tips and outer casings in modern turbomachines require complex formulations and subsequent expensive computational efforts when the classical finite element method is considered. The construction of reduced-order models through component mode synthesis techniques usually improves the computational efficiency and may be used for fast parameter studies yielding a better knowledge of the phenomena of interest.In this highly nonlinear framework, the present study is dedicated to the investigation of the capabilities of fixed- and free-interface reduction strategies to handle accurately such problems through a realistic 2D model and complements former results involving a direct modal projection with respective strong kinematic restrictions.The equations of motion are solved using an explicit time integration scheme together with the Lagrange multiplier method where friction is accounted for. The presented work discusses the notions of both displacement and motion convergences and the possibility to conduct fast parameter studies with the use of relevant reduction bases. It also shows that kinematic restrictions artificially enhance the detection of modal interactions.     

Feedback control of flow resonances using balanced reduced-order models

This paper investigates the use of balanced reduced-order models for the feedback control of flow resonances. Specifically, the Eigensystem Realization Algorithm is used to find balanced reduced-order models of the linear dynamics of such flow resonances. The method is applied first to a computational problem in direct numerical simulations of cavity resonances, and then to a lab-scale experiment of combustion oscillations. Although the resulting reduced-order models both have fewer than 10 degrees of freedom, the feedback controllers that are based on them perform very well, with closed-loop stability achieved over a wide range of operating conditions.     

Reduced-order modelling of thermoacoustic instabilities in a two-heater Rijke tube

The topic of thermoacoustic instabilities in combustors is well-investigated, as it is important in the field of combustion, primarily in gas-turbine engines. In recent years, much attention has been focused on monitoring, diagnosis, prognosis, and control of high-amplitude pressure oscillations in confined combustion chambers. The Rijke tube is one of the most simple, yet very commonly used, laboratory apparatuses for emulation of thermoacoustic instabilities, which is also capable of capturing the physics of the thermally driven acoustics. A Rijke tube apparatus can be constructed with an electrical heater acting as the heat source, thus making it more flexible to operate and safer to handle than a fuel-burning Rijke tube or a fuel-fired combustor. Augmentation of the heat source of the Rijke tube with a secondary heater at a downstream location facilitates better control of thermoacoustic instabilities. Along this line, much work has been reported on the investigation of thermoacoustics by using computational fluid dynamics (CFD) modelling as well as reduced-order modelling for both single-heater and two-heater Rijke tube systems. However, since reduced-order models are often designed and built upon certain empirical relations, they may not account for the dynamic behaviour of the heater itself, which is a critical factor in the analysis and synthesis of real-time robust control systems. This issue is addressed in the current paper, where modifications have been made to existing models by incorporating heater dynamics. The model results are systematically validated with experimental data, generated from an in-house (electrically heated) Rijke tube apparatus.     

风力机翼型气动计算的降阶模型研究

将基于POD的降阶模型应用于风力机翼型的气动研究。首先应用CFD数值模拟得到一系列快照结果;应用基于本征正交分解(POD)的方法得到流场的一组基模态,认为对于所研究的问题,任一流场可以由这些基模态通过线性表达得到;对控制方程进行Galerkin投影,得到降阶模型,将离散求解N-S方程的问题转化为一组只有十几个自由度的常微分方程,从而减少计算时间,提高计算效率。并对二维翼型的绕流的定常和非定常问题进行了分析,计算结果表明,降阶模型可以较好地捕捉流动的特征,与直接CFD模拟相比计算精度相当,但大幅有效地提高了计算效率。     

Problems of angular momentum projection in nuclear physics

In nuclear models approximate wave functions are often used which do no have sharp angular momentum as required of the exact wave functions. It seem obvious that model wave functions of this type should be improved by projection onto states of good angular momentum. It is not the purpose of this paper to discuss the technical difficulties of projection (which can be formidable for many particle systems), but rather to present in an elementary way certain fundamental ambiguities in the use of projection. An application to high spin states near the yrast line is suggested.     

The spin-1/2XXZ Heisenberg chain,the quantum algebra Uq[sl(2)], and duality transformations for minimal models

The finite-size scaling spectra of the spin-1/2XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central chargec < 1, including the unitary and nonunitary minimal series. Taking into account the half-integer angular momentum sectors—which correspond to chains with an odd number of sites—in many cases leads to new spinor operators appearing in the projected systems. These new sectors in theXXZ chain correspond to new types of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which, however, differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finiteXXZ chain. The observed degeneracies in the energy and momentum spectra are shown to be the consequence of intertwining relations involvingU _q [sl(2)] quantum algebra transformations.     

创新三维立体投影装置的设计和制作

受四棱锥立体投影模型的启发,本文探索了圆锥式和前后平行板式立体投影装置的针对性设计和具体制作方法,在此基础上实现了良好的三维立体投影效果。这两种立体投影装置是最多和最少面多棱锥设计的极限,是大学物理实验大胆创新的一个尝试。     

一类不确定混沌系统的观测器同步

基于降维观测器的方法实现了一类具有外部扰动的混沌系统的同步. 无需知道系统外部扰动项的任何信息，就可对驱动系统设计基于降维观测器的响应系统，从而实现了混沌系统的同步. 数值仿真表明该方法是有效的. 关键词： 混沌同步 混沌系统 观测器     

Sensitivity of friction-induced vibration in idealised systems

Friction-induced vibration occurs in many contexts: vehicle brake squeal in particular remains surprisingly unpredictable and poorly understood. Testing theory against measurements has been hindered by the difficulty in obtaining repeatable results suggesting that the phenomenon is sensitive to small changes in parameters. This paper explores highly idealised cases as a starting point to understanding sensitivity. Using a stability criterion based on the roots of the characteristic equations of the system, the sensitivity of predictions to parameter changes is studied, focussing on a single-mode model. The effects of contact stiffness, non-proportional damping and a velocity-dependent coefficient of friction are considered. It is found that each physical effect can significantly alter predictions; each physical effect can lead to extreme sensitivity; and high sensitivity can sometimes occur when modal amplitudes are small such that they might normally be considered insignificant. With a large body of literature focussing on reduced-order models this study provides an important warning when interpreting their results.     

A new measure of efficiency for model reduction: Application to a vibroimpact system

The aim of this paper is to propose a new way to measure the efficiency of the proper orthogonal decomposition (POD) to construct a reduced-order model in Structural Dynamics. It investigates the efficiency of three reduced-order models for a vibroimpact problem: (1) POD_dir-basis, which is the basis constructed using the direct method of the proper orthogonal decomposition; (2) POD_snap-basis, which is the basis constructed using the snapshot method of the POD; and (3) LIN-basis, which is the basis composed by the normal modes of the associated linear (LIN) conservative system. The efficiency is measured in terms of (1) number of elements to represent the dynamics with a given precision and (2) computational cost to simulate the time response within a given precision.