Multi-cluster dynamics in coupled phase oscillator networks

In this paper, we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number of oscillators N and a single scalar function g(?) (the coupling function). Previous work has shown that (a) any clustering can stably appear via choice of a suitable coupling function and (b) open sets of coupling functions can generate heteroclinic network attractors between cluster states of saddle type, though there seem to be no examples where saddles with more than two nontrivial clusters are involved. In this work, we clarify the relationship between the coupling function and the dynamics. We focus on cases where the clusters are inequivalent in the sense of not being related by a temporal symmetry, and demonstrate that there are coupling functions that give robust heteroclinic networks between periodic states involving three or more nontrivial clusters. We consider an example for N = 6 oscillators where the clustering is into three inequivalent clusters. We also discuss some aspects of the bifurcation structure for periodic multi-cluster states and show that the transverse stability of inequivalent clusters can, to a large extent, be varied independently of the tangential stability.     

平动矩形贮箱刚-液耦合非线性动力学研究

首先应用H-O原理建立了矩形贮箱刚-液耦合系统平动的耦合动力学模型,在贮箱水平运动情况下,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,在给定贮箱运动规律和给定外力规律两种形式下,分析了刚-液耦合系统固有频率变化规律,并应用多尺度法对系统的一阶主共振进行解析分析,研究了液体稳态解的幅频曲线,均发现跳跃及软、硬特性随液深转换的现象,在给定水平外力下,得到液体稳态解的同时还可得到刚体稳态解,两者定性性态相同。最后用数值法验证了解析解的正确性。     

MFXRLS‐based adaptive feed‐forward controller implemented with velocity sensor identified by frequency response to improve actuator speaker performance in ANC systems

Abstract

To improve performance of a “dual voice coil” (DVC) actuator speaker in an active noise control (ANC) system, a speaker model that includes coupling dynamics and source of noise pressure is first derived to design an adaptive feed‐forward controller based on modified, filtered‐X, recursive‐least‐squares (MFXRLS) algorithm in this investigation. A novel velocity sensor measuring velocity of the speaker face is further developed by use of a frequency‐response method. Two transfer functions required for the velocity sensor are identified in two steps: (i) the adaptive feed‐forward controller is applied to keep speaker face velocity zero to identify the first transfer function; and (ii) the second transfer function is then obtained experimentally using the first transfer function. Performance of the established velocity sensor is similar to that of a Polytec OFV2100 laser velocity transducer. This velocity sensor is then incorporated with the adaptive feed‐forward controller to control the DVC actuator speaker in the ANC system. For a sinusoidal command input of frequency below 390 Hz, the controlled speaker acquires a unit‐gain magnitude and zero phase degree, showing that the controller can effectively reduce effects of the speaker dynamics, including coupling dynamics.     

空间桁架结构动力刚化有限元分析

作高速大范围运动的弹性体,由于运动和变形的耦合将产生动力刚化现象,传统的动力学理论难以计及这种影响。本文在有限元方法中首次引入了单元耦合形函数(阵),以此将单元弹性位移表示成为单元结点位移的二阶小量形式。利用几何非线性的应变—位移关系式,在小变形假设条件下确定了单元耦合形函数。在此基础上,根据Kane方程,运用模态坐标压缩,并通过适当的线性化处理,得到了一致线性化的动力学方程。编制了空间桁架结构动力刚化有限元分析程序,仿真算例证明了理论和算法的正确性。     

弹性胶泥阻尼器的冲击实验研究及建模分析

通过实验与理论分析相互结合的方法,以纯硅油和不同体积比例的固体颗粒为介质的弹性胶泥阻尼器为研究对象,对各阻尼器分别进行不同高度下的冲击实验,分析在固液耦合作用下弹性胶泥阻尼器的冲击性能变化。并且在冲击实验的基础上建立阻尼器的动力学模型,通过数值方法辨识模型中方程的各参数并与实测数值进行对比。研究工作对含固体颗粒的弹性胶泥阻尼器的冲击实验分析与动力学建模以及该类阻尼器的工程应用有着理论指导意义。     

Collective spin waves in high-density two-dimensional arrays of FeCo nanowires

Brillouin measurements have been made of the spin dynamics of high-density two-dimensional hexagonally ordered 20 nm diameter Fe48Co52 nanowire arrays, with various interwire spacings, as a function of longitudinal magnetic field. The experimental data are analyzed within the Arias-Mills theory based on interwire dipolar couplings in the arrays. The results provide conclusive evidence of collective spin waves arising from the dipolar coupling which is manifested as a reduction in spin wave frequency with decreasing interwire spacing.     

Constrained optimization using a multipoint type chaotic Lagrangian method with a coupling structure

This article proposes a new constrained optimization method using a multipoint type chaotic Lagrangian method that utilizes chaotic search trajectories generated by Lagrangian gradient dynamics with a coupling structure. In the proposed method, multiple search points autonomously implement global search using the chaotic search trajectory generated by the coupled Lagrangian gradient dynamics. These points are advected to elite points (which are chosen by considering their objective function values and their feasibility) by the coupling in order to explore promising regions intensively. In this way, the proposed method successfully provides diversification and intensification for constrained optimization problems. The effectiveness of the proposed method is confirmed through application to various types of benchmark problem, including the coil spring design problem, the benchmark problems used in the special session on constrained real parameter optimization in CEC2006, and a high-dimensional and multi-peaked constrained optimization problem.     

基于频响函数合成的浮筏隔振系统的响应研究

运用频响函数合成法并结合运用刚体动力学,探讨一种基于子结构频响函数合成的新型浮筏隔振系统分析方法——频响函数合成法。该方法可以针对含有弹性基座的浮筏隔振系统进行分析,避免传统模态合成分析方法在模态分解时可能引入的误差,而与传统导纳合成法相比,本方法能够充分考虑连接点处的弹性,并且其对实验数据的应用更为便利,结构无关性更好。     

转子-轴承系统裂纹-碰摩耦合故障的非线性特性研究

研究了带有裂纹和碰摩耦合故障的弹性转子系统的复杂运动。在同时考虑轴承油膜力和碰摩发生时转静件间的相对速度对非线性摩擦力的影响基础上,构造了含有裂纹-碰摩耦合故障转子系统的动力学模型。针对短轴承油膜力和裂纹-碰摩转子系统的强非线性特点,本文用Runge-Kutta法对转子-轴承系统由裂纹和碰摩耦合故障导致的非线性动力学行为进行了数值仿真研究,发现该类系统在运行过程中存在周期运动、拟周期运动和混沌运动等丰富的非线性现象,研究结果为转子-轴承系统故障诊断、动态设计和安全运行提供了理论参考。     

基于双向流固耦合的机载导弹分离动力学研究

导弹与载机之间的安全与稳定分离过程对导弹飞行稳定性和载机安全具有非常重要作用。为了研究大长径比机载导弹弹射分离过程中与载机之间的相互干扰以及导弹在分离过程中相对于载机的运动轨迹,该文分别使用刚体六自由度（6DOF）方法和计算流体力学/计算结构动力学（CFD/CSD）双向流固耦合方法对典型空空导弹发射分离过程进行了数值模拟,刚体6DOF方法基于对流体力学控制方程与外弹道6DOF运动方程的耦合求解,而CFD/CSD双向流固耦合方法基于对流体力学控制方程与结构运动方程的耦合求解。两种方法得到了导弹分离时的整个气动流场及其变化特性,揭示了不同时刻导弹气动系数随时间的变化曲线和导弹弹道参数,比较与分析了两种计算结果的异同,并对导弹结构弹性变形对其分离运动的影响进行了讨论。     

基于状态空间模型的机床加工精度分析

伺服进给系统的机电耦合特性直接影响数控机床的加工精度，单独针对伺服系统或机械系统建立的模型不足以准确分析系统参数对机床整机加工精度的影响。因此，综合考虑机床伺服系统与机械结构之间的耦合关系，建立伺服进给系统机电耦合动力学模型具有重要意义。首先，为保证伺服进给系统建模精度，利用状态空间法建立了机床机电耦合状态空间方程。其次，建立了伺服进给系统机电耦合Simulink模型，在此基础上采用复合控制提高系统的响应速度和加工精度。随后，利用多体动力学软件建立机床进给系统的刚柔耦合动力学模型，添加摩擦、阻尼等非线性因素，并导入Simulink与伺服系统建立耦合关系。最终，建立了卧式加工中心伺服进给系统的刚柔-机电耦合仿真加工平台，通过模拟机床加工轨迹以验证机电耦合状态空间模型的可靠性。结果表明：该状态空间模型能准确描述系统内部参数和系统输入输出的耦合关系；采用复合控制结构能有效提高系统的响应速度和加工精度。研究结果为数控机床的仿真建模和提高加工精度提供理论依据，为机床机电系统的设计提供有效指导。     

一种基于应变插值大变形梁单元的刚-柔耦合动力学分析

柔性多体系统动力学中的“动力刚化”现象起因于变形间的耦合。一次近似模型成功地解决了小变形情况下的刚柔耦合建模问题,但在大变形情况下则需要考虑更多的耦合效应。本文选取表征梁弯曲应变的曲率和轴向应变作为单元参数进行离散;在大变形大转动基础上得到了单元两端节点运动学参数的递推关系,构造出了能够自动计及“动力刚化项”且适用于大变形刚柔耦合动力学分析的平面梁单元。最后采用本文所提应变插值单元求解了包含大变形和刚柔耦合动力学柔性梁的数值算例,验证了文中算法的正确性和有效性。     

Modeling and optimization of add-drop dynamics in gain-clamped fiber amplifiers

A new dynamic model for gain-clamped fiber amplifiers is presented. The model can simulate the transient behavior of a gain-clamped erbium-doped fiber amplifier as a function of its controlling parameters. Results show the detailed dependence of the amplifier gain dynamics on launched pump power and reveal the pump-power penalty incurred in implementing gain control with minimal transients to power disturbances. The effect on the transients of varying the laser cavity feedback coupling is also presented. Model accuracy is verified by the excellent quantitative agreement with dynamic measurements over a range of operating conditions. Results show how an increase in pump power can effectively suppress both the dynamic and the steady-state signal power transients in wavelength-division multiplexing channel add-drop operations.     

Discrete symmetries of chaotic strings

Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. In this article we look at two important properties of chaotic strings, namely (i) the behaviour under discrete symmetry transformations and (ii) the loss of ergodic behaviour in certain coupling regions. We show that several of the chaotic string dynamics can be transformed into each other by simple discrete coordinate transformations. We investigate how expectation values converge in the various coupling parameter regions and single out those stable zeros of the correlation function that correspond to ergodic states with well-defined convergence properties.     

The effect of a linear mode coupling dispersionon the wave packet dynamics in an optical waveguide with Kerr nonlinearity

The influence of a dispersion of the linear mode coupling coefficient of an optical waveguide (OWG) with Kerr nonlinearity on the dispersion parameters and dynamics of an optical pulse propagating in such a system is studied. In OWGs with a strong linear mode coupling, the presence of a dispersion of the mode coupling may lead to a significant decrease in the energy threshold for nonlinear self-compression of pulses as compared to the case of a single-mode OWG.     

充液挠性航天器俯仰运动分岔特性初步研究

该文考虑了带弹性帆板与液体燃料的航天器做俯仰运动时刚-液-弹之间的相互耦合作用,采用已推导的刚-液-弹耦合系统非线性动力学方程组,应用多尺度法解析分析耦合系统的液体一阶主共振,利用奇异性理论对分岔方程进行分析,得到多种分岔模式,随后根据该文研究的耦合系统物理系数范围,确定只存在滞后点分岔,表现为幅频曲线软、硬特性的转换现象。     

车辆—轨道耦合系统垂横模型及其验证

本文根据车辆－轨道耦合动力学原理,建立车辆－轨道垂横耦合模型,并进行全面的验证：首先与国际著名软件NUCARS进行对比;其次与车辆－轨道垂向耦合模型得到的车辆和轨道系统垂向随机响应对比;然后与鹰厦线小半径曲线试验结果对比;最后与货物列车的线路试验结果对比。对比结果有力地验证了车辆－轨道耦合系统垂横模型及其求解方法的正确性和合理性,为车辆－轨道耦合系统垂横模型的广泛应用奠定了基础。     

Modeling of fracture behavior in polymer composites using concurrent multi-scale coupling approach

ABSTRACT

Embedded statistical coupling method was originally developed to provide computational efficiency, to decrease coupling complexities, and to avoid the need to discretize the continuum model to atomic scale resolution in concurrent multi-scale modeling. An embedded statistical coupling method scheme is relatively easy to implement within a conventional finite element method code and has been tested in standard solid lattice structures. However, this method encounters difficulties when being implemented for amorphous materials like polymers, due to the fact that they lack specific ordered lattice structure and atoms may not be covalently bonded with each other, which are the requirements of common coupling schemes. Therefore, a new approach needs to be developed to resolve this problem. In this article, details of a modified embedded statistical coupling method approach for atomistic-continuum coupling developed to perform simulations of macroscale crack growth in polymers is presented. The presence of the continuum domain surrounding the molecular dynamics region allows for the application of far field loading, and prevents stress wave reflections from the external boundary impinging back on the crack tip. In our approach, a material point method, which is a meshless particle-in-cell method based on an arbitrary Euler-Lagrange scheme and has been proven to have good performance in large deformation problems, is used to model the continuum domain. It is concurrently coupled with molecular dynamics, a widely used method in atomistic simulations, using a so-called handshake region. Anchor points, the equilibrium positions of the constrained particles, which are designed to transmit displacements and forces between nanoscale and macroscale model, are defined in the handshake region. A concurrently coupled material point method-molecular dynamics simulation of crack propagation inside a polymer is performed to verify this new coupling approach, thereby providing a better understanding of the fracture mechanisms at the nanoscale to predict the macro-scale fracture toughness of a polymer system. Results are presented for concurrently coupled simulation of crack initiation and crack propagation in a di-functional cross-linked thermoset polymer, EPON 862.     

Modulation Instability and Pattern Formation in Two-component Bose-Einstein Condensates

No Heading We investigate the dynamics of pattern formation caused by the modulation instability of two-component Bose-Einstein condensates in trapping potentials based on the numerical analysis of the coupled Gross-Pitaevskii equations. The modulation instability induced by the intercomponent mean-field coupling occurs in the out-of-phase fluctuation of the wave function and leads to the formation of multiple domains. We especially focus on the dimensional dependence of the dynamics by varying the aspect ratio of the trapping potential, finding the two-step dynamic process of the pattern formation due to the different time scales of the instability in the different spatial dimensions.PACS numbers: 03.75.Lm, 03.75.Mn