Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study

The two-dimensional evolution of Stokes waves over a long fetch has been studied only by means of the cubic Schrödinger equation which is accurate up to the third order in wave slope (Yuen and Ferguson [1], Martin and Yuen [2] and Litvak et al. [3]). For uniform Stokes waves unstable sidebands are known to induce modulation and demodulation at the beginning but energy leakage to higher frequencies leads to chaos eventually and invalidates the theory. For one-dimensional evolution, the fourth-order extension by Dysthe [4] has been shown to corroborate better with experiments that the third-order (Lo and Mei [5]). In this paper we pursue further the implications of the fourth-order theory on two-dimensional evolutions. For the instability of uniform wave trains due to oblique sidebands, we find that the narrower instability region and the presence of a higher-order dispersion term tend to delay the trend toward chaos. We also study the evolution of a single three-dimensional envelope with various aspect ratios. Comparisons between the third- and fourth-order theories are made. Specifically, if the initial envelope is elongated in the direction of the crests, new groups are first born near the center, with ridges parallel to the crests, then everything flattens out. If the initial envelope is elongated in the direction of wave propagation, then the tendency of group-splitting is reduced. Furthermore, the envelope elongates crest-wise to form a ridge before eventual flattening.     

Chaos detection and parameter identification in fractional-order chaotic systems with delay

The paper first applies the 0–1 test for chaos to detecting chaos exhibited by fractional-order delayed systems. The results of the test reveal that there exists chaos in some fractional-order delayed systems with specific parameter values, which coincides with previous reports based on the phase portrait. In addition, it is very important to identify exactly the unknown specific parameters of fractional-order chaotic delayed systems in chaos control and synchronization. Thus, a method for parameter identification of fractional-order chaotic delayed systems based on particle swarm optimization (PSO) is presented. By treating the orders as parameters, the parameters and orders are identified through minimizing an objective function. PSO can efficiently find the optimal feasible solution of the objective function. Finally, numerical simulations on fractional-order chaotic logistic delayed system and fractional-order chaotic Chen delayed system show that the proposed method has effective performance of parameter identification.     

一类冲击振动系统在强共振条件下的亚谐分叉与Hopf分叉

通过理论分析和数值仿真,研究了一类二维冲击振动系统在一种强共振条件下的Hopf分叉与亚谐分叉。分析并证实了该类系统在此共振条件下可由稳定的周期1 1振动分叉为周期4 4振动或概周期振动,讨论了亚谐振动和概周期振动向混沌运动的演化过程。     

具有单侧刚性约束的两自由度振动系统在强共振条件下的拟周 …

采用理论分析和数值仿真相结合的方法,研究了一类两自由度碰撞振动系统在一种强共振条件下的Ｈｏｐｆ分叉问题,分析并证实了碰撞振动系统在此共振条件下可由稳定的周期１－１振动分叉为不稳定的周期３－３振动,讨论了亚谐振动向混沌运动的演化过程。     

Analysis of fluctuations induced by a scale hierarchy of interacting particles

We investigate the two-point averaging over space of fluctuations arising from a multiscale hierarchy of interacting particles. We assume this will satisfy a condition of homogeneity with respect to scale. We consider the second-order correlation of fluctuations arising from particles of a single scale in the hierarchy; we then form an average over the set of such single-scale correlations. As the hierarchy is refined, a condition of scale continuum is approached. We use the limiting value of this procedure to define a two-point correlation function for the multiscale system as a whole, and identify this with the experimental measurement of correlation in such a multiscale context. In the energy spectrum which emerges in this limit, one term comes to dominate the spectrum for large k; this term has the form ‘k ⁻² ln k’. In fact, a variety of different shape functions (intended to represent correlation functions) leads to this energy spectrum, which bears a qualitative resemblance to a Kolmogorov power-law. In this sense a degree of universality is exhibited. The ideas are illustrated for two simple one-dimensional test cases before a more general treatment in one and three dimensions is developed.     

Spatial and Dynamical Chaos Generated by Reaction–Diffusion Systems in Unbounded Domains

We consider in this article a nonlinear reaction–diffusion system with a transport term (L,∇ _x )u, where L is a given vector field, in an unbounded domain Ω. We prove that, under natural assumptions, this system possesses a locally compact attractor in the corresponding phase space. Since the dimension of this attractor is usually infinite, we study its Kolmogorov’s ɛ-entropy and obtain upper and lower bounds of this entropy. Moreover, we give a more detailed study of the spatio-temporal chaos generated by the spatially homogeneous RDS in . In order to describe this chaos, we introduce an extended (n + 1)-parametrical semigroup, generated on the attractor by 1-parametrical temporal dynamics and by n-parametrical group of spatial shifts ( = spatial dynamics). We prove that this extended semigroup has finite topological entropy, in contrast to the case of purely temporal or purely spatial dynamics, where the topological entropy is infinite. We also modify the concept of topological entropy in such a way that the modified one is finite and strictly positive, in particular for purely temporal and for purely spatial dynamics on the attractor. In order to clarify the nature of the spatial and temporal chaos on the attractor, we use (following Zelik, 2003, Comm. Pure. Appl. Math. 56(5), 584–637) another model dynamical system, which is an adaptation of Bernoulli shifts to the case of infinite entropy and construct homeomorphic embeddings of it into the spatial and temporal dynamics on . As a corollary of the obtained embeddings, we finally prove that every finite dimensional dynamics can be realized (up to a homeomorphism) by restricting the temporal dynamics to the appropriate invariant subset of .     

基于混合行为博弈的多目标仿生设计方法

将多个设计目标视为不同的博弈方,通过计算设计变量对目标函数的影响因子和模糊聚类, 将设计变量集合分割为各博弈方拥有的策略空间. 对蜥蜴种群的繁衍生存机理进行仿生,将 3种蜥蜴的行为方式分别定义为利己主义、集体主义和投机主义,并赋予相应的博弈方, 各博弈方根据所仿生蜥蜴的行为特点,建立自身博弈得益函数与目标函数之间的映射关系. 各博弈方分别以自身博弈得益函数为目标,在各自的策略空间中进行单目标优化,获得本博 弈方对其余博弈方的最佳对策,所有博弈方的最佳对策形成一轮博弈的策略组合,并根据收 敛判别,通过多轮博弈,获得最终的博弈解. 以白鹤滩拱坝体型的三目标优化设计为例,设 计结果显示坝体体积方量减少了16.412万方,或2.38%; 最大主拉应力降低 了0.036MPa, 或0.31%; 整体应变能下降了0.167GJ 或4.47% 体现了基 于混合行为博弈方式的多目标仿生设计方法的有效性.     

冰雹撞击下泡沫铝夹芯板的动态响应

在传统单层泡沫夹芯结构的上、下面板之间插入中面板,通过移动中面板的位置,获得了外形尺寸相同、质量相等的5种构型夹芯结构,其上层芯材与芯材总厚度比分别为0:30、10:30、15:30、20:30和30:30。在量纲分析的基础上,应用非线性动力有限元程序LS-DYNA对5种构型夹芯结构进行了冰雹撞击数值分析,研究了中面板位置对夹芯板的能量吸收、能量耗散和动态响应的影响。结果表明:中面板的存在对下层芯材能形成有效的保护;随着中面板位置由上向下移动,夹芯板的抗撞击性能呈现由大到小再增大的态势。数值计算结果对抗冰雹撞击夹芯结构的优化设计具有一定的参考价值。     

Circuit implementation of a piezoelectric buckled beam and its response under fractional components considerations

In this paper, an analog testing circuit and determinist averaging method for a vibration energy harvesting system with fractional derivative and nonlinear damping under a sinusoidal vibration source is proposed in order to predict the system response and its stability. The objective of this paper is to show that there is a possibility to make a pre-experimental design of the structure by using analog circuit and discussing the performance of a system with fractional derivative. Bifurcation diagram, poincaré maps and power spectral density are provided to deeply characterize the dynamic of the system. These results are corroborated by using 0–1 test. By using the Melnikov method, we find the necessary condition for which homoclinic bifurcation occurs. Understanding and predicting this bifurcation is very judicious in the energy harvesting field because it may lead to different types of motion in the perturbed system. The appearance of chaotic vibrations increases the frequency’s bandwidth of the harvester thereby, allowing to harvest more energy. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim^®). The corresponding electronic circuit is designed exhibiting transient to chaos in accord with numerical simulations. The impact of fractional derivatives is presented upon the power generated by the system. In addition, by combining the harmonic force and a random excitation, the stochastic resonance appears, giving rise to large amplitude of vibration and consequently, enhancing the performance of the system. The results obtained in this work show the interest of using the electronic circuit to make the experiment analysis of the physical structure and also, the effects of the use of piezoelectric material exhibiting fractional properties in this research field.     

The Post-Hopf-Bifurcation Response of a Loosely Supported Cylinder in an Array Subjected to Cross-Flow. Part II: Theoretical Model and Comparison with Experiments

A nonlinear quasi-steady model for the analysis of the dynamics of a loosely supported cylinder, which takes into account position-dependent nonlinear fluid forces as well as nonuniform flow, is formulated. The model includes an approximation for the equivalent viscous damping associated with energy dissipation on impact at the support. The nonlinear model shows reasonably good agreement with experiments, in predicting the observed bifurcations in the cylinder response. Comparison criteria include the standard orbital plots, time traces and response spectra. A borderline chaotic response is found to be predominant over the test velocity range. In this chaotic regime, the theoretical results were verified via attractor fractal-dimension calculations and saddle orbit distributions; theoretical values of these invariant measures compare reasonably well with their experimental counterparts. Two mechanisms leading to chaos have been identified for this system. The first is a switching mechanism , at the onset of impacting. The second, and more prevalent, is the type I intermittency route to chaos.     

Origins of group coordination: nonlinear dynamics and the role of verbalization

Coordination occurs when two or more people do the same or complimentary tasks simultaneously; its explanation game theory, nonlinear dynamics, and implicit learning theory. In the experiment, 12 four-person groups were allowed to discuss the coordination (card game) task while performing it; 12 other groups worked nonverbally. One to three group members were replaced during the game. Split-plot ANOVA showed that verbalizing groups performed better than nonverbalizing groups overall and showed more acute coordination learning curves, but verbalization did not compensate for the replacement of personnel. Groups that changed one or two players showed positive coordination transfer, but groups that changed three players did not. Nonlinear regression for temporal dynamics within verbalizing and nonverbalizing groups showed asymptotic stability for initial coordination learning and transfer to a difficult rule, a chaotic function when replacements were introduced, and asymptotic stability again when the team with replacements switched to the difficult rule.     

Wind tunnel simulation of wind effect on a group of high Cooling towers

Aerodynamic interference between high cooling towers in the atmospheric boundary layer (ABL) and uniform flow has been discussed. For the 1/1000 ABL model set up in the 2.25m low speed wind tunnel at Peking University, the similarity condition of the cooling tower in the ABL, the simulation results of a single tower and some typical tower groups have been provided. Experiments showed that the Circumferential pressure distributions were consistent between the smooth model tower and the prototype tower, and between the rough model tower and the prototype tower with ribs; the two dimensional characteristics in the circumferential pressure distribution were also noticeable around the middle 1/3 part of the tower after nondimensionalization by local dynamic pressure. Results demonstrate that, in the flow with strong turbulence the lift coefficient of the downstream cylinder approaches 0.4. In the flow with weak turbulence, the pressure distribution reflects a strong nonsymmetry, and the lift coefficient or stagnation pressure of the downstream cylinder switches alternately between 1 and 0, where a concentrated vortex rolls up and then sheds toward the front of the downstream cylinder and exerts a decisive influence on the aerodynamic properties of the downstream cylinder.     

The study on the chaotic motion of a nonlinear dynamic system

ｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｃｈａｏｓｉｎｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃｓｙｓｔｅｍｓｈａｓｂｅｎａｒｏｕｓｉｎｇｍｏｒｅａｎｄｍｏｒｅｉｎｔｅｒｅｓｔ［１～３］．Ｔｈｅｃｈａｏｔｉｃｍｏｔｉｏｎｉｓｒｅｇａｒｄｅｄａｓａｎａ...     

非线性函数的混沌优化方法比较研究

已有的混沌优化方法几乎都是利用Logistic映射作为混沌序列发生器，而Logistic映射产生的混沌序列的概率密度函数服从两头多、中间少的切比雪夫型分布，不利于搜索的效率和能力。为此，首先根据Logistie映射混沌轨道点密度函数的特点，建立改进的混沌-BFGS混合优化算法。之后，考虑到Kent映射混沌轨道点密度为均匀分布，建立了基于Kent映射的混沌-BFGS混合优化算法。然后对五种混合优化方法——不加改进的和改进的基于Logistic映射的混沌-BFGS法，基于Kent映射的混沌-BFGS法，Monte Carlo试验-BFGS法，网格-BFGS法进行了研究，分别对3个低维和2个高维非线性复杂测试函数进行优化计算，对它们的全局优化计算效率和寻优能力做了比较，并探讨了混合优化方法全局优化性能差异的原因。结果表明，混沌优化方法是与Monte Carlo方法类似的一种随机性试验优化方法。而且，这类优化方法的计算性能至少与以下因素有关：混沌／随机序列的统计性质，优化问题全局最优点位置。     

Analysis and control of a class of uncertain linear periodic discrete-time systems

Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.     

氧化锆增韧陶瓷与A95陶瓷抗侵彻性能对比实验研究

使用穿甲弹对两种陶瓷材料,10%氧化锆增韧陶瓷和A95陶瓷,开展了系列弹道实验研究。分析了各自的抗弹防护系数随射弹入射速度的变化规律,并分析了材料强度和韧性对其抗侵彻性能的影响。实验表明:两种陶瓷材料的质量防护系数都明显高于1,但在射弹入射速度为1000.0~1300m/s的范围内,A95陶瓷靶的抗侵彻能力高于增韧陶瓷的抗侵占能力。随着入射速度的提高,增韧陶瓷的抗侵彻能力提高的更快,并在某点出现转折入射速度以上,大约1300m/s,其与A95陶瓷的抗侵彻能力趋于相同,显示了增韧陶瓷在抗高速侵彻方面的适用性。     

结构设计中的混沌优化方法及其改进

在变尺度混沌优化方法研究中．结合结构优化问题的特点,提出了一种改进的混沌优化求解算法,用来解决带有多种约束条件的结构优化设计问题。在有限元分析和优化设计软件JEFIX中实现了上述算法．并通过数值算例讨论了变尺度混沌优化方法在结构优化中的可行性及存在的问题,得到了一些重要结论。     

混沌系统延迟反馈控制的理论与实验研究

综述了近年来控制混沌的延迟反馈控制技术------DFC控制的相关进展,总结了延迟反馈控制在不动点和不稳定周期轨道镇定方面的局限性和可控性研究的理论成果,介绍了延迟反馈控制在电子线路和磁弹性梁混沌控制方面的实验,并对延迟反馈控制技术未来的研究方向和发展前景进行了预测和展望。      

Erratum to: Parameter identification of electronic throttle using a hybrid optimization algorithm

Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach.