周期场中片状束输运的分叉与混沌行为

强流技术的基本问题之一是它的空间电荷和束流的稳定性。利用片状束在周期场中的聚焦和输运可将问题减至最小。引入非线性和运动阻尼,在经典物理框架内,把周期场中片状束的冷腔运动方程化为广义的Mathieu方程。利用Melnikov方法分析了系统的次谐分叉和Smale马蹄混沌;并对系统的临界条件进行了讨论。结果表明,系统稳定性与它的参数有关,只需适当调节参数原则上可以保证系统的稳定性。     

基于改进Duffing理论的轴承微弱故障信号判断

分析了传统Duffing振子混沌系统的基本理论对检测微弱信号的不足,给出了基于改进之后的Duffing振子检测微弱信号的新方法。改进后的方法能够弥补传统方法对系统固有频率的限制,检测具有较大固有频率的微弱信号。本文主要利用传统方法和改进方法分别对轴承外圈故障信号进行验证性分析,发现改进方法能更好的找出微弱故障信号。通过对仿真信号分析和轴承故障诊断实验,结果验证了本文方法的有效性。     

一种新型离散指数混沌映射的实现及其研究

针对Logistic映射参数简单、混沌区间范围小的缺点,提出一种新型的离散指数混沌映射。通过引入指数项和增加参数个数,进而扩大映射的混沌区间。利用常规的动力学分析方法,对指数混沌映射进行了动力学特性分析,包括Lyapunov指数图、分岔图等。在此基础上,对Logistic映射和离散指数混沌映射进行了特性比较。最后对由该离散混沌映射产生的序列进行NIST测试,测试结果表明序列性能更良好。     

Error estimation in a stochastic finite element method in electrokinetics

Input data to a numerical model are not necessarily well known. Uncertainties may exist both in material properties and in the geometry of the device. They can be due, for instance, to ageing or imperfections in the manufacturing process. Input data can be modelled as random variables leading to a stochastic model. In electromagnetism, this leads to solution of a stochastic partial differential equation system. The solution can be approximated by a linear combination of basis functions rising from the tensorial product of the basis functions used to discretize the space (nodal shape function for example) and basis functions used to discretize the random dimension (a polynomial chaos expansion for example). Some methods (SSFEM, collocation) have been proposed in the literature to calculate such approximation. The issue is then how to compare the different approaches in an objective way. One solution is to use an appropriate a posteriori numerical error estimator. In this paper, we present an error estimator based on the constitutive relation error in electrokinetics, which allows the calculation of the distance between an average solution and the unknown exact solution. The method of calculation of the error is detailed in this paper from two solutions that satisfy the two equilibrium equations. In an example, we compare two different approximations (Legendre and Hermite polynomial chaos expansions) for the random dimension using the proposed error estimator. In addition, we show how to choose the appropriate order for the polynomial chaos expansion for the proposed error estimator. Copyright © 2009 John Wiley & Sons, Ltd.     

Identification of composite uncertain material parameters from experimental modal data

Stochastic analysis of structures using probability methods requires the statistical knowledge of uncertain material parameters. This is often quite easier to identify these statistics indirectly from structure response by solving an inverse stochastic problem. In this paper, a robust and efficient inverse stochastic method based on the non-sampling generalized polynomial chaos method is presented for identifying uncertain elastic parameters from experimental modal data. A data set on natural frequencies is collected from experimental modal analysis for sample orthotropic plates. The Pearson model is used to identify the distribution functions of the measured natural frequencies. This realization is then employed to construct the random orthogonal basis for each vibration mode. The uncertain parameters are represented by polynomial chaos expansions with unknown coefficients and the same random orthogonal basis as the vibration modes. The coefficients are identified via a stochastic inverse problem. The results show good agreement with experimental data.     

Pyragas stabilizability via delayed feedback with periodic control gain

In this paper for the unstable periodic solution of nonlinear differential equation, Pyragas stabilizability problem is studied. An algorithm of stabilization via periodical delayed feedback is obtained. The consideration is based on the theory of nonstationary stabilization.     

Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules

We develop a nonlinear dynamic Cournot duopoly model in discrete time, where two bounded rational quantity-setting firms, both endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. One of the two competing firms adopts best-reply behaviour, whereas the other adjusts its production according to the gradient of its profit. Although excessive reaction of the latter firm generally results in destabilization of the ‘Cournot–Nash’ equilibrium and brings about complex dynamic scenarios, this occurs via qualitatively different bifurcation routes, depending on the ratio between firms’ marginal costs. The paper also provides a preliminary exploration of the long-run sustainability of the heterogeneous duopoly competition, by investigating numerically the impact of fixed costs on firms’ survival, along different output trajectories.     

Efficient stochastic structural analysis using Guyan reduction

This paper introduces the application of the Guyan reduction within the stochastic finite element (SFE) analysis, which employs a Galerkin-based Polynomial chaos (P-C) expansion formulation. It is shown that by reducing the size of the deterministic FE model, a substantial improvement in the overall computational efficiency can be achieved. An implementation exploiting the features of the proposed formulation is presented. In this regard, especially the interaction with the 3rd party FE solvers has been addressed. The suggested method has been tested on a simple grid structure and also on a large building model, where the accuracy and efficiency of the introduced approach have been quantified.     

Shil’nikov chaos in the oxidation of formic acid with bismuth ion on Pt ring electrode

We report experimental observations of potential oscillations in electrocatalytic oxidation of formic acid with bismuth ion on the Pt ring electrode. Potential oscillations were investigated under galvanostatic conditions. The presence of bismuth ion enables to get the low and stable potential values at larger current range. Periodic and Shil’nikov chaotic potential oscillations were observed at fixed current. To extract information from the oscillation pattern, we used time series, reconstructed attractor, next-maximum map, pattern formation of interfacial potential above ring electrode.     

Complicated motion of particles on vibration screen surface

lINTRODUCTIONToday,them0tiontheoryofparticlesonscreensurfaceisanimp0rtantresearchdirectionofscreeningtechn0logyandtheory['~8].Bymeansofstudyingmotionregularityofparticles,wecanobtaintheoptimumkineticparametersfortheindustrialscreeningandraiseitsefficien-cy.Thematerialbeingscreenedhasvariableshapeandsize,withdifferentsurfacemoistureandclaymineralscontents.Themotionofparti-clesisaffectedbydisplacement,velocity,accel-erationofscreensurfaceandfrictionamongpar-ticles.S0theparticles'motiononscr…