Stochastic analysis of strongly non-linear elastic impact system with Coulomb friction excited by white noise

The stochastic response of frictionally damped strongly non-linear elastic impact oscillator subjected to white noise excitation and its stochastic bifurcation are considered. By the stochastic averaging method based on generalized harmonic function, one can obtain the stationary probability density function of this system. The effects of system parameters on the responses are investigated and the analytical results were verified by comparing with numerical results from Monte Carlo simulations. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that the coefficient of friction, damping constant of the elastic impact force respectively, can be treated as bifurcation parameters.     

Saddle-node equilibrium points on the stability boundary of nonlinear autonomous dynamical systems

A complete characterization of the stability boundary of an asymptotically stable equilibrium point in the presence of type-k saddle-node non-hyperbolic equilibrium points, with k ≥ 0, on the stability boundary is developed in this paper. Under the transversality condition, it is shown that the stability boundary is composed of the stable manifolds of the hyperbolic equilibrium points on the stability boundary, the stable manifolds of type-0 saddle-node equilibrium points on the stability boundary and the stable centre and centre manifolds of the type-r saddle-node equilibrium points with r ≥ 1 on the stability boundary. This characterization is the first step to understanding the behaviour of stability regions and stability boundaries in the occurrence of saddle-node bifurcations on the stability boundary.     

二甲醚球形扩散火焰的熄火机理研究

采用改进的PREMIX模型及"化学爆炸模式分析(CEMA)"方法,对二甲醚(DME)球形扩散火焰的熄火机理进行数值诊断,分析环境氧气摩尔分数(X_(O_2))及详细基元反应对熄火极限的影响,利用"爆炸因子"和"分岔因子"的概念,确定控制DME球形扩散火焰熄火的关键反应动力学因素。结果表明:DME冷焰具有比热焰更宽的可燃范围;冷焰对X_(O_2)的敏感性弱很多,热焰中具有正特征值的CEM首次出现在最高温度处;在熄火极限附近,CEM的特征值变为虚数,说明熄火伴随着振荡;热焰的熄火主要由小分子所参与的高温反应所控制,而冷焰熄火主要由大分子所参与的低温反应所控制。     

二维反三角超混沌系统及其在图像加密上的应用

为了进一步提高混沌系统的混沌特性，为图像加密算法提供更可靠的混沌系统，增强图像加密算法的安全性，提出了一种基于二维反三角超混沌系统的新型图像加密算法。首先，在一维三角混沌函数的基础上构建了一个二维反三角超混沌系统，通过分岔图和Lyapunov指数等仿真实验，验证了该系统具有更广的混沌区间和更强随机性的迭代序列，遍历性更加优秀；然后，基于此混沌系统，采用"置乱-扩散"策略，根据不同密钥生成的不同超混沌序列，对图像矩阵进行无重复置乱和循环移位扩散，循环三次得到密文，完成加密过程；最后，对图像加密方案进行了直方图分析、密钥空间分析、相邻像素相关性分析、明文敏感性分析和信息熵分析等性能测试。其中密文图像的相关指标参数像素变化率（NPCR）和统一平均变化强度（UACI）的测试值非常接近于它们的理想期望值，信息熵的测试结果约为7.997，也非常接近于理想期望值8。实验结果表明，此图像加密系统具有更可靠的安全性，抵抗攻击能力强，在图像安全领域具有较好的应用前景。     

Two‐Parameter Continuation and Bifurcation Strategies for Oscillatory Behavior Elimination from a Zymomonas mobilis Fermentation System

Two‐parameter continuation and bifurcation analysis strategies were applied to deal with the oscillatory phenomena of a Zymomonas mobilis ethanol fermentation system. A structured verified non‐linear mathematical model considering the physiological limitations of microorganisms for a single continuous fermenter for ethanol production using Z. mobilis was built to identify the Hopf bifurcation (HB) points, which indicate the oscillatory behavior, using the inlet substrate concentration and the dilution rate as bifurcation parameters. The path of the HB points can be determined with different controlling operating parameters. It was found that with the addition of a small amount of cells or ethanol to the feed stream or by increasing the dilution rate, the oscillations could be eliminated and steady‐state behavior was attained. Using a two‐parameter continuation strategy, the Z. mobilis fermentation system could operate at steady state without oscillatory behavior.     

方腔内耦合传热传质非对称流动数值模拟

对带有质热源的方腔内流体传热传质进行数值研究。针对不同Ra、Nc、Sr和Df，探究对称方腔内流体传热传质的分岔特性。结果表明：存在临界Ra_c使流体流动形态发生转变，当Ra<Ra_c时，流体流线、温度场和浓度场对称分布；当Ra>Ra_c时，流体发生偏斜。增大浮升力，流体更易发生分岔现象。增强Soret和Dufour效应可增强传热对称性并增大流体发生分岔的临界Rayleigh数。     

断裂顶板锚拉支架支护系统的分叉行为

应用弹性系统稳定性理论对断裂顶板－锚拉支架系统建立了动力系统稳定性分析的力学模型．对该模型分别考虑因块ＡＢ（或ＢＣ）沿对角线变形和支座处的水平变形引起的稳定性进行了求解；讨论了解曲线即平衡路径的稳定性及系统的静态分叉特征；进而分析了断裂顶板结构的运动失稳机制，并给出了该系统的运动稳定条件，证实了借助当代非线性科学研究岩土工程问题的必要性和理论意义．     

真三维应力状态下土体应变局部化的非共轴理论

判别土体应变局部化的产生条件强烈依赖于土体塑性流动的非共轴特性。本文分析表明,由于传统的非共轴塑性理论是基于二维共轴应力空间得到的,为此,本文基于三维共轴应力空间建立了三维非共轴塑性理论框架,并利用三维非共轴塑性理论预测土体的变形分叉状态。数值模拟与试验结果对比分析表明,传统的本构模型有必要引入非共轴塑性流动理论才能有效地提高模型预测土体变形分叉特性的能力。研究表明:针对平面应变状态的变形分叉问题,由于考虑了应力第三不变量对非共轴性的影响,三维非共轴理论预测结果比二维非共轴理论更为合理。     

土体变形分叉的非共轴理论

土体的变形分叉特性强烈依赖于土体的本构模型。由于传统的本构理论隐含了应力和塑性应变率的共轴条件,从而基于传统本构模型的变形分叉理论不能准确地预测土体变形分叉的失稳状态。由此引入本构模型的非共轴理论来分析土体变形分叉的失稳现象。通过与共轴的本构理论进行对比分析,研究结果表明,采用非共轴理论的本构模型能够合理地判别土体的失稳状态,理论预测剪切带的倾角随围压增大而减小的变化规律也与试验结果一致。     

开孔薄板过屈曲分析的边界元法

从开孔薄板大挠度问题的一般数学理论出发．建立了一组新型边界积分方程用以求解开孔薄板的临界载荷、过屈曲分析。并且从分支理论出发，对离散的边界积分方程进行了分析和求解。通过算例．计算了环形板在中面内受均匀推力．横向为简支、夹紧情况下的屈曲载荷以及过屈曲状态。与已知结果吻合良好．证明边界元法对开孔薄板后屈曲状态的分析是有效的。与区域型解法比较．具有处理的矩阵维数少．输入数据量少．计算时间短等优点。