带有随机时滞的非线性网络控制系统的镇定

考虑了一类非线性离散系统的网络控制问题.通过齐次马尔可夫链描述采样器-控制器和控制器-执行器的时延,将网络控制系统建模为带跳非线性系统.利用Lyapunov方法和线性矩阵不等式技巧,得到了系统随机稳定的充分条件,并给出了镇定控制器的设计方法.数值例子的仿真结果验证了所得方法的有效性.     

基于脑电功率谱-连续隐马尔科夫链的精神疲劳分级模型

提取多通道脑电（EEG）功率谱特征,训练连续高斯密度混合隐马尔科夫模型（CHMM）,建立了基于功率谱-CHMM的精神疲劳分级模型.分级结果表明：EEG各节律功率谱及其比值是精神疲劳的敏感指标,CHMM对于不同的精神疲劳状态具有较高的分类精度,最高分类正确率达到97.5%;在训练样本相同的情况下,CHMM比反向传输人工神经网络具有更高的分类精度.     

一类快速非线性预测控制的分析与改进

针对仿射非线性系统,分析了一类快速预测控制算法稳态误差的来源,给出了误差的解析表达式.通过反馈校正消除稳态误差,提高了算法对模型失配的鲁棒性.对水箱液位控制系统的仿真和实验研究,结果验证了分析和改进的有效性.     

Nonlinear interactions between gravity waves and background winds

Using the nonlinear propagating gravity waves (GW) model in the two-dimensional compressible atmosphere and the linear GW theory, the process of GW propagation in different background winds, e.g. the direction of the background wind is opposite to (dead wind) or the same as (tail wind) the direction of the horizontal phase velocity of GW, is studied. The results show that the dead wind prolongs the vertical wavelength and accelerates GW propagation. Therefore, GW propagates up to a higher height becomes instable in a short time and eventually induces an inverse jet flow. Then, the vertical wavelength is becoming short due to the nonlinear interactions between GW and the inverse jet flow. The vertical wavelength and group velocity decrease after GW propagates into the tail wind. The initial instable time is delayed. Although most of GW is trapped in the instable region, some of GW propagates above the instable region. Compared with GW propagation in the tail wind, the nonlinear interactions between GW and the dead wind are also strong. In contrast, the linear GW theory predicts that GW can propagate freely in the dead wind. The vertical wavelength simulated by the nonlinear numerical model is different from that predicted by the linear theory greatly after GW propagates into the dead wind.     

Linear and third-order nonlinear optical properties for the heptamethine cyanine chromophore H-aggregates thin film

The thin film of a heptamethine cyanine chromophore HC was prepared by spin-coating technique. Its surface morphology and linear optical property were characterized by atomic force microscopy (AFM) and UV-visible absorption spectroscopy. The results show that HC molecules are arranged in a well-ordered H-aggregate type. The third-order nonlinear optical properties of the spin-coating film were also measured by degenerate four-wave mixing (DFWM) measurement. Enhanced third-order nonlinear susceptibility can be attributed to molecular aggregation effects, and the corresponding mechanism was dealt with by collective electronic oscillator (CEO) approach.     

一类非线性奇摄动方程的渐近解

讨论了一类二阶弱非线性常微分方程,利用Lindstedt-Poincare法,引入参量变换,消去形式解中出现的长期项,得到了解的一阶一致有效的渐近展开式.再用多重尺度法,引入多个变量尺度,把原常微分方程转化为几个相应的偏微分方程,再根据不出现长期项的原则,构造了解的渐近展开式.最后,比较了上述两种方法得到的解的展开式,得到了相同的结果.     

一类非线性抛物方程全离散Legendre拟谱逼近的大时间性态

运用Legendre拟谱方法研究一类非线性抛物方程的大时间问题,建立了全离散的拟谱格式.在有限时间区域及0≤t≤+∞上,讨论了半离散系统解的长时间误差估计.     

高阶非线性中立型微分方程的振动性

研究具有连续分布滞量的高阶非线性中立型微分方程x(t) ∑mi=1ci(t)x[τi(t)](n) x(t) ∑mi=1ci(t)x[τi(t)](n-1) ∫abF(t,ζ,x[g(t,ζ)])dσ(ζ)=0(其中t≥t0,n≥2为偶数)的振动性,获得了该类方程所有解振动的一些充分条件.     

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.     

基于流-固耦合的压裂裂缝形态影响因素分析

压裂裂缝形态易受储层物性、地应力、施工参数及压裂液黏度的影响.基于多孔介质流-固耦合的基本方程,根据损伤力学基本理论,利用cohesive黏结单元模拟压裂过程中裂缝起裂、扩展造成的损伤,以此建立水力压裂垂直裂缝扩展的三维有限元模型.模型可以对垂直缝扩展进行动态模拟,定量描述压裂过程中裂缝长度、高度、宽度.通过模拟发现:①储隔层弹性模量差值较小、施工排量过大、储隔层最小水平主应力差值较小均可能造成泥岩穿层,裂缝长度急剧下降,严重影响压裂效率;②渗透率对裂缝长度的影响最大,高弹性模量、低渗透的储层容易造长缝,但是高弹性模量、高渗透或高滤失的储层裂缝长度较短;③弹性模量对裂缝宽度的影响最大.