Synthesis and optical properties of polyacetylenes containing nonlinear optical chromophores

High molecular weight polyacetylenes bearing nonlinear chromophoric pendants poly[4-ethynyl-4′-(N,N-diethylamino)azobenzene-co-phenylacetylene]s [poly(EAAB-co-PA)s] were synthesized in moderate yields by [Rh(nbd)Cl]₂-Et₃N. The azo unit in the copolymers can be effectively controlled by the monomer feed ratio. Whereas the homopolymer of EAAB possessed low solubility, all the copolymers, however, dissolved readily in common organic solvents when the poly(EAAB) molar content was less than 41.7%. The structures and properties of the polymers were characterized and evaluated by UV, NMR, optical limiting, and nonlinear optical analyses. All the copolymers possessed high stereoregularity and thermal stability (≥300 °C). They can attenuate intense laser pulses, with solutions of high concentrations showing better performances. The third-order nonlinear susceptibility of the copolymers was as high as 4.62×10⁻¹¹ esu, which are two orders of magnitude larger than those of poly(PA), and larger than that of poly(N-carbazoylacetylene), and poly(1-naphthylacetylene).     

基于优进策略的遗传算法对重油热解模型参数的估计

针对常规遗传算法全局寻优效率偏低的弱点，提出了一种优进策略，用以改进常规遗传算法。该策略将从繁衍过程中获取进化信息，自适应地改进子代分布，适时引入确定性操作，以提高全局寻优性能。提出的相关技术包括维持种群的多样性、改进交叉算子、增加Powell寻优算子等。实例测试表明这种优进策略效果良好，并已成功地应用于重油热解三集总动力学复杂数学模型的非线性参数估计。     

The effective diffusivities in porous media with and without nonlinear reactions

The question of whether effective diffusivities in porous materials under reactive and nonreactive conditions are equal is addressed. Previous studies had considered the problem with first-order reactions. We study the issue with two nonlinear reactions—a second-order reaction and one governed by the Michaelis-Menten kinetics. Pore network and continuum models of porous media are utilized to estimate the effective diffusivities under reactive and nonreactive conditions. We show that the two effective diffusivities are significantly different. The difference is due to the heterogeneities of the porous material, and the fluctuations that they cause in the spatially varying local concentrations and diffusivities, and can be as large as a few orders of magnitude. Theoretical analysis of diffusion and reactions in porous media is also presented that supports the results of the simulations. In particular, it is shown that the results of pore network simulations cannot be fitted to the classical continuum equation of diffusion and reaction, and that a more complex continuum equation should be used for this purpose.     

GRIP管混凝土组合结构压弯构件非线性全过程分析

本文应用细观力学、经典层板理论、平截面假定、FRP约束混凝土本构模型及数值积分对GFRP管混凝土组合结构压弯构件进行了非线性全过程分析。通过理论计算发现GFRP管混凝土组合结构能有效地提高构件的承载力，且构件具有良好的变形能力。FRP壳体参与承载且有效地约束混凝土的变形，显著提高核心混凝土强度和变形能力。文中讨论了轴压比、长细比、径厚比、混凝土强度等级、纵筋配筋率、铺层角变化对极限水平荷载和极限水平位移的影响，从而得到了一些有益的结论。     

广义线性模型与非线性模型参数的统计推断

概述了广义线性模型(含半参数广义线性模型)与非线性模型研究的新进展,着重讨论了它们参数估计的统计推断。近年来,广义线性模型与非线性模型的研究发展迅速,有着广泛的应用前景。     

Non-existence of finite-time stable equilibria in fractional-order nonlinear systems

We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems.     

Consistent hierarchical economic NMPC for a class of hybrid systems using neighboring-extremal updates

A hierarchical two-layer control algorithm is developed for a class of hybrid (discrete-continuous dynamic) systems to support economically optimal operation of batch or continuous processes with a predefined production schedule. For this class of hybrid systems, the optimal control moves as well as the controlled switching times between two adjacent modes are determined online. In contrast to closely related schemes for integrated scheduling and control, the sequence of modes is not optimized. On the upper layer, the economic optimal control problem is solved rigorously by a slow hybrid economic model predictive controller at a low sampling rate. On the lower layer, a fast hybrid neighboring-extremal controller is based on the same economic optimal control problem as the slow controller to ensure consistency between both layers. The fast neighboring-extremal controller updates rather than tracks the optimal trajectories from the upper layer to account for disturbances. Consequently, the fast controller steers the process to its operational bounds under disturbances and the economic potential of the process is exploited anytime. The suggested two-layer control algorithm provides fully consistent control action on the fast and slow time-scale and thus avoids performance degradation and even infeasibilities which are commonly encountered if inconsistent optimal control problems are formulated and solved.     

Fast economic model predictive control based on NLP-sensitivities

This study adapts the advanced step NMPC framework to Economic NMPC. Here, sufficient conditions for nominal stability are derived for NMPC controllers that incorporate economic stage costs with appropriate regularization. To guarantee these conditions, we derive a constructive strategy to calculate the regularization term directly. Moreover, we extend the sensitivity components in the advanced step NMPC framework to consider a rigorous path-following algorithm. This approach accounts for active set changes and allows much weaker constraint qualifications. Moreover, using an ℓ₁ formulation of the NMPC problem satisfies these constraint qualifications and allows more reliable solution of the moving horizon optimization problem, even in the presence of noise. Finally, all of these concepts are demonstrated on a detailed case study with a continuously stirred tank reactor.     

无约束非线性lp问题的区间极大熵方法

针对信号处理、系统识别等领域中涉及到的无约束非线性lp问题,为减小由于二进制编码的舍入误差对该问题计算结果的影响,对求解该问题的极大熵方法进行了区间扩张.证明了区间扩张后的极大熵函数至少具有二阶收敛性,并设计了具有多项式时间复杂度的区间算法进行求解,举例进行了数值计算.数值计算结果显示,该区间算法可靠,计算结果与区间扩张前相比,结果更加精确.