Selkov模型不同扩散和流速下非Turing不稳定化学反应机制

建立了Selkov模型中间反应物具有不同扩散和不同流速条件下的反应-扩散-流动方程,理论分析了非Turing不稳定形成的条件,求得其参数区间,对Andresen的结论作了拓展.研究还发现,在振荡Hopf区域之外,静止波动(空间周期结构FDS)仍然可以存在.因而,此结构存在的参数空间大于Andresen的结果.同时,还将此种不稳定参数区间与Turing不稳定和差速流动引起不稳定(DIFI)的结果进行了比较,结果发现静态FDS值总是处于DIFI临界曲线相应的最小值之上,这表明动力学机制是由DIFI不稳定造成的,DIFI不稳定区是产生静止波FDS不稳定结构的必要条件.     

多定态转变化学反应体系与环境传热-扩散耦合导致的环面型化学振荡

以Schlögl模型作为多定态转变化学反应体系的范例, 研究了通过传热及扩散与环境耦合的多定态转变化学反应体系中诱发的新动力学行为, 其中特别重要的是沿慢变量方向的环面型化学振荡的出现. 建立了慢流型上的准定态的线形化稳定性分析法, 揭示了由极限环振荡蜕变为环面型振荡的动力学机制, 不同于小寄生参数存在引起的非连续极限环振荡. 通过以慢流型上准定态稳定性分区为基础的定性分析, 进一步揭示了该类体系中可能出现间歇性、反复持续式和骤发式3种亚类环面振荡. 最后以第三亚类作为示例, 以相应的计算机模拟证实理论分析的正确性.     

苯的振动量子能级的非线性量子理论计算

用最近发展起来的非线性量子学的定态本征方程的理论去计算蒸气和液体的苯（Ｃ６Ｈ６）和重苯（Ｃ６Ｄ６）的ＣＨ和ＣＤ键的振动所产生的量子能态，同时用非线性简并微扰理论计算在弱色散极限下苯的稳定的能态劈裂，得到较为满意的结果。     

铂电极BZ反应系双电层稀疏区中的Turing结构

将扩散流作为场函数, 考虑φ电势的空间分布, 建立了铂电极BZ反应系在双电层稀疏区的动力学演化机制, 确立了纳入稀疏区φ电势效应的反应-扩散型演化方程. 采用Boltzmann分布近似, 解决了演化方程中含φ电势的流项的线性化问题; 导出了可在算法上实现的三变量体系线性化算子本征值的解析形式. 分别以静态铂电极BZ反应系双电层稀疏区和对应的纯粹BZ反应系作为参考模型系, 分析了经空间对称性破缺产生Turing结构的参数范围. 数值模拟发现, φ电场的存在使铂电极BZ反应系的输运过程在静态双电层稀疏区趋于电化学平衡时, 在对应的纯粹BZ反应体系中可呈现的Turing结构已趋于消失; 而在电流强度不太大的恒流不可逆铂电极BZ反应体系双电层稀疏区中, 鲜明稳定的Turing结构又重新出现在原参数区间内. 同时, 在静态双电层稀疏区不出现Turing结构的参数范围内也可找到类似的恒流稳定空间结构.     

铜电极阳极溶解过程恒电位电流振荡的动力学模型

研究了铜电极在酸性氯化钠溶液中的恒电位电流振荡行为,分析了电极过程中的非线性步骤及电化学耦合因素,提出了一个可能的电极过程动力学模型,并借助线性稳定性分析及分支分析得到了参数坐标空间中的动力学行为区域图。在此基础上,将极化曲线视为稳定非平衡定态区态函（电流）与外控参数（电位）的关系,同时将恒电位电流振荡模拟为稳定极限环振荡,分别计算出了极化曲线与时间－电流振荡曲线,其结果与实验数据相符,表明该类电     

Benesi-Hildebrand方程的正确性与可靠性

Benesi-Hildebrand(B-H)方程现被广泛地应用于各种非键作用体系, 特别是作用比为1:1型和1:2型的体系. 该方程可以用来确定作用体系的平衡常数以及作用比. 通过计算机模拟, 发现在某些情况下, 对于1:2型的作用体系, B-H方程会给出错误的作用比信息. 无论是弱的作用体系还是强的作用体系, 都可能会出现1:1的B-H方程曲线呈现出线性, 同时(或者)1:2的B-H方程曲线呈现出非线性的情况. 此外, 本文还研究了体系中两种作用物质的初态浓度比对于1:1型作用的平衡常数计算的影响, 发现最小的初态浓度比(r0)等于100是可以确保B-H方程近似条件C0B≈CB成立的安全阈值. 当作用很弱的时候, 比如说作用的平衡常数K小于25 L·mol-1 (C0P=4×10-4 mol·L-1)时, 则不需要对最小初态浓度比值r0进行限制, 就可以满足B-H方程的近似条件. 通过计算机模拟还分析了文献中提出的两个边界条件. 研究表明1/(KC0P)≥10可以保证处于平衡状态时的CB/C0B≥0.91. 而另一个条件KC0B>0.1 并不是确保B-H方程近似条件成立的充分条件.     

受高斯白噪声影响的有限化学反应体系的随机热力学——外噪声对化学反应体系影响的有效热力学量度

通过分析噪声对跃迁概率的不同影响,借助Novikov定理及MSR理论,建立了受多源白噪声影响的有限化学反应体系的有效主方程及有效熵平衡方程,导出非平衡定态时这类噪声体系熵产生的一般表达式,揭示涨落熵产生的统计内涵及噪声贡献,并针对非宏观量级的外噪声,借助扰动按分布参数分离法及有效主方程的Kramers-Moyal展开,进一步对简单加合性噪声建立了非平衡定态宏观稳定性判据的随机模拟,论证了噪声对化学反应体系定态稳定性的弱化作用.     

不对称五氮齿镉和铟大环配合物的激发态性能研究

本文研究了不对称五氮齿镉和铟大环配合物的激发态性能及其光稳定性。结果表明:它们的三重态能量在120kJ/mol左右,最低激发三重态敏化产生单重态氧的量子产率在0.6～0.9,它们的分子一阶超极化率在～10^-28esu,在光照的条件下,配合物Ⅰ相当稳定,而配合Ⅱ则形成不稳定化合物导致光褪色。     

RuB-PVP胶态催化剂的制备及苯选择加氢性能研究

系统研究了制备时间、Ru/PVP(聚乙烯吡咯烷酮)比及钌浓度对PVP稳定的RuB胶态催化剂粒径及分布的影响; 制备了粒径在1.3～3.9 nm的RuB-PVP催化剂, 研究了不同粒径的催化剂对苯选择加氢反应的影响. 结果表明RuB粒径越小, 催化剂的苯选择加氢性能越好. 在粒径为1.3 nm的RuB-PVP催化剂上, 环己烯得率达到16.8%. 在无机添加剂ZnSO₄的存在下, 环己烯得率可进一步提高至23.2%. 在相同实验条件下, 无PVP稳定的RuB催化剂上的苯选择加氢性能则远低于RuB-PVP胶态催化剂.     

苯醚甲环唑在芹菜及其土壤中的残留测定和消解动态研究

采用气相色谱-电子捕获检测, 对芹菜及其土壤中的苯醚甲环唑消解动态和最终残留量进行了研究, 评价了苯醚甲环唑在芹菜上使用后的残留行为和环境安全性. 苯醚甲环唑在芹菜及土壤中的残留消解动态均符合一级动力学方程, 苯醚甲环唑在芹菜上消解快; 苯醚甲环唑最终残留量与施药的剂量、施药次数及采样的间隔时间有关; 水解研究表明, 苯醚甲环唑是稳定的农药, 在不同温度和不同pH的研究条件下水解半衰期均大于166 d, 碱性条件更有利于苯醚甲环唑的降解.     

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.     

Spontaneous Formation of Microgroove Arrays on the Surface of p‐Type Porous Silicon Induced by a Turing Instability in Electrochemical Dissolution

Self‐organization plays an imperative role in recent materials science. Highly tunable, periodic structures based on dynamic self‐organization at micrometer scales have proven difficult to design, but are desired for the further development of micropatterning. In the present study, we report a microgroove array that spontaneously forms on a p‐type silicon surface during its electrodissolution. Our detailed experimental results suggest that the instability can be classified as Turing instability. The characteristic scale of the Turing‐type pattern is small compared to self‐organized patterns caused by the Turing instabilities reported so far. The mechanism for the miniaturization of self‐organized patterns is strongly related to the semiconducting property of silicon electrodes as well as the dynamics of their surface chemistry.     

Superlattice patterns and spatial instability induced by delay feedback

Various oscillatory superlattice patterns in a reaction-diffusion system are observed by means of delay feedback (DF) in the parametric domain where the system without DF displays uniform bulk oscillation. By varying DF parameters within an appropriate range, the system undergoes transitions to oscillatory hexagons, stripes and squares, and square superlattices with different wavenumbers are also obtained. Linear stability analysis reveals that the patterns do not result from the Turing instability and a possible mechanism of pattern formation is suggested and proved analytically: DF induces instability of a homogeneous limit cycle with respect to spatial perturbations even if the Turing instability does not occur, so that oscillatory patterns possessing the corresponding spatial modes are produced. The different behavior of the dominant characteristic multiplier seems to be connected to the pattern selection. Here it is clearly demonstrated that DF can play a destabilizing role in spatially extended system instead of stabilizing the periodic orbits or turbulent states, which most earlier works have usually focused on.     

糖酵解模型双曲型反应-扩散方程的非线性行为

The Stability and chemical oscillation of the hyperbolic reaction-diffusion equations for glycolysis model are studied and compared with that of the corresponding parabolic equations. The results show that the parabolic equation is the limiting case of the hyperbolic system when the reaction-diffusion number Nrd →∞, and that the divergence of the wave speed, which exists in the parabolic system, does not appear in the hyperbolic one. The stabilities of these two systems are significantly different. The hyperbolic system may exist in chaos state under certain conditions. It is shown that the hyperbolic system is more suitatle to be used as the model for studying chemical oscillations.     

A graph-theoretic method for detecting potential Turing bifurcations

The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Modeling (Nauka, Moscow, 1987) (in Russian), p. 57] for Turing instabilities in a mass-action reaction-diffusion system involving n substances. The method is based on the representation of a reaction mechanism as a bipartite graph with two types of nodes representing chemical species and reactions, respectively. The condition for diffusion-driven instability is related to the existence of a structure in the graph known as a critical fragment. The technique is illustrated using a substrate-inhibited bifunctional enzyme mechanism which involves seven chemical species.     

Turing pattern amplitude equation for a model glycolytic reaction-diffusion system

For a reaction-diffusion system of glycolytic oscillations containing analytical steady state solution in complicated algebraic form, Turing instability condition and the critical wavenumber at the Turing bifurcation point, have been derived by a linear stability analysis. In the framework of a weakly nonlinear theory, these relations have been subsequently used to derive an amplitude equation, which interprets the structural transitions and stability of various forms of Turing structures. Amplitude equation also conforms to the expectation that time-invariant amplitudes are independent of complexing reaction with the activator species.     

Formation and control of Turing patterns and phase fronts in photonics and chemistry

We review the main mechanisms for the formation of regular spatial structures (Turing patterns) and phase fronts in photonics and chemistry driven by either diffraction or diffusion. We first demonstrate that the so-called ‘off-resonance’ mechanism leading to regular patterns in photonics is a Turing instability. We then show that negative feedback techniques for the control of photonic patterns based on Fourier transforms can be extended and applied to chemical experiments. The dynamics of phase fronts leading to locked lines and spots are also presented to outline analogies and differences in the study of complex systems in these two scientific disciplines.     

Mobility-induced instability and pattern formation in a reaction-diffusion system

Ions undergoing a reaction-diffusion process are susceptible to electric field. We show that a constant external field may induce a kind of instability on the state stabilized by diffusion in a reaction-diffusion system giving rise to formation of pattern even when the diffusion coefficients of the reactants are equal. The origin of the pattern is due to the difference in mobilities of the two species and is thus markedly different from that of deformed Turing pattern in presence of the field. While this differential flow instability had been shown earlier to result in traveling waves, we realize in the context of stationary pattern formation in a typical reaction-diffusion-advective system. Our analysis is based on a numerical simulation of a generic model on a two-dimensional domain.     

Analysis of a model scheme incorporating reactant inhibition: Instability of homogeneous solution and formation of spatio–temporal structures

A model scheme incorporating reactant inhibition in the rate process has been analyzed with a view to study the instability of homogeneous solution due to diffusion. Conditions for the occurrence of Turing as well as phase instability are derived and show the existence of multiplicity in the parameter space. The Ginzburg-Landau equation for the system is developed and solved numerically in various regions of the parameter space. The simple model system shows the existence of very rich behavior including normal and inverted bifurcations in the super and subcritical regimes. The various results are analyzed and discussed. © 1993 John Wiley & Sons, Inc.