Nucleation theory for a model bistable chemical reaction

The theory of homogeneous nucleation is developed for a model nonlinear bistable chemical reaction driven far from equilibrium (trimolecular Schlögl model). The theory is restricted to the vicinity of the stable/unstable transition, where the nucleation barrier is small but nonvanishing. The nucleation rates are derived for two types of fluctuations: first, fluctuations due to a homogeneous external white noise source, and second, internal chemical fluctuations, described by a reastion-diffusion multivariate master equation. In the white noise case, a Landau-Ginzburg potential can be defined, and the standard nucleation formalism can be applied; this is not true for the internal case and a new result is used. The inhomogeneous chemical fluctuations, due to the coupling between the nonlinear reaction and diffusion, are shown to have an influence on the nucleation rate. Quantitative conditions are also given to evaluate the possibility of homogeneous nucleation in nonlinear chemical systems.     

非线性吸收诱导掺镱光纤激光器中的光学双稳

研究了在掺镱光纤激光器中观察到的光学双稳态现象.激光信号光和驻留泵浦光的双稳特性来源于激光器在小信号和增益饱和两种情况下,掺镱光纤对信号的非线性吸收导致的激光器内腔非线性损耗.同时分析了把泵浦光中的光学双稳行为通过分叉的腔结构扩展到切换式双波长光纤激光器的可行性.     

Selective tunnelling effects in collinear chemical reactions

Summary Tunnelling contributions to the reactive probability of both early- and late-barrier reactions are investigated. For the first class of reactions a new type of tunnelling effect taking place at high translational energy is discussed. For both reactions relations linking tunnelling features to the type of energy promoting reactivity are discussed with regard to the barrier location.

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Riassunto Si esamina il contributo dell'effetto tunnel alla probabilità reattiva per reazioni con barriera anticipata e con barriera posticipata. Per la prima classe di reazioni si discute un nuovo tipo di effetto tunnel che ha luogo ad alte energie traslazionali. Per ambedue i tipi di reazione si discute il nesso esistente tra le caratteristiche dell'effetto tunnel e la forma di energia che è capace di favorire la reazione in relazione alla posizione della barriera.

     

Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers

Switching between the bistable soliton states in a doubly and inhomogeneously doped fiber system is studied numerically. Both the cases of lossless as well as lossy couplers are considered. It is shown that both up-switching (from the low state to the high state) and down-switching (from the high state to the low state) of solitons between bistable states are realizable, if the amplification of the input soliton for up-switching and the extraction of energy from it for down-switching are suitably adjusted.     

色噪声对光学双稳态的影响

采用统一色噪声近似构建了由乘法色噪声驱动的纯吸收型光学双稳态状态方程,并分析了色噪声对光学双稳态的影响,将结果与白噪声驱动的光学双稳态进行比较.结果表明:当乘法噪声与加法噪声处在正关联时,增加乘法色噪声的自关联时间r,光学双稳性的区域显著变宽,即磁滞回线面积变大;当乘法噪声与加法噪声处在负关联时,只有乘法噪声较小时,改变乘法色噪声的自关联时间r,光学双稳态才发生改变;当乘法噪声的自相关时间等于零时,本文模型退化为乘法白噪声驱动的光学双稳性状态方程.     

Frequency dependence of microwave-assisted electron-transfer chemical reactions

In this paper, the electron transfer reactions in the microwave field are studied. A classical theory is developed for a mix of reagents and polar frequency-dispersive and lossy solvent filling vessels excited by microwaves. These reactors are described by a system of non-linear partial self-consistent differential equations for non-stationary microwave field, heat and liquid dynamics, and chemical molecular kinetics. A particular solution of this system is considered for the isothermic electron-transfer reactions in the microwave field varying its frequency with the calculation of the normalised Marcus rate coefficient. It is found that for the small normalised reaction free energy, the chemical reactions are supported by microwaves in a wide frequency band with an increased value of the exponent in the Marcus rate coefficient. At higher values of this energy, these reactions are driven only by conventional microwave heating. The restrictions for the given theory are reviewed, and further experimental and semi-classical and quantum-mechanical studies are found essential for practical applications of these findings.     

The polarization of chemical reactions

Microwaves have been widely used in organic chemical syntheses, but the mechanism is still unclear. The aim of this paper is to study the polarization of polar molecule reactions in the liquid phase. A novel model is proposed to describe the polarization of chemical reactions. In this model, the polarization is expressed by the summation of the orientational polarization of the liquid mixture and the polarization increment due to the chemical process. On the basis of the assumption of local equilibrium, the chemical process is divided into a series of equilibrium systems. We derive the general expression for the polarization increment according to the mass balance equations. By considering a simple chemical process, we give a specific expression for the polarization. Copyright © 2015 John Wiley & Sons, Ltd.     

A class of collision processes with memory and application to simple chemical reactions in a solvent

We apply the general formalism of a class of non-Markovian processes which we have studied elsewhere to three simple models of chemical reactions: dissociation, isomerization, and diffusion in a double-well potential. Our method leads to explicitly solvable models and numerical computations. The results are in agreement with numerical simulation and stochastic dynamics studies of other authors.     

含负折射率介质非线性Bragg腔的双稳态特性

研究了含负折射率介质一维光子晶体非线性Bragg腔的透射特性、光学增强和双稳态特性.对负折射率介质无色散和有色散非线性Bragg腔及由两种正折射率介质构成的非线性Bragg腔的透射谱、光学增强、缺陷模的线宽、入射光的红移量、双稳态开关阈值进行了比较.含负折射率介质的非线性Bragg腔可显著增大腔内光学增强效应,降低缺陷模的线宽、入射光的红移量和双稳态开关阈值.     

The elimination of fast variables in complex chemical reactions. I. Macroscopic level

The kinetics of complex chemical reactions is considered. Different time scales exist if one or more of the rate constants of the individual reaction steps is much larger than the others. Examples of specific reactions are given in which the intermediates vary on the fast time scale. They can be eliminated according to a standard scheme, the lowest order of which coincides with the steady-state approximation usually employed in textbooks on chemical kinetics.     

Diffusion-influenced reactions

We summarize three of our recent results on diffusion-influenced reactions in solutions. All deal with the concentration dependence of the reaction rate when the reactants must first diffuse together before reaction can occur. When one species (the sink species) is not dilute, the rate cannot be obtained by solution of a pair diffusion equation; the correlations among the sinks for the diffusing species must be accounted for. First, we consider fluorescence quenching when the quenchers are not dilute. For charged quenchers and fluorophores we discuss how the solution dielectric constant and ionic strength can strongly influence the deviations from the linear Stern-Volmer behavior (the dilute sink result) which arise due to the sink correlations. Second, we consider heterogeneous catalysis where a reactive species is adsorbed onto a surface and must surface diffuse to reactive sites (the sinks). We find that surface diffusion can be an important factor contributing to the rate of reaction; especially when surface diffusion is rapid relative to the adsorption/desorption rate. Third, we discuss diffusion influenced reactions with sinks which are long ellipsoids. Dilute long ellipsoids provide a large rate enhancement relative to a spherical sink; we show that this rate enhancement survives when nondilute ellipsoids are considered.     

Correlations in stochastic theories of chemical reactions

A comprehensive study of correlations in linear and nonlinear chemical reactions is presented using coupled chemical and diffusion master equations. As a consequence of including correlations in linear reactions the approach to the steady-state Poisson distribution from an initial non-Poissonian distribution is given by a power law rather than the exponential predicted by neglecting correlations. In nonlinear reactions we show that a steadystate Poisson distribution is achieved in small volumes, whereas in large volumes a non-Poissonian distribution is built up via the correlation. The spatial correlation function is calculated for two examples, one which exhibits an instability, the other which exhibits a second-order phase transition, and correlation length and correlation time are calculated and shown to become infinite as the critical point is approached. The critical exponents are found to be classical.     

Bistable Optically Writable Image Memory Using Optical Feedback

A novel, parallel aligned optically addressed liquid crystal spatial light modulator has been used to implement an optically writable image memory. The memory uses a two-beam interferometer with optical feedback which exhibits thresholding, hysteresis, and bistability. We discuss the characteristics of the system, and present the results of an experimental demonstration.Presented at the International Commission for Optics Topical Meeting, Kyoto, 1994.     

Mechanism and nonlinear dynamics of an oscillating chemical reaction

A mechanism and a model of a ferroin-catalyzed oscillating chemical system are descrined. This reaction presents an excellent example of a far-from-equilibrium system that forms spatial and temporal dissipative structures. The model shows that while the well-stirred system has a unique and stable stationary state, the same reagent spread in a thin layer may form complex spatiotemporal paterns. Stationary periodic patterns of both small and large amplitude, standing waves, and inhomogeneous chaotic oscillations are found in the model.     

Intrinsic fluctuations in explosive reactions

A reaction is called explosive when the amount of a reactant becomes infinite in a finite time. When the intrinsic stochastic character of the reaction is taken into account, the explosion time is a random quantity. We compute its probability distribution, or at least its average and variance, for various kinds of reactions. If a reaction is unstable, so that a reactant can either explode or disappear, one first has to compute the probability for an explosion to occur at all, and then the average explosion time. Finally, the same ideas are applied to more general Markov processes.     

Stochastic models of firstorder nonequilibrium phase transitions in chemical reactions

The steady states of a simple nonlinear chemical system kept far from equilibrium are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability causing a transition analogous to a thermodynamic first-order phase transition. Near this transition the system exhibits hysteresis between two alternative steady states. Fluctuations are introduced into this model using a stochastic master equation. The solution of this master equation is unique, preventing two alternative exactly stable states. However, a quasi-hysteresis occurs involving transitions between alternative metastable steady states on a time scale that is longer than that of the fluctuations around the mean steady state values by a factor of the forme , where ø is the height of a generalized thermodynamic potential barrier between the two states. In the thermodynamic limit this time scale tends to infinity and we have essentially two alternative stable steady states.     

Stochastic aspects of pattern formation during the catalytic oxidation of CO on Pd(111) surfaces

We present experimental results on rare transitions between two states due to intrinsic noise between two states in a bistable surface reaction, namely the catalytic oxidation of CO on Pd(111) surfaces. The mean time scales involved are typically of order 10⁴ s and the probability distribution shows two peaks over a large part of the bistable regime of this surface reaction. We use measurements of the resulting CO₂ rate as well as photoelectron emission microscopy (PEEM) to characterize these rare transitions. From our dynamic data we can extract probability distributions for the CO₂ rate. We use x-t plots from PEEM measurements to describe the transitions, which are-as we demonstrate-characterized by one wall moving through the field of view in PEEM measurements. The resulting probability distributions for the CO₂ rate are shown to depend strongly on the value, Y, of the CO fraction in the reactant flux inside the bistable regime. We find that the probability distribution is strongly asymmetric indicating that the two basins of attraction are rather different in depth and width. This is also concluded from the PEEM measurements, which show in one case a rather sharp and narrow domain wall going one way, while it is rather wide and diffuse for the motion in the opposite direction. To have two basins of attraction in the bistable regime, which are rather different in nature is reminiscent of other bistable systems such as, for example, optical bistability, although the time scales involved in the present system are entirely different.     

棱镜非线性波导耦合光学双稳器件

通过K/Na离子交换方法在掺CdS_xSe_1-x玻璃表面制成单模光波导,采用三种不同的光束耦合方式观测到了棱镜非线性波导耦合本征光学双稳态。