Transitions induced by the discreteness of molecules in a small autocatalytic system

The autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as an extinction of molecule species alternately in the autocatalytic reaction loop. Phase transition to this state with changes of the system size and flow is studied, while a single-molecule switch of the molecule distributions is reported. The relevance of the results to intracellular processes is briefly discussed.     

Autocatalytic nature of the bainitic transformation in steels: a new hypothesis

To ensure improvements in predicting the kinetics of bainite formation, it is important to understand the autocatalytic nature of the transformation so that this accelerating effect can be rigorously incorporated in kinetic models. In the present paper, it is assumed that the broad faces of bainitic plates in particular provide new potential nucleation sites for autocatalytic nucleation. The dislocations in the austenite near a bainitic plate are thought to stimulate autocatalysis because carbon is assumed to pile up at these regions and thereby other austenite–bainite interface regions may contain less carbon which promotes nucleation. Based on these assumptions, it is derived that the autocatalytic contribution is proportional to the volume fraction of as-formed bainite, which is consistent with the dependence proposed by Entwisle [V. Raghavan and A.R. Entwisle, Special Report No. 93, The Iron and Steel Institute, London, 1965, p.30] on the basis of empirical knowledge. In addition, it is assumed that autocatalytic nucleation can also depend on the morphology of bainite due to the associated difference in cementite precipitation. This new hypothesis for autocatalysis offers a viable explanation for the irregular variation in kinetics associated with the transition from upper to lower bainite measured for an alloy with eutectoid composition. Furthermore, comparison with experimental data of a Si-rich steel demonstrates that the isothermal kinetics of bainite formation can only be satisfactorily described when the autocatalytic factor is inversely proportional to the thickness of bainitic plates, which is consistent with the model proposed.     

Buoyant plumes and vortex rings in an autocatalytic chemical reaction

Buoyant plumes, evolving free of boundary constraints, may develop well-defined mushroom-shaped heads. In conventional plumes, overturning flow in the head entrains less buoyant fluid from the surroundings as the head rises, robbing the plume of its driving force. We consider here a new type of plume in which the source of buoyancy is an autocatalytic chemical reaction. The reaction occurs at a sharp front which separates reactants from less dense products. In this type of autocatalytic plume, entrainment assists the reaction, producing new buoyancy which fuels an accelerating plume head. When the head has grown to a critical size, it detaches from the upwelling conduit, forming an accelerating, buoyant vortex ring. A second-generation head then develops at the point of detachment. Multiple generations of autocatalytic vortex rings can detach from a single triggering event.     

Weber's law for biological responses in autocatalytic networks of chemical reactions

Biological responses often obey Weber's law, according to which the magnitude of the response depends only on the fold change in the external input. In this study, we demonstrate that a system involving a simple autocatalytic reaction shows such a response when a chemical is slowly synthesized by the reaction from a faster influx process. We also show that an autocatalytic reaction process occurring in series or in parallel can obey Weber's law with an oscillatory adaptive response. Considering the simplicity and ubiquity of the autocatalytic process, our proposed mechanism is thought to be commonly observed in biological reactions.     

Multiple time scale based reduction scheme for nonlinear chemical dynamics

A chemical reaction is often characterized by multiple time scales governing the kinetics of reactants, products and intermediates. We eliminate the fast relaxing intermediates in autocatalytic reaction by transforming the original system into a new one in which the linearized part is diagonal. This allows us to reduce the dynamical system by identifying the associated time scales and subsequent adiabatic elimination of the fast modes. It has been shown that the reduced system sustains the robust qualitative signatures of the original system and at times the generic form of the return map for the chaotic system from which complex dynamics stems out in the original system can be identified. We illustrate the scheme for a three-variable cubic autocatalytic reaction and four-variable peroxidase-oxidase reaction.     

Comparison of the oxidation of two porphyrin complexes by bromate with respect to wave propagation

The kinetics and mechanism of the oxidation of iron(III) protoporphyrin IX (hemin) and iron(III) meso-tetra(4-sulfonatophenyl)porphine (TPPSFe) were compared. Both reactions exhibit sigmoid-shaped time dependence of the absorbance of the porphyrin complexes during the course of the reaction. The oxidation of hemin was proved to be an autocatalytic reaction resembling very much the autocatalytic subset reaction of the BZ oscillators. The oxidation of TPPSFe was proved not to be autocatalytic. It consists of consecutive reaction steps without any feedback. One of the intermediates absorbing in the same region as TPPSFe could be identified as an iron(V)-oxo complex of TPPS. According to the kinetic differences, single autocatalytic wave fronts could be observed in the autocatalytic hemin-bromate reaction if hemin was fixed and stabilized in silica gels, while no wave formation appeared in the TPPSFe-bromate system. The kinetic differences are in agreement with the different structures of the two porphyrin complexes.     

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

Exothermic autocatalytic fronts traveling in the gravity field can be deformed by buoyancy-driven convection due to solutal and thermal contributions to changes in the density of the product versus the reactant solutions. We classify the possible instability mechanisms, such as Rayleigh-Benard, Rayleigh-Taylor, and double-diffusive mechanisms known to operate in such conditions in a parameter space spanned by the corresponding solutal and thermal Rayleigh numbers. We also discuss a counterintuitive instability leading to buoyancy-driven deformation of statically stable fronts across which a solute-light and hot solution lies on top of a solute-heavy and colder one. The mechanism of this chemically driven instability lies in the coupling of a localized reaction zone and of differential diffusion of heat and mass. Dispersion curves of the various cases are analyzed. A discussion of the possible candidates of autocatalytic reactions and experimental conditions necessary to observe the various instability scenarios is presented.     

Metal nanorod production in silicon matrix by electroless process

Metal filled Si nanopores, that is, metal nanorods in an Si matrix, are produced by an electroless process that consists of three steps: (1) electroless displacement deposition of metal nanoparticles from a metal salt solution containing HF; (2) Si nanopore formation by metal-particle-enhanced HF etching; and (3) metal filling in nanopores by autocatalytic electroless deposition. Ag nanoparticles produce Si nanopores whose sizes are a few tens of nm in diameter and ca. 50 nm deep. Au nanoparticles produce finer and straighter nanopores on Si than the Ag case. These nanopores are filled with a Co or a Co-Ni alloy by autocatalytic deposition using dimethylamine-borane as a reducing agent. Phosphinate can be used as a reducing agent for the Au-deposited-and-pore-formed Si. The important feature of this process is that the metal nanoparticles, that is, the initiation points of the autocatalytic metal deposition, are present on the bottoms of the Si nanopores.     

Spatiotemporal chaos in the dynamics of buoyantly and diffusively unstable chemical fronts

Nonlinear dynamics resulting from the interplay between diffusive and buoyancy-driven Rayleigh-Taylor (RT) instabilities of autocatalytic traveling fronts are analyzed numerically for various values of the relevant parameters. These are the Rayleigh numbers of the reactant A and autocatalytic product B solutions as well as the ratio D=D(B)/D(A) between the diffusion coefficients of the two key chemical species. The interplay between the coarsening dynamics characteristic of the RT instability and the constant short wavelength modulation of the diffusive instability can lead in some regimes to complex dynamics dominated by irregular succession of birth and death of fingers. By using spectral entropy measurements, we characterize the transition between order and spatial disorder in this system. The analysis of the power spectrum and autocorrelation function, moreover, identifies similarities between the various spatial patterns. The contribution of the diffusive instability to the complex dynamics is discussed.     

On some dynamical diagrams of chemical reaction engineering

A brief historical survey of some of the influential types of diagrams that have been used in chemical reaction engineering is given. These include the phase plane, the simple autocatalytic diagram, and the stroboscopic phase plane. (c) 1999 American Institute of Physics.     

Quantum description of five-particle systems in principal-axis hyperspherical coordinates

To describe a 5-particle system, ‘principal-axis hyperspherical’ coordinates (made up of one hyperradius and eight angles as internal coordinates) and three Euler angles as external (rotational) coordinates are used. A mathematical procedure to derive, in a systematic manner, the exact quantum mechanical Hamiltonian of the system in terms of these coordinates is presented. A generalized angular momentum vector operator, which allows the generation of a profitable standard representation for the angular part of the problem, is introduced.     

Statistics of rare strong bursts in autocatalytic stochastic growth with diffusion

A general model of autocatalytic stochastic growth with diffusion is analytically and numerically investigated. Exact analytical results for the intermittency exponents and the probability of rare strong bursts in an infinite system are presented. Finite-size saturation effects, leading to the stretched exponential growth of statistical moments, are further considered. These analytical predictions are checked in numerical simulations.     

Modification of hyperspherical coordinates in the classical three-particle problem

A new version of the hyperspherical coordinates in the classical three-particle problem is considered, that leads to a modification of the Delves coordinates. A type of the kinetic and potential energy is obtained for the system. The problem is reduced in these coordinates for different cases of the classical motion. From geometrical reasonings a formula is chosen for the reduced mass of the three-body system. The triangle of masses and the relevant basic quantities and relations are introduced.     

Euclidean Special Relativity

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications.     

采用RBF神经网络求解反向条纹的研究

提出了一种利用RBF神经网络来确定摄像机和投影器坐标映射关系的方法。首先在投影器坐标系中将数据分为若干个16×16的子区域,然后以（l,m,lm,l2,m2）为输入层的5个神经元（其中l、m为投影器像素坐标）,以摄像机像素坐标i为输出层的神经元,建立RBF神经网络。利用RBF神经网络求解在投影器坐标系中摄像机像素坐标的分布模型,最后得到投影器像素点对应的摄像机像素坐标值。计算机模拟和实验结果表明,与已有的算法相比,该方法能更有效地提高反向条纹投影的求解精度。为反向条纹的求解提供了新方法。     

Mean relaxation time approximation for dynamical correlation functions in stochastic systems near instabilities

We present a simple approximation for dynamical correlation functions in stochastic systems which reproduces the high as well as the low frequency behaviour of the exact correlation functions. The approximation is applied in its lowest order to diffusion in a quartic potential and to autocatalytic chemical reaction systems as described by the Schlögl models. The results are compared to those from the conventional Mori-Zwanzig projection operator approach which reproduces only the short-time relaxation of the systems considered. The new approximation describes correctly slow relaxation processes, e.g. barrier crossing in a quartic potential and the slowing down of dynamic processes in finite autocatalytic systems near first and second order transitions.     

Determination of a Potential Energy Surface for CO2 Using Generalized Internal Vibrational Coordinates

A potential energy surface for CO2 is determined from experimental data using generalized internal vibrational coordinates. These coordinates are defined as two arbitrary distances and the angle between them and depend on two external parameters, which can be properly optimized. An optimal generalized internal coordinate system is obtained for CO2 by minimizing unconverged vibrational energies with respect to the external parameters. The optimal coordinates are shown to be superior to previously derived normal hyperspherical coordinates for this molecule. A nonlinear least-squares fit of the potential energy surface of CO2 to observed vibrational frequencies is made by using the optimal internal coordinates and fully variational calculations. The potential function is represented by a fourth-order Morse-cosine expansion and its quality is checked by computing highly excited vibrational transition frequencies which were not included in the fit. Copyright 1999 Academic Press.     

Mechano-chemical oscillations of a gel bead

We present a formalism which describes the spatio-temporal evolution of a gel submitted to an autocatalytic chemical reaction to which it is responsive. This theory is based on an extension of a hydrodynamical multi-diffusional approach of the gel dynamics, which is plunged into a chemically active mixture. Emergent and autonomous volume self-oscillation dynamics of the gel are obtained from the nonlinear coupling of the elastic deformation, the chemical kinetics and the transport phenomena, that take place in the system. We apply this formalism to a spherical bead of gel plunged in a Belouzov-Zhabotinsky oscillatory chemical reaction, for which Yoshida et al. have obtained numerous experimental results. The case of a gel immersed in an autocatalytic bistable chemical reaction is also considered. We show that such formalism describes the autonomous volume self-oscillation dynamics of the gel beads.     

Solid-state NMR and the thermal polymerization of 2,4-hexadiyne-1,6-diol bis-(p-toluenesulfonate)

The solid-state thermal polymerization of crystalline 2,4-hexadiyne-1,6-diol bis-(p-toluenesulfonate) (PTS) was investigated by solid-state 13C NMR, the first application of this technique to such a process. The kinetics of the thermal process was examined at temperatures of 40.5, 51.0, and 59.5 degrees C, with a magic angle spinning (MAS) rate of 5 kHz. The first-order rate constants associated with the induction (k0) and autocatalytic (k max) periods were calculated by monitoring signal intensities (conversion) throughout the course of the thermal polymerization. While estimations of the activation energy (E(a) approximately 20 kcal/mol) from the NMR experiments are similar to values obtained by other analytical techniques, estimations of the autocatalytic effect (k max/k0 approximately 22) were significantly lower. Likely causes for the unusually small autocatalytic effect are discussed.     

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A complex network of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.