Pattern formation in reaction-diffusion system in crossed electric and magnetic fields

We consider a reaction-diffusion system in crossed electric and magnetic fields lying on the reaction plane. It is shown that a charge separation along the direction normal to the reaction plane resulting in a diffusional flux may cause a differential flow induced chemical instability and stationary pattern formation on a homogeneous steady state. This pattern is generically different from a Turing pattern modified by the crossed fields. The special role of magnetic field is emphasized. Our theoretical analysis is corroborated by numerical simulation on a reaction-diffusion system in three dimensions.     

Bifurcation analysis of Liesegang ring pattern formation

Bifurcation analysis is introduced to a prototype Liesegang ring (LR) model to explain pattern formation as an instability of a propagating plane reaction front. A theoretical criterion for the onset of patterning is derived and numerically tested. The uneven spacing law of LR bands is explained as a consequence of the time varying velocity of the moving reaction front. Suggestions for controlling pattern formation are provided.     

Entropy production in a two-dimensional reversible Gray-Scott system

The entropy production sigma is calculated in the time evolution processes toward a Turing-like pattern and a chaotic pattern in a two-dimensional reaction-diffusion system. The contributions of reaction and diffusion to the entropy production are evaluated separately. Though its contribution to total sigma is about 5%, the entropy production in diffusion foretells the moving direction of the dots (reaction spots) and the line-shaped patterns. The entropy production of the entire system sigma depicts well the cooperative dynamics and evolution of chaotic dot patterns. It is suggested that sigma can be a scalar measure for quantitative studies of hierarchic pattern dynamics. The relation is also discussed between the bifurcation parameter and the distance from thermodynamic equilibrium.     

双层耦合非对称反应扩散系统中的超点阵斑图

通过线性耦合Brusselator模型和Lengyel-Epstein模型,数值研究了双层耦合非对称反应扩散系统中图灵模之间的相互作用以及斑图的形成机理.模拟结果表明,合适的波数比以及相同的对称性是两个图灵模之间达到空间共振的必要条件,而耦合强度则直接影响了图灵斑图的振幅大小.为了保证对称性相同,两个图灵模的本征值高度要位于一定的范围内.只有失稳模为长波模时,才能对另一个图灵模产生调制作用,并形成多尺度时空斑图.随着波数比的增加,短波模子系统依次经历黑眼斑图、白眼斑图以及时序振荡六边形斑图的转变.研究表明失稳图灵模与处于短波不稳定区域的高阶谐波模之间的共振是产生时序振荡六边形的主要原因.     

Spatio-temporal pattern formation during CO oxidation on Pt(100) at low and intermediate pressures: A comparative study

Experimental studies of CO oxidation on Pt(100) over two different ranges of reactant pressures will be reviewed. Using photoemission electron microscopy (PEEM), spatio-temporal pattern formation was observed at temperatures between 420 and 540 K in the 10(-5) mbar pressure range. In an attempt to bridge the "pressure-gap," ellipsomicroscopy for surface imaging was used to follow pattern formation at temperatures around 600 K in the 10(-2) mbar pressure range. The features of the nonlinear phenomena, observed in these two different pressure regimes, are markedly different. This is shown by comparison of various qualitative and quantitative features of spatio-temporal pattern formation as well as the dynamics of the macroscopic reaction rate. Subsurface oxygen is proposed as a tentative alternative to the surface phase transition for oscillations in the reaction rate at higher temperatures and intermediate pressures. (c) 2002 American Institute of Physics.     

Real time imaging of catalytic reactions on surfaces: Past,present and future

Simple surface reactions like the CO-oxidation on single crystal platinum surfaces show a rich scenario of non-linear behavior under specific reaction parameters. Gerhard Ertl started in the late 1980s a new research group focusing on imaging of surface reactions to discover possible spatio-temporal pattern formation. Necessarily we conceived several unique imaging methods, which are discussed in the first part of the paper. An unexpected wealth of adsorbate patterns during the CO-oxidation on Pt was soon discovered and can be modeled by a reconstruction model. But the interaction of a multitude of micrometer scale concentration waves and fronts on the surface complicate our understanding of the underlying mechanisms for such patterns. We tackled those complications by constraining pattern formation within inactive or active boundaries formed by different metals evaporated onto the Pt single crystal, thereby isolating individual features of reaction diffusion systems (for example single pulses). Since 2001 we have been able to dynamically change the surface catalytic activity in real time and space by focusing an addressable laser beam to differentially heat a single crystal surface. Combining fixed microstructures made with different catalytic activities and the local heating of the surface opens new avenues of controlling pattern formation. In contrast to these approaches, varying one of the control parameters in time creates a globally coupled system, with the choice between direct forcing or a feedback experiment. In the last part temperature effects arising from the reaction heat are discussed, which become dominant at higher partial pressures for the reactants or on ultra thin samples where the reaction heat cannot be effectively dissipated into the bulk.     

局域浓度调控扩散系数的次氯酸-碘离子-丙二酸系统图灵斑图形成中的反常扩散

通过数值模拟及振幅方程解析解方法,从实空间和倒空间分析了受局域浓度扩散系数调控下次氯酸-碘离子-丙二酸反应扩散系统图灵斑图形成的扩散机理.在零扩散系数调节下,斑图形成为典型的菲克扩散;而在负向正向扩散系数调节下,斑图的形成依赖欠扩散和超扩散.图灵系统的浓度稳态振幅对随机初始条件敏感性随局域浓度扩散调控系数k的增大而增加.     

The Possible Contribution of Isotope Effects on Ester- and Aldol Condensations to Isotope Discriminations and Isotopic Patterns of Natural Compounds

Abstract

Acetyl-CoA provides the C-2-units for the formation of many secondary compounds. The primary pattern of this intermediate is originating from glucose, further modifications are introduced by isotope effects on the pyruvate-dehydrogenase-reaction and on ester- and aldol-reactions in the course of the biosynthesis of secondary products. The overlap of these various effects is demonstrated through the pattern of some natural products.

The partial pattern of limonene and pulegone, respectively, products from different origin are not identical, this is interpreted as a consequence of individual relative contributions of the above mentioned effects in the plants in question.

On the other hand the distinct relative depletion in a position of sinigrin, a glucosinolate from Brassica nigra, originating from CH₃ of acetate can be assigned to an isotope effect of the aldol reaction between a precursor and acetyl-CoA. An corresponding depletion has been measured in position 5 of citrate. Therefore the kinetic isotope effect on the citrate synthase reaction is studied in vitro at present.     

Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.     

Pattern formation in the thiourea-iodate-sulfite system: Spatial bistability, waves, and stationary patterns

We present a detailed study of the reaction-diffusion patterns observed in the thiourea-iodate-sulfite (TuIS) reaction, operated in open one-side-fed reactors. Besides spatial bistability and spatio-temporal oscillatory dynamics, this proton autoactivated reaction shows stationary patterns, as a result of two back-to-back Turing bifurcations, in the presence of a low-mobility proton binding agent (sodium polyacrylate). This is the third aqueous solution system to produce stationary patterns and the second to do this through a Turing bifurcation. The stationary pattern forming capacities of the reaction are explored through a systematic design method, which is applicable to other bistable and oscillatory reactions. The spatio-temporal dynamics of this reaction is compared with that of the previous ferrocyanide-iodate-sulfite mixed Landolt system.     

Specific features of the unsteady combustion of planar Ti–2B–αCu samples

The modes of spin gasless combustion of plate- and disk-shaped Ti–2B–Cu samples are investigated using frame-by-frame filming. The combustion process takes place under unsteady conditions. An increase in the diameter of the reaction sample makes the pattern of movement of the reaction front more complicated.     

Chemical instability induced by a shear flow

We predict a new type of instability induced by shear flow in chemical systems. A homogeneous steady state solution of a reaction-diffusion system loses stability in a Poiseuille flow. The instability appears as the speed of the flow increases beyond a certain threshold. This results in a steady pattern moving with the average fluid velocity. The chemical reaction consists of two species (activator and inhibitor) moving with identical velocities. Contrary to Turing's instability, the pattern arises when the activator has a higher diffusivity than the inhibitor.     

ORDER AND CHAOS IN NATURE-PHENOMENA AT SURFACES

In chemical reaction systems far from thermodynamical equlibrium rate oscillations and chemical wave patterns develop. This paper presents a condensed overview of recent developments in the study of self-organization processes during heterogeneously catalyzed reactions, whereby the main emphasis is focused on low pressure single crystal studies of oscillatory and pattern forming reactions on Pt and Rh surfaces. Chemical wave patterns on a macroscopic scale as well as reaction induced-microscopic roughening and coverage fluctuations in nano-scale systems are discussed.     

Influence of gas pressure on the pattern evolutions of dust clusters and fractals in a dusty plasma system

Dusty plasma has been produced through chemical reaction in a capacitively coupled radio frequency (rf) discharge system. Dust clusters with a few particles and dust fractals are observed. As gas pressure is increased, the suspended height of dust particles descends and the average interparticle distance decreases accordingly. The influence of gas pressure on the pattern evolutions is investigated. Dust clusters or fractals not only can evolve regularly on a horizontal plane, but also can evolve from a horizontal plane to a vertical line array. Under appropriate conditions, the evolutions are reversible. When the evolution is from a symmetrical pattern with a centre particle to another pattern, the centre particle will first show its unsteadiness.     

New direct reaction: two-proton knockout from neutron-rich nuclei

The reaction 9Be(28Mg,26Ne+gamma)X has been studied at 82 MeV/nucleon together with two similar cases, 30Mg and 34Si. Strong evidence that the reactions are direct is offered by the parallel-momentum distributions of the reaction residues and by the inclusive cross sections. The pattern of the partial cross sections for 28Mg suggests the presence of correlations. A preliminary theoretical discussion based on eikonal reaction theory and the many-body shell model is presented. The reaction holds great promise for the study of neutron-rich nuclei.     

Spontaneous symmetry breaking turing-type pattern formation in a confined Dictyostelium cell mass

We have discovered a new type of patterning which occurs in a two-dimensionally confined cell mass of the cellular slime mold Dictyostelium discoideum. Besides the longitudinal structure reported earlier, we observed a spontaneous symmetry breaking spot pattern whose wavelength shows similar strain dependency to that of the longitudinal pattern. We propose that these structures are due to a reaction-diffusion Turing instability similar to the one which has been exemplified by CIMA (chlorite-iodide-malonic acid) reaction. The present finding may exhibit the first biochemical Turing structure in a developmental system with a controllable boundary condition.     

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.     

Phase-transfer catalysis and ultrasonic waves. I. Cannizzaro reaction

The aim of this work is to study the effect of an ultrasonic wave on the Cannizzaro reaction catalyzed by a phase-transfer catalyst. The reaction of benzaldehyde with potassium hydroxide was chosen as the reference reaction. The kinetics of the reaction was followed by the amount of benzoic acid which is well characterized and easily isolatable. Investigations were made on variables such as the kind of aldehyde, the phase-transfer catalyst, the temperature and the frequency of ultrasonic wave. As the phase-transfer catalyst depends strongly on mass transfer between two phases, it is well understood that ultrasonic waves have a greater efficiency of interface mixing than conventional agitation. The results showed that an ultrasonic wave of 20 kHz dramatically accelerates on the reaction.     

Mechanism of Excited State Double Proton Transfer in 2-Amino-3-Methoxypyridine and Acetic Acid Complex

The excited-state double-proton transfer(ESDPT) mechanism of 2-amino-3-methoxypyridine and acetic acid complex is studied by the density functional theory(DFT) and time-dependent DFT with CAM-B3LYP functional.The complex is connected through two different types of inter-molecular hydrogen bonds. After photo-excitation,both hydrogen bonds get strengthened, which can facilitate the ESDPT reaction. The scanned potential energy curve along the proton transfer coordinate indicates that the ESDPT reaction proceeds in a stepwise pattern.     

Stochastic Simulation of Turing Patterns

We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction-diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie＇s algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion pro- cesses are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Sfochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.