Highly efficient photoinitiation in the cerium(III)-catalyzed aqueous autoxidation of sulfur(IV). An example of comprehensive evaluation of photoinduced chain reactions

The photoinitiated and cerium(III)-catalyzed aqueous reaction between sulfite ion and oxygen has been studied in a diode-array spectrophotometer using the same light beam for excitation and detection. Cerium(III) is identified as the photoactive absorbing species, and the production of cerium(IV) initiates a radical chain reaction. To interpret all the experimental findings, a simple scheme is proposed, in which the additional chain carriers are sulfite ion radical (SO3(-.)), sulfate ion radical (SO4(-.), and peroxomonosulfate ion radical (SO5(-.). The overall rate of oxidation is proportional to the square root of the light intensity per unit volume, which is readily interpreted by the second-order termination reaction of the proposed scheme. It is also shown that the reaction proceeds for an extended period of time in the dark following illumination, and a quantitative analysis is presented for this phase as well. The postulated model predicts that cerium(III) should have a cocatalytic or synergistic effect on the autoxidation of sulfite ion in the presence of other catalysts. This prediction was confirmed in the iron(III)-sulfite ion-oxygen system. The experimental method and the mathematical treatment used might be applicable to a wide range of photoinduced chain reactions.     

Oscillatory photochemical decomposition of tetrathionate ion

When subject to illumination, tetrathionate ion decomposes in an oscillatory fashion with a period of about 1 h to yield products identified as colloidal sulfur and trithionate ion. This system represents the first experimental example of a stirred, batch photochemical oscillator. A simple model consisting of four reaction steps and four adjustable rate parameters gives good agreement with the observed oscillatory behavior.     

Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics

We propose a method for the determination of a characteristic oscillation frequency for a broad class of chaotic oscillators generating complex signals. It is based on the locking of standard periodic self-sustained oscillators by an irregular signal. The method is applied to experimental data from chaotic electrochemical oscillators, where other approaches of frequency determination (e.g., based on Hilbert transform) fail. Using the method we characterize the effects of phase synchronization for systems with ill-defined phase by external forcing and due to mutual coupling.     

Book reviews

Unsigned book reviews are by the Book Review Editor.     

Wave propagation in a wooden bar

In this paper we will present a method to determine the material properties of a wooden bar with rectangular cross-section using guided waves in the measurement. We modelled the wood as an orthotropic material with nine independent constants. We determined the dispersion curves theoretically in the three-dimensional case using a semi-analytical finite element method. In our laboratory we excited transversal and longitudinal waves in wooden bars of 2.5-4 m length by piezoceramic transducers. We measured the displacement or the velocity of the surface of the bar by a laser-interferometer. The dispersion curves of the bar are determined from the measurement by the linear prediction method. We related the dispersion curves and the material properties. We found the material properties by parametric model fitting.     

On Discretization Schemes for Stochastic Evolution Equations

Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved. Mathematics Subject Classifications (2000) Primary: 60H15; Secondary: 65M60.István Gyöngy: This paper was written while the first named author was visiting the University of Paris X. The research of this author is partially supported by EU Network HARP.Annie Millet: The research of the second named author is partially supported by the research project BMF2003-01345.     

Noise-sustained coherent oscillation of excitable media in a chaotic flow

Constructive effects of noise in spatially extended systems have been well studied in static reaction-diffusion media. We study a noisy two-dimensional Fitz Hugh-Nagumo excitable model under the stirring of a chaotic flow. We find a regime where a noisy excitation can induce a coherent global excitation of the medium and a noise-sustained oscillation. Outside this regime, noisy excitation is either diluted into homogeneous background by strong stirring or develops into noncoherent patterns at weak stirring. These results explain some experimental findings of stirring effects in chemical reactions and are relevant for understanding the effects of natural variability in oceanic plankton bloom.     

Synchronization and oscillator death in oscillatory media with stirring

The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the stirring rate can control the macroscopic behavior of the system producing collective oscillations (synchronization) or complete quenching of the oscillations (oscillator death). We interpret the homogenization rate due to mixing as a measure of global coupling and compare the phase diagrams of stirred oscillatory media and of populations of globally coupled oscillators.