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.     

Geometrical consequences of resonance-assisted intramolecular hydrogen-bond formation from Ab initio MO calculations on 2-nitroresorcinol

Ab initio orbital calculations on phenol, nitrobenzene, and 2-nitroresorcinol have been performed with the GAUSSIAN 92 series of programs. Initial RHF/6-31G^* and RHF/6-31G^** optimizations were followed by second-order MØller-Plesset MP2(FC)/6-31G^* optimizations. The general geometrical features of these molecules, and, in particular, the characteristic changes as going from phenol to 2-nitroresorcinol and from nitrobenzene to 2-nitroresorcinol are in good agreement with recent gas-phase electron diffraction studies and with the notion of resonance-assisted intramolecular hydrogen-bond formation in 2-nitroresorcinol.