Chemical waves curvature

A great deal is known about the behavior of spiral waves in excitable media from both the mathematical and the experimental points of view. One feature of particular interest is the center or core from which the spiral waves emanate. The eikonal equation (6.31) allows us to obtain a rough estimate of the size of a spiral core. Chemical waves typically travel at speeds of millimeters per minute, or perhaps (4-10) xl0 cms. Diffusion constants of monomeric species in aqueous solution tend to be around 2 x 10 cm s. If we consider an expanding circle (which has a negative curvature) on the perimeter of the core, and plug these values for c and D into eq. (6.31), we find that A = 0 when... 

Foerster, P. Muller, S. C. Hess, B. 1988. Curvature and Propagation Velocity of Chemical Waves, Science 241, 685-687. 

The rise times of the elastic wave may be quite narrow in elastic single crystals, but in polycrystalline solids the times can be significant due to heterogeneities in physical and chemical composition and residual stresses. In materials such as fused quartz, negative curvature of the stress-volume relation can lead to dispersive waves with slowly rising profiles. 

The deficiency can be made up, if no energy is added from the outside, only from the detonation products, with a resulting drop in their temperature from the isochoric adiabatic flame temperature. This may quench the chemical reaction. The deficiency diminishes with decrease of wave-front curvature. For point initiation , enough energy must be added from the outside to make up for the total deficit which accumulates during the time the wave is reaching a diameter at which the curvature drops below a critical value... 

Two examples of shift data with nonuniform curvature (unsymmetrical shift data) which can be fitted by this approach are shown in Figures 14 and 15. The study of iodide solvation by uv CTTS and 127I chemical shifts is the only one where both approaches have been used on the same ion (44). The accuracy of the results is questionable but 127I peaks are very broad and measurement of shifts difficult (5). The treatment leading to Equation 53 is not valid for a CTTS transition, and its application is intuitive, but a difference in wave number shifts rather than wavelengths should be plotted. However, the discrepancy resulting is numerically trivial. 

From a chemical point of view the most important result is that number theory predicts two alternative periodic classifications of the elements. One of these agrees with experimental observation and the other with a wave-mechanical model of the atom. The subtle differences must be ascribed to a constructionist error that neglects the role of the environment in the wave-mechanical analysis. It is inferred that the wave-mechanical model applies in empty space Z/N = 0.58), compared to the result, observed in curved non-empty space, (Z/N = t). The fundamental difference between the two situations reduces to a difference in space-time curvature. 

A detailed experimental study of the chemical conditions for which instable wave fronts appear was carried out, as previously, in the cerium-catalyzed BZ reaction [46]. The purpose of this study was to verify a simple hypothesis by Pertsov et al. [47] from which the authors calculated that the onset of instabilities at a marginal excitability is strongly associated with the critical curvature relative to the width of the autocatalyst band in the wave front, L. In a series of solutions with decreasing excitability the critical diameter. 

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