Excitable wave propagation

We see that kd decreases with e, i.e. it becomes smaller for smaller excitabilities. Suppose that a curved excitation wave propagates through the medium and enters a region where excitability is locally decreased, so that the local value of the critical curvature kd becomes smaller than the curvature of the arrived wave. Then the wave will break in this region and two free ends will be formed. 

Y. Tang and H. G. Othmer, Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum. Philos. Trans. R. Soc. Land. B. Biol. Sci. 349, 179-195 (1995). 

This equation has an extremely important interpretation. In its differential form it means that, in two dimensions (with the x-axis lying in the plane of the interface between the solid and the fluid and the z-axis lying normal to the plane), if a pressure pjnc(x ) with implicit frequency dependence exp(iwt) acts along a strip in the y-direction at x of width dx, then the Rayleigh wave that is excited will propagate and the response in the fluid immediately above the surface at x will be... 

Even if with the present system the external conditions were adjusted in a way to enable the initiation of wave propagation, additional requirements had to be fullfilled. The laser power had to exceed a threshold in order to cause sufficient CO desorption, and a second laser pulse only excited another wave if the preceding excursion had decayed completely, i.e., the system exhibits a refractory period. 

To test the fit of the theoretical mechanism to the experimentally observed phenomena, it seemed principally important to try to realize experimentally the second mode of the autowave process. Its initiation was performed, in accordance with the theory, not by pulse heating but with the help of a heater whose temperature could be raised slowly. Under such conditions the slower wave could not be excited either in liquid helium or nitrogen, that is, there was only one mode of wave propagation. This was possibly connected with the fact that under conditions of intense heat release into liquid media, high (close to critical) transverse temperature gradients occurred in the samples, which might be a source of severe disturbances impeding the realization of the slower wave mode. 

The use of heterodyne detection to monitor vibrational oscillations even after traveling wave propagation out of the excitation region has also been demonstrated in the case of acoustic modes in bulk and thin... 

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