Spiral wave stability

Qu, Z., Weiss, J., and Garfinkel, A., Cardiac electrical restitution properties and stability of reentrant spiral waves A simulation study, American Journal of Physiology, Vol. 276, No. 1(2), 1999, pp. H269-283. 

D. Barkley. Linear stability analysis of rotating spiral waves in excitable media. Phys. Rev. Lett., 68 2090-2093, 1994. 

Spiral waves ofCa" 396 ofcAMP, 215,232,233 Stability analysis, see Linear stability analysis... 

In this section we derive the analytical solutions for a spiral wave steadily rotating around a circular obstacle and for a free spiral wave and investigate their stability. It was found in Section 2, following Wiener and Rosenblueth [6], that a steadily rotating spiral wave is an involute of the obstacle s boundary and approaches an Archimedean spiral far from it. However, the conditions of applicability of the WR approximation break down near the tip of a steadily rotating spiral because the curvature diverges there. Therefore we must use... 

The stability investigation of steadily rotating free spiral waves is given in [13, 26, 29]. Its main result is that, as time goes on, the local perturbations of the curve move outwards to the periphery and fade away by spreading. Only the perturbations originating within a narrow zone of width about lo near the... 

The question of stability of spiral waves was not studied in detail by Hagan. An indirect way to approach this problem is to consider the limit r —> oo, for which the spiral wavetrains behave like plane waves. It is known that plane wave solutions of Equation (1) are stable with respect to small perturbations if their wave number satisfies the Eckhaus condition [10] ... 

If a drifting spiral meets a small region where the medium is not excitable at all, it can start to circulate around this region thus, small obstacles can anchor and stabilize spiral waves in nonuniform media [50]. 

At time zero (top) the circular wave is subject to a plane parallel electric (ohmic) field. The part of the circle propagating towards the negative electrode is annihilated beyond a critical field strength and a crescent wave is observed to propagate (bottom). Note the free ends which are stabilized by the applied field and which become Winfree spirals when the field is turned off. (See Ref. 13 for details.)... 

For antiferromagnetic materials there exists some other spin arrangement (q 0). Here q is the wave vector of some spin spiral structure (see fig. 14.2) whose wavelength A is equal to 2ir/q. Conical spin arrangements need not be considered here since they are only stabilized by the presence of anisotropy. 

It is known [17-27] that the loss of frontal modes stability as a rule is followed by occurrence of oscillatory, periodical, single-, two-, three-and multiple-start spin modes. Herewith, on the surfaces of polymerized samples in the specified papers [17-27] the spiral hollows which are typical for imstable modes of frontal pol5mierization are revealed. In this case, as is seen from the data in Figure 7.1b and Figure 7.2 (samples 1-6), the stability of co-polymerization thermal waves is lost when adding the nanotubes in amount of 20% and higher. Indeed, when filling the polymerized medium with nanotubes up to 19%, the frontal... 

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