Local geometry hypothesis

Computational previews of stable particle-like organizing centers have been completed using excitable media with electrophysiological rather than chemical mechanisms [23, 30, 31]. There seems no reason to expect qualitatively different behavior in the Oregonator mechanism or the Belousov-Zhabotinsky reagent, but this expectation has thus far been tested both computationally and in the laboratory only for the dynamical consequences of twist on an arc of initially straight filament (see Sections 4 and 5 below). How are we to quantitatively inquire into the dynamics of vortex filaments The only approach undertaken to date is based on the Local Geometry Hypothesis . 

In this chapter we describe the successes of the local geometry hypothesis, whereas Winfree, in another chapter in this book, describes many interesting situations where nonlocal interactions are more important. More details can be found in Winfree [18] and Keener and Tyson [19], and for a third perspective on the problem one should consult the review by Davydov et al. [20]. 

It was suggested also that the local geometry, in particular the Al-O-Si angle could be correlated to the OH frequency a hypothesis supported by ab initio calculations on small clusters, where the regression coefficient is practically... 

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