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I. , and S c h o p m a n , F . J. G. (1977). Circ. Res. 41, 9. Andronov, Α. , Vitt, Α. , and Khaikin, S. Ε. (1966). In " T h e o r y of O s c i l l a t o r s " (W. ), pp. 468-478. P e r g a m o n Press, Oxford. Aris, R. (1975). " T h e M a t h e m a t i c a l T h e o r y of Diffusion a n d Reaction in Permeable Catalysts," Vols. I and II. Oxford Univ. Press (Clarendon), L o n d o n and N e w York. 48 A. T. Winfree Arshavskii, Y. I. (1964). Biofizika 9, 365. Arshavskii, Y. , Berkenblit, Ν . , and Dunin-Barkovskii, V.
T h e pivotal cell m a p s t o ( - 2 , 7). T h e four corners are indicated on the border. This is the anticlockwise r o t o r of Winfree (1974b), Fig. 7, at Τ — 164 sec. composition space? 1) with k = \ and S = 20. The wave circulating outward along the disk's border extends continuously inward, ultimately pivoting about a cell of unvarying composition. Annuli concentric to this point m a p into composition space very nearly as d o the isolated rings of Fig. 14, except that rings too small to sustain a wave independently are here supported by their outer neighbors in the disk.
T. Winfree impermeable boundary because gradients have n o normal components at the boundary. The inside or " core " is the region that so conspicuously fills the interior of the disk's image in composition space. The geometry here is determined by a balancing of the image's elasticity (corresponding to molecular diffusion) and the divergence of the flow (corresponding to reaction). Curiously, and quite unlike linearized reaction-diffusion equations (Gmitro and Scriven, 1966), the boundary conditions play little role in determining the core's rotation period or diameter or the wavelength of the surrounding involute spiral.
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