By V.A. Vasiliev, Yu.M. Romanovskii, D.S. Chernavskii, V.G. Yakhno
Probably, we're obliged to technology, greater than to the other box of the human task, for the foundation of our feel that collective efforts are helpful certainly. F. Joliot-Curie The research of autowave methods is a tender technological know-how. Its uncomplicated recommendations and techniques are nonetheless within the strategy of formation, and the sector of its functions to varied domain names of typical sciences is increasing continually. staggering examples of assorted autowave procedures are saw experimentally in different laboratories of rather diversified orientations, facing investigations in physics, chemistry and biology. it truly is O1). r opinion, even though, that if a heritage of the invention of autowaves will he written a few day its writer should still definitely point out 3 basic phenomena that have been the assets of the area in view. "Ve suggest combustion and section transition waves, waves in chemical reactors the place oxidation-reduction strategies happen, and propagation of excitations in nerve fibres. the most instruments of the idea of autowave tactics are quite a few equipment used for investigating nonlinear discrete or dispensed oscillating structures, the mathe matical concept of nonlinear parabolic differential equations, and techniques of the idea of finite automata. it truly is noteworthy that the speculation of autowave,. , has been vastly contributed to be paintings of excellent mathematicians who expected the experimental discoveries of their summary experiences. One may still point out R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).
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Extra resources for Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine
At the qualitative lcvel, however, cclls can be rcpresented as rectangular bodies and fluxes can be considered as being quasistationary; in other words, one can suppose that the relaxation times for fluxes between adjacent cells is substantially less than the specific times of intracellular reactions. Let the distance between the cell centres along the Orl axis be Rv the membrane thickness be l, the diffusion coefficient for a component x with respect to water be Dx [cm2/s], and the membrane penetrability be P (cm/s).
First of all, replace the fluxes measured in the coordinate frame referred to the k-th component by the fluxes measured with respect to the convection velocity. 32) n where 1) is a characteristic velocity. Summing over all the fluxes, we get E (b;/Ci) Ii = 0, A similar identity, n E (b;' ICi) It' = i=1 i=1 0, holds for fluxes in another characteristic frame. Comparing these identities we get the desired formula for the transformation of fluxes corresponding to 8ubstitution of one characteristic velocity by another, I;' = Ii - Ci n E (b/ICj) I j .
Similar effects are known for diffusion of ions in plasmas. Second, though in passive systems the ratio Dij/D ii is small enough to neglect crossing fluxes, in an active system a "local" autocatalysis results in qualitatively new AW properties even for small, but nonzero, values of DijjD ii . In other words, in such cases one can decide whether Dij (i =t= j) can be neglected only with a due account for local kinetics (cf. 3). Let us dwell on some problems of the theory of crossing effects and consider the example of mass transfer in multicomponent systems.
Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine by V.A. Vasiliev, Yu.M. Romanovskii, D.S. Chernavskii, V.G. Yakhno