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 job, for the starting place of our feel that collective efforts are helpful certainly. F. Joliot-Curie The examine of autowave strategies is a tender technology. Its easy techniques and techniques are nonetheless within the technique of formation, and the sector of its functions to varied domain names of typical sciences is increasing always. dazzling examples of assorted autowave tactics are saw experimentally in several laboratories of particularly assorted orientations, facing investigations in physics, chemistry and biology. it truly is O1). r opinion, in spite of the fact that, that if a background of the invention of autowaves will he written a few day its writer should still without doubt 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 approaches ensue, and propagation of excitations in nerve fibres. the most instruments of the idea of autowave approaches are a number of tools used for investigating nonlinear discrete or disbursed oscillating structures, the mathe matical concept of nonlinear parabolic differential equations, and techniques of the idea of finite automata. it really is noteworthy that the speculation of autowave,. , has been drastically contributed to be paintings of awesome mathematicians who expected the experimental discoveries of their summary experiences. One should 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 info for Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine
The coefficients D~j in the Stefan-Maxwell equation have a weak concentration dependence, in contrast to the Fick coefficients D ij ; the dependence is totally absent for ideal dilute mixtures. 40) provide a correct representation of the concentration dependence for the Fick diffusion coefficients. These expressions suggest a number of important conclusions. The mutual diffusion coefficients for the components, D32 and D 23 , vanish for C3 = 0 and C2 = 0, respectively. The matrix D jj in Eqs. 39) is not symmetrical.
Suppose, for definiteness, that 8(17) is a Gaussian distribution, 8(1)) = exp (-1)2/1'0 2 ) where To is the distribution width. 5 .. (2l - 1) (ro)2i+1]/(2i)! 2i = f3 iToi+l (f3i < 1 for i > 2). g. for quasiharmonical processes the scale is given by wavelengths. The order of magnitude of the terms in the expansion is f3i(To/W. 49) 44 2 Physical premises for the construction of basic models where Dxx = Dyy = Dxy = Dyx = oB - ox oB = - oy = bq"W2C2([(X + y)2 + W 2C2]. 49) can be reduced to the basic model describing a number of AWPs including the localized stationary dissipative structures, travelling fronts.
2). 5) to the basic models. From this viewpoint, the basic models are intermediate, as to the complication level of the proposed description of the objects and phenomena themselves. As compared with the axiomatic models (finite automates) they provide a possibility to investigate the mutual stability of AWP under study. It is difficult, and sometimes impossible in principle, however, to account in their framework for specific features of space interactions which take place in some media. 2) only in separate, though very important, cases.