Autowave Processes in Kinetic Systems: Spatial and Temporal by V.A. Vasiliev, Yu.M. Romanovskii, D.S. Chernavskii, V.G.

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 beginning of our feel that collective efforts are helpful certainly. F. Joliot-Curie The examine of autowave techniques is a tender technological know-how. Its uncomplicated innovations and techniques are nonetheless within the technique of formation, and the sector of its purposes to varied domain names of common sciences is increasing continually. stunning examples of assorted autowave approaches are saw experimentally in different laboratories of rather diverse orientations, facing investigations in physics, chemistry and biology. it truly is O1). r opinion, even though, that if a background of the invention of autowaves will he written a few day its writer should still without doubt point out 3 primary phenomena that have been the assets of the area in view. "Ve suggest combustion and part transition waves, waves in chemical reactors the place oxidation-reduction approaches happen, and propagation of excitations in nerve fibres. the most instruments of the speculation of autowave approaches are a number of equipment used for investigating nonlinear discrete or allotted oscillating platforms, the mathe­ matical idea of nonlinear parabolic differential equations, and strategies of the idea of finite automata. it's noteworthy that the idea of autowave,. , has been drastically contributed to be paintings of extraordinary mathematicians who expected the experimental discoveries of their summary stories. 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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Additional resources for Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine

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The model is named after 1. Prigogine's Brussel School, members of which contributed greatly to its investigation (see monographs by Glansdorff and Prigogine 1971 and Nicolis and Prigogine 1977; other references are given in Chapter 7). The scheme of chemical reactions which is the basis for the local kinetics of a Brussellator originated in the pioneering work of A. Turing 1952; it is kl-+ (i) A+-_X, k-l k (iii) B+X+-'~Y+D, k_. (ii) 2X + Y +- k, -+ k_, 3X, (iv) X~-+ +c--'- E. k_. L D, while the ingredients X and Yare intermediate.

The nonequilibrium properties and diffusion coupling between the points of the system can lead to the existence of several inhomogeneous stationary solutions, which are either structures that do not change with time or stationary waves that propagate at a constant speed. 2. One of the main problems arising here is choosing the basic characteristics of these AW processes: front velocity, TP width, and others. 3) by the small perturbation method. For small nonlinearities (or quasi-harmonic systems), concepts of increments or decrements of harmonics, dispersion, etc.

Propagation of electric excitations along nerve fibres and other similar systems (Fig. 1) must be described, strictly speaking, by means of the Maxwell equations (cf. g. Scott 1977). 3 Om) and the fibre radius is small (less than 1 mm), the damping factor is high for passive propagation of travelling pulses. Active properties are due to membranes. Evidently, these properties can manifest theirselves only in presence of transverse magnetic waves (ER =f= 0, He = Hr = E6 = 0) which are shown in Fig.

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