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

By V.A. Vasiliev, Yu.M. Romanovskii, D.S. Chernavskii, V.G. Yakhno

ISBN-10: 9400937512

ISBN-13: 9789400937512

ISBN-10: 9401081727

ISBN-13: 9789401081726

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 worthwhile certainly. F. Joliot-Curie The research of autowave strategies is a tender technological know-how. Its simple techniques and techniques are nonetheless within the technique of formation, and the sphere of its purposes to varied domain names of average sciences is increasing constantly. dazzling examples of varied autowave techniques are saw experimentally in different laboratories of rather assorted orientations, facing investigations in physics, chemistry and biology. it really is O1). r opinion, even though, that if a historical past of the invention of autowaves will he written a few day its writer may still definitely point out 3 primary phenomena which have been the assets of the area in view. "Ve suggest combustion and part transition waves, waves in chemical reactors the place oxidation-reduction techniques happen, and propagation of excitations in nerve fibres. the most instruments of the idea of autowave approaches are numerous tools used for investigating nonlinear discrete or allotted oscillating structures, the mathe­ matical thought of nonlinear parabolic differential equations, and techniques of the speculation of finite automata. it really is noteworthy that the idea of autowave,. , has been significantly contributed to be paintings of terrific mathematicians who expected the experimental discoveries of their summary stories. 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).

Show description

Read or Download Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine PDF

Similar system theory books

New PDF release: An Elementary Course in Synthetic Projective Geometry

This e-book used to be switched over from its actual version to the electronic structure by means of a group of volunteers. you could locate it at no cost on the net. buy of the Kindle version comprises instant supply.

Get Low-Complexity Controllers for Time-Delay Systems PDF

This quantity within the newly tested sequence Advances in Delays and Dynamics (ADD@S) offers a suite of modern effects at the layout and research of Low Complexity Controllers for Time hold up platforms. A widespread oblique technique to receive low order controllers for time hold up structures is to layout a controller for the diminished order version of the plant.

Read e-book online Mathematical Control Theory I: Nonlinear and Hybrid Control PDF

This therapy of recent subject matters regarding mathematical platforms idea varieties the court cases of a workshop, Mathematical platforms idea: From Behaviors to Nonlinear keep an eye on, held on the college of Groningen in July 2015. The workshop celebrated the paintings of Professors Arjan van der Schaft and Harry Trentelman, honouring their sixtieth Birthdays.

Extra resources for Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine

Example text

Thus in this domain the variable x has autocatalytic properties. In the following x stands for the autocatalytic variable, unless specified otherwise. A particular, but vast, family of models has a special name: the Fitz-Hew-Nagumomodel (Scott 1975). In this case P(x, y) = -y +x - x 3, Q(x, y) = b - y + yx. This model enables one to investigate stationary propagation and formation of TPs (Chapter 4), fission of TP fronts, AW "echo" regimes (Chapter 5) and other phenomena. If band y acquire values such that the point system has three singular points, only TF can propagate in the distributed system.

8), reducing the hyperbolic equation to the form specific for Eqs. 3). 9) would be used in models. 3. Active lines with high linear conductances, like nerve fibres, may be investigated in the framework of a basic model which has been obtained by reduction from Eqs. 8) (or from an analoguous equation). Propagation of excitation waves is due to active (but not wave) properties of such media. 11) where r E (-00, (0), 0 < Xo < 1, and all parameters of the model are positive. The left-hand side is similar to that in Eqs.

52) 02y + Dy 8r2' The variables involved here are usually: X - temperature of the medium, y - concentration of a reagent limiting the combustion reaction. e. Q(x, y) = yq exp {-Ejkx} , where E is the activation energy, k Boltzmann's constant, q a constant. A simplified representation of the source function is used in qualitative investigations, Q""' (x - Xl) (X - x 2) y. If Dx = Dy, after a change of variables, x' = x - yy, y' = x + yy, we get the single equation discussed above. Thus, the simplest model of a TP is a particular case of the model represented as Eqs.

Download PDF sample

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


by William
4.2

Rated 4.24 of 5 – based on 9 votes