Download Dissipative Structures and Chaos by Professor Hazime Mori, Professor Dr. Yoshiki Kuramoto PDF

By Professor Hazime Mori, Professor Dr. Yoshiki Kuramoto (auth.)

ISBN-10: 3642803768

ISBN-13: 9783642803765

ISBN-10: 3642803784

ISBN-13: 9783642803789

This monograph involves elements and provides an method of the physics of open nonequilibrium structures. half I derives the phenomena of dissipative buildings at the foundation of decreased evolution equations and comprises Bénard convection and Belousov-Zhabotinskii chemical reactions. half II discusses the physics and constructions of chaos. whereas offering a development of the statistical physics of chaos, the authors unify the geometrical and statistical descriptions of dynamical platforms. the form of chaotic attractors is characterised, as are the blending and diffusion of chaotic orbits and the fluctuation of strength dissipation exhibited by way of chaotic systems.

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Extra info for Dissipative Structures and Chaos

Sample text

Let us now determine a new orthogonal coordinate system ~-'T/, obtained from the x-y system through a rotation

and qx < 0, respectively). According to our assumption, the defect moves in the 17 direction at constant speed. We thus look for a solution of the form ° W = w(E, 17- ct)eiq~ .

It is interesting that the equation found here to describe an anisotropic fluid has been reduced to a form that is more simple than the NW equation, used to describe an isotropic fluid. 3 Topological Defects and Their Motion In the NW equation, or alternatively the GP equation, let us write the complex amplitude W as W = Aexp{i1/J) with the real amplitude A and phase 1/J. 4b) applies to A for the case of steady rolls. In this case, A assumes a constant value throughout space. When such a periodic pattern is disturbed, A becomes spatially nonuniform.

Thus the defect moves in such a way as to remove a single roll from the system, thereby slightly increasing the spacing between rolls. Contrastingly, when q < 0, the defect rises, and in so doing acts to increase the number of rolls in the system by 1. As a result, the periodic structure of the system becomes slightly finer. In this manner, the motion of defects acts to push the system toward the wavelength Ac. A pure glide occurs in the case qx = O. Here, t; = y, 1] = -x, and q = qy. If q > 0, the roll axis is somewhat tilted with respect to the y-axis.

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Dissipative Structures and Chaos by Professor Hazime Mori, Professor Dr. Yoshiki Kuramoto (auth.)

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