By Krzysztof Murawski

ISBN-10: 9812381554

ISBN-13: 9789812381552

Mathematical aesthetics isn't really frequently mentioned as a separate self-discipline, although it is affordable to consider that the principles of physics lie in mathematical aesthetics. This e-book provides an inventory of mathematical ideas that may be categorised as "aesthetic" and exhibits that those rules should be forged right into a nonlinear set of equations. Then, with this minimum enter, the ebook exhibits that possible receive lattice options, soliton structures, closed strings, instantons and chaotic-looking platforms in addition to multi-wave-packet recommendations as output. those options have the typical characteristic of being nonintegrable, ie. the result of integration rely on the combination course. the subject of nonintegrable structures is mentioned Ch. 1. creation -- Ch. 2. Mathematical description of fluids -- Ch. three. Linear waves -- Ch. four. version equations for weakly nonlinear waves -- Ch. five. Analytical tools for fixing the classical version wave equations -- Ch. 6. Numerical tools for a scalar hyperbolic equations -- Ch. 7. evaluate of numerical equipment for version wave equations -- Ch. eight. Numerical schemes for a approach of one-dimensional hyperbolic equations -- Ch. nine. A hyperbolic process of two-dimensional equations -- Ch. 10. Numerical tools for the MHD equations -- Ch. eleven. Numerical experiments -- Ch. 12. precis of the e-book

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**Additional info for Analytical and numerical methods for wave propagation in fluid media**

**Example text**

Lou and Rosner (1986) showed that the Alfven wave is damped owing to the time-dependent fluctuations. Kawahara (1976) proved that a time-dependent random field, that is associated with bottom inhomogeneities, leads to amplitude attenuation and increase (decrease) of low (high) frequency self-modulated surface gravity waves. Benilov and Pelinovsky (1989) provided an example of a time-dependent random media whose high (low) frequency fluctuations lead to wave amplification (damping). Muzychuk (1975) pointed out that space- and time- Waves in inhomogeneous fluids 37 dependent fluctuations lead to a reduction of the mean field damping and eventually to enhancement of this field.

Evaluation of the integral in Eq. 69) leads to the following expression: lx -^2 coh = 7^K{2-i^K), 3 2 8TT / cr = -l. 71) As the real (imaginary) part of Q2 is positive (negative) we conclude that the rightwardly propagating sound waves are speeded up and attenuated by the wave noise which moves to the left with its speed cr = — 1. For cr ^ ± 1 Eq. 69) can be rewritten as follows: (Crk - c-/r)2e-(*-*>a h^-^L c-c+(K-K)(k-<±Ky •dK. 73) Real and imaginary parts of U2lx/(coh) which follow from Eq. 73) are displayed in Fig.

In this case, electric charge density fluctuations are important and the electrostatic field is evaluated from Eq. 54). Both ions and electrons are often represented in this case kinetically with the relevant spatial and temporal scales equal to the electron Debye length and the inverse of the electron plasma frequency, respectively. For frequencies lower than the ion plasma frequency, electrons are treated adiabatically with the electron number density, ne = neo exp (j^f-) - (2-55) Mathematical description of fluids 18 where

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