Download e-book for iPad: Wave Turbulence Under Parametric Excitation: Applications to by Professor Dr. Victor S. L’vov (auth.)

By Professor Dr. Victor S. L’vov (auth.)

ISBN-10: 3642752950

ISBN-13: 9783642752957

ISBN-10: 3642752977

ISBN-13: 9783642752971

WAVE TURBULENCE is a kingdom of a method of many concurrently excited and interacting waves characterised by means of an strength distribution which isn't in any experience as regards to thermodynamic equilibrium. Such events in a uneven sea, in a scorching plasma, in dielectrics below come up, for instance, a strong laser beam, in magnets put in a robust microwave box, and so forth. one of the nice number of actual occasions within which wave turbulence arises, it's attainable to pick huge proscribing teams which permit an in depth research. the 1st is absolutely constructed wave turbulence coming up while strength pumping and dissipation have primarily various house scales. to that end there's a huge energy spectrum of turbulence. this sort of turbulence is defined intimately e. g. in Zakharov et al. 1 within the moment restricting case the scales within which power pumping and dissipation ensue are an analogous. in general, to that end a slim, nearly singular spectrum of turbulence looks that is focused close to surfaces, curves or maybe issues in k-space. the most very important, largely investigated and instructive examples of this sort of turbulence is parametric wave turbulence showing as a result of evolution of a parametric instability of waves in media below powerful exterior periodic modulation (laser beam, microwave electromagnetic box, and so forth. ). the current publication bargains with parametric wave turbulence.

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Extra info for Wave Turbulence Under Parametric Excitation: Applications to Magnets

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The state of the nonlinear wave system may be strongly excited. These waves will be described in detail by means of dynamic equations of motion for the wave amplitudes b(k, t). Let us assume that the "medium" weakly interacts with nonlinear waves and is in thermodynamic equilibrium. Then it can act as a thermal bath for the nonlinear wave systems. The physical characteristics of the remaining part of the medium that we assume to be a thermal bath may be absolutely different for specific cases. If our aim is a detailed description of long-wave length motions of the continuous medium (liquid or plasma) by means of dynamical equations, smallscale non-cooperative motions of the individual particles (liquid molecules, electrons and ions in plasma) will act as a thermal bath.

6) w( k) will be expanded in terms of Ii up to the terms ex ",2 and we shall take T(1,2;3,4) = T(ko,ko;ko,ko) = T/47f 3 . 16) This approach is correct if there are no long-range forcing in the medium and if T(l, 2; 3,4) is a continuous function of its arguments. 28). We have as a result: [i (:t + v . 20) Here v = 8w/8k , w" = 8 2 w/8k 2 . 5 Four-Wave Processes 31 with a group velocity, the terms 82 j 8z 2 and ill. describe the dispersion and the diffraction, and the last term describes the nonlinear self-action of the waves in the package.

This contribution to the energy is usually much greater than all the others and the magnetic moments of the valence electrons may be considered rigidly connected to one another. They are manifested in interatomic interactions as a single big magnetic moment with respective atomic spin S> 1/2. 3 Interatomic Exchange of Large Spins Consider the exchange interaction of two atoms in the state with a total spin Sa > 1/2 and Sb > 1/2. The wave functions are antisymmetric under rearrangement of N electrons on the atom a and N electrons on the atom b.

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Wave Turbulence Under Parametric Excitation: Applications to Magnets by Professor Dr. Victor S. L’vov (auth.)


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