By Sitenko A.G., Zakharov V.E., Chernousenko V.M.

ISBN-10: 5120020860

ISBN-13: 9785120020862

The lawsuits include contributed papers submitted to the IV foreign Workshop on Nonlinear and Turbulent techniques in Physics "NONLINEAR international" (Kiev, October 9-22, 1989) and approved by way of the Organizing Committee. The ebook is an instantaneous replica of the camera-ready manuscripts provided by means of the authors. No corrections were made within the texts. quantity 2 contains the next themes: difficulties in quantum box concept and statistical physics, nonlinear phenomena within the surroundings and the sea, mathematical equipment, chaos and turbulence.

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**Extra resources for Nonlinear and turbulent processes in physics**

**Example text**

Therefore, the functions T (E9 ω\Ε09ω0; X)9 Τ (Ε9 ω\Ε09 ω 0 ; X)9 and R(E9 ω \ E0, ω0; X) vanish for energy Ε greater than source energy E0. From Eqs. 3) The initial condition for the function is evidently given by Τ^(Ε9ω\Εθ9ωο;0) (8 In terms of the function f \ rewritten in the form = 0. 1 : DERIVATION Τ^(Ε,ω\Ε0,ω0;Χ OF EQUATIONS FOR NUMERICAL + Χ') = Γ" dE' f άω' P*\E, ω \ Ε', ω'; Χ')Ρ»(Ε', Jo 43 SOLUTIONS Jo + exp(- X'} • P'\E, + Τ <"(£, ω\Ε0, ω ; Χ') 0 ω\Ε0, exp(- ω'\ E0, ω0; Χ) ω0; Χ) χ). 5) The relation between the modified transmission function and the or dinary one [Eq.

For this purpose, it is more convenient to introduce the energy reflection and transmission functions for multigroup approximations. They are defined by the equations #Ertm(">, ω 0 ; X) = -τι— ί dE f dE0 ω0;Χ) is = - ¡ L - f dE f dE0-^-T \E, m T$nm{o>, ω0;Χ) R(E> ω\Ε0,ω0; J η J m Jm ω \ E0y ω0;Χ), 0 ( ? " ( £ , ω | E0> ω 0 ; X ) . 24) 48 4 : METHOD OF NUMERICAL SOLUTIONS The equations for the energy reflection and transmission functions have the same form as Eqs. 2 í dE ί dE0 - J - ΣΆ(Ε0, -^=r- Jη Jm ω0 -> Ε, ω).

From the solution for the initial thickness h. Thus, one can obtain solutions for very thick slabs without difficulty, even though one starts from the solution for a very thin slab. From Eq. 21) we also have f £ » t o , ω,; nX + X) = £ l=m Σ CkT%(o>it ω,; X)T%(cok, ω,; nX) k=l + exp(- - Α. «z). 37) can be used to generate solutions for thicknesses 2X, 3Xy ... , nX, . . from the solution for a thickness X. 37) can be reduced further to a simpler form for the case when transmission due to an incident current of a specific energy spectrum and angular distribution is desired.

### Nonlinear and turbulent processes in physics by Sitenko A.G., Zakharov V.E., Chernousenko V.M.

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