By Yu.L. Klimontovich
ISBN-10: 9401055157
ISBN-13: 9789401055154
ISBN-10: 940113426X
ISBN-13: 9789401134262
analyzing the experimental information and developing math.ematical versions of the strategies less than research, one has to depend really at the actual instinct than at the strict calculations. Now allow us to cross one step larger and clarify the most name of the ebook. The thoughts of "laminary" and "turbulent" motions have been first brought in hydrodynamics. because the previous days those thoughts have significantly broadened; now the laminar and the turbulent motions were came across and investigated in any respect degrees of description of nonequilibrium procedures within the open platforms, from kinetics to response diffusion. at the least, one of many crucial features of the turbulent movement is the lifestyles of a giant variety of well-developed macroscopic levels of freedom. accordingly the turbulent movement is very advanced and to a wide volume unpredictable. because the laminar and the turbulent flows play a big position within the tactics of evolution within the open platforms, and particularly, within the strategies of self-organization, you have to for assessing the relative measure of order of laminar and turbulent motions, and likewise for evaluating the measure of order of varied turbulent motions. with no with the ability to make such estimates will probably be most unlikely to figure out no matter if the evolution goes in the direction of larger or in the direction of decrease association whilst one turbulent kingdom is changed by means of another.
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Extra resources for Turbulent Motion and the Structure of Chaos: A New Approach to the Statistical Theory of Open Systems
Example text
11): ~ 2rr 00 = - nfPdPfd Accordingly, Bogolyubov's condition implicitly assumes that the large-scale (kinetic, hydrodynamic, diffusion) fluctuations are neglected. This is exactly it becomes possible, by getting the approximate solution of the BBGKY chain of equations, to obtain the closed irreversible kinetic Boltzmann equation for the statistical distribution f(x,t), or the equation of fluid mechanics in sixdimensional phase space. The plan for deriving the Boltzmann equation, pro'posed by Kirkwood (1946; 1947), is somewhat different. 7). 8), used in the BBGKY theory. 20). 1)1 and use the identity (rr) = Ff + (oror). 1)2 We also define the smoothed correlation function (oror)x,x,,t 1[o(x = Ii , 1 't)) + '" - x )f(x,t) - vf(x. ' t). 20) yields an extra term with the two-particle correlation in the integrand, together with the product of one-particle distributions f. Since the integration range with respect to r (the target distance p) is of the order of r~ = V o and the genuine (not smoothed over V ) correlation g2 in this range ph is of the order of unity, g2 g = Jg (r )dr 2 2 V /V V0 ph r '" V 3 0 '" (1. Turbulent Motion and the Structure of Chaos: A New Approach to the Statistical Theory of Open Systems by Yu.L. Klimontovich
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