Renormalization group approach and short-distance expansion in theory of developed turbulence: Asymptotics of the triplex equal-time correlation function

1995 ◽  
Vol 105 (3) ◽  
pp. 1556-1565 ◽  
Author(s):  
L. Ts. Adzhemyan ◽  
S. V. Borisenok ◽  
V. I. Girina
Keyword(s):  
Correlation Function ◽  
Renormalization Group ◽  
Short Distance ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Group Approach ◽  
Equal Time ◽  
Developed Turbulence ◽  
Renormalization Group Approach ◽  
Short Distance Expansion

scholarly journals NUMERICAL INVESTIGATION OF ANISOTROPICALLY DRIVEN DEVELOPED TURBULENCE

2007 ◽  
Vol 12 (3) ◽  
pp. 325-342 ◽  
Author(s):  
Edik Hayryan ◽  
Eva Jurcisinova ◽  
Marian Jurcisin ◽  
Milan Stenlik
Keyword(s):  
Renormalization Group ◽  
Parallel Programming ◽  
Numerical Investigation ◽  
Group Approach ◽  
Strongly Nonlinear ◽  
Developed Turbulence ◽  
Renormalization Group Equations ◽  
Renormalization Group Approach ◽  
Anisotropy Parameters ◽  
The Stability

The fully developed turbulence with axial anisotropy for dimensions d > 2 is investigated by means of renormalization group approach. The corresponding system of strongly nonlinear renormalization group equations which contain angle integrals is solved numerically. Possible utilization of the parallel programming methods is discussed. As a result, the influence of anisotropy on the stability of the Kolmogorov scaling regime is analyzed. The borderline dimension between stable scaling regime and unstable one is calculated as a function of the anisotropy parameters. Obtained results are compared with results calculated in [7].

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

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