RENORMALIZATION GROUP METHOD APPLIED TO LARGE SCALE LANGMUIR TURBULENCE

1979 ◽  
Vol 40 (C7) ◽  
pp. C7-657-C7-658
Author(s):  
G. Pelletier
Keyword(s):  
Renormalization Group ◽  
Large Scale ◽  
Group Method ◽  
Renormalization Group Method ◽  
Langmuir Turbulence

Langmuir turbulence as a critical phenomenon. Part 2. Application of the dynamical renormalization group method

1980 ◽  
Vol 24 (3) ◽  
pp. 421-443 ◽  
Author(s):  
Guy Pelletier
Keyword(s):  
Renormalization Group ◽  
Large Scale ◽  
Critical Phenomenon ◽  
Critical Curve ◽  
Group Method ◽  
Renormalization Group Method ◽  
Scaling Invariance ◽  
Correlation Spectrum ◽  
Scale Properties ◽  
Modulation Regime

In part 1 of this work, we have found a ‘critical curve’ which separates the unstable self-modulation regime from the stable one for a Gibbs ensemble of interacting modes. On this critical curve, the correlation length diverges and scaling invariance occurs; in particular, the Langmuir correlation spectrum is proportional to k-2. Simple laws have been derived for the neighbourhood of the critical curve. However these derivations are based on equilibrium statistical mechanics and the results are obtained with a Hartree approximation which has not been checked. So, in this second part, we elaborate a direct statistical theory of Zakharov's equations completed by excitation sources and dissipations. In spite of infra-red divergences and a large fluctuation level, large-scale properties are derived in the neighbourhood of the critical curve, by the renormalization group method. The laws obtained in part 1 are slightly modified; however, the same spectrum is obtained.

scholarly journals New applications of the renormalization group method in physics: a brief introduction

2011 ◽  
Vol 369 (1946) ◽  
pp. 2602-2611 ◽  
Author(s):  
Y. Meurice ◽  
R. Perry ◽  
S.-W. Tsai
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Dynamical Systems ◽  
Particle Physics ◽  
Recent Progress ◽  
Condensed Matter ◽  
Group Method ◽  
Renormalization Group Method ◽  
Theme Issue ◽  
New Applications

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

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