scholarly journals Additive blending of local approximations into a globally-valid approximation with application to the dilogarithm

2001 ◽  
Vol 14 (4) ◽  
pp. 477-481 ◽  
Author(s):  
J.P. Boyd
Keyword(s):  
Local Approximations

scholarly journals Combining global and local approximations

AIAA Journal ◽  
1991 ◽  
Vol 29 (9) ◽  
pp. 1523-1525 ◽  
Author(s):  
Raphael T. Haftka
Keyword(s):  
Local Approximations ◽  
Global And Local

scholarly journals Inverse cascade anomalies in fourth-order Leith models

2021 ◽  
Author(s):  
Simon Thalabard ◽  
Sergey Medvedev ◽  
Vladimir Grebenev ◽  
Sergey Nazarenko
Keyword(s):  
Fourth Order ◽  
Field Model ◽  
Kinetic Equations ◽  
Vacuum Field ◽  
Wave Turbulence ◽  
Anomalous Scaling ◽  
Time Singularity ◽  
Linear Diffusion ◽  
Local Approximations ◽  
Finite Time Singularity

Abstract We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

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