A derivation of the scaling law, the power law and the scaling relation for fetch-limited wind waves using the renormalization group theory

1998 ◽  
Vol 54 (6) ◽  
pp. 641-649
Author(s):  
Koji Ueno
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Power Law ◽  
Wind Waves ◽  
Scaling Law ◽  
Renormalization Group Theory ◽  
Scaling Relation

Statistical Damage Mechanics— Part I: Theory

2005 ◽  
Vol 72 (1) ◽  
pp. 76-85 ◽  
Author(s):  
D. Krajcinovic ◽  
A. Rinaldi
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Damage Mechanics ◽  
Renormalization Group Theory ◽  
Scaling Relation ◽  
Simulation Data ◽  
The Family ◽  
Damage Process ◽  
Statistical Damage

Statistical damage mechanics in this work establishes the connection between damaged random heterogeneous micromaterial and the system macroparameter. Renormalization group theory provides the bridge from the microscale to the macroscale. Delaunay lattices, which simulate and capture the role of the disordered microstructure in damage process, substitute a polycrystal specimen assuming that microcracks are grain-boundaries cracks. The macroparameters of the system, in the form of algebraic functions, are obtained applying the Family–Vicsek scaling relation on simulation data.

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