On the derivation of the Debye theory of dielectric relaxation from the Langevin equation in the presence of the driving field. II. Inclusion of inertial effects for rotation in three dimensions

1991 ◽  
Vol 95 (3) ◽  
pp. 2026-2035 ◽  
Author(s):  
W. T. Coffey
Keyword(s):  
Dielectric Relaxation ◽  
Langevin Equation ◽  
Three Dimensions ◽  
Inertial Effects ◽  
Debye Theory ◽  
Driving Field

scholarly journals Inertial effects in the anomalous dielectric relaxation of rotators in space

2002 ◽  
Vol 65 (5) ◽  
Author(s):  
William T. Coffey ◽  
Yuri P. Kalmykov ◽  
Sergey V. Titov
Keyword(s):  
Dielectric Relaxation ◽  
Inertial Effects

THE STATISTICS OF CRACK BRANCHING DURING FAST CRACK PROPAGATION

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1051-1058 ◽  
Author(s):  
E. BOUCHAUD ◽  
J.-P. BOUCHAUD ◽  
J. PLANÈS ◽  
G. LAPASSET
Keyword(s):  
Crack Propagation ◽  
Langevin Equation ◽  
Scaling Laws ◽  
Percolation Cluster ◽  
Three Dimensions ◽  
Crack Branching ◽  
Directed Percolation ◽  
Fracture Surfaces ◽  
Affine Structures ◽  
Branched Structures

We present simple theoretical ideas which allow an understanding of part of the scaling laws recently observed on branched fracture surfaces. Some of these are argued to be common to all critical branched structures, which barely survive when propagating. This is exemplified by numerical results on the directed percolation cluster, which serves as a good toy-model. Finally, we propose a Langevin equation for unbranched cracks in three dimensions, which naturally leads to self-affine structures.

Sign in / Sign up

Export Citation Format

Share Document