scholarly journals Phase Transition for the Speed of the Biased Random Walk on the Supercritical Percolation Cluster

2013 ◽  
Vol 67 (2) ◽  
pp. 173-245 ◽  
Author(s):  
Alexander Fribergh ◽  
Alan Hammond
Keyword(s):  
Phase Transition ◽  
Random Walk ◽  
Percolation Cluster ◽  
Biased Random Walk

Random walk in a percolation cluster: external field dependence

1991 ◽  
Vol 24 (3) ◽  
pp. 735-740
Author(s):  
Jae Woo Lee ◽  
Ho Chui Kim ◽  
Jong-Jean Kim
Keyword(s):  
Random Walk ◽  
External Field ◽  
Field Dependence ◽  
Percolation Cluster

A Biased Random Walk with Symmetry

1992 ◽  
Vol 65 (5) ◽  
pp. 330
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury
Keyword(s):  
Random Walk ◽  
Biased Random Walk

RANDOM WALK ON ANISOTROPICALLY GENERATED PERCOLATION CLUSTER AND ANISOTROPIC RANDOM WALK ON PERCOLATION CLUSTER

1989 ◽  
Vol 03 (10) ◽  
pp. 765-770
Author(s):  
C.S. KIM ◽  
MIN-HO LEE
Keyword(s):  
Random Walk ◽  
Fractal Dimensionality ◽  
Percolation Cluster ◽  
Asymptotic Convergence ◽  
Spectral Dimensionality

We studied two subjects related to anisotropy: random walk on percolation cluster having anisotropy (RWAC) and direction dependent (anisotropic) random walk on percolation cluster (AWIC). We find that the anisotropy of the cluster has only time-delaying effect on asymptotic convergence of the spectral dimensionality ds and fractal dimensionality of walk dw, however, the anisotropy of the walk results in lower spectral dimensionality and higher fractal dimensionality, as anisotropy grows larger.

scholarly journals A phase transition in the random transposition random walk

2005 ◽  
Vol 136 (2) ◽  
pp. 203-233 ◽  
Author(s):  
Nathanaël Berestycki ◽  
Rick Durrett
Keyword(s):  
Phase Transition ◽  
Random Walk ◽  
Random Transposition

COMPUTATIONAL INVESTIGATION OF THE EFFECTS OF SPHERICAL FILLER MORPHOLOGY AND LOADING ON DIFFUSION TORTUOSITY AND RUBBER PERMEABILITY

2013 ◽  
Vol 86 (2) ◽  
pp. 175-189 ◽  
Author(s):  
T. C. Gruber ◽  
S. D. Crossley ◽  
A. P. Smith
Keyword(s):  
Random Walk ◽  
Rolling Resistance ◽  
Diffusion Path ◽  
Filler Loading ◽  
Pressure Losses ◽  
Biased Random Walk ◽  
Gas Molecule ◽  
Path Lengths ◽  
Path Tortuosity ◽  
Spherical Filler

ABSTRACT Inflation pressure loss in tires degrades performance, raises rolling resistance, and reduces fuel economy. The incorporation of solid fillers, such as carbon black, at relatively high loadings in tire innerliners helps minimize these pressure losses by reducing innerliner permeability due to increases in average gas molecule diffusion path lengths (tortuosity), as well as reductions in diffusion pathway density (capacity). The effects of filler morphology and loading on diffusion path tortuosity can be explored by modeling biased random-walk diffusion through impermeable sphere-filled matrices. Modeled diffusion rate was found to decrease with increased filler loading, reduced filler sphere sizes, increased random-walk step sizes, and the aggregation of filler spheres. Initial correlations with limited empirical permeability measurements are used to validate the model approach.

A Biased Random Walk with Symmetry

1992 ◽  
Vol 65 (5) ◽  
pp. 330-333
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury
Keyword(s):  
Random Walk ◽  
Biased Random Walk
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