scholarly journals The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions

2011 ◽  
Vol 16 (0) ◽  
pp. 775-780
Author(s):  
Artem Sapozhnikov
Keyword(s):  
Percolation Cluster ◽  
Two Dimensions ◽  
Invasion Percolation ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster

Dynamic Contrast-Enhanced MRI and Fractal Characteristics of Percolation Clusters in Two-Dimensional Tumor Blood Perfusion

1999 ◽  
Vol 121 (5) ◽  
pp. 480-486 ◽  
Author(s):  
O. I. Craciunescu ◽  
S. K. Das ◽  
S. T. Clegg
Keyword(s):  
Tumor Tissue ◽  
Blood Perfusion ◽  
Percolation Cluster ◽  
Three Dimensions ◽  
Invasion Percolation ◽  
Two Dimensional ◽  
Tumor Perfusion ◽  
Dynamic Contrast Enhanced ◽  
Contrast Enhanced ◽  
Fractal Characteristics

Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool is used to study tumor tissue perfusion. The results are then analyzed using percolation models. Percolation cluster geometry is depicted using the wash-in component of MRI contrast signal intensity. Fractal characteristics are determined for each two-dimensional cluster. The invasion percolation model is used to describe the evolution of the tumor perfusion front. Although tumor perfusion can be depicted rigorously only in three dimensions, two-dimensional cases are used to validate the methodology. It is concluded that the blood perfusion in a two-dimensional tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. For all the cases studied, the front starts to grow from the periphery of the tumor (where the feeding vessel was assumed to lie) and continues to grow toward the center of the tumor, accounting for the well-documented perfused periphery and necrotic core of the tumor tissue.

scholarly journals Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions

2008 ◽  
Vol 278 (2) ◽  
pp. 385-431 ◽  
Author(s):  
Martin T. Barlow ◽  
Antal A. Járai ◽  
Takashi Kumagai ◽  
Gordon Slade
Keyword(s):  
Random Walk ◽  
Oriented Percolation ◽  
High Dimensions ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster

Fragmentation of Invasion Percolation Cluster in Two-Dimensional Porous Media

1995 ◽  
Vol 31 (3) ◽  
pp. 139-144 ◽  
Author(s):  
G Wagner ◽  
A Birovljev ◽  
P Meakin ◽  
J Feder ◽  
T Jøssang
Keyword(s):  
Porous Media ◽  
Percolation Cluster ◽  
Invasion Percolation ◽  
Two Dimensional

Gravity invasion percolation in two dimensions: Experiment and simulation

1991 ◽  
Vol 67 (5) ◽  
pp. 584-587 ◽  
Author(s):  
A. Birovljev ◽  
L. Furuberg ◽  
J. Feder ◽  
T. Jssang ◽  
K. J. Mly ◽  
...  
Keyword(s):  
Two Dimensions ◽  
Invasion Percolation ◽  
Experiment And Simulation

scholarly journals Relations between invasion percolation and critical percolation in two dimensions

2009 ◽  
Vol 37 (6) ◽  
pp. 2297-2331 ◽  
Author(s):  
Michael Damron ◽  
Artëm Sapozhnikov ◽  
Bálint Vágvölgyi
Keyword(s):  
Two Dimensions ◽  
Invasion Percolation ◽  
Critical Percolation
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