Effect of anisotropy on the scaling of connectivity and conductivity in continuum percolation theory.
We investigate the effects of anisotropy on the finite-size scaling of connectivity and conductivity of continuum percolation in three dimensions. We consider a system of size X×Y×Z in which cubic bodies of size a×b×c are placed randomly. We define two aspect ratios to request anisotropy then we expect that the displacement of average connected fraction P (averaged over the realizations), about the isotropic universal curves will be a function of the two aspect ratios. This is accounted by considering an apparent percolation threshold in each direction which leads to 50% of realizations connecting in that direction. We find the aspect ratios' dependency of the apparent threshold and investigate the finite-size scaling transformations for the mean connected fraction and its associated fluctuations. Moreover, we apply a single phase pressure solver to determine the conductivity of various realizations of the system. Finally we apply the same idea to account for the effect of anisotropy on the conductivity scaling.
Sadeghnejad
S
S
Department of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 11365-9465, Azadi Avenue, Tehran, Iran. s_sadeghnejad@mapsaeng.com
Masihi
M
M
King
P R
PR
Shojaei
A
A
Pishvaei
M
M