Yoshiyuki Shimosako

Shigeki Matsutani, Yoshiyuki Shimosako, Yunhong Wang

We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear the {\it{quasi-equipotential clusters}} which approximately and locally have the same values like steps and stairs. Since the quasi-equipotential clusters has the fractal structure, we compute the fractal dimension of equipotential curves and its dependence on the volume fraction over $[0,1]$. The fractal dimension in [1.00, 1.257] has a peak at the percolation threshold $p_c$.

Shigeki Matsutani, Yoshiyuki Shimosako

In this article, we introduce a novel geometrical index $δ_{agg}$, which is associated with the Euler number and is obtained by an image processing procedure for a given digital picture of aggregated particles such that $δ_{agg}$ exhibits the degree of the agglomerations of the particles. In the previous work (Matsutani, Shimosako, Wang, Appl.Math.Modeling {\bf{37}} (2013), 4007-4022), we proposed an algorithm to construct a picture of agglomerated particles as a Monte-Carlo simulation whose agglomeration degree is controlled by $γ_{agg} \in (0,1)$. By applying the image processing procedure to the pictures of the agglomeration particles constructed following the algorithm, we show that $δ_{agg}$ statistically reproduces the agglomeration parameter $γ_{agg}$.