Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal Structure of Equipotential Curves on a Continuum Percolation
  Model   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
$p_c$.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ