Internal Percolation Problem

TL;DR

This paper introduces the internal percolation problem (IP), a new variation where current flows through internal holes, and compares its properties to the traditional external percolation problem (EP), revealing similarities in conductance but differences in noise characteristics.

Contribution

The study defines the internal percolation problem, explores its parameters, and compares its critical indexes and noise behavior to the external percolation problem.

Findings

Critical conductance indexes are similar in IP and EP.

Relative spectral noise density differs significantly between IP and EP.

Higher moments of noise also show notable differences.

Abstract

Introduced and investigated new kind of percolation problem - so called internal percolation problem (IP). In usual percolation problem current flows from top to bottom of the system and here it can be called as external percolation problem (EP) despite of the IP case when voltage is applied to the system through bars which are inside of the hole in system. EP problem has two major parameters: M size of system and a0 size of inclusion, lattice size etc. IP holds one more parameter the size of hole - L. Results of computer simulation show that critical indexes of conductance for IP problem are very close to those in EP problem. In opposite indexes of relative spectral noise density of 1/f noise and higher moments are really differs from EP problem. The source of such behaviour is discussed.