By Jiantong Li

RIT, Sweden

A Monte Carlo simulator to study percolation characteristics of two-dimensional stick systems

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Version 1.01 - published on 24 Mar 2014

doi:10.4231/D3X921J6V cite this

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Stick2D is a tool to study, by Monte Carlo simulations, the behaviors of two-dimensional stick percolation systems. In percolation theory, stick systems are one of the most important continuum percolations. In practice, stick percolation is also very useful for electronics, material science and engineering, and nanotechnology which rely on networks of stick-like (or rod-like) nanoparticles, including a variety of nanotubes, nanoribbons and nanowires, such as carbon nanotubes, silicon nanowires.

Stick2D is somewhat similar to NanoNet, but focuses more on the percolation characteristics. It features using high-efficiency algorithms to effectively study large-size stick systems.

In the present version, Stick2D can only study those percolation systems with identical width-less sticks. It includes the following components:

Spanning Probability
This component produces the spanning probability function of a stick percolation. This function describes how the spanning probability (the probability a stick system contains at least one continuous path connecting its two opposite boundaries) varies with the stick number density (the number of sticks per unit area). The results include both the direct simulation observables (mircocanonical percolation ensemble) and their convolution with Poisson distribution (canonical percolation ensemble). The sub-cell algorithm [1] and the tree-based algorithm [2,3] are integrated in this component to improve the efficiency.

This component produces the dependence of the system conductivity on the stick number density. The sample standard deviation (relative) is also included in the simulation results. Besides the sub-cell algorithm and tree-based algorithm, this component employs preconditioned conjugate gradient method [4] to solve the large systems of linear equations.


Cite this work

Researchers should cite this work as follows:

  • Jiantong Li (2014), "Stick2D," (DOI: 10.4231/D3X921J6V).

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