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Stick2D
A Monte Carlo simulator to study percolation characteristics of twodimensional stick systems
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Abstract
Stick2D is a tool to study, by Monte Carlo simulations, the behaviors of twodimensional 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 sticklike (or rodlike) 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 highefficiency algorithms to effectively study largesize stick systems.
In the present version, Stick2D can only study those percolation systems with identical widthless 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 subcell algorithm [1] and the treebased algorithm [2,3] are integrated in this component to improve the efficiency.
Conductivity
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 subcell algorithm and treebased algorithm, this component employs preconditioned conjugate gradient method [4] to solve the large systems of linear equations.
Stick2D is somewhat similar to NanoNet, but focuses more on the percolation characteristics. It features using highefficiency algorithms to effectively study largesize stick systems.
In the present version, Stick2D can only study those percolation systems with identical widthless 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 subcell algorithm [1] and the treebased algorithm [2,3] are integrated in this component to improve the efficiency.
Conductivity
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 subcell algorithm and treebased algorithm, this component employs preconditioned conjugate gradient method [4] to solve the large systems of linear equations.
References
[1] T. Vicsek and J. Kertész, J. Phys. A 14, L31 (1981).
[2] M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85, 4104 (2000).
[3] M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001).
[4] http://en.wikipedia.org/wiki/Conjugate_gradient_method
[2] M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85, 4104 (2000).
[3] M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001).
[4] http://en.wikipedia.org/wiki/Conjugate_gradient_method
Cite this work
Researchers should cite this work as follows:

For the Spanning Probability, please refer to
J. Li and S.L. Zhang, Physical Review E 80, 040104(R) (2009).
For the Conductivity, please refer to
J. Li and S.L. Zhang, Physical Review E 81, 021120 (2010).
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