# Site-percolation threshold of carbon nanotube fibers—Fast inspection of percolation with Markov stochastic theory

@article{Xu2014SitepercolationTO, title={Site-percolation threshold of carbon nanotube fibers—Fast inspection of percolation with Markov stochastic theory}, author={Fangbo Xu and Zhiping Xu and Boris I. Yakobson}, journal={Physica A-statistical Mechanics and Its Applications}, year={2014}, volume={407}, pages={341-349} }

## 9 Citations

### Percolation thresholds for discrete-continuous models with nonuniform probabilities of bond formation.

- Computer SciencePhysical review. E
- 2016

A class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties are introduced and it is found that it compares favorably to well-known algorithms for simpler systems.

### Field percolation-switching in soft ternary anisotropic system

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2019

### Polycrystalline morphology and mechanical strength of nanotube fibers

- Materials Science, Physicsnpj Computational Materials
- 2022

Correlating mechanical performance with mesoscale structure is fundamental for the design and optimization of light and strong fibers (or any composites), most promising being those from carbon…

### Percolation thresholds on a triangular lattice for neighborhoods containing sites up to the fifth coordination zone.

- PhysicsPhysical review. E
- 2021

We determine thresholds p_{c} for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their…

### A unified electrical model based on experimental data to describe electrical transport in carbon nanotube-based materials

- EngineeringNano Research
- 2020

Understanding the electrical transport in carbon nanotube (CNT) materials is one key to reach very high electrical conductivities. All CNT material resistivity ( ρ ( T )) as function of the…

### Large improvement of CNT yarn electrical conductivity by varying chemical doping and annealing treatment

- Engineering
- 2020

### Fatigue in assemblies of indefatigable carbon nanotubes

- Materials ScienceScience advances
- 2021

Description

### A Computational Approach to Determine the Percolation Threshold for Various Materials in Construction

- Materials ScienceBDET
- 2020

This work proposed using Monte Carlo simulation to computationally simulating the percolation probability for materials with different grain size and probability of open sites, and further explores the combination of two materials, which provide a useful computational framework to when analyzing a wide array of questions.

## References

SHOWING 1-10 OF 100 REFERENCES

### Analysis of electrical percolation thresholds in carbon nanotube networks using the Weibull probability distribution

- Engineering
- 2010

We suggest a method for the a priori determination of the electrical percolation threshold in carbon nanotube (CNT) networks, of relevance in electronic devices, polymer composites, etc. The…

### Fast Monte Carlo algorithm for site or bond percolation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

An efficient algorithm is described that can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system.

### Efficient Monte Carlo algorithm and high-precision results for percolation.

- MathematicsPhysical review letters
- 2000

A new Monte Carlo algorithm is presented that is able to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice.

### Critical behavior of the site percolation model on the square lattice in aL×M geometry

- Mathematics
- 1991

Relevant aspects of the critical behavior of the site percolation model in aL×M geometry (L≪M) are studied. It is shown that this geometry favors the growth of percolating clusters in theL-direction…

### Convergence of threshold estimates for two-dimensional percolation.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

This work shows that the convergence of the average-probability estimate is described by a nontrivial correction-to-scaling exponent as predicted previously, and measures the value of this exponent to be 0.90+/-0.02.

### Universality at the three-dimensional percolation threshold

- Physics
- 1994

The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The…

### Aspect-ratio dependence of percolation probability in a rectangular system

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

The dependence of the percolation probability R on a is shown and analyzed on the basis of a modified finite-size scaling function and a method for evaluating R without statistical simulations is proposed for given conditions of the system.

### Markov chain analysis of random walks in disordered media.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1994

A new technique of relating the velocity autocorrelation function and the return to the starting point probability to the asymptotic spectral properties of the hopping transition probability matrix of the diffusing particle is used, and the latter is numerically analyzed using the Arnoldi-Saad algorithm.

### Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The percolation properties derived here are useful to account for finite-size effects on percolated systems in natural or man-made correlated systems.

### Conduction in rectangular quasi-one-dimensional and two-dimensional random resistor networks away from the percolation threshold.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

A linear approximation for conduction in two-dimensional systems far away from the percolation threshold p(c) is proposed, which is useful for engineering purposes and of potential interest in fields such as nanostructured or composite materials and sensing applications.