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

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Percolation models are crucial for understanding material properties and phase transitions.
• Existing models often lack the flexibility to capture complex phenomena like activated carbon disintegration.
• Efficient computational methods are needed to analyze these complex systems.

Purpose of the Study:

• Introduce a versatile class of discrete-continuous percolation models.
• Develop and validate an efficient Monte Carlo algorithm for property computation.
• Apply the model and algorithm to a nanotube model of activated carbon disintegration.

Main Methods:

• Developed a generalized discrete-continuous percolation model framework.
• Implemented an efficient Monte Carlo simulation algorithm.
• Calculated exact critical thresholds in 2D and estimated in 3D for the nanotube model.
• Analyzed algorithm efficiency using critical exponents and properties.

Main Results:

• The proposed model class encompasses existing discrete and continuous percolation models.
• Exact critical threshold determined in 2D for the activated carbon nanotube model.
• Monte Carlo estimation of the critical threshold achieved in 3D.
• The algorithm demonstrated favorable efficiency compared to established methods for simpler systems.

Conclusions:

• The new discrete-continuous percolation models offer a unified framework for diverse systems.
• The developed Monte Carlo algorithm is efficient and accurate for analyzing complex materials.
• This approach provides valuable insights into the disintegration of activated carbon at the nanoscale.