A new dynamic Monte Carlo method satisfying n-particle diffusion equation with position-dependent diffusion...

Area of Science:

• Computational Physics
• Chemical Physics
• Statistical Mechanics

Background:

• Single-particle diffusion in heterogeneous media is challenging to model.
• Existing methods often lack accuracy or are computationally expensive for complex systems.

Purpose of the Study:

• To generalize a dynamic Monte Carlo (MC) method for single-particle diffusion to n-particle dynamics.
• To accurately describe the diffusion of interacting molecules in heterogeneous environments.

Main Methods:

• Extension of a dynamic MC method to n-particle systems with position-dependent diffusion and free energy.
• Algebraic proof using the master equation for MC transition probabilities.
• Comparison of MC calculations with molecular dynamics (MD) for 2D heterogeneous Lennard-Jones systems.

Main Results:

• MC transition probabilities satisfy the n-particle diffusion equation.
• Excellent agreement between MC and MD for global diffusion coefficients.
• Demonstrated extension of Metropolis MC to heterogeneous dynamics with position-dependent coefficients.

Conclusions:

• The generalized dynamic MC method accurately describes n-particle diffusion in heterogeneous media.
• The method offers a computationally efficient approach for simulating complex, large-scale particle dynamics.
• This provides a valuable tool for investigating sub-micrometer diffusion over millisecond timescales.