Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion

Area of Science:

• Physics
• Computational Science
• Statistical Mechanics

Background:

• Subdiffusive random walks are crucial for modeling anomalous transport in various physical systems.
• Existing methods for simulating these walks often face computational challenges, especially with memory effects.
• Fractional Langevin equations provide a theoretical framework for describing subdiffusion driven by viscoelastic forces.

Purpose of the Study:

• To introduce a novel kinetic Monte Carlo (KMC) method for simulating subdiffusive random walks on a Cartesian lattice.
• To incorporate viscoelastic forces, computed via the fractional Langevin equation, into the random walk model.
• To develop a computationally efficient simulation technique that handles n-step memory effects.

Main Methods:

• The proposed method employs a kinetic Monte Carlo approach where walkers move one lattice unit per step.
• Viscoelastic forces are calculated from individual walker trajectories using the fractional Langevin equation.
• An approximation with O(log n) complexity is used for memory and memory kernel functions, with numerical adjustments to compensate for artifacts.

Main Results:

• The developed KMC method successfully simulates subdiffusive random walks on a lattice.
• The simulations accurately capture the behavior dictated by viscoelastic forces and fractional Langevin dynamics.
• The method demonstrates consistency with the theory of fractional Brownian motion.

Conclusions:

• The new kinetic Monte Carlo method provides an efficient and accurate way to simulate subdiffusive random walks with viscoelastic forces.
• This approach offers a valuable tool for studying anomalous transport phenomena governed by fractional dynamics.
• The method's computational efficiency and theoretical consistency make it suitable for complex simulations.