Wavelet Monte Carlo dynamics: A new algorithm for simulating the hydrodynamics of interacting Brownian particles

Area of Science:

• Computational physics and chemistry
• Soft matter physics
• Statistical mechanics

Background:

• Simulating soft matter systems requires accurate modeling of hydrodynamic interactions.
• Existing Brownian dynamics and lattice Boltzmann algorithms have limitations in computational cost and accuracy.

Purpose of the Study:

• To develop a novel algorithm for Brownian dynamics of soft matter.
• To achieve efficient and accurate simulation of hydrodynamic interactions in low Reynolds number regimes.
• To improve computational scaling for large numbers of particles.

Main Methods:

• Developed a new algorithm utilizing spatially correlated Monte Carlo moves based on vector wavelets.
• Incorporated plane wave moves for long-range correlations in both infinite and periodic systems.
• Algorithm's computational cost scales as N log N in homogeneous systems and N in dilute systems.

Main Results:

• The wavelet method approximates the Rotne-Prager tensor, improving upon the Oseen tensor.
• Demonstrated competitive computational cost, outperforming lattice Boltzmann and Brownian dynamics at large N in dilute systems.
• Validated the algorithm by reproducing equilibrium and dynamic properties of single polymer systems.

Conclusions:

• The new wavelet-based Brownian dynamics algorithm offers an efficient and accurate approach for soft matter simulations.
• The method provides a significant speedup over established algorithms, particularly for large, dilute systems.
• The algorithm correctly captures hydrodynamic interactions and system properties, including the effects of periodicity.