Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models

Area of Science:

• Computational physics
• Soft matter physics
• Multiscale modeling

Background:

• Particle-based coarse-grained models are crucial for simulating complex systems.
• Accurate modeling requires capturing non-Markovian dynamics and frequency-dependent interactions.
• Efficient simulation techniques are needed for systems with incomplete time scale separation.

Purpose of the Study:

• To introduce a generalized Langevin dynamics (GLD) technique for constructing and simulating non-Markovian particle-based coarse-grained models.
• To develop an efficient simulation algorithm for these GLD models.
• To assess the accuracy and transferability of the GLD method for soft matter systems.

Main Methods:

• Developed a discretized generalized Langevin equation with distance-dependent memory kernels.
• Iteratively reconstructed memory kernels from fine-grained simulation dynamical correlation functions.
• Implemented a linear-scaling simulation algorithm for the GLD method.
• Applied the GLD method to a nanocolloid suspension with frequency-dependent hydrodynamic interactions.

Main Results:

• GLD simulations accurately reproduced the dynamics of the fine-grained reference system.
• Achieved an effective speedup of approximately 10^4 compared to fine-grained simulations.
• Demonstrated model transferability to systems with nanocolloid densities differing by up to one order of magnitude.

Conclusions:

• The proposed GLD technique provides an efficient and accurate approach for non-Markovian coarse-grained modeling.
• GLD is suitable for simulating soft matter systems with incomplete time scale separation.
• The developed method shows excellent transferability and significant computational advantages.