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

Abstract

We propose a Generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a discretized generalized Langevin equation with distance-dependent two-particle contributions to the self-and pair-memory kernels. The memory kernels are iteratively reconstructed from the dynamical correlation functions of an underlying fine-grained system. We develop a simulation algorithm for this class of non-Markovian models that scales linearly with the number of coarse-grained particles. Our GLD method is suitable for coarse-grained studies of systems with incomplete time scale separation, as is often encountered, e.g., in soft matter systems.We apply the method to a suspension of nanocolloids with frequency-dependent hydrodynamic interactions. We show that the results from GLD simulations perfectly reproduce the dynamics of the underlying fine-grained system. The effective speedup of these simulations amounts to a factor of about 10 4 . Additionally, the transferability of the coarse-grained model with respect to changes of the nanocolloid density is investigated. The results indicate that the model is transferable to systems with nanocolloid densities that differ by up to one order of magnitude from the density of the reference system. t 0 ds j K NM-DPD ij (t, s)V j (s) (3) = t 0 ds j =i K ij (t − s) (V j (s) − V i (s)).arXiv:1808.00270v4 [cond-mat.soft]

Fluctuation–dissipation relations far from equilibrium: a case study

“…This uniquely defines the relationship between the dissipative and the random forces in the system, which is then given by the 2FDT, and it is applicable to systems far away from equilibrium and also non-stationary dynamics. Such a separation is crucial for consistent modeling and should enable to use dynamic coarse-graining techniques developed in recent years [42,63,64] for non-equilibrium systems. From a practical point of view, it could sometimes be convenient to use equivalent versions of the GLE that violate the 2FDT.…”

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

“…Additionally, the authors proposed two different methods for efficient implementation of a colored-noise generator. Very recently, Jung et al [68,69] have proposed a generalization of the approach of Li et al [39], which can be interpreted as generalized Brownian dynamics with frequency-dependent friction kernels. In contrast to the previous approach, this method is not Galilean invariant and, thus, more applicable to the movement of CG particles in an implicit environment.…”

On the dynamics of reaction coordinates in classical, time-dependent, many-body processes

“…which is such thatC(t, t ′ ) = Ã (t)Ã(t ′ ) . For this modified variable, the arguments presented above show that the derivation leading to (16) and (17) still holds true and we can hence write…”

“…The formalism developed in the previous paragraph would then remain valid and the structure of eqn. (16) would still be valid, together with the FDT-like relation (41). In order to recover the true dependence of the observable A, we make sure that the initial augmented phase-space density ρ ′ (γ ′ , s) has a Dirac peak at τ = s, i.e.…”

“…Note that the relation is independent from the reference time t ′ and that it might be a practical tool if one wants to generate trajectories that are solutions of eqn. (16).…”