Li Zhen, Bian Xin, Li Xiantao, Karniadakis George Em
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA.
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
J Chem Phys. 2015 Dec 28;143(24):243128. doi: 10.1063/1.4935490.
The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.
用于对复杂动力学系统进行粗粒化的森-茨万齐格形式通常会引入记忆效应。通常采用与δ相关的涨落力的马尔可夫假设来简化粗粒化（CG）模型的公式和数值实现。然而，当系统的时间尺度没有明显分离时，记忆效应会变强，马尔可夫假设就会变得不准确。为此，我们通过保留CG变量之间的非马尔可夫相互作用将记忆效应纳入CG建模，并且直接从微观动力学评估记忆核。对于一个具体例子，在将许多键合原子分组为单个簇来定义相应的CG系统的同时，进行了星形聚合物熔体的分子动力学（MD）模拟。然后，从MD模拟中获得CG簇之间的有效相互作用以及记忆核。构建的带有记忆核的CG力场导致了非马尔可夫耗散粒子动力学（NM-DPD）。具有马尔可夫和非马尔可夫近似的CG模型之间的定量比较表明，如果系统具有清晰的时间尺度分离，使用NM-DPD包含记忆效应会产生与基于马尔可夫的DPD相似的结果。然而，对于时间尺度分离较小的系统，NM-DPD可以重现与系统对高频扰动的响应方式相关的正确短时特性，而基于马尔可夫的DPD模型无法捕捉这些特性。
