Uneyama Takashi
JST, PRESTO, and Center for Computational Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan.
Phys Rev E. 2020 Mar;101(3-1):032106. doi: 10.1103/PhysRevE.101.032106.
We show that a mesoscopic coarse-grained dynamics model which incorporates the transient potential can be formally derived from an underlying microscopic dynamics model. As a microscopic dynamics model, we employ the overdamped Langevin equation. By utilizing the path probability and the Onsager-Machlup type action, we calculate the path probability for the coarse-grained mesoscopic degrees of freedom. The action for the mesoscopic degrees of freedom can be simplified by incorporating the transient potential. Then the dynamic equation for the mesoscopic degrees of freedom can be simply described by the Langevin equation with the transient potential (LETP). As a simple and analytically tractable approximation, we introduce additional degrees of freedom which express the state of the transient potential. Then we approximately express the dynamics of the system as the the combination of the LETP and the dynamics model for the transient potential. The resulting dynamics model has the same dynamical structure as the responsive particle dynamics type models [W. J. Briels, Soft Matter 5, 4401 (2009)1744-683X10.1039/b911310j] and the multichain slip-spring type models [T. Uneyama and Y. Masubuchi, J. Chem. Phys. 137, 154902 (2012)JCPSA60021-960610.1063/1.4758320]. As a demonstration, we apply our coarse-graining method with the LETP to a single particle dynamics in a supercooled liquid, and compare the results of the LETP with the molecular dynamics simulations and other coarse-graining models.
我们表明，一个包含瞬态势的介观粗粒化动力学模型可以从一个潜在的微观动力学模型正式推导出来。作为微观动力学模型，我们采用过阻尼朗之万方程。通过利用路径概率和昂萨格 - 马赫卢普型作用量，我们计算了粗粒化介观自由度的路径概率。通过纳入瞬态势，可以简化介观自由度的作用量。然后，介观自由度的动力学方程可以简单地用带有瞬态势的朗之万方程（LETP）来描述。作为一种简单且易于解析处理的近似，我们引入了额外的自由度来表示瞬态势的状态。然后，我们将系统的动力学近似表示为LETP和瞬态势动力学模型的组合。所得的动力学模型与响应粒子动力学类型模型[W. J. Briels，Soft Matter 5，4401（2009）1744 - 683X10.1039/b911310j]以及多链滑弹簧类型模型[T. Uneyama和Y. Masubuchi，J. Chem. Phys. 137，154902（2012）JCPSA60021 - 960610.1063/1.4758320]具有相同的动力学结构。作为一个示例，我们将带有LETP的粗粒化方法应用于过冷液体中的单粒子动力学，并将LETP的结果与分子动力学模拟和其他粗粒化模型进行比较。
