【作者】 陈含爽； 侯中怀； 辛厚文；

【Author】 Hanshuang Chen1,Zhonghuai Hou1,2,Houwen Xin1 1Department of Chemical Physics 2Hefei National Laboratory for Physical Sciences at Microscale University of Science and Technology of China,Hefei,Anhui 230026,China

【机构】 中国科学技术大学化学物理系； 中国合肥微尺度物质科学国家实验室；

【摘要】 人们已经建立了适用于不同时间和空间尺度的模拟和计算方法,微观层次上分子动力学方法、动力学蒙特卡罗方法,宏观层次的唯象动力学方程。然而,这些微观方法目前仍只能处理相对较小的时间和空间尺度,而宏观方法又缺少对微观机理的理解。为深入理解这些多尺度的动力学过程,人们迫切需要建立介于微观和宏观之间的介观理论方法,实现在微观-介观-宏观层次间的有机过渡与衔接。本文以复杂网络为研究对象,发展复杂网络上动力学过程的多尺度粗粒化方法。基于Ising模型和流行病传播SIS模型,我们提出了多尺度粗粒化的蒙特卡罗和动力学蒙特卡罗方法。我们讨论了在不同网络拓扑和不同节点合并原则下粗粒化方法的实用性。通过与微观模拟的方法和宏观平均场方法比较,粗粒化方法不仅可以节省计算时间,还可以计算涨落相关的动力学信息。更多还原

【Abstract】 People have developed many simulation and calculation methods that span different temporal and spatial scales,for instances,molecular dynamics and kinetic Monte Carlo(KMC) simulation in microscopic scale,and phenomenologically dynamical equation in macroscopic scale.However,these microscopic methods are limited to relatively short length and time scales,while macroscopic methods are lack of the understanding of microscopic-based mechanism.In order to overcome the above difficulties,mesoscopic models should be introduced to establish the bridge between microscopic scale and macroscopic scale.We here focus on dynamical processes taking place on top of complex networks and explore multiscale coarse-grained(CG) methods.Based on Ising model and SIS model of epidemic spreading,coarse-grained Monte Carlo(CGMC) and coarse-grained kinetic Monte Carlo(CGKMC) are introduced.The effects of networks types and the rules of merging nodes on the practicability of CG methods are discussed.By comparing with microscopic simulation and macroscopic mean field equations,CG methods not only save the calculation expense,but also calculate dynamical information related to fluctuation.更多还原