Homogenizing atomic dynamics by fractional differential equations

doi:10.1016/j.jcp.2017.06.038

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	Homogenizing atomic dynamics by fractional differential equations
	Tang, Shaoqiang ; Ying, Yuping
刊名	JOURNAL OF COMPUTATIONAL PHYSICS
	2017
关键词	Homogenization Atomic chain Fractional differential equation Dispersion relation Symbol INTERFACIAL CONDITIONS
DOI	10.1016/j.jcp.2017.06.038
英文摘要	In this paper, we propose two ways to construct fractional differential equations (FDE) for approximating atomic chain dynamics. Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers. This approximate function leads to an FDE after considering both directions for wave propagation. As an alternative, we consider the symbol of the force term, and approximate it by a similar function. It also induces an FDE. Both approaches produce excellent agreement with the harmonic chain dynamics. The accuracy may be improved by optimizing the selected wave numbers, or starting with higher order Taylor expansions. When resolved in the lattice constant, the resulting FDE's faithfully reproduce the lattice dynamics. When resolved in a coarse grid instead, they systematically generate homogenized algorithms. Numerical tests are performed to verify the proposed approaches. Moreover, FDE's are also constructed for diatomic chain and anharmonic lattice, to illustrate the generality of the proposed approaches. (C) 2017 Elsevier Inc. All rights reserved.; NSFC [11521202, 11272009]; key subject Computational Solid Mechanics of CAEP; SCI(E); ARTICLE; 539-551; 346
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/470708]
专题	工学院
推荐引用方式 GB/T 7714	Tang, Shaoqiang,Ying, Yuping. Homogenizing atomic dynamics by fractional differential equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017.
APA	Tang, Shaoqiang,&Ying, Yuping.(2017).Homogenizing atomic dynamics by fractional differential equations.JOURNAL OF COMPUTATIONAL PHYSICS.
MLA	Tang, Shaoqiang,et al."Homogenizing atomic dynamics by fractional differential equations".JOURNAL OF COMPUTATIONAL PHYSICS (2017).