Molecular dynamics boundary conditions for regular crystal lattices

Gregory J. Wagner; Eduard G. Karpov; Wing Kam Liu

doi:10.1016/j.cma.2003.12.012

Molecular dynamics boundary conditions for regular crystal lattices

Gregory J. Wagner, Eduard G. Karpov, Wing Kam Liu^*

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

87 Scopus citations

Abstract

We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon.

Original language	English (US)
Pages (from-to)	1579-1601
Number of pages	23
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	193
Issue number	17-20
DOIs	https://doi.org/10.1016/j.cma.2003.12.012
State	Published - May 7 2004

Keywords

Boundary conditions
Generalized Langevin equation
Molecular dynamics
Multiple scale simulations

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2003.12.012

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title = "Molecular dynamics boundary conditions for regular crystal lattices",

abstract = "We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon.",

keywords = "Boundary conditions, Generalized Langevin equation, Molecular dynamics, Multiple scale simulations",

author = "Wagner, {Gregory J.} and Karpov, {Eduard G.} and Liu, {Wing Kam}",

note = "Funding Information: The work of G.J. Wagner is supported by U.S. DOE Contract AC04-94AL85000. E.G. Karpov and W.K. Liu gratefully acknowledge the support of NSF and NSF IGERT. ",

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doi = "10.1016/j.cma.2003.12.012",

language = "English (US)",

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T1 - Molecular dynamics boundary conditions for regular crystal lattices

AU - Wagner, Gregory J.

AU - Karpov, Eduard G.

AU - Liu, Wing Kam

N1 - Funding Information: The work of G.J. Wagner is supported by U.S. DOE Contract AC04-94AL85000. E.G. Karpov and W.K. Liu gratefully acknowledge the support of NSF and NSF IGERT.

PY - 2004/5/7

Y1 - 2004/5/7

N2 - We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon.

AB - We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon.

KW - Boundary conditions

KW - Generalized Langevin equation

KW - Molecular dynamics

KW - Multiple scale simulations

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DO - 10.1016/j.cma.2003.12.012

M3 - Article

AN - SCOPUS:1842708887

SN - 0045-7825

VL - 193

SP - 1579

EP - 1601

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 17-20

ER -

Molecular dynamics boundary conditions for regular crystal lattices

Abstract

Keywords

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