Theil, Florian. (2011) Surface energies in a two-dimensional mass-spring model for crystals. ESAIM : Mathematical Modelling and Numerical Analysis, Vol.45 (No.5). pp. 873-899. ISSN 0764-583X

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Abstract

We study an atomistic pair potential-energy E((n))(y) that describes the elastic behavior of two-dimensional crystals with n atoms where y is an element of R(2xn) characterizes the particle positions. The main focus is the asymptotic analysis of the ground state energy as n tends to infinity. We show in a suitable scaling regime where the energy is essentially quadratic that the energy minimum of E((n)) admits an asymptotic expansion involving fractional powers of n: min(y) E((n)) (y) = n E(bulk) + root n E(surface) + o(root n), n -> infinity. The bulk energy density E(bulk) is given by an explicit expression involving the interaction potentials. The surface energy E(surface) can be expressed as a surface integral where the integrand depends only on the surface normal and the interaction potentials. The evaluation of the integrand involves solving a discrete algebraic Riccati equation. Numerical simulations suggest that the integrand is a continuous, but nowhere differentiable function of the surface normal.

Item Type:	Journal Article
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	ESAIM : Mathematical Modelling and Numerical Analysis
Publisher:	E D P Sciences
ISSN:	0764-583X
Date:	2011
Volume:	Vol.45
Number:	No.5
Page Range:	pp. 873-899
Identification Number:	10.1051/m2an/2010106
Status:	Peer Reviewed
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/41809

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