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Surface energies in a two-dimensional mass-spring model for crystals

Florian Theil (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with natoms where y 2 × n characterizes the particle positions. The main focus is the asymptotic analysis of the ground state energy asn 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 + n E surface + o ( n ) , n . The bulk energy densityEbulk is given by an explicit expression...

Surface energies in a two-dimensional mass-spring model for crystals

Florian Theil (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We study an atomistic pair potential-energy E(n)(y) that describes the elastic behavior of two-dimensional crystals with n atoms where y 2 × n 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 + n E surface + o ( n ) , n . The bulk energy density Ebulk is given by an explicit expression...

Sweeping preconditioners for elastic wave propagation with spectral element methods

Paul Tsuji, Jack Poulson, Björn Engquist, Lexing Ying (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a parallel preconditioning method for the iterative solution of the time-harmonic elastic wave equation which makes use of higher-order spectral elements to reduce pollution error. In particular, the method leverages perfectly matched layer boundary conditions to efficiently approximate the Schur complement matrices of a block LDLT factorization. Both sequential and parallel versions of the algorithm are discussed and results for large-scale problems from exploration geophysics are presented....

Synchronization with error bound of non-identical forced oscillators

Jian Gen Wang, Jianping Cai, Mihua Ma, Jiuchao Feng (2008)

Kybernetika

Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.

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