Analysis of Coarse-Grained Lattice Models and Connections to Nonlocal Interactions

Analysis of Coarse-Grained Lattice Models and Connections to Nonlocal Interactions

Year:    2020

Author:    Qiang Du, Xiantao Li, Liming Yuan

CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 1 : pp. 155–185

Abstract

We study coarse-grained models of some linear static lattice models with interactions up to second nearest neighbors. It will be demonstrated how nonlocal interactions, as described by a nonlocal kernel function, arise from a coarse-graining procedure. Some important properties of the nonlocal kernels will be established such as its decay rate and positivity. We also study the scaling behavior of the kernel functions as the level of coarse-graining changes. In addition, we suggest closure approximations of the nonlocal interactions that can be expressed in local PDE forms by introducing auxiliary variables.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.2020-0009

CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 1 : pp. 155–185

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    31

Keywords:    Linear static models coarse-graining next nearest neighbor interactions nonlocal models.

Author Details

Qiang Du

Xiantao Li

Liming Yuan