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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.