TY - JOUR
T1 - Analysis of Coarse-Grained Lattice Models and Connections to Nonlocal Interactions
AU - Du , Qiang
AU - Li , Xiantao
AU - Yuan , Liming
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 155
EP - 185
PY - 2020
DA - 2020/03
SN - 1
DO - http://doi.org/10.4208/csiam-am.2020-0009
UR - https://global-sci.org/intro/article_detail/csiam-am/16798.html
KW - Linear static models, coarse-graining, next nearest neighbor interactions, nonlocal models.
AB - <p style="text-align: justify;">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.</p>