@Article{CSIAM-AM-3-3,
author = {Xu, Jie},
title = {Symmetry-Consistent Expansion of Interaction Kernels Between Rigid Molecules},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2022},
volume = {3},
number = {3},
pages = {383--427},
abstract = {<p style="text-align: justify;">We discuss the expansion of interaction kernels between anisotropic rigid
molecules. The expansion decouples the correlated orientational variables, which is
the crucial step to derive macroscopic free energy. It is at the level of kernel expansion,
or equivalently the free energy, that the symmetries of the interacting rigid molecules
can be fully recognized. Thus, writing down the form of expansion consistent with the
symmetries is significant. Symmetries of two types are considered. First, we examine
the symmetry of an interacting cluster, including the translation and rotation of the
whole cluster, and label permutation within the cluster. The expansion is expressed
by symmetric traceless tensors, with the linearly independent terms identified. Then,
we study the molecular symmetry characterized by a point group in $O(3).$ The proper
rotations determine what symmetric traceless tensors can appear. The improper rotations decompose these tensors into two subspaces and determine how the tensors in
the two subspaces are coupled. For each point group, we identify the two subspaces,
so that the expansion consistent with the point group is established.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2021-0034},
url = {https://global-sci.com/article/82323/symmetry-consistent-expansion-of-interaction-kernels-between-rigid-molecules}
}