Pattern formation for a local/nonlocal interaction functional arising in colloidal systems
Analysis of PDEs
2021-03-10 v3 Optimization and Control
Abstract
In this paper we study pattern formation for a physical local/nonlocal interaction functional where the local attractive term is given by the -perimeter and the nonlocal repulsive term is the Yukawa (or screened Coulomb) potential. This model is physically interesting as it is the -limit of a double Yukawa model used to explain and simulate pattern formation in colloidal systems \cite{BBCH,CCA,IR,GCLW}. Following a strategy introduced in~\cite{DR} we prove that in a suitable regime minimizers are periodic stripes, in any space dimension.
Cite
@article{arxiv.1810.11884,
title = {Pattern formation for a local/nonlocal interaction functional arising in colloidal systems},
author = {Sara Daneri and Eris Runa},
journal= {arXiv preprint arXiv:1810.11884},
year = {2021}
}