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arXiv · 1810.11884

Pattern formation for a local/nonlocal interaction functional arising in colloidal systems

Sara Daneri·Eris Runa
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Abstract

In this paper we study pattern formation for a physical local/nonlocal interaction functional where the local attractive term is given by the $1$-perimeter and the nonlocal repulsive term is the Yukawa (or screened Coulomb) potential. This model is physically interesting as it is the $\Gamma$-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.

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Sara Daneri, Eris Runa. 2018-10-28. Pattern formation for a local/nonlocal interaction functional arising in colloidal systems. https://doi.org/10.1137/19m1276005

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