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. Following a strategy introduced in [S. Daneri and E. Runa, Arch. Ration. Mech. Anal., 231 (2019), pp. 519--589] we prove that in a suitable regime minimizers are periodic stripes in any space dimension.

Pattern Formation for a Local/Nonlocal Interaction Functional Arising in Colloidal Systems

Daneri, Sara;
2020

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. Following a strategy introduced in [S. Daneri and E. Runa, Arch. Ration. Mech. Anal., 231 (2019), pp. 519--589] we prove that in a suitable regime minimizers are periodic stripes in any space dimension.
Pattern formation, Yukawa potential, symmetry breaking
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/25725
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