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Pattern formation for a local/nonlocal interaction functional arising in colloidal systems. (English) Zbl 07245265
The ability of matter to arrange itself in periodic structures is often referred to as spontaneous pattern formation. This phenomenon is of fundamental importance in science, technology, engineering, and mathematics, and it is often caused by the interaction between local attractive and nonlocal repulsive forces. In this paper, the authors 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 [B. Derjaguin and L. Landau, “Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes”, Acta Phys. Chem. USSR, 14, 633–662 (1941)]. 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. The authors prove that in a suitable regime minimizers are periodic stripes in any space dimension.
MSC:
 82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics 49N20 Periodic optimal control problems 49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
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