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

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.

References in corpus (12)

• Ising models with long-range dipolar and short-range ferromagnetic interactions
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• The $\mathbf{\Gamma }$-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density
• Striped phases in two dimensional dipole systems
• Periodic minimizers in 1D local mean field theory
• Two-dimensional colloidal fluids exhibiting pattern formation
• Exact periodic stripes for a minimizers of a local/non-local interaction functional in general dimension
• Periodic striped ground states in Ising models with competing interactions
• Modulated phases of a 1D sharp interface model in a magnetic field
• Pattern formation of a nonlocal, anisotropic interaction model
• Pattern formation in binary fluid mixtures induced by short-range competing interactions
• Stability analysis of line patterns of an anisotropic interaction model

Cited by in corpus (2)

• On the Ternary Ohta-Kawasaki Free Energy and Its One-dimensional Global Minimizers
• Emergence of non-trivial minimizers for the three-dimensional Ohta-Kawasaki energy