Nonlocal effects on a 1D generalized Ohta–Kawasaki model

Abstract

We propose a generalized Ohta–Kawasaki model to study the nonlocal effect on the pattern formation of some binary systems with general long-range interactions. While in the 1D case, the generalized Ohta–Kawasaki model displays similar bubble patterns as the standard Ohta–Kawasaki model, by performing Fourier analysis, we find that the optimal number of bubbles for the generalized model may have an upper bound no matter how large the repulsive strength is. The existence of such an upper bound is characterized by the eigenvalues of the nonlocal kernels. Additionally, we explore the conditions under which the nonlocal horizon parameter may promote or demote the bubble splitting, and apply the analysis framework to several case studies for various nonlocal operators.