  We propose a nonlocal Ohta-Kawasaki model to study the nonlocal effect on the
pattern formation of some binary systems with general long-range interactions.
While the nonlocal 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 nonlocal 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.
