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- W4220786719 abstract "<abstract><p>We investigate pattern formation in a two-dimensional manifold using the Otha-Kawasaki model for micro-phase separation of diblock copolymers. In this model, the total energy includes a short-range and a long-range term. The short-range term is a Landau-type free energy that is common in phase separation problems and favors large domains with minimum perimeter. The inhibitory long-range interaction term is the Otha-Kawasaki functional derived from the theory of diblock copolymers and favors small domains. The balance of these terms leads to equilibrium states that exhibit a variety of patterns, including disk-like droplets, droplet assemblies, elongated droplets, dog-bone shaped droplets, stripes, annular rings, wriggled stripes and combinations thereof. For problems where analytical results are known, we compare our numerical results and find good agreement. Where analytical results are not available, our numerical methods allow us to explore the solution space revealing new stable patterns. We focus on the triaxial ellipsoid, but our methods are general and can be applied to higher genus surfaces and surfaces with boundaries.</p></abstract>" @default.
- W4220786719 created "2022-04-03" @default.
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- W4220786719 date "2022-01-01" @default.
- W4220786719 modified "2023-09-25" @default.
- W4220786719 title "Numerical investigations of pattern formation in binary systems with inhibitory long-range interaction" @default.
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- W4220786719 doi "https://doi.org/10.3934/era.2022081" @default.
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