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arXiv · 2507.18968

Double Fourier Sphere Methods with Low Rank Approximation for Block Copolymer Systems on Sphere

Wangbo Luo·Yanxiang Zhao
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Abstract

We introduce spectral methods for the Ohta-Kawasaki (OK) and Nakazawa-Ohta (NO) models on a spherical domain, examining their coarsening dynamics and equilibrium pattern formations. We employed the Double Fourier Sphere (DFS) method for spatial discretization and the second-order Backward Differentiation Formula (BDF2) scheme for time evolution, resulting in an efficient energy-stable scheme to simulate the OK and NO models on the unit sphere. Our numerical experiments reveal various self-assembled patterns, such as single-bubble assemblies in binary systems and double-bubble and mixed-bubble assemblies in ternary systems. These patterns closely resemble experimental biomembrane patterns, demonstrating the effectiveness of the OK model in real-world applications. Additionally, our study explores the relationship between repulsive strength and the number of bubbles in assemblies, confirming the two-thirds law in the OK model. This provides quantitative evidence of how self-assembled patterns depend on system parameters in copolymer systems.

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Wangbo Luo, Yanxiang Zhao. 2025-07-25. Double Fourier Sphere Methods with Low Rank Approximation for Block Copolymer Systems on Sphere. https://arxiv.org/abs/2507.18968

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