Double Fourier Sphere Methods with Low Rank Approximation for Block Copolymer Systems on Sphere
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916866746744832 |
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| author | Luo, Wangbo Zhao, Yanxiang |
| author_facet | Luo, Wangbo Zhao, Yanxiang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double Fourier Sphere Methods with Low Rank Approximation for Block Copolymer Systems on Sphere Luo, Wangbo Zhao, Yanxiang Numerical Analysis Mathematical Physics 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. |
| title | Double Fourier Sphere Methods with Low Rank Approximation for Block Copolymer Systems on Sphere |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2507.18968 |