标题： 球面上块共聚物系统的低秩近似双傅里叶球方法 显示英文标题

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

摘要： 我们介绍了在球面域上用于Ohta-Kawasaki（OK）和Nakazawa-Ohta（NO）模型的谱方法，研究了它们的粗化动力学和平衡模式形成。我们采用了双傅里叶球面（DFS）方法进行空间离散化，以及二阶后向微分公式（BDF2）方案进行时间演化，从而得到了一种高效的能量稳定方案，用于在单位球面上模拟OK和NO模型。我们的数值实验揭示了各种自组装模式，如二元系统中的单泡组装和三元系统中的双泡和混合泡组装。这些模式与实验生物膜模式非常相似，证明了OK模型在实际应用中的有效性。此外，我们的研究探讨了排斥强度与组装中气泡数量之间的关系，确认了OK模型中的三分之二定律。这提供了自组装模式如何依赖于共聚物系统中系统参数的定量证据。 显示英文摘要

摘要： 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.