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

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Title: Double Fourier Sphere Methods With Low Rank Approximation for Block Copolymer Systems on Sphere.
Authors: Luo, Wangbo1 (AUTHOR), Zhao, Yanxiang2 (AUTHOR) yxzhao@email.gwu.edu
Source: Numerical Methods for Partial Differential Equations. May2026, Vol. 42 Issue 3, p1-28. 28p.
Subjects: Block copolymers, Pattern formation (Physical sciences), Mathematical models, Numerical analysis, Phase separation, Numerical solutions to partial differential equations
Abstract: We introduce Double Fourier Sphere (DFS) 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 DFS 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. [ABSTRACT FROM AUTHOR]
Copyright of Numerical Methods for Partial Differential Equations is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 194139473
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  Data: Double Fourier Sphere Methods With Low Rank Approximation for Block Copolymer Systems on Sphere.
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  Data: <searchLink fieldCode="AR" term="%22Luo%2C+Wangbo%22">Luo, Wangbo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhao%2C+Yanxiang%22">Zhao, Yanxiang</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> yxzhao@email.gwu.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Numerical+Methods+for+Partial+Differential+Equations%22">Numerical Methods for Partial Differential Equations</searchLink>. May2026, Vol. 42 Issue 3, p1-28. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Block+copolymers%22">Block copolymers</searchLink><br /><searchLink fieldCode="DE" term="%22Pattern+formation+%28Physical+sciences%29%22">Pattern formation (Physical sciences)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Phase+separation%22">Phase separation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+partial+differential+equations%22">Numerical solutions to partial differential equations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We introduce Double Fourier Sphere (DFS) 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 DFS 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Numerical Methods for Partial Differential Equations is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/num.70091
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 28
        StartPage: 1
    Subjects:
      – SubjectFull: Block copolymers
        Type: general
      – SubjectFull: Pattern formation (Physical sciences)
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Phase separation
        Type: general
      – SubjectFull: Numerical solutions to partial differential equations
        Type: general
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      – TitleFull: Double Fourier Sphere Methods With Low Rank Approximation for Block Copolymer Systems on Sphere.
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            NameFull: Luo, Wangbo
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            NameFull: Zhao, Yanxiang
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 42
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            – TitleFull: Numerical Methods for Partial Differential Equations
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