Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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DIRECT COMPARISON STUDY OF THE CAHN-HILLIARD EQUATION WITH REAL EXPERIMENTAL DATA

  • DARAE, JEONG (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY) ;
  • SEOKJUN, HAM (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
  • JUNSEOK, KIM (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
  • Received : 2022.10.18
  • Accepted : 2022.12.20
  • Published : 2022.12.25
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Abstract

In this paper, we perform a direct comparison study of real experimental data for domain rearrangement and the Cahn-Hilliard (CH) equation on the dynamics of morphological evolution. To validate a mathematical model for physical phenomena, we take initial conditions from experimental images by using an image segmentation technique. The image segmentation algorithm is based on the Mumford-Shah functional and the Allen-Cahn (AC) equation. The segmented phase-field profile is similar to the solution of the CH equation, that is, it has hyperbolic tangent profile across interfacial transition region. We use unconditionally stable schemes to solve the governing equations. As a test problem, we take domain rearrangement of lipid bilayers. Numerical results demonstrate that comparison of the evolutions with experimental data is a good benchmark test for validating a mathematical model.

Keywords

Acknowledgement

The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2020R1F1A1A01075937). The corresponding author (J.S. Kim) was supported by the National Research Foundation(NRF), Korea, under project BK21 FOUR. The authors appreciate the reviewers for the valuable comments on the revision of this article.

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