Basic principles and practical applications of the Cahn–Hilliard equation

J Kim, S Lee, Y Choi, SM Lee… - … Problems in Engineering, 2016 - Wiley Online Library
The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase
separation in binary alloys by Cahn and Hilliard. Since then the equation has been …

A robust and efficient fingerprint image restoration method based on a phase-field model

Y Li, Q **a, C Lee, S Kim, J Kim - Pattern Recognition, 2022 - Elsevier
In this study, we present a robust and efficient fingerprint image restoration algorithm using
the nonlocal Cahn–Hilliard (CH) equation, which was proposed for modeling the …

Linear energy-stable method with correction technique for the Ohta–Kawasaki–Navier–Stokes model of incompressible diblock copolymer melt

J Yang - Communications in Nonlinear Science and Numerical …, 2024 - Elsevier
An efficiently linear time-marching method is proposed for the incompressible fluid flows
coupled Ohta–Kawasaki model of diblock copolymer melt. Although this model satisfies the …

[HTML][HTML] Energy stable compact scheme for Cahn–Hilliard equation with periodic boundary condition

S Lee, J Shin - Computers & Mathematics with Applications, 2019 - Elsevier
We present a compact scheme to solve the Cahn–Hilliard equation with a periodic boundary
condition, which is fourth-order accurate in space. We introduce schemes for two and three …

A polynomial-augmented RBF collocation method using fictitious centres for solving the Cahn–Hilliard equation

D Cao, X Li, H Zhu - Engineering Analysis with Boundary Elements, 2022 - Elsevier
In this paper, we consider the radial basis function collocation method with fictitious centres
for solving the Cahn–Hilliard equation in one-dimensional and two-dimensional settings …

A benchmark problem for the two-and three-dimensional Cahn–Hilliard equations

D Jeong, Y Choi, J Kim - … in Nonlinear Science and Numerical Simulation, 2018 - Elsevier
This paper proposes a benchmark problem for the two-and three-dimensional Cahn–Hilliard
(CH) equations, which describe the process of phase separation. The CH equation is highly …

Analytical solutions of Cahn-Hillard phase-field model for spinodal decomposition of a binary system

A Tozar, O Tasbozan, A Kurt - Europhysics Letters, 2020 - iopscience.iop.org
Spinodal decomposition is a very important and challenging issue not for only materials
science but for also many other fields in science. Phase-field models, which have become …

Determine source of Cahn–Hilliard equation with time‐fractional derivative by iterative variational regularization method

J Li, H Cheng - Mathematical Methods in the Applied Sciences, 2024 - Wiley Online Library
In this paper, we consider the inverse problem for the time‐fractional two‐dimensional Cahn–
Hilliard equation. The ill‐posedness and a conditional stability of the inverse problem are …

Doubly Nonlocal Cahn–Hilliard Equations: Well-posedness and Asymptotic Behavior

MD Foss, P Radu, L White - Research in Mathematics of Materials …, 2022 - Springer
This chapter focuses on a doubly nonlocal Cahn–Hilliard system that involves weakly
singular kernels in the operators and which allows discontinuous solutions. The system is …

Fourth-order spatial and second-order temporal accurate compact scheme for Cahn–Hilliard equation

S Lee - International Journal of Nonlinear Sciences and …, 2019 - degruyter.com
We propose a fourth-order spatial and second-order temporal accurate and unconditionally
stable compact finite-difference scheme for the Cahn–Hilliard equation. The proposed …