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Linear Stability Analysis of the Cahn–Hilliard Equation in Spinodal Region
We study a linear stability analysis for the Cahn–Hilliard (CH) equation at critical and off-critical compositions. The CH equation is solved by the linearly stabilized splitting scheme and the Fourier-spectral method. We define the analytic and numerical growth rates and compare these growth rates...
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Published in: | Journal of function spaces 2022, Vol.2022, p.1-11 |
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creator | Ham, Seokjun Jeong, Darae Kim, Hyundong Lee, Chaeyoung Kwak, Soobin Hwang, Youngjin Kim, Junseok |
description | We study a linear stability analysis for the Cahn–Hilliard (CH) equation at critical and off-critical compositions. The CH equation is solved by the linearly stabilized splitting scheme and the Fourier-spectral method. We define the analytic and numerical growth rates and compare these growth rates with respect to the different average levels. In this study, the linear stability analysis is conducted by classifying three average levels such as zero average, spinodal average, and near critical point levels of free energy function, in the one-dimensional (1D) space. The numerical results provide insight for the dynamics of CH equation at critical and off-critical compositions. |
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The CH equation is solved by the linearly stabilized splitting scheme and the Fourier-spectral method. We define the analytic and numerical growth rates and compare these growth rates with respect to the different average levels. In this study, the linear stability analysis is conducted by classifying three average levels such as zero average, spinodal average, and near critical point levels of free energy function, in the one-dimensional (1D) space. The numerical results provide insight for the dynamics of CH equation at critical and off-critical compositions.</description><identifier>ISSN: 2314-8896</identifier><identifier>EISSN: 2314-8888</identifier><identifier>DOI: 10.1155/2022/2970876</identifier><language>eng</language><publisher>New York: Hindawi</publisher><subject>Composition ; Critical point ; Energy ; Experiments ; Free energy ; Growth rate ; Numerical analysis ; Partial differential equations ; Spectral methods ; Stability analysis</subject><ispartof>Journal of function spaces, 2022, Vol.2022, p.1-11</ispartof><rights>Copyright © 2022 Seokjun Ham et al.</rights><rights>Copyright © 2022 Seokjun Ham et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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subjects | Composition Critical point Energy Experiments Free energy Growth rate Numerical analysis Partial differential equations Spectral methods Stability analysis |
title | Linear Stability Analysis of the Cahn–Hilliard Equation in Spinodal Region |
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