Geometric evolution of bilayers under the functionalized cahn-hilliard equation
Shibin Dai,Keith Promislow +1 more
TLDR
In this article, a multi-scale analysis based on a sharp interface limit for the dynamics of bilayer structures of the functionalized Cahn-Hilliard equation is presented, which yields a quenched mean-curvature-driven normal velocity at O( e −1) whereas on the longer O(e −2) time scale, it leads to a total surface area preserving Willmore flow.Abstract:
We use a multi-scale analysis to derive a sharp interface limit for the dynamics of bilayer structures of the functionalized Cahn–Hilliard equation. In contrast to analysis based on single-layer interfaces, we show that the Stefan and Mullins–Sekerka problems derived for the evolution of single-layer interfaces for the Cahn–Hilliard equation are trivial in this context, and the sharp interface limit yields a quenched mean-curvature-driven normal velocity at O ( e −1), whereas on the longer O ( e −2) time scale, it leads to a total surface area preserving Willmore flow. In particular, for space dimension n =2, the constrained Willmore flow drives collections of spherically symmetric vesicles to a common radius, whereas for n =3, the radii are constant, and for n ≥4 the largest vesicle dominates.read more
Citations
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The phase field method for geometric moving interfaces and their numerical approximations
Qiang Du,Xiaobing Feng +1 more
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High accuracy solutions to energy gradient flows from material science models
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A second-order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection
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A Uniquely Solvable, Energy Stable Numerical Scheme for the Functionalized Cahn–Hilliard Equation and Its Convergence Analysis
TL;DR: A uniquely solvable and unconditionally energy stable numerical scheme for the Functionalized Cahn–Hilliard equation, including an analysis of convergence, which confirms the stability and accuracy of the proposed numerical scheme.
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Meander and Pearling of Single-Curvature Bilayer Interfaces in the Functionalized Cahn--Hilliard Equation
TL;DR: This work addresses the existence and linear stability of $\alpha$-single curvature bilayer structures in $d\geq2$ space dimensions for a family of gradient flows associated to the strong functionalization scaling.
References
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