2D Phase Diagram for Minimizers of a Cahn-Hilliard Functional with Long-Range Interactions

被引：41

作者：

Choksi, Rustum ^{[1
]}

Maras, Mirjana ^{[2
]}

Williams, J. F. ^{[2
]}

机构：

[1] McGill Univ, Dept Math, Montreal, PQ H3A 2K6, Canada

[2] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2011年 / 10卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

simulation of the phase diagram; long-range interactions; Cahn-Hilliard equation; spectral weighting; SWIFT-HOHENBERG EQUATION; NONLOCAL ISOPERIMETRIC PROBLEM; DIBLOCK COPOLYMER PROBLEM; MICROPHASE SEPARATION; BLOCK-COPOLYMERS; UNIFORM ENERGY; DYNAMICS; SYSTEM; EQUILIBRIUM; DIMENSIONS;

D O I：

10.1137/100784497

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a two-dimensional investigation of the phase diagram for global minimizers to a Cahn-Hilliard functional with long-range interactions. Based upon the H(-1) gradient flow, we introduce a hybrid numerical method to navigate through the complex energy landscape and access an accurate depiction of the ground state of the functional. We use this method to numerically compute the phase diagram in a (finite) neighborhood of the order-disorder transition. We demonstrate a remarkably strong agreement with the standard asymptotic estimates for stability regions based upon a small parameter measuring perturbation from the order-disorder transition curve.

引用

页码：1344 / 1362

页数：19

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