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

被引：42

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

共 43 条

[1]

Alberti G, 2009, J AM MATH SOC, V22, P569

[2]

[Anonymous], 2003, MATH BIOL

[3]

[Anonymous], 1998, An unconditionally stable one-step scheme for gradient systems

[4] CELL DYNAMIC SYSTEM APPROACH TO BLOCK COPOLYMERS [J].

BAHIANA, M ;

OONO, Y .

PHYSICAL REVIEW A, 1990, 41 (12) :6763-6771

[5] Block copolymers - Designer soft materials [J].

Bates, FS ;

Fredrickson, GH .

PHYSICS TODAY, 1999, 52 (02) :32-38

[6] Localized states in the generalized Swift-Hohenberg equation [J].

Burke, John ;

Knobloch, Edgar .

PHYSICAL REVIEW E, 2006, 73 (05)

[7] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY [J].

CAHN, JW ;

HILLIARD, JE .

JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) :258-267

[8]

Chaparova J. V., 2003, ADV DIFFERENTIAL EQU, V8, P1237

[9] An application of the modular function in nonlocal variational problems [J].

Chen, Xinfu ;

Oshita, Yoshihito .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 186 (01) :109-132

[10] On the derivation of a density functional theory for microphase separation of diblock copolymers [J].

Choksi, R ;

Ren, XF .

JOURNAL OF STATISTICAL PHYSICS, 2003, 113 (1-2) :151-176

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