Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity

被引：75

作者：

Thiele, Uwe ^{[1
]}

Archer, Andrew J. ^{[1
]}

Robbins, Mark J. ^{[1
]}

Gomez, Hector ^{[2
]}

Knobloch, Edgar ^{[3
]}

机构：

[1] Univ Loughborough, Dept Math Sci, Loughborough LE11 3TU, Leics, England

[2] Univ A Coruna, La Coruna 15192, Spain

[3] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA

来源：

PHYSICAL REVIEW E | 2013年 / 87卷 / 04期

基金：

美国国家科学基金会;

关键词：

TRAVELING-WAVE CONVECTION; GINZBURG-LANDAU EQUATION; PATTERN-FORMATION; ISOGEOMETRIC ANALYSIS; BIFURCATIONS; INSTABILITY; DYNAMICS; NUCLEATION; MORPHOLOGY; SEPARATION;

D O I：

10.1103/PhysRevE.87.042915

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter. DOI: 10.1103/PhysRevE.87.042915

引用

页数：19

共 85 条

[1] Nonlinear driven response of a phase-field crystal in a periodic pinning potential [J].