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Title: Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
Authors: Thiele, Uwe
Archer, Andrew J.
Robbins, Mark J.
Gomez, Hector
Knobloch, Edgar
Issue Date: 2013
Publisher: © American Physical Society
Citation: THIELE, U. ... et al., 2013. Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 87 (4), 042915, 19pp.
Abstract: 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. © 2013 American Physical Society.
Description: This article was published in the journal, Physical Review E [© American Physical Society].
Version: Published
DOI: 10.1103/PhysRevE.87.042915
URI: https://dspace.lboro.ac.uk/2134/12306
Publisher Link: http://dx.doi.org/10.1103/PhysRevE.87.042915
ISSN: 1539-3755
Appears in Collections:Published Articles (Maths)

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