Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity
journal contributionposted on 2013-05-17, 10:31 authored by Uwe Thiele, Andrew ArcherAndrew Archer, Mark J. Robbins, Hector Gomez, Edgar Knobloch
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.
- Mathematical Sciences
CitationTHIELE, 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.
Publisher© American Physical Society
- VoR (Version of Record)
NotesThis article was published in the journal, Physical Review E [© American Physical Society].