Faceting and coarsening dynamics in the complex Swift-Hohenberg equation

by Gelens, L. and Knobloch, E.
Abstract:
The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and finds applications in lasers, optical parametric oscillators, and photorefractive oscillators. We show that with real coefficients this equation exhibits two classes of localized states: localized in amplitude only or localized in both amplitude and phase. The latter are associated with phase-winding states in which the real and imaginary parts of the order parameter oscillate periodically but with a constant phase difference between them. The localized states take the form of defects connecting phase-winding states with equal and opposite phase lag, and can be stable over a wide range of parameters. The formation of these defects leads to faceting of states with initially spatially uniform phase. Depending on parameters these facets may either coarsen indefinitely, as described by a Cahn-Hilliard equation, or the coarsening ceases leading to a frozen faceted structure.
Reference:
Faceting and coarsening dynamics in the complex Swift-Hohenberg equation (Gelens, L. and Knobloch, E.), In Physical Review E, volume 80, 2009.
Bibtex Entry:
@article{gelens_faceting_2009,
	title = {Faceting and coarsening dynamics in the complex {Swift}-{Hohenberg} equation},
	volume = {80},
	url = {http://link.aps.org/doi/10.1103/PhysRevE.80.046221},
	doi = {10.1103/PhysRevE.80.046221},
	abstract = {The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and finds applications in lasers, optical parametric oscillators, and photorefractive oscillators. We show that with real coefficients this equation exhibits two classes of localized states: localized in amplitude only or localized in both amplitude and phase. The latter are associated with phase-winding states in which the real and imaginary parts of the order parameter oscillate periodically but with a constant phase difference between them. The localized states take the form of defects connecting phase-winding states with equal and opposite phase lag, and can be stable over a wide range of parameters. The formation of these defects leads to faceting of states with initially spatially uniform phase. Depending on parameters these facets may either coarsen indefinitely, as described by a Cahn-Hilliard equation, or the coarsening ceases leading to a frozen faceted structure.},
	number = {4},
	urldate = {2016-11-07},
	journal = {Physical Review E},
	author = {Gelens, L. and Knobloch, E.},
	month = oct,
	year = {2009},
	pages = {046221},
	file = {APS Snapshot:/home/jan/.zotero/zotero/djuw86a6.default/zotero/storage/G2KVWNNW/PhysRevE.80.html:text/html}
}