Front-type solutions of fractional Allen–Cahn equation

• Published in: Physica. D Vol. 237; no. 24; pp. 3237 - 3251
• Main Authors: Nec, Y., Nepomnyashchy, A.A., Golovin, A.A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-12-2008; Elsevier
• Subjects: Anomalous front; Domain wall dynamics; Exact sciences and technology; Fractional Allen–Cahn equation; Physics; Fractional Allen–Cahn equation; 64.60.-i; Domain wall dynamics; Anomalous front; Time dependence; Variational methods; Dynamics; Domain walls; Anomaly; Kinks; Non linear phenomenon; Fractional Allen-Cahn equation
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2008.08.002

Super-diffusive front dynamics have been analysed via a fractional analogue of the Allen–Cahn equation. One-dimensional kink shape and such characteristics as slope at origin and domain wall dynamics have been computed numerically and satisfactorily approximated by variational techniques for a set of anomaly exponents
1
<
γ
<
2
. The dynamics of a two-dimensional curved front has been considered. Also, the time dependence of coarsening rates during the various evolution stages was analysed in one and two spatial dimensions.