Front-type solutions of fractional Allen–Cahn equation

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 o...

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Bibliographic Details
Published in:Physica. D 2008-12, Vol.237 (24), p.3237-3251
Main Authors: Nec, Y., Nepomnyashchy, A.A., Golovin, A.A.
Format: Article
Language:English
Subjects:
Anomalous front
Domain wall dynamics
Exact sciences and technology
Fractional Allen–Cahn equation
Physics
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Summary: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.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2008.08.002