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Title: Snaking without subcriticality: grain boundaries as non-topological defects
Abstract Non-topological defects in spatial patterns such as grain boundaries in crystalline materials arise from local variations of the pattern properties such as amplitude, wavelength and orientation. Such non-topological defects may be treated as spatially localized structures, i.e. as fronts connecting distinct periodic states. Using the two-dimensional quadratic-cubic Swift–Hohenberg equation, we obtain fully nonlinear equilibria containing grain boundaries that separate a patch of hexagons with one orientation (the grain) from an identical hexagonal state with a different orientation (the background). These grain boundaries take the form of closed curves with multiple penta-hepta defects that arise from local orientation mismatches between the two competing hexagonal structures. Multiple isolas occurring robustly over a wide range of parameters are obtained even in the absence of a unique Maxwell point, underlining the importance of retaining pinning when analysing patterns with defects, an effect omitted from the commonly used amplitude-phase description. Similar results are obtained for quasiperiodic structures in a two-scale phase-field model.  more » « less
Award ID(s):
1908891
PAR ID:
10275906
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
IMA Journal of Applied Mathematics
ISSN:
0272-4960
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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