Strain and defects in oblique stripe growth
Files
First author draft
Date
2021-01
Authors
Chen, Kelly
Deiman, Zachary
Goh, Ryan
Jankovic, Sally
Scheel, Arnd
Version
First author draft
OA Version
Citation
K. Chen, Z. Deiman, R. Goh, S. Jankovic, A. Scheel. 2021. "Strain and Defects in Oblique Stripe Growth." Multiscale Modeling & Simulation, Volume 19, Issue 3, pp. 1236 - 1260. https://doi.org/10.1137/21m1397210
Abstract
We study stripe formation in two-dimensional systems under directional quenching in a phase-diffusion approximation including non-adiabatic boundary effects. We find stripe formation through simple traveling waves for
all angles relative to the quenching line using an analytic continuation procedure. We also present comprehensive
analytical asymptotic formulas in limiting cases of small and large angles as well as small and large quenching
rates. Of particular interest is a regime of small angle and slow quenching rate which is well described by the
glide motion of a boundary dislocation along the quenching line. A delocalization bifurcation of this dislocation
leads to a sharp decrease of strain created in the growth process at small angles. We complement our results with
numerical continuation reliant on a boundary-integral formulation. We also compare results in the phase-diffusion
approximation numerically to quenched stripe formation in an anisotropic Swift Hohenberg equation.