  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.
