Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry

Details Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry

2002-03-19

arxiv.org/abs/cond-mat/0203389v1

Phys. Rev. Lett. 89, 055501 (2002).

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1103/PhysRevLett.89.055501

We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation appropriate for hexagonal patterns, a multiple scale analysis leads to an analytical equation of motion for the boundary that shares many properties with that of a crystalline solid. We find that defect motion is generically opposed by a pinning force that arises from non-adiabatic corrections to the standard amplitude equation. The magnitude of this force depends sharply on the mis-orientation angle between adjacent domains so that the most easily pinned grain boundaries are those with an angle between four and eight degrees. Although pinning effects may be small, they do not vanish asymptotically near the onset of this subcritical bifurcation, and can be orders of magnitude larger than those present in smectic phases that bifurcate supercritically.

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