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Stepping

We show that stepping is never favored for SALK at regular (non-topological) times.

There are two cases to consider: stepping a facet with and stepping one with .

Consider stepping with . Three new facets are produced: one zero length facet with and its two neighbors. One neighbor must have its and the other will have a . Equation 16 implies that the difference in velocities is , where has been taken to have the nonzero . If that difference is negative, so disappears; the same holds for .

Consider stepping with . After the stepping, either or . (The step has the sense that the new neighbors have with opposite sign, or they both have ). If , then is necessarily negative and stepping is not favorable, and similarly for (Figure 1). However, if the both new neighbors have , then all three will move with the same velocity. The small facet is neutrally stable; if it was inserted, it will travel to one of the nearby corners at with constant speed where it will subsequently annihilate. The inserted facet does not lengthen, and thus it not inserted.


roosen@borax.nist.gov