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.