  In this paper, we discuss filamentations on oriented chord diagrams. When a
filamentation cannot be realized on an oriented chord diagram, then the
corresponding flat virtual knot is non-trivial. If a flat knot diagram is
non-trivial, then any virtual diagram whose shadow is the flat diagram must
also be non-trivial. We introduce a class of flat diagrams for which no
filamentations exist. This class gives the first example of an infinite set of
virtual knots for which the Jones polynomial and the fundamental group both
evaluate trivially. The related generalized Alexander polynomials for the
virtual knots in this class turn out to be distinct, proving that the class is
indeed infinite.
