  Models of symmetry breaking in the early universe can produce networks of
cosmic strings threading 't Hooft-Polyakov monopoles. In certain cases there is
a larger global symmetry group and the monopoles split into so-called
semipoles. These networks are all known as cosmic necklaces. We carry out
large-scale field theory simulations of the simplest model containing these
objects, confirming that the energy density of networks of cosmic necklaces
approaches scaling, i.e. that it remains a constant fraction of the background
energy density. The number of monopoles per unit comoving string length is
constant, meaning that the density fraction of monopoles decreases with time.
Where the necklaces carry semipoles rather than monopoles, we perform the first
simulations large enough to demonstrate that they also maintain a constant
number per unit comoving string length. We also compare our results to a number
of analytical models of cosmic necklaces, finding that none explains our
results. We put forward evidence that annihilation of poles on the strings is
controlled by a diffusive process, a possibility not considered before. The
observational constraints derived in our previous work for necklaces with
monopoles can now be safely applied to those with semipoles as well.
