Evolution of Axionic Strings and Spectrum of Axions Radiated from Them
  Cosmological evolution of axionic strings is investigated by numerically solving field equations of a complex scalar field in 3+1 dimensions. It is shown that the global strings relax to the scaling solution with a significantly smaller number density than the case of local strings. The power spectrum of axions radiated from them is calculated from the simulation data, which is found to be highly peaked around the Hubble scale, and a more accurate constraint on the Peccei-Quinn breaking scale is obtained. 
Masahide Yamaguchi, M. Kawasaki, and Jun'ichi Yokoyama