High Harmonic Configurations of Cosmic Strings: An Analysis of   Self-Intersections
  A general formulation for describing odd-harmonic cosmic strings is developed and used to determine the self-intersection properties of high-harmonic loops. This is important because loop formation mechanisms produce high-harmonic components (kinks) which can only be eliminated very slowly by gravitational radiation, damping by the dense surrounding plasma in the era of string formation, or by the expansion of the Universe. For the class of loops examined it has been found that in the high-harmonic limit, essentially all cosmic loops self-intersect. 
Xavier A. Siemens and T.W.B. Kibble