Interactions between $U(1)$ Cosmic Strings: An Analytical Study
  We derive analytic expressions for the interaction energy between two general $U(1)$ cosmic strings as the function of their relative orientation and the ratio of the coupling constants in the model. The results are relevant to the statistic description of strings away from critical coupling and shed some light on the mechanisms involved in string formation and the evolution of string networks. 
L. M. A. Bettencourt and R. J. Rivers