Semi-scaling cosmic strings

We develop a model of string dynamics with back-reaction from both scaling and non-scaling loops taken into account. The evolution of a string network is described by the distribution functions of coherence segments and kinks. We derive two non-linear equations which govern the evolution of the two distributions and solve them analytically in the limit of late times. We also show that the correlation function is an exponential, and solve the dynamics for the corresponding spectrum of scaling loops.