Quantitative evolution of global strings from the Lagrangian viewpoint

We clarify the quantitative nature of the cosmological evolution of a global string network, that is, the energy density, peculiar velocity, velocity squared, Lorentz factor, formation rate of loops, and emission rate of Nambu-Goldstone bosons, based on a new type of numerical simulation of scalar fields in Eulerian meshes. We give a detailed explanation of a method to extract the above-mentioned quantities to characterize string evolution by analyzing scalar fields in Eulerian meshes from a Lagrangian viewpoint. We confirm our previous claim that the number of long strings per horizon volume in a global string network is smaller than in the case of a local string network by a factor of $\sim$10 even under cosmological situations, and its reason is clarified.