Quantitative evolution of global strings from the Lagrangian view point

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