Lagrangian evolution of global strings

We establish a method to trace the Lagrangian evolution of extended objects consisting of a multicomponent scalar field in terms of a numerical calculation of field equations in three dimensional Eulerian meshes. We apply our method to the cosmological evolution of global strings and evaluate the energy density, peculiar velocity, Lorentz factor, formation rate of loops, and emission rate of Nambu-Goldstone (NG) bosons. We confirm the scaling behavior with a number of long strings per horizon volume smaller than the case of local strings by a factor of $\sim$ 10. The strategy and the method established here are applicable to a variety of fields in physics.Comment: 5 pages, 2 figure