E. P. S. Shellard modeled the evolution of cosmic string networks with C. J. A. P. Martins. Their velocity-dependent one-scale description evolves a characteristic network length together with a typical string velocity, incorporating expansion, energy loss into loops and curvature-driven acceleration.[ref]
Extending the Velocity-dependent One-scale String Evolution Model by C. J. A. P. Martins and E. P. S. Shellard. Section II.A: averaged length, velocity and loss equations
This replaces the full network by a small set of macroscopic variables, making scaling behaviour and cosmological evolution tractable while leaving model coefficients to physical arguments and simulation tests.
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