Transient dynamics of pinning of domain wall

We study the evolution of an elastic string, serving as model for a domain wall, into the pinned state at driving forces slightly below the depinning threshold force F c. We quantify the temporal evolution of the string by an activity function A( t) representing the fraction of active nodes at time t and find three distinct dynamic regimes. There is an initial stage of fast decay of the activity; in the second, intermediate, regime, an exponential decay of activity is observed; and, eventually, the fast collapse of the string towards its final pinned state results in decay in the activity with A r∼( t p− t) ψ , where t p is the pinning time in the finite system involved.