  In this thesis we study synchronization phenomena in natural and artificial
coupled multi-component systems, applicable to the scalability of parallel
discrete-event simulation for systems with asynchronous dynamics. We analyze
the properties of the virtual time horizon or synchronization landscape
(corresponding to the progress of the processing elements) of these networks by
using the framework of non-equilibrium surface growth. When the communication
topology mimics that of the short-range interacting underlying system, the
virtual time horizon exhibits Kardar-Parisi-Zhang-like kinetic roughening.
Although the virtual times, on average, progress at a nonzero rate, their
statistical spread diverges with the number of processing elements, hindering
efficient data collection. We show that when the synchronization topology is
extended to include quenched random communication links (small-world links)
between the processing elements, they make a close-to-uniform progress with a
nonzero rate, without global synchronization. We also provide a coarse-grained
description for the small-world-synchronized virtual-time horizon and compare
the findings to those obtained by simulating the simulations based on the exact
algorithmic rules. We also present numerical results for the evolution of the
virtual-time horizon on scale-free Barabasi-Albert networks serving as
communication topology among the processing elements. Finally, we investigate
to what extent small-world couplings (extending the original local relaxational
dynamics through the random links) lead to the suppression of extreme
fluctuations in the synchronization landscape.
