Engineering networks fall into the category of large-scale networks with heterogeneous nodes such as sources and sinks. The survivability analysis of such networks requires the analysis of the connectivity of the network components for every possible
combination of faults to determine a network response to each combination of faults. From the computational complexity point of view, the problem belongs to the class of exponential time problems at least. Partially, the problem complexity can be reduced by mapping the initial topology of a complex large-scale network with multiple sources and multiple sinks onto a set of smaller sub-topologies with multiple sources and a single sink connected to the network of sources by a single link. In this paper, the mapping procedure is applied to the Florida power grid.
We study by kinetic Monte Carlo simulations the catalytic oxidation of carbon monoxide on a surface in the presence of contaminants in the gas phase. The process is simulated by a Ziff-Gulari-Barshad (ZGB) model that has been modified to include the
effect of the contaminants and to eliminate the unphysical oxygen-poisoned phase. The impurities can adsorb and desorb on the surface, but otherwise remain inert. We find that, if the impurities can not desorb, no matter how small their proportion in the gas mixture, the first order transition and the reactive window that characterize the ZGB model disappear. The coverages become continuous, and once the surface has reached a steady state there is no production of CO$_2$. This is quite different from the behavior of a system in which the surface presents a fixed percentage of impurities. When the contaminants are allowed to desorb, the reactive window appears again, and disappears at a value that depends on the proportion of contaminants in the gas and on their desorption rate.
The nanoscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (ele
ctro)chemical potential, are studied by an analytic nonlinear-response approximation together with kinetic Monte Carlo simulations. Here we consider the case that the system is coupled to a two-dimensional phonon bath. In the resulting dynamic, transitions that conserve the system energy are forbidden, and the effects of the applied force and the interaction energies do not factorize (a so-called hard dynamic). In full agreement with previous general theoretical results we find that the local interface width changes dramatically with the applied force. However, in contrast with other hard dynamics, this change is nonmonotonic in the driving force. However, significant differences between theory and simulation are found near two special values of the driving force, where certain transitions allowed by the solid-on-solid model become forbidden by the phonon-assisted dynamic. Our results represent a significant step toward providing a solid physical foundation for kinetic Monte Carlo simulations.
