We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value $N$, a blockage occurs and the particle flux is definitively interrupted. B
y introducing an integral representation of the $n$ particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particle and their time correlation. We generalize previous results for $N=2$ to an arbitrary distribution of entry times and obtain new, exact solutions for $N=3$ for a Poisson distribution and partial results for $Nge 4$.
The interaction of two resonant impurities in graphene has been predicted to have a long-range character with weaker repulsion when the two adatoms reside on the same sublattice and stronger attraction when they are on different sublattices. We revea
l that this attraction results from a single energy level. This opens up a possibility of controlling the sign of the impurity interaction via the adjustment of the chemical potential. For many randomly distributed impurities (adatoms or vacancies) this may offer a way to achieve a controlled transition from aggregation to dispersion.
