We present a numerical study of a reaction-diffusion model on a small-world network. We characterize the models average activity $F_T$ after $T$ time steps and the transition from a collective (global) extinct state to an active state in parameter sp
ace. We provide an explicit relation between the parameters of our model at the frontier between these states. A collective active state can be associated to a global epidemic spread, or to a persistent neuronal activity. We found that $F_T$ does not depends on disorder in the network if the transmission rate $r$ or the average coordination number $K$ are large enough. The collective extinct-active transition can be induced by changing two parameters associated to the network: $K$ and the disorder parameter $p$ (which controls the variance of $K$). We can also induce the transition by changing $r$, which controls the threshold size in the dynamics. In order to operate at the transition the parameters of the model must satisfy the relation $rK=a_p$, where $a_p$ as a function of $p/(1-p)$ is a stretched exponential function. Our results are relevant for systems that operate {it at} the transition in order to increase its dynamic range and/or to operate under optimal information-processing conditions. We discuss how glassy behaviour appears within our model.
We study experimentally gravity-driven granular discharges of laboratory scale silos, during the initial instants of the discharge. We investigate deformable wall silos around their critical collapse height, as well as rigid wall silos. We propose a
criterion to determine a maximum time for the onset of the collapse and find that the onset of collapse always occurs before the grains adjacent to the wall are sliding down. We conclude that the evolution of the static friction toward a state of maximum mobilization plays a crucial role in the collapse of the silo.
