The main objective of a water distribution network is to provide water to users in compliance with quality and service standards under different conditions. The ability to meet the water demand at the nodes, under the required pressures head, depends on many characteristic factors of the water network, such as various infrastructural components. A water distribution network is a complex system consisting of numerous structural elements and dependent by several factors. Resilience, robustness and vulnerability are of great interest, for these systems, in relation to the possible failure conditions which may compromise the network’s ability to fulfill the project conditions. Vulnerability measures how much the network is fragile: a higher value of vulnerability means that the network is prone to fail in achieving the project conditions. In the present work, a new vulnerability measure based on a topological approach is proposed. A first application of the proposed vulnerability measure on two water networks known in the literature is described, and the obtained results are compared with other performance indices showing a significant correlation.

This work presents a quantum chemical study of Zn and Sb doping and co-doping in SnO₂ carried out by a DFT+U method. The analysis has been developed by introducing three different modifications in the otherwise pure SnO₂ system. In the first place, an oxygen vacancy was introduced within the crystal. Following, such a system was doped (separately) by Zn or Sb impurities. Finally, the best energetic positions for both Zn and Sb atoms were simultaneously introduced within the lattice. Results of the simulations show that the confined charge that appeared due to the introduction of the oxygen vacancy interacts with the dopants atoms, being this interaction mostly responsible of the observed effects, i.e., E_G shrinkage, F-centers formations, and magnetic momentum rise.