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In this paper, we propose a scenario-based robust optimization model for the design of a water supply system considering the risk of facility failure, which is represented as an uncertainty set generated by a finite set of scenarios. New facilities are planned to be built to hedge against the possible failure of existing system facilities that would potentially damage the capacity of the system to meet given user demands. The goal is to build facilities that are both cost-effective and make the system robust. The system robustness is defined as the ability to satisfy user demands for every data realization in the uncertainty set. The proposed model is shown to be equivalent to a large-scale mixed-integer linear program that is solved by a Benders decomposition algorithm. Computational results demonstrate the efficiency of the proposed algorithm, and show that substantial improvement in system robustness can be achieved with minimal increase in system cost. [ABSTRACT FROM AUTHOR]

Structural heterogeneity has been proposed as a key intrinsic feature and mechanism underline unique properties and dynamic behavior of metallic glasses; however, it is still challenging in precisely describing and effectively characterizing the atomic-scale heterogeneity in metallic glasses. In this work, we employed the Meissner effect of superconductivity in magnetic susceptibility measurements as a sensitive bulk probe and successfully revealed the three-dimensional structural heterogeneity and its two-way evolution tuned by structural aging or rejuvenation in a La-based metallic glass. Compared with the resistivity measurements which only signal the most superconductive loop in inhomogeneous materials, the diamagnetic susceptibility signal of the Meissner effect maps the volumetric distribution of all superconductive regions and the corresponding structural heterogeneity in metallic glasses with high sensitivity. The experimental results reported in this article can be well interpreted based on a structural model of tunable "soft liquid-like" regions with soft vibration modes mixed with "hard solid-like" regions, validating the heterogeneity models of metallic glasses with new experimental data and approach. • The Meissner effect can be used to uncover the intrinsic structural heterogeneity in superconductive metallic glasses. • The heterogeneity degree and volumetric distribution of metallic glasses can be estimated by the diamagnetic susceptibility. • The diamagnetic susceptibility is susceptible to structural changes caused by aging or rejuvenation of metallic glasses. [ABSTRACT FROM AUTHOR]