Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description.

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The protection of riverine ecosystems downstream from dams requires reservoir operations to satisfy environmental flow (e-flow) requirements. In practice, this often involves re-regulation of downstream river flows within the constraints of water resource demands for human supplies and irrigation. In this paper, we develop a method to assess how reservoir storage may be used more effectively to meet both water supply and downstream ecosystem needs. The latter are met by providing seasonally variable baseflows, including dry season flow recession at natural rates, and high-flow pulses and bankfull flows synchronized with natural events. A series of reservoir operating rules are derived based on both reservoir storage and reservoir inflows to trigger reservoir releases. For a given water supply reliability, the method seeks to minimize the degree of hydrological alteration below a dam. We present a case study of the Tanghe Reservoir in China's Tang river basin to show that the proposed method could help reservoir managers and planners evaluate e-flow scenarios to reduce the negative impacts of dams and reservoirs on riverine ecosystems.

The paper studies grid connected photovoltaic(PV)-hydrogen/battery systems. The storage component capacities and the rule-based operation strategy parameters are simultaneously optimized by the Genetic Algorithm. Three operation strategies for the hydrogen storage, namely conventional operation strategy, peak shaving strategy and hybrid operation strategy, are compared under two scenarios based on the pessimistic and optimistic costs. The results indicate that the hybrid operation strategy, which combines the conventional operation strategy and the peak shaving strategy, is advantageous in achieving higher Net Present Value (NPV) and Self Sufficiency Ratio (SSR). Hydrogen storage is further compared with battery storage. Under the pessimistic cost scenario, hydrogen storage results in poorer performance in both SSR and NPV. While under the optimistic cost scenario, hydrogen storage achieves higher NPV. Moreover, when taking into account the grid power fluctuation, hydrogen storage achieves better performance in all three optimization objectives, which are NPV, SSR and GI (Grid Indicator).