Use of advanced operations research methods for optimal water allocation modelling

Three mathematical models named the Single Objective Economic (SOE), Compromised Water Allocation (CWA), and Multiple Economic Objectives (MEO) models were developed for modelling equitable and efficient water allocation among competing users of a transboundary basin, based on a multi-period node-link river basin network. Furthermore, the Integrated Water & Dam Allocation (IWDA) method was proposed in order to integrate water allocation modelling and locating and sizing new water projects of a transboundary basin. The SOE model is a single economic objective model that allocates water to competing stakeholders such that the overall profit of the basin is maximised, subjects to river water system constraints and the environmental water requirement satisfaction in the entire basin. The CWA model challenges multi-objective programming with aggregated objective functions for providing a sustainable water allocation. Three basin-wide aggregated objective functions, addressed the overall basin’s profit, the environmental water supply in the entire basin, and the limitation of transferring water from upstream to downstream are considered in this model. The environment is considered as a stakeholder in this model, which competes with other stakeholders for more water supplies in the CWA model. The MEO model involves directly the profits of stakeholders in water allocation modelling. It maximizes the profits of all stakeholders simultaneously, while the environmental water satisfaction in the entire basin is considered as a firm constraint. In order to solve this model, two three-step approaches (the Single Lambda and Multiple Lambda solution methods) were introduced. These solution methods are established based on maximizing the minimum ratio of achieved profits of the stakeholders from their water shares to their highest possible profits. The IWDA method, which is treated as the key contribution of this thesis, consists of three steps. The first step runs the Multi-Objective Water & Dams Allocation (MOWDA) model in order to allocate equitably water to the stakeholders of the basin along with providing the optimal locations and capacities of new proposed dams for various scenarios (number of dams). The second step utilizes a sensitivity analysis approach for comparing the results of the MOWDA model for various scenarios (number of dams) in order to provide the optimal number of required reservoirs in the basin. The third step runs the Minimum Capacity (MinCap) model to find another optimal water allocation scheme for the basin which leads to the lowest required dams’ capacities, for the final number of required dams (determined by step 2). Throughout the study, both the feasibility and the effectiveness of incorporating equity concepts into economic optimal water resources management modelling were addressed. The applications of all aforementioned models to the Sefidrud Basin in Iran demonstrate the models can serve as a powerful tool for sustainable water resource management and conflict resolution between the stakeholders. It can be stated that the IWDA method can be utilized for providing the maximum welfare in a transboundary river basin. This method satisfies the environmental water requirements, locates and sizes optimally dams, and distributes available water resources between the stakeholders such that their achieved profits are satisfactory

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum