In this paper, a new Specific Breakpoint Algorithm (SBA), which can efficiently search appropriate breakpoints of parametric maximum-flow-related problems, is presented. The algorithm is used to solve Lagrangian Relaxed Precedence Constrained Knapsack Problem (LRPCKP) and Linear Programming Relaxed Precedence Constrained Knapsack Problem (LPRPCKP) in mine pushback design. The relaxed solutions are then processed through Rounded Topo-Sort (RoTS) heuristic to produce feasible solutions. The study results on seven bench mark datasets on Minelib for two approaches, referred here as LRPCKP-SBA and LPRPCKP-SBA, indicate that LRPCKP-SBA in spite of being faster, produces inferior quality solutions than well known BZ and CPLEX solutions. However, LPRPCKP-SBA produces a comparable quality of solutions as BZ in a computationally more efficient manner. Furthermore, the RoTS heuristics operated on relaxed solutions produce a better quality of feasible solutions than an existing technique, Expected Topo-Sort heuristic (ExTS).
The hunt for a cleaner energy carrier leads us to consider a source that produces no toxic byproducts. One of the targeted alternatives in this approach is hydrogen energy, which, unfortunately, suffers from a lack of efficient storage media. Solid-state hydrogen absorption systems, such as lithium amide (LiNH2) systems, may store up to 6.5 weight percent hydrogen. However, the temperature of hydrogenation and dehydrogenation is too high for practical use. Various molar ratios of LiNH2 with sodium hydride (NaH) and potassium hydride (KH) have been explored in this paper. The temperature of hydrogenation for LiNH2 combined with KH and NaH was found to be substantially lower than the temperature of individual LiNH2. This lower temperature operation of both LiNH2-NaH and LiNH2-KH systems was investigated in depth, and the eutectic melting phenomenon was observed. Systematic thermal studies of this amide-hydride system in different compositions were carried out, which enabled the plotting of a pseudo-binary phase diagram. The occurrence of eutectic interaction increased atomic mobility, which resulted in the kinetic modification followed by an increase in the reactivity of two materials. For these eutectic compositions, i.e., 0.15LiNH2-0.85NaH and 0.25LiNH2-0.75KH, the lowest melting temperature was found to be 307 °C and 235 °C, respectively. Morphological studies were used to investigate and present the detailed mechanism linked with this phenomenon.
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