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The construction of bounded-degree plane geometric spanners has been a focus of interest since 2002 when Bose, Gudmundsson, and Smid proposed the first algorithm to construct such spanners. To date, 11 algorithms have been designed with various tradeoffs in degree and stretch-factor. We have implemented these sophisticated spanner algorithms in C ++ using the CGAL library and experimented with them using large synthetic and real-world pointsets. Our experiments have revealed their practical behavior and real-world efficacy. We share the implementations via GitHub for broader uses and future research. We design and engineer EstimateStretchFactor , a simple practical algorithm, which can estimate stretch-factors (obtains lower bounds on the exact stretch-factors) of geometric spanners—a challenging problem for which no practical algorithm is known yet. In our experiments with bounded-degree plane geometric spanners, we found that EstimateStretchFactor estimated stretch-factors almost precisely. Further, it gave linear runtime performance in practice for the pointset distributions considered in this work, making it much faster than the naive Dijkstra-based algorithm for calculating stretch-factors. 

In this study, hydrophilic silica nanoparticles (Si NPs) were used to modify α-alumina tubular membranes to improve their performance in terms of flux, oil rejection, and anti-fouling properties. Our work focuses on enhancing membrane performance, particularly for difficult applications such as produced water treatment. The prepared membranes were applied for oil-in-water emulsion treatment. After coating hydrophilic Si NPs, the oil contact angle improved from 133.8° to 171.4°. To prevent Si NPs from leaching off the surface of α-alumina tubular membranes, polyvinyl alcohol was used to coat the membranes as a pre-treatment step before Si NP modification. After coating the membrane with Si NPs, the roughness of the membrane surface decreased, likely leading to less fouling. After coating Si NPs, Total Organic Carbon rejection increased from 93.1% for pristine α-alumina tubular membranes to 97.7% for silica-modified membranes because of hydrophilic improvements of the modified membranes. The Si NP coating improved the anti-fouling property of membranes with the flux recovery ratio increasing from 71.3% for pristine α-alumina tubular membranes to 85.9% for silica-modified membranes. Scanning Electron Microscopy, Energy- dispersive X-ray spectroscopy, oil contact angle, and Atomic Force Microscopy characterization tests were done. The tests showed successful Si NPs impregnation and altered wettability.