Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

Optimization of Pathogen Capture in Flowing Fluids with Magnetic Nanoparticles

Magnetic nanoparticles have been employed to capture pathogens for many biological applications; however, optimal particle sizes have been determined empirically in specific capturing protocols. Here, a theoretical model that simulates capture of bacteria is described and used to calculate bacterial collision frequencies and magnetophoretic properties for a range of particle sizes. The model predicts that particles with a diameter of 460 nm should produce optimal separation of bacteria in buffer flowing at 1 L h⁻¹. Validating the predictive power of the model, Staphylococcus aureus is separated from buffer and blood flowing through magnetic capture devices using six different sizes of magnetic particles. Experimental magnetic separation in buffer conditions confirms that particles with a diameter closest to the predicted optimal particle size provide the most effective capture. Modeling the capturing process in plasma and blood by introducing empirical constants (c_e), which integrate the interfering effects of biological components on the binding kinetics of magnetic beads to bacteria, smaller beads with 50 nm diameters are predicted that exhibit maximum magnetic separation of bacteria from blood and experimentally validated this trend. The predictive power of the model suggests its utility for the future design of magnetic separation for diagnostic and therapeutic applications.     

Experimental investigation of unconfined spherical and cylindrical flame propagation in hydrogen-air mixtures

This paper presents results of experimental investigations on spherical and cylindrical flame propagation in pre-mixed H₂/air-mixtures in unconfined and semi-confined geometries. The experiments were performed in a facility consisting of two transparent solid walls with 1 m² area and four weak side walls made from thin plastic film. The gap size between the solid walls was varied stepwise from thin layer geometry (6 mm) to cube geometry (1 m). A wide range of H₂/air-mixtures with volumetric hydrogen concentrations from 10% to 45% H₂ was ignited between the transparent solid walls. The propagating flame front and its structure was observed with a large scale high speed shadow system. Results of spherical and cylindrical flame propagation up to a radius of 0.5 m were analyzed. The presented spherical burning velocity model is used to discuss the self-acceleration phenomena in unconfined and unobstructed pre-mixed H₂/air flames.     

Fully renewable limonene‐derived polycarbonate as a high‐performance alkyd resin

Limonene‐derived polycarbonate‐based alkyd resins (ARs) have been prepared by copolymerization of limonene dioxide with CO₂, catalysed by a β‐diiminate zinc–bis(trimethylsilyl)amido complex, and subsequent chemical modification with soybean oil fatty acids using triphenylethylphosphonium bromide as the catalyst. This quantitative partial modification was realized via epoxy–carboxylic acid chemistry, affording ARs with higher oil lengths, lower polydispersities and higher glass transition temperatures (T_g) in comparison to a conventional polyester AR based on phthalic acid, multifunctional polyol pentaerythritol and soybean fatty acid. The novel limonene polycarbonate AR and the conventional polyester AR were evaluated as coatings and both the physical drying (without the presence of the oxidative drying accelerator Borchi® Oxy Coat) and chemical curing (with Borchi® Oxy Coat) processes of these coatings were monitored by measuring the König hardness and complex modulus development with time. A better performance was obtained for the alkyd paint containing polycarbonates modified with fatty acids (FA‐PCs), which showed a faster chemical drying, a higher König hardness and a higher T_g in coating evaluation, demonstrating that the fully renewable FA‐PCs are promising resins for alkyd paint applications. © 2019 Society of Chemical Industry