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  1. Meyer, J. P. (Ed.)
    Air-water evaporation systems are ubiquitous in industrial applications, including processes such as fuel combustion, inkjet printing, spray cooling, and desalination. In these evaporation-driven systems, a fundamental understanding of mass accommodation at the liquid-vapour interface is critical to predicting and optimizing performance. Interfacial mass accommodation depends on many factors, such as temperature, vapour concentration, non-volatile impurity content, and non-condensable gasses present. Elucidating how these factors interact is essential to designing devices to meet demanding applications. Hence, high precision measurements are needed to quantify accommodation at the liquid-vapour interface accurately. Our previous study has shown surface averaged accommodation coefficients close to 0.001more »for pure water droplets throughout evaporation. While it is well established that saline non-volatile impurities reduce the evaporation rate of sessile droplets, the dynamic effect on mass accommodation during the droplet's lifespan is yet to be determined. In this work, we combine experimental and computational techniques to determine the accommodation coefficient over the lifespan of 10-3 to 1 molar potassium chloride-water droplets evaporating on a gold-coated surface into dry nitrogen. This study uses a quartz crystal microbalance as a high-precision contact area sensor. It also determines the non-volatile impurities in the droplet with a precision on the order of nanograms. The computational model couples macroscopic measurements with the microscopic kinetic theory of gasses to quantify hard-to-measure physical quantities. We believe this study will provide a basis for predicting evaporative device performance in conditions where non-volatile impurities are intrinsic to the application.« less
    Free, publicly-accessible full text available July 28, 2022
  2. Free, publicly-accessible full text available June 1, 2022
  3. Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems. We study its application to two clustering problems: the facility location problem, and the single-linkage hierarchical clustering problem, which is equivalent to computing the minimum spanning tree. We show that if we project the input pointset 𝑋 onto a random 𝑑=𝑂(𝑑𝑋)-dimensional subspace (where 𝑑𝑋 is the doubling dimension of 𝑋), then the optimum facility location cost in the projected space approximates the original cost up to a constant factor. We show an analogous statement for minimum spanning tree, but with the dimension 𝑑 having an extramore »loglog𝑛 term and the approximation factor being arbitrarily close to 1. Furthermore, we extend these results to approximating solutions instead of just their costs. Lastly, we provide experimental results to validate the quality of solutions and the speedup due to the dimensionality reduction. Unlike several previous papers studying this approach in the context of 𝑘-means and 𝑘-medians, our dimension bound does not depend on the number of clusters but only on the intrinsic dimensionality of 𝑋.« less
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