Proper Orthogonal Decomposition of Flexible Clap and Fling Elastic Motions via High-Speed Deformation Measurements

Many complex unsteady mechanisms are thought to facilitate the high efficiency and agility commonly observed in small biological flyers. One of these, the flexible clap and fling maneuver, has not been extensively studied; an experimental characterization is the focus of this work. The clap–fling mechanism is approximated with a single flexible membrane flapping wing, replacing the symmetry plane between two wings with a splitter plate simulating the pair wing. This produces a complex vibro-impact aeroelastic problem, the deformation resulting from which is measured with a high-speed visual image correlation system. A low-dimensional representation of the ensuing large data set is obtained with proper orthogonal decomposition. The POD modes, and the relative importance of each, can help elucidate crucial mechanisms and relationships within the flapping system, and are computed for various membrane wing structures and flapping frequencies, with or without the presence of the splitter plate.     

Exploded manifolds

This paper provides an introduction to exploded manifolds. The category of exploded manifolds is an extension of the category of smooth manifolds with an excellent holomorphic curve theory. Each exploded manifold has a tropical part which is a union of convex polytopes glued along faces. Exploded manifolds are useful for defining and computing Gromov–Witten invariants relative to normal crossing divisors, and using tropical curve counts to compute Gromov–Witten invariants.     

Nitrile Rubber Reactor Operation Troubleshooting with Principal Component Analysis

Principal Component Analysis (PCA) is employed as a tool in order to demonstrate yet another application of the technique, and, most importantly, to show that results from the statistical multivariate technique do make physico-chemical sense. The operation of a typical emulsion copolymerization of acrylonitrile and butadiene (nitrile butadiene rubber, NBR) is used as an example of process troubleshooting. In more general terms, a statistical tool is used to aid process data analysis and process operation (recipe, product property) troubleshooting.

The goal is to produce consistent Mooney Viscosity (MV) among different batches. The observation is that varying induction times lead to Mooney Viscosity inconsistencies. Firstly, we show results from the application of PCA to process data. Secondly, we deal with an even more important (and often ignored) question by examining whether the trends indicated by PCA make process sense.