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In short-carbon-fiber-reinforced polyamide 66 articles shaped by 3D printing (3D-SCFRPA66), the interfaces between printed layers are often susceptible to damage, and the composite is excessively brittle. Therefore, a novel treatment for 3D-printed short-carbon-fiber-reinforced polyamide (3D-SCFRPA66) using homogeneous low-potential electron beam irradiation (HLEBI) to enhance tensile properties was investigated. In 3D-SCFRPA66 samples, ductility was measured based on the following parameters: strain at tensile strength (corresponding to homogeneous deformation) (εts) and resistance energy to homogeneous deformation, a measure of toughness (Ehd), which were both substantially increased. An HLEBI dose of 43.2 kGy at an acceleration potential of 210 kV for the finished 3D-SCFRPA66 samples increased the εts and Ehd values from 0.031 and 1.20 MPa·m for the untreated samples to 0.270 and 6.05 MPa·m for the treated samples, increases of 771% and 504%, respectively. Higher HLEBI doses of 86, 129, or 215 kGy also increased the εts and Ehd values to lesser degrees. Electron spin resonance (ESR) data in the literature show that HLEBI creates dangling bonds in Nylon 6. Since PA66 and Nylon 6 are constructed of C, N, and O and have similar molecular structures, HLEBI apparently severs the (-C-N-) bonds in the backbone of PA66, which have the lowest bond-dissociation energy (BDE) of ~326 to 335 kJ mol−1. This shortens the PA66 chains for higher ductility. In addition, for Nylon 6, X-ray photoelectron spectroscopy (XPS) data in the literature show that HLEBI reduces the N peak while increasing the C peak, indicating the occurrence of shortening chains via dangling bond formation accompanied by increases in crosslinking with carbon bonds. However, caution is advised, since HLEBI was found to decrease the tensile strength (σts) and initial elasticity ([dσ/dε]i) of 3D-SCFRPA66. This tradeoff can possibly allow the HLEBI dose to be adjusted for the desired ductility and strength while minimizing energy consumption. [ABSTRACT FROM AUTHOR]

We describe how one department moved from skepticism to wide-spread embrace of coordinated Calculus I. Data played a crucial role in this process. Details of this journey, including successful strategies and missteps, may provide insight and perspective to other departments starting on, or immersed in, similar transformational adventures.

CANWA (Comparative Analytical Numerical Wave Algorithm), written in MATLAB, provides a fast, direct comparison of a general finite volume solution to the 1+1 shallow water wave equations with a robust analytical solution recently presented by Nicolsky et al. (2018). The implementation of the method for data projection, introduced in Nicolsky et al. (2018), solves the initial value problem produced by the Carrier-Greenspan transformation, allows for highly accurate simulations of waves with nonzero initial velocities. Additionally, an L2analysis of error grants a comparison of solutions across the entire spatial domain. Simulations of both solitary and N-waves reveal that the numerical method consistently yields larger inundation zones than the analytical solution.

An edge-colored graph is properly connected if for every pair of vertices u and v there exists a properly colored uv-path (i.e. a uv-path in which no two consecutive edges have the same color). The proper connection number of a connected graph G, denoted pc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is properly connected. An edge-colored graph is flexibly connected if for every pair of vertices u and v there exist two properly colored paths between them, say P and Q, such that the first edges of P and Q have different colors and the last edges of P and Q have different colors. The flexible connection number of a connected graph G, denoted fpc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is flexibly connected. In this paper, we demonstrate several methods for constructing graphs with pc(G) = 2 and fpc(G) = 2. We describe several families of graphs such that pc(G) ≥ 2 and we settle a conjecture from [BFG+12]. We prove that if G is connected and bipartite, then pc(G) = 2 is equivalent to being 2-edge-connected and fpc(G) = 2 is equivalent to the existence of a path through all cut-edges. Finally, it is proved that every connected, k-regular, Class 1 graph has flexible connection number 2.

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G̅ to G results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum size is the well studied extremal number, ex(n,H). The saturation spectrum for a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this paper we completely determine the saturation spectrum of stars and we show the saturation spectrum of paths is continuous from sat(n, Pk) to within a constant of ex(n, Pk) when n is sufficiently large.