Translational Covering of Closed Planar Cubic B-Spline Curves

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B‐splines. Inner and outer polygonal approximations to the spline regions are generated using enclosures that are inside two different types of piecewise‐linear envelopes. Our recent polygonal covering technique is then applied to seek translations of the covering shapes that allow them to fully cover the target shape. A feasible solution to the polygonal instance provides a feasible solution to the spline instance. We use our recent proof that 2D translational polygonal covering is NP‐hard to establish NP‐hardness of our planar translational spline covering problem. Our polygonal approximation strategy creates approximations that are tight, yet the number of vertices is only a linear function of the number of control points. Using recent results on B‐spline curve envelopes, we bound the distance from the spline curve to its approximation. We balance the two competing objectives of tightness vs. number of points in the approximation, which is crucial given the NP‐hardness of the spline problem. Examples of the results of our spline covering work are provided for instances containing as many as six covering shapes, including both convex and nonconvex regions. Our implementation uses the LEDA and CGAL C++ libraries of geometric data structures and algorithms.     

Microstructure,mechanical properties,and corrosion resistance of Ti-20Zr alloy in undoped and NaF doped artificial saliva

The corrosion behavior of a new, advanced Ti-20Zr alloy with α+β microstructure (determined by optical microscopy, XRD, and SEM) and very good mechanical properties (obtained from the stress-strain curve) is studied in this paper. The composition of the alloy native passive film was determined from a XPS analysis and the long-term corrosion resistance in undoped and doped states with 0.05M NaF artificial Carter-Brugirard saliva of different pH values, simulating the severe functional conditions of a dental implant, was analyzed by electrochemical methods. This alloy possesses an advantageous balance between good mechanical resistance and plasticity and Young’s modulus and exhibits more favorable electrochemical parameters and corrosion resistance than CP Ti due to its more resistant passive layer containing Ti₂O₃, TiO₂, and ZrO₂ protective oxides. After 1000 h of immersion in saliva, the protective properties of the alloy were enhanced due to the deposited surface layer that incorporated protective phosphates (shown by SEM and XPS).     

Total and individual carotenoids and phenolic acids content in fresh,refrigerated and processed spinach (Spinacia oleracea L.)

The carotenoid and phenolic acid contents in fresh, stored and processed (blanched, frozen and boiled) spinach were comparatively determined by spectrophotometric and HPLC analyses. The major carotenoids identified after HPLC analysis in saponified samples were lutein (37–53 μg/kg), β-carotene (18–31 μg/kg), violaxanthin (9–23 μg/kg) and neoxanthin (10–22 μg/kg). These carotenoids were all affected by storage and/or heating. The content of carotenoids was best preserved after storage for one day at 4 °C.     

Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source

We describe and demonstrate a new nanometer-scale broadband light source. It is based on the grating-coupled excitation of surface plasmon polaritons (SPPs) on the shaft of a sharp conical metal taper with a tip radius of few tens of nanometers. Far-field excitation of linear nanoslit gratings results in the resonant generation of SPPs traveling over more than 10 mum to the tip apex and converging to an intense radiative local light spot. Such nanofabricated tips are expected to find various applications in nanospectroscopy, overcoming problems with background illumination in apertureless microscopy.     

Antioxidant flavonoids from knotwood of Jack pine and European aspen

Flavonoids have recently been found in large amounts in knotwood and stemwood of several tree species. Six flavonoids, two flavonoid glucosides, and one cinnamic acid derivative were isolated from Jack pine and European aspen knotwood and structurally characterised using GC-MS, HR-MS, and NMR spectroscopic analyses. Isolated compounds were further assessed on basis of their potency to inhibit lipid peroxidation and scavenge peroxyl radicals. All tested compounds possessed antioxidant properties close to that of the reference compound Trolox.     

Structural Analysis,Electrochemical Behavior,and Biocompatibility of Novel Quaternary Titanium Alloy with near β Structure

This article analyses the microstructure, electrochemical behavior, and biocompatibility of a novel Ti-20Nb-10Zr-5Ta alloy with low Young’s modulus (59 GPa) much closer to that of bone, between 10 and 30 GPa, than Ti and other Ti alloys used as implant biomaterial. XRD and SEM measurements revealed a near β crystalline microstructure containing β phase matrix and secondary α phase, with a typical grain size of around 200 μm. The corrosion behavior in neutral Ringer solution evidenced: self-passivation behavior characterizing a very resistant passive film; an easy passivation as a result of favorable influence of the alloying elements Nb, Zr, and Ta that participate with their passive oxides to the formation of the alloy passive film; low corrosion and ion release rates corresponding with very low toxicity. In MEM solution, the novel alloy demonstrated very high corrosion resistance and no susceptibility to localized corrosion. Biocompatibility was evaluated on in vitro human osteoblast-like and human immortalized pulmonary fibroblast cell (Wi-38) lines and the new Ti-20Nb-10Zr-5Ta alloy exhibited no cytotoxicity. The new Ti-20Nb-10Zr5Ta alloy is a promising material for implants due to combined properties of low elastic modulus, very low corrosion rate, and good biocompatibility.     

A phenomenological model for fiber tow saturation of dual scale fabrics in liquid composite molding

Advanced composites are manufactured by liquid composite molding by impregnating a thermoset resin into a stationary woven or stitched preform. For a successful injection, the manufactured part should fill all the empty spaces between the fiber tows and inside the fiber tows with the resin. The fiber tows in such preforms have orders of magnitude lower permeability than the regions between the fiber tows, which makes them difficult to fill and hence susceptible to formation of microvoids. Numerical simulations can address the filling of fiber tows but it is difficult to capture the essential physics of their filling in a model created entirely from first principles due to the complexity of the flow which involves anisotropic permeability of flow along and across a fiber tow, uneven packing, fiber sizing, capillarity and the treatment of entrapped air. Hence, in this article we adopt a phenomenological approach in which we compare some of the possible models with an experimental procedure. The experimental procedure provides a quantitative measure of the filling of fiber tows during the impregnation process. A numerical simulation based on the dual scale flow was developed with different constitutive models that described the filling of the fiber tows. The predictions of the different models are compared with the experimental results under different processing conditions to select the model that most accurately describes the tow filling behavior. POLYM. COMPOS., 31:1881–1889, 2010. © 2010 Society of Plastics Engineers.     

Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM

Traditionally, capillary effects have been neglected when modeling the filling stage of Liquid Composite Molding processes. This simplification is justified because the inlet resin pressures are much higher than the capillary pressure. This simplification is also acceptable when impregnating fabrics in which their fiber tows saturate at the same rate as the bulk preform. However, this assumption is questionable for fabrics that exhibit dual scale in which the fiber tows saturate at a much slower rate than the bulk preform. In such cases, the capillary pressure can influence the time to saturate a fiber tow significantly and impact the overall impregnation dynamics. Since the flow front velocity inside the fiber tows is significantly smaller than the flow around them, it is important to include the capillary pressure that may aid the saturation of the tow. In this paper, we modify our existing simulation that can predict the filling of the bulk preform and the saturation of the fiber tows to include the capillary forces at the fiber tow level. Important parameters are identified and grouped in non-dimensional form. A parametric study is conducted to examine the role of these dimensionless parameters on the overall tow saturation levels. The modeling is extended to include the effect of entrapped air inside the tows on the overall saturation of the preform. An experimental technique using the optical properties of vinyl ester and glass fiber was used to qualitatively validate the proposed model.