Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.

Changes in the flavonoid and phenolic acid contents and antioxidant activity of red leaf lettuce (Lollo Rosso) due to cultivation under plastic films varying in ultraviolet transparency

Red leaf lettuce (Lollo Rosso) was grown under three types of plastic films that varied in transparency to UV radiation (designated as UV block, UV low, and UV window). Flavonoid composition was determined by high-performance liquid chromatography (HPLC), total phenolics by the Folin-Ciocalteu assay, and antioxiclant capacity by the oxygen radical absorbance capacity (ORAC) assay. Exposure to increased levels of UV radiation during cultivation caused the leaves to redden and increased concentrations of total phenols and the main flavonoids, quercetin and cyanidin glycosides, as well as luteolin conjugates and phenolic acids. The total phenol content increased from 1.6 mg of gallic acid equivalents (GAE)/g of fresh weight (FW) for lettuce grown under UV block film to 2.9 and 3.5 mg of GAE/g of FW for lettuce grown under the UV low and UV window films. The antioxiclant activity was also higher in lettuce exposed to higher levels of UV radiation with ORAC values of 25.4 and 55.1 mu mol of Trolox equivalents/g of FW for lettuce grown under the UV block and UV window films, respectively. The content of phenolic acids, quantified as caffeic acid, was also different, ranging from 6.2 to 11.1 mu mol/g of FW for lettuce cultivated under the lowest and highest UV exposure plastic films, respectively. Higher concentrations of the flavonoid glycosides were observed with increased exposure to UV radiation, as demonstrated by the concentrations of aglycones after hydrolysis, which were cyanidin (ranging from 165 to 793 mu g/g), quercetin (ranging from 196 to 880,mu g/g), and luteolin (ranging from 19 to 152 mu g/g). The results demonstrate the potential of the use of UV-transparent plastic as a means of increasing beneficial flavonoid content of red leaf lettuce when the crop is grown in polytunnels.