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.

Designing Temperature-Responsive Biocompatible Copolymers and Hydrogels Based on 2-Hydroxyethyl(meth)acrylates

Free-radical copolymerization of 2-hydroxyethyl methacrylate with 2-hydroxyethyl acrylate can be successively utilized for the synthesis of water-soluble polymers and hydrogels with excellent physicochemical properties, thus showing promise for pharmaceutical and biomedical applications. In the work presented it has been demonstrated that water-soluble copolymers based on 2-hydroxyethyl methacrylate and 2-hydroxyethyl acrylate exhibit lower critical solution temperature in aqueous solutions, whereas the corresponding high molecular weight homopolymers do not have this unique property. The temperature-induced transitions observed upon heating the aqueous solutions of these copolymers proceed via liquid−liquid phase separation. The hydrogels were also synthesized by copolymerizing 2-hydroxyethyl methacrylate and 2-hydroxyethyl acrylate in the absence of a bifunctional cross-linker. The cross-linking of these copolymers during copolymerization is believed to be due to the presence of bifunctional admixtures or transesterification reactions. Transparency, swelling behavior, mechanical properties, and porosity of the hydrogels are dependent upon the monomer ratio in the copolymers. Hydrogel samples containing more 2-hydroxyethyl methacrylate are less transparent, have lower swelling capacity, higher elastic moduli, and pores of smaller size. The assessment of the biocompatibility of the copolymers using the slug mucosal irritation test revealed that they are also less irritant than poly(acrylic acid).

Solvent Effects on the Formation of Nanoparticles and Multilayered Coatings Based on Hydrogen-Bonded Interpolymer Complexes of Poly(acrylic acid) with Homo- and Copolymers of N-Vinyl Pyrrolidone

The formation of hydrogen-bonded interpolymer complexes between poly(acrylic acid) and poly(N-vinyl pyrrolidone) as well as amphiphilic copolymers of N-vinyl pyrrolidone with vinyl propyl ether has been studied in aqueous and organic solutions. It was demonstrated that introduction of vinyl propyl ether units into the macromolecules of the nonionic polymer enhances their ability to form complexes in aqueous solutions due to more significant contribution of hydrophobic effects. The complexation was found to be a multistage process that involves the formation of primary polycomplex particles, which further aggregate to form spherical nanoparticles. Depending on the environmental factors (pH, solvent nature), these nanoparticles may either form stable colloidal solutions or undergo further aggregation, resulting in precipitation of interpolymer complexes. In organic solvents, the intensity of complex formation increases in the following order: methanol < ethanol < isopropanol < dioxane. The multilayered coatings were developed using layer-by-layer deposition of interpolymer complexes on glass surfaces. It was demonstrated that the solvent nature affects the efficiency of coating deposition.

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.

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.

Temperature-responsive properties and drug solubilization capacity of amphiphilic copolymers based on N-vinylpyrrolidone and vinyl propyl ether

A series of amphiphilic copolymers were synthesized by free-radical copolymerization of N-vinylpyrrolidone (NVP) with vinyl propyl ether (VPE), and the structure of the copolymers was characterized by elemental analysis and gel permeation chromatography. The reactivity of VPE in copolymerization was found to be significantly lower than the reactivity of NVP, which resulted in a decrease of copolymers’ yields and molecular weights with higher content of VPE in the feed mixture. An investigation of the behavior of the copolymers in aqueous solutions at different temperatures by dynamic light scattering revealed the presence of lower critical solution temperature, which depending on the content of VPE ranged within 23−38 °C. Aqueous solutions of these copolymers were studied by fluorescent spectroscopy with pyrene as a polarity probe to reveal the formation of hydrophobic domains. The copolymers were found to be useful for enhancing the solubility of riboflavin in water.