Solving the radiation diffusion and energy balance equations using pseudo-transient continuation

We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks.     

Nematic Equilibria on a Two‐Dimensional Annulus

We study planar nematic equilibria on a two‐dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect‐free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral‐like equilibrium which emerges as the defect‐free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect‐free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.     

A-type cranberry proanthocyanidins inhibit the RANKL-dependent differentiation and function of human osteoclasts

This study investigated the effect of A-type cranberry proanthocyanidins (AC-PACs) on osteoclast formation and bone resorption activity. The differentiation of human pre-osteoclastic cells was assessed by tartrate-resistant acid phosphatase (TRAP) staining, while the secretion of interleukin-8 (IL-8) and matrix metalloproteinases (MMPs) was measured by ELISA. Bone resorption activity was investigated by using a human bone plate coupled with an immunoassay that detected the release of collagen helical peptides. AC-PACs up to 100 μg/mL were atoxic for osteoclastic cells. TRAP staining evidenced a dose-dependent inhibition of osteoclastogenesis. More specifically, AC-PACs at 50 μg/mL caused a 95% inhibition of RANKL-dependent osteoclast differentiation. This concentration of AC-PACs also significantly increased the secretion of IL-8 (6-fold) and inhibited the secretion of both MMP-2 and MMP-9. Lastly, AC-PACs (10, 25, 50 and 100 μg/ml) affected bone degradation mediated by mature osteoclasts by significantly decreasing the release of collagen helical peptides. This study suggests that AC-PACs can interfere with osteoclastic cell maturation and physiology as well as prevent bone resorption. These compounds may be considered as therapeutic agents for the prevention and treatment of periodontitis.     

Inf–sup conditions for twofold saddle point problems

Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented.     

Palladium-catalyzed carbohalogenation: bromide to iodide exchange and domino processes

Aryl bromides have been used to prepare a variety of nitrogen- and oxygen-containing heterocycles featuring new carbon-carbon and carbon-iodine bonds. This palladium-catalyzed carbohalogenation requires potassium iodide for the reaction to proceed in high yields. Additionally, the first examples of domino carbohalogenation reactions have been demonstrated using both aryl iodide and aryl bromide starting materials. Complex products with multiple rings and stereogenic centers are generated in excellent yields with moderate to excellent diastereoselectivities.     

Adsorption of anionic and cationic dyes by activated carbons, PVA hydrogels, and PVA/AC composite

The textural and adsorption characteristics of a series of activated carbons (ACs), porous poly(vinyl alcohol) (PVA) gels, and PVA/AC composites were studied using scanning electron microscopy, mercury porosimetry, adsorption of nitrogen (at 77.4 K), cationic methylene blue (MB), anionic methyl orange (MO), and Congo red (CR) from the aqueous solutions. Dye-PVA-AC-water interactions were modeled using the semiempirical quantum chemical method PM6. The percentage of dye removed (C(rem)) by the ACs was close to 100% at an equilibrium concentration (C(eq)) of less than 0.1 mM but decreased with increasing dye concentration. This decrease was stronger at C(eq) of less than 1 mM, and C(rem) was less than 50% at a C(eq) of 10-20 mM. For PVA and the PVA/AC composite containing C-7, the C(rem) values were minimal (<75%). The free energy distribution functions (f(ΔG)) for dye adsorption include one to three peaks in the -ΔG range of 1-60 kJ/mol, depending on the dye concentration range used and the spatial, charge symmetry of the hydrated dye ions and the structural characteristics of the adsorbents. The f(ΔG) shape is most complex for MO with the most asymmetrical geometry and charge distribution and adsorbed at concentrations over a large C(eq) range. For symmetrical CR ions, adsorbed over a narrow C(eq) range, the f(ΔG) plot includes mainly one narrow peak. MB has a minimal molecular size at a planar geometry (especially important for effective adsorption in slit-shaped pores) which explains its greater adsorptive capacity over that of MO or CR. Dye adsorption was greatest for ACs with the largest surface area but as molecular size increases adsorption depends to a greater extent on the pore size distribution in addition to total and nanopore surface areas and pore volume.     

Thermal characteristics of precursors to a difunctional imide monomer

A difunctional imide monomer may be produced from 4-nitrophthalic anhydride and m-phenylenediamine. The requisite anhydride may be generated by nitration of phthalimide followed by hydrolysis to the corresponding acid and dehydration. All intermediate compounds have been fully characterized using spectroscopic and thermal methods.     

UV polymerization of hydrodynamically shaped fibers

Most natural and man-made fibers have circular cross-sections; thus the properties of materials composed of non-circular fibers are largely unexplored. We demonstrate the technology for fabricating fibers with predetermined cross-sectional shape. Passive hydrodynamic focusing and UV polymerization of a shaped acrylate stream produced metre-long fibers for structural and mechanical characterization.     

Two new promelacacinidin dimers,including a novel flavanone-flavanol dimer characterized by a unique C(3)-C(4) linkage,from the heartwood of <Emphasis Type="Italic">Acacia nigrescens</Emphasis>

Two new promelacacinidin biflavonoids, mesquitol-(4α,5)-epimesquitol-4β-ol and a 3′,4′,7,8-tetrahydroxyflavanone(3,4)-ent-epimesquitol, were isolated among others from the heartwood of Acacia nigrescens. The flavanone derived dimer, characterized by a unique C(3) to C(4) bridge, which links the monomers via two stereogenic and sp³ hybridized C-atoms, is the prototype of a new subgroup of the flavonoid family. Assessment of the absolute configuration of all five stereogenic centers of this novel flavanone-derived biflavonoid was achieved by correlating the chiroptical properties of the benzoyl chromophore to the absolute configuration of C(2) of the flavanone moiety and hence the absolute stereochemistry of the other four chiral centers. Published in Khimiya Prirodnykh Soedinenii, No. 5, pp. 437–441, September–October, 2007. Dedicated to Prof. E. Malan, who initiated and supervised this research project, for a noteworthy contribution in the flavonoid field, and who has since retired.     

The hearing aid feedback path: mathematical simulations and experimental verification

Acoustic feedback in hearing aids has received little attention in the literature. Feedback occurs when stability conditions of the open-loop transfer function of an in situ hearing aid are violated. Solving the feedback problem will first require knowledge of the open-loop transfer function. Included in the open-loop transfer function is the acoustical path by which sound emanating from the earmold vent returns to the microphone (i.e., the feedback path). Reported herein are two different mathematical procedures for simulating transfer functions of the feedback path of an eyeglass-type hearing aid. In one procedure the vent exit was modeled as a point source of sound located on a flat plane, while it was treated as a point source on a sphere in the other. Results of laboratory experiments indicate that the mathematical models accurately predict those acoustic phenomena for which they were intended: point sources on plane and spherical baffles. Results of manikin experiments showed both models to be less accurate for simulating the feedback path around the human head. The maximum difference between experiment and theory was 6 dB at one frequency. Surprisingly, the flat-baffle model produced better agreement with experimental results than did the sphere model.