A posteriori error estimates for mixed finite element approximations of parabolic problems

We derive residual based a posteriori error estimates for parabolic problems on mixed form solved using Raviart–Thomas–Nedelec finite elements in space and backward Euler in time. The error norm considered is the flux part of the energy, i.e. weighted L ²(Ω) norm integrated over time. In order to get an optimal order bound, an elementwise computable post-processed approximation of the scalar variable needs to be used. This is a common technique used for elliptic problems. The final bound consists of terms, capturing the spatial discretization error and the time discretization error and can be used to drive an adaptive algorithm.     

Chelation-mediated palladium(II)-catalyzed domino Heck-Mizoroki/Suzuki-Miyaura reactions using arylboronic acids: increasing scope and mechanistic understanding

A palladium(II)-catalyzed Heck-Mizoroki/Suzuki-Miyaura domino reaction involving metal coordinating dimethylaminoethyl vinyl ethers and a number of electron-rich and electron-deficient arylboronic acids has been developed. Through variation of the temperature and the concentration of the p-benzoquinone (p-Bq) ligand/reoxidant, conditions for the robust and convenient one-pot generation of diarylated-saturated ethers were identified. With the aid of coordination of the dimethylamino group to the arylpalladium intermediate, the otherwise predominant formation of the β-arylated olefin could be reversed. A reaction route involving a chelation-controlled carbopalladation, providing a p-Bq stabilized six-membered palladacycle, followed by transmetalation and reductive elimination is suggested to explain the selective formation of saturated diarylated ether products.     

Microwave-assisted synthesis of Weinreb and MAP aryl amides via Pd-catalyzed Heck aminocarbonylation using Mo(CO)6 or W(CO)6

A simple and expedient process for the Heck aminocarbonylative synthesis of Weinreb and MAP amide acylating agents, from aryl halides, is reported. This methodology utilizes solid sources of CO making it readily accessible to chemists working in small-scale laboratory applications.     

Contribution from a hole-conducting dye to the photocurrent in solid-state dye-sensitized solar cells

The hole transporting medium in solid-state dye-sensitized solar cells can be utilized to harvest sunlight. Herein we demonstrate that a triphenylamine-based dye, used as hole-transporting medium, contributes to the photocurrent in a squaraine-sensitized solid-state dye-sensitized solar cell. Steady-state photoluminescence measurements have been used to distinguish between electron transfer and energy transfer processes leading to energy conversion upon light absorption in the hole-transporting dye.     

A note on global stability of three-dimensional Ricker models

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.     

Influence of soot aggregate structure on particle sizing using laser-induced incandescence: importance of bridging between primary particles

Soot aggregates formed in combustion processes are often described as clusters of carbonaceous particles in random fractal structures. For theoretical studies of the physical properties of such aggregates, they have often been modelled as spherical primary particles in point contact. However, transmission electron microscopy (TEM) images show that the primary particles are more connected than in a single point; there is a certain amount of bridging between the primary particles. Particle sizing using the diagnostic technique laser-induced incandescence (LII) is crucially dependent on the heat conduction rate from the aggregate to the ambient gas, which depends on the amount of bridging. In this work, aggregates with bridging are modelled using overlapping spheres, and it is shown how such aggregates can be built to fulfil specific fractal parameters. Aggregates with and without bridging are constructed numerically, and it is investigated how the bridging influences the heat conduction rate in the free-molecular regime. The calculated heat conduction rates are then used in an LII model to show how LII particle sizing is influenced by different amounts of bridging. For realistic amounts of bridging ( $C_{\rm{ov}}\leq0.25$ ), the primary particle diameters were overestimated by up to 9 % if bridging was not taken into account.     

In situ Polymerization Technique for Obtaining Composite Materials Based on Polyethylene,Multi-walled Carbon Nanotubes and Cobalt Nanoparticles

Specific features of formation of composite materials based on polyethylene, multi-walled carbon nanotubes, and cobalt nanoparticles (MWCNT–PE and Co/MWCNT–PE) by in situ polymerization were revealed. The in situ polymerization technique is based on ethylene polymerization on a highly dispersed Ti-containing catalyst supported on the surface of MWCNT and Со/MWCNT. This method ensures uniform distribution of MWCNT and Co/MWCNT in the polyethylene matrix. The effect of MWCNT and Со/MWCNT on the final properties of the composite materials was determined. Introduction of MWCNT into the polyethylene matrix increases the specific electrical conductivity of the material. Such composite materials can be used for preparing concentrates with preset composition for the subsequent preparation of antistatic coatings. Introduction of the Со/MWCNT filler into the polyethylene matrix makes the material paramagnetic owing to Co nanoparticles and allows its use for preparing coatings that efficiently protect from electromagnetic radiation.     

Dioxygen-promoted regioselective oxidative heck arylations of electron-rich olefins with arylboronic acids

Arylations of electron-rich heteroatom-substituted olefins were performed with arylboronic acids. This appears to constitute the first example of palladium(II)-catalyzed internal Heck arylations. The novel protocol exploits oxygen gas for environmentally benign reoxidation and a stable 1,10-phenanthroline bidentate ligand to promote the palladium(II) regeneration and to control the regioselectivity. Internal arylation is strongly favored with electron-rich arylboronic acids. DFT calculations support a charge-driven selectivity rationale, where phenyls substituted with electron-donating groups prefer the electron-poor alpha-carbon of the olefin. Experiments, verified by calculations, confirm the cationic nature of the catalytic route. This Heck methodology provides a facile and mild access to functionalized enamides. Controlled microwave heating and increased oxygen pressure were used to further reduce the reaction time to 1 h.     

N-Aryl Isoleucine Derivatives as Angiotensin?II AT2 Receptor Ligands

A novel series of ligands for the recombinant human AT₂ receptor has been synthesized utilizing a fast and efficient palladium-catalyzed procedure for aminocarbonylation as the key reaction. Molybdenum hexacarbonyl [Mo(CO)₆] was employed as the carbon monoxide source, and controlled microwave heating was applied. The prepared N-aryl isoleucine derivatives, encompassing a variety of amide groups attached to the aromatic system, exhibit binding affinities at best with K_i values in the low micromolar range versus the recombinant human AT₂ receptor. Some of the new nonpeptidic isoleucine derivatives may serve as starting points for further structural optimization. The presented data emphasize the importance of using human receptors in drug discovery programs.