Application of the dissipation theorem to turbulent flow and mass transfer in a pipe

The dissipation theorem is applied to turbulent pipe flow. The eddy-viscosity profiles can be made to agree with some in the literature in the sense that the eddy viscosity starts at zero on the solid pipe wall, rises to a maximum, and declines again toward the center line. A relationship between the volumetric dissipation and the eddy viscosity is derived by means of an energy balance on a core of fluid of radius r. The question of what exponent to use on the radius in another governing equation is clarified, thereby giving better agreement with experimental data than other values tried. Negative values of the eddy viscosity can be obtained in some regions of the flow field, such as near the center line, and it is suggested that these can be eliminated by slight modification of the decay term. Better agreement with the shapes of friction-factor and mass-transfer curves could be achieved by further (empirical) modification of the stress dependence of parameters in the model.     

An infinite family of convex Brunnian links in $${\mathbb{R}^n}$$

This paper proves that convex Brunnian links exist for every dimension n ≥ 3 by constructing explicit examples. These examples are three-component links which are higher-dimensional generalizations of the Borromean rings.     

Existence of solutions to a new model of biological pattern formation

In this paper we study the existence of classical solutions to a new model of skeletal development in the vertebrate limb. The model incorporates a general term describing adhesion interaction between cells and fibronectin, an extracellular matrix molecule secreted by the cells, as well as two secreted, diffusible regulators of fibronectin production, the positively-acting differentiation factor (“activator”) TGF-β, and a negatively-acting factor (“inhibitor”). Together, these terms constitute a pattern forming system of equations. We analyze the conditions guaranteeing that smooth solutions exist globally in time. We prove that these conditions can be significantly relaxed if we add a diffusion term to the equation describing the evolution of fibronectin.     

Tomato polyphenol oxidase B is spatially and temporally regulated during development and in response to ethylene

Plant polyphenol oxidases (PPOs) are ubiquitous plastid-localized enzymes. A precise analysis of PPO function in plants has been complicated by the presence of several family members with immunological cross reactivity. Previously we reported the isolation of genomic clones coding for the seven members of the tomato (Solanum lycopersicum) PPO family (A, A', B, C, D, E, and F). Here we report the complex spatial and temporal expression of one of the members, PPO B. The PPO B promoter was sequenced and subjected to homology analysis. Sequence similarities were found to nucleotide sequences of genes encoding enzymes/proteins active in the following systems: phenylpropanoid biosynthesis, signal transduction and responsiveness to hormones and stresses, fruit and seed proteins/enzymes, and photosynthesis. Chimeric gene fusions were constructed linking PPO B 5' flanking regions to the reporter gene, b-glucuronidase (GUS). The resultant transgenic plants were histochemically analyzed for GUS activity in various vegetative and reproductive tissues, and evaluated for PPO B responsiveness to ethylene induction. It was shown that PPO B expression was tissue specific, developmentally regulated, ethylene induced, and localized predominantly to mitotic or apoptotic tissues.     

Rhodium and iridium complexes of an asymmetric bicyclic NHC bearing secondary pyridyl donors

A tridentate N^C^N ligand, 1, containing a bicyclic central NHC ring and two flanking pyridyl groups has been coordinated to Rh(I) and Ir(I) to give complexes of the type [M(κ(3)-1)(1,5-COD)]PF(6) (2 M = Rh; 3 M = Ir). In contrast to our earlier study with this ligand, the complexes have been shown to approximate to a trigonal bipyramidal geometry in the solid state and exist as an isomeric mixture in solution as determined by (1)H and (13)C NMR spectroscopy. Electrochemical studies revealed that both complexes undergo a 1-electron oxidation with the potential of the Rh complex 0.1 V less than that of the Ir complex in CH(2)Cl(2). Preliminary DFT studies confirm the lowest energy conformations as those seen in the solid state and show the location and energy of the HOMOs to be identical in 2 and 3. Partial charge analysis shows a greater positive charge on the Ir in 3 compared to the Rh in 2. Some preliminary studies of hydrogenation reactivity have shown the complexes to be efficient for both transfer and direct hydrogenation of prochiral ketones and alkenes at moderate temperatures but without any discernible enantioselectivity.     

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.     

Integration of a macro/micro architectured compartmentalised neuronal culture device using a rapid prototyping moulding process

The rapid prototyping of a reversible and one step moulded compartmentalised neuron glass/PDMS device with a thin wall barrier directly adjacent to the reservoirs is presented. A simple moulding technique to produce these devices results in a barrier of 560 μm where the 3 μm deep by 8 μm wide channels can be reversibly fabricated in either the glass base or PDMS compartmentalised mould depending on the type of application required. Using glass substrates with commercially laser engraved microchannels, both the PDMS planar and PDMS channelled device can be easily fabricated in a standard laboratory. The compartmentalised device has several advantages including good experimental accessibility and versatility with a variety of end user applications.