The cell Reynolds number myth

The commonly accepted linear stability analysis for the forward-time centred-space (FTCS) algorithm applied to the transport equation has led to the concept of a cell Reynolds number restriction on the spatial grid size. This paper shows where the commonly accepted original analysis is in error and presents the correct stability restrictions, which are restrictions on the time step, not the spatial grid size. There is no cell Reynolds number restriction. The results are confirmed by numerical computations for the two-dimensional driven cavity problem.     

Demetallation of α,β,γ,δ-tetrakis(p-sulfophenyl) porphiniron(III) in mineral acid–alcohol–water media

Demetallation rates of α,β,γ,δ-tetrakis(p-sulfophenyl)porphiniron(III) in hydrochloric acid–ethanol–water, perchloric acid–ethanol–water, and sulfuric acid–alcohol–water media were determined. For a given acidity value H₀ the order of the rates for the three acids was HCl > H₂SO₄ > HClO₄. This is also the order for complex formation between acid anion and iron(III). Consequently ligands as well as protons are involved in the breaking of bonds between the metal and the porphyrin leading to the formation of the activated complex. The log k values for HCl and HClO₄ media were not linearly related to the Hammett acidity function as they were for sulfuric acid–ethanol–water media. The average ΔH? and ΔS?values for the HCl media were 18.4 ± 1.4 kcal/mol and ? 19 ± 3 cal K mol, respectively, in very close agreement with those for H₂SO₄ media despite the difference in H ₀ dependence. For H₂SO₄–alcohol–water media the order of the rates was butanol > propanol > ethanol with little difference between isomeric alcohols.     

Thermoresponsive Block Copolymer–Protein Conjugates Prepared by Grafting‐from via RAFT Polymerization

Well‐defined “smart” block copolymer–protein conjugates were prepared by two consecutive “grafting‐from” reactions via reversible addition–fragmentation chain transfer (RAFT) polymerization. The initiating portion (R‐group) of the RAFT agent was anchored to a model protein such that the thiocarbonylthio moiety was readily accessible for chain transfer with propagating chains in solution. Well‐defined polymer‐protein conjugates of poly(N‐isopropylacrylamide) (PNIPAM) and bovine serum albumin (BSA) were prepared at room temperature in aqueous media. The retained trithiocarbonate moiety on the free end group of the immobilized polymer allowed the homopolymer conjugate to be extended by polymerization of N,N‐dimethylacrylamide. Polyacrylamide gel electrophoresis, size exclusion chromatography, and NMR spectroscopy confirmed the synthesis of the various conjugates and revealed that the polymerizations were well controlled. As expected, the resulting block copolymer–protein conjugates demonstrated thermoresponsive behavior due to the temperature‐sensitivity of the PNIPAM block, as evidenced by turbidity measurements and dynamic light scattering analysis.

     

Reflection absorption infrared spectroscopy during atomic layer deposition of HfO2 films from tetrakis(ethylmethylamido)hafnium and water

Tetrakis(ethylmethylamido)hafnium and water are commonly used precursors for atomic layer deposition of HfO₂. Using reflection absorption infrared spectroscopy with a buried-metal-layer substrate, we probe surface species present during typical deposition conditions. We observe evidence for thermal decomposition of alkylamido ligands at 320 °C. Additionally, we find that complete saturation of the SiO₂ substrate occurs in the first cycle at ≈100 °C whereas incomplete coverage is apparent even after many cycles at higher temperatures. The use of this technique as an in situ diagnostic useful for process optimization is demonstrated.     

A forest building process on simple graphs

Consider the following process on a simple graph without isolated vertices: order the edges randomly and keep an edge if and only if it contains a vertex which is not contained in some preceding edge. The resulting set of edges forms a spanning forest of the graph.The probability of obtaining $k$ components in this process for complete bipartite graphs is determined as well as a formula for the expected number of components in any graph. A generic recurrence and some additional basic properties are discussed.     

Automorphism Groups of Schur Rings

In 1993, Muzychuk [23 Muzychuk , Mikhail E. ( 1993 ). The structure of rational Schur rings over cyclic groups . European Journal of Combinatorics 14 : 479 – 490 .[Crossref], [Web of Science ®] , [Google Scholar]] showed that the rational Schur rings over a cyclic group Z _n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z _n . This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G in a natural way. Our main result is that any finite group may be represented as the (algebraic) automorphism group of such a rational Schur ring over an abelian p-group, for any odd prime p. In contrast, over a cyclic group the automorphism group of any Schur ring is abelian. We also prove a converse to the well-known result of Muzychuk [24 Muzychuk , Mikhail E. ( 1994 ). On the structure of basic sets of Schur rings over cyclic groups . Journal of Algebra 169 : 655 – 678 .[Crossref], [Web of Science ®] , [Google Scholar]] that two Schur rings over a cyclic group are isomorphic if and only if they coincide; namely, we show that over a group which is not cyclic, there always exist distinct isomorphic Schur rings.     

Beyond microstructures: Using the Kerr Effect to characterize the macrostructures of synthetic polymers

The macrostructures of synthetic polymers are essentially the complete molecular chain architectures, including the types and amounts of constituent short‐range microstructures, such as the regio‐ and stereosequences of the inserted monomers, the amounts and sequences of monomers found in co‐, ter‐, and tetra‐polymers, branching, inadvertent, and otherwise, etc. Currently, the best method for characterizing polymer microstructures uses high field, high resolution ¹³C‐nuclear magnetic resonance (NMR) spectroscopy observed in solution. However, even ¹³C‐NMR is incapable of determining the locations or positions of resident polymer microstructures, which are required to elucidate their complete macrostructures. The sequences of amino acid residues in proteins, or their primary structures, cannot be characterized by NMR or other short‐range spectroscopic methods, but only by decoding the DNA used in their syntheses or, if available, X‐ray analysis of their single crystals. Similarly, there are currently no experimental means to determine the sequences or locations of constituent microstructures along the chains of synthetic macromolecules. Thus, we are presently unable to determine their macrostructures. As protein tertiary and quaternary structures and their resulting ultimate functions are determined by their primary sequence of amino acids, so too are the behaviors and properties of synthetic polymers critically dependent on their macrostructures. We seek to raise the consciousness of both synthetic and physical polymer scientists and engineers to the importance of characterizing polymer macrostructures when attempting to develop structure–property relations. To help achieve this task, we suggest using the electrical birefringence or Kerr effects observed in their dilute solutions. The molar Kerr constants of polymer solutes contributing to the birefringence of their solutions, under the application of a strong electric field, are highly sensitive to both the types and locations of their constituent microstructures. As a consequence, we may begin to characterize the macrostructures of synthetic polymers by means of the Kerr effect. To simplify implementation of the Kerr effect to characterize polymer macrostructures, we suggest that NMR first be used to determine the types and amounts of constituent microstructures present. Subsequent comparison of observed Kerr effects with those predicted for different microstructural locations along the polymer chains can then be used to identify the most likely macrostructures. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 155–166     

Investigation of the structure of detonation waves in a non-premixed hydrogen–air rotating detonation engine using mid-infrared imaging

The structure of detonation waves propagating through the annular channel of an optically accessible non-premixed rotating detonation engine (RDE) are investigated using mid-infrared imaging. The RDE is operated on hydrogen–air mixtures for a range of air mass flow rates and equivalence ratios. Instantaneous images of the radiation intensity from water vapor are acquired using a mid-infrared camera and a band-pass filter (2.890?±?0.033?µm). The instantaneous mid-infrared images reveal the stochastic nature of the detonation wave structure, position and angle of oblique and reflected shock waves, presence of shear layer separating products from the previous and current cycles, and extent of mixing between the reactants and products in the reactant fill zone in front of the detonation wave. The images show negligible signal directly in front of the detonation waves suggesting that there is minimal mixing between the reactants and products from the previous cycle ahead of the detonation wave for most operating conditions. The mid-infrared images provide insights useful for improving fundamental understanding of the detonation structure in RDEs and benchmark data for evaluating modeling and simulation results of RDEs.     

Cross‐Linked Aptamer–Lipid Micelles for Excellent Stability and Specificity in Target‐Cell Recognition

The specific binding ability of DNA–lipid micelles (DLMs) can be increased by the introduction of an aptamer. However, supramolecular micellar structures based on self‐assemblies of amphiphilic DLMs are expected to demonstrate low stability when interacting with cell membranes under certain conditions, which could lead to a reduction in selectivity for targeting cancer cells. We herein report a straightforward cross‐linking strategy that relies on a methacrylamide branch to link aptamer and lipid segments. By an efficient photoinduced polymerization process, covalently linked aptamer–lipid units help stabilize the micelle structure and enhance aptamer probe stability, further improving the targeting ability of the resulting nanoassembly. Besides the development of a facile cross‐linking method, this study clarifies the relationship between aptamer–lipid concentration and the corresponding binding ability.