Smoothing Windows for the Synthesis of Gaussian Stationary Random Fields Using Circulant Matrix Embedding

When generating Gaussian stationary random fields, a standard method based on circulant matrix embedding usually fails because some of the associated eigenvalues are negative. The eigenvalues can be shown to be nonnegative in the limit of increasing sample size. Computationally feasible large sample sizes, however, rarely lead to nonnegative eigenvalues. Another solution is to extend suitably the covariance function of interest so that the eigenvalues of the embedded circulant matrix become nonnegative in theory. Though such extensions have been found for a number of examples of stationary fields, the method depends on nontrivial constructions in specific cases.

In this work, the embedded circulant matrix is smoothed at the boundary by using a cutoff window or overlapping windows over a transition region. The windows are not specific to particular examples of stationary fields. The resulting method modifies the standard circulant embedding, and is easy to use. It is shown that this straightforward approach works for many examples of interest, with the overlapping windows performing consistently better. The method even outperforms in the cases where extending the covariance leads to nonnegative eigenvalues in theory, in the sense that the transition region is considerably smaller. The Matlab code implementing the method is included in the online supplementary materials and also publicly available at www.hermir.org.     

Affine Slice for the Coadjoint Action of a Class of Biparabolic Subalgebras of a Semisimple Lie Algebra

In this article, we give a simple explicit construction of an affine slice for the coadjoint action of a certain class of biparabolic (also called seaweed) subalgebras of a semisimple Lie algebra over an algebraically closed field of characteristic zero. In particular, this class includes all Borel subalgebras.     

Structural Wall-modeled LES Using a High-order Spectral Difference Scheme for Unstructured Meshes

The combination of the high-order unstructured Spectral Difference (SD) spatial discretization scheme with Sub-Grid Scale (SGS) modeling for Wall-Modeled Large-Eddy Simulation (WMLES) is investigated. Particular focus is given to the use of wall-function approaches and to the relevant optimal coupling with the numerical scheme and the SGS model, a similarity mixed type model featuring newly designed discrete filters with specified cutoff length scale. To take full advantage of the discontinuous Finite Element (FE) structure which characterizes the SD scheme, wall-modeling is accomplished within the first wall element by using the information from the farthest solution points from the wall. Compared to the customary used first off-wall node, this point provides more accurate information to the wall-function, thus improving the quality of the solution. Two different law-of-the-wall are tested, a classical three-layers wall-function based on the equilibrium assumption and a more general formulation to account for the pressure gradient in more complex configurations. Moreover, the mixed scale-similarity SGS model is used in the entire computational domain without any particular adjustment inside the wall-modeled region. Numerical tests on the classical test case of the turbulent channel flow at different Reynolds numbers and on the channel with periodic constrictions at Re _h = 10,595 give evidence that the results are extremely sensitive to the choice of the solution points used to provide the informations to the law-of-the-wall. In particular, it is shown that significant improvements in the results can be attained by solving the wall-function away from the wall, rather than at the first off-wall solution point as customary done. The combination of the selected wall-modeling strategies and the similarity mixed formulation proves to be remarkably accurate, even in the presence of boundary layer separation, thus opening the path to further exploit the high-order SD platform, as well as a broad range of other similar methodologies, for WMLES. Extensions of the methodology are envisaged to include more sophisticated wall-modeling approaches incorporating turbulent sensors to switch to no-slip conditions in laminar regions.     

Enantioselective Approach for Expanding the Three-Dimensional Space of Tetrahydroquinoline to Develop BET Bromodomain Inhibitors**

The pharmaceutical industry has a pervasive need for chiral specific molecules with optimal affinity for their biological targets. However, the mass production of such compounds is currently limited by conventional chemical routes, that are costly and have an environmental impact. Here, we propose an easy access to obtain new tetrahydroquinolines, a motif found in many bioactive compounds, that is rapid and cost effective. Starting from simple raw materials, the procedure uses a proline-catalyzed Mannich reaction followed by the addition of BF₃ ⋅ OEt₂, which generates a highly electrophilic aza-ortho-quinone methide intermediate capable of reacting with different nucleophiles to form the diversely functionalized tetrahydroquinoline. Moreover, this enantioselective one-pot process provides access for the first time to tetrahydroquinolines with a cis-2,3 and trans-3,4 configuration. As proof of concept, we demonstrate that a three-step reaction sequence, from simple and inexpensive starting compounds and catalysts, can generate a BD2-selective BET bromodomain inhibitor with anti-inflammatory effect.     

Tuneable pseudorotaxane formation between a biotin-avidin bioconjugate and CBPQT4+

A biotinylated 1,5-dialkoxynaphthalene derivative has been shown to have the ability to bind strongly to avidin and thus act as an artificial binding site for cyclobis(paraquat-p-phenylene) thereby facilitating the formation of a tuneable pseudorotaxane-based bioconjugate.     

One-electron reduction of superoxide radical-anions by 3-alkylpolyhydroxyflavones in micelles. Effect of antioxidant alkyl chain length on micellar structure and reactivity

In micellar solutions, one-electron reduction of (*)O 2 (-) radical-anions by 3-alkylpolyhydroxyflavones (FnH) with alkyl chains of n = 1, 4, 6, 10 carbons produces phenoxyl radicals ( (*)Fn) identical to those obtained by one-electron oxidation by (*)Br 2 (-) radical-anions or by repair of tryptophan radicals. In cetyltrimethylammonium bromide (CTAB), F1H localizes in the Stern layer, and alkyl chains of other FnH solubilize in the hydrophobic interior, interacting with cetyl tails. This interaction produces more compact micelles with lower intramicellar fluidity, as suggested by the increase in the pseudo-first-order rate constant of (*)Fn formation ( k 1) from approximately 390 s (-1) for n = 1 to 610 s (-1) for n = 10, leading to an intramicellar bimolecular rate constant of 1 x 10 (5) M (-1) s (-1). Additionally, (*)F1 and (*)F4 decay by intermicellar bimolecular reaction (2 k = 20 and 2 x 10 (5) M (-1) s (-1), respectively) whereas other (*)Fn radicals are stable over seconds due to increased localization with regards to the Stern layer. In contrast, the thick uncharged hydrophilic palisade layer and the compact hydrophobic core of Triton X100 micelles are responsible for a much higher microviscosity resulting in a decrease in k 1 from approximately 15.6 s (-1) for n = 1 to 9.6 s (-1) for n = 10.     

Aqueous behaviour of cationic surfactants containing a cleavable group

The aggregation behaviour of two novel cationic RAFT agents (transfer surfactants); N,N-dimethyl-N-(4-(((phenylcarbonothioyl)thio)methyl)benzyl)ethanammonium bromide (PCDBAB) and N-(4-((((dodecylthio)-carbonothioyl)thio)methyl)benzyl)-N,N-dimethylethanammonium bromide (DCTBAB) in diluted solutions have been investigated by surface tension, conductimetry and microcalorimetry measurements. The thermodynamic parameters i.e. the critical micelle concentration (cmc), the degree of micelle ionization (alpha), the head group surface area (a 0), Delta H mic, Delta G mic and T Delta S mic are reported at 303 K. The thermodynamic parameters have been compared to those of the conventional surfactant cetyltrimethylammonium bromide (CTAB) in order to specify structural relationships. The obtained results have been discussed considering the hydrophobic behaviour of the S-C=S- linkage and the specific interactions that arise from the introduction of the benzene ring into the hydrophobic part.     

Synthesis of P,N-heterocycles from omega-amino-H-phosphinates: conformationally restricted alpha-amino acid analogs

P,N-heterocycles (3-hydroxy-1,3-azaphospholane and 3-hydroxy-1,3-azaphosphorinane-3-oxide) are synthesized in moderate yield from readily available omega-amino-H-phosphinates and aldehydes or ketones via an intramolecular Kabachnik-Fields reaction. The products are conformationally restricted phosphinic analogs of alpha-amino acids. The multigram-scale syntheses of the H2N(CH2)(n)PO2H2 phosphinic precursors (n = 1, 2, 3) and some derivatives are also described.     

Simultaneous Determination of Nickel and Cobalt as Chelates with 1-(2-Pyridylazo)-2-naphthol Using an LC Switching Column Method

A simple liquid chromatographic method was developed for the separation and simultaneous determination of cobalt and nickel as chelates with 1-(2-pyridylazo)-2-naphthol (PAN). The method, using a switching column technique for the on-line purification and separation, enables to reach the sub-microgram per litre concentration level excluding off-line sample treatment with the exception of the derivatization reaction. Two small-sized columns packed with CN- and C₄-bonded stationary phases were selected and used considering their complementary behaviour with respect to chelated Co and Ni ions. The analysis was performed within 10 min using an optimised eluent (water–acetonitrile–methanol–tetrahydrofuran, 40:45:10:5, v/v/v/v) containing Tween 40 (10^?3 M) and acetate buffer (5 × 10^?3 M, pH 4.8). Detection was performed by UV-vis spectrophotometry (λ = 565 nm) permitting to reach quantification limits of 0.9 and 0.5 μg L^?1 for Co and Ni, respectively.