Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Synthesis of polyphosphodiesters by ring‐opening polymerization of cyclic phosphates bearing allyl phosphoester protecting groups

The allyl phosphoester group is shown to be a protecting group for the synthesis of anionic polyphosphodiesters. Our strategy relies on the synthesis of a cyclic phosphate monomer bearing a pendant allyl phosphoester group, its easy purification by fractional distillation, its organocatalyzed ring‐opening polymerization by 1,8‐diazobicyclo[5.4.0]undec‐7‐ene (DBU) and 1‐[3,5‐bis(trifluoromethyl)phenyl]‐3‐cyclohexyl‐thiourea (TU). Finally, the deprotection of the allyl phosphoester group is carried out by reaction with sodium benzenethiolate in the absence of any detectable degradation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2642–2648     

CdS quantum dot sensitized p-type NiO as photocathode with integrated cobaloxime in photoelectrochemical cell for water splitting

CdS sensitized NiO electrode was used as the photoactive cathode in a photoelectrochemical cell for water splitting,avoiding the use of a sacrificial electron donor.Photocurrent increment under visible light irradiation was observed after integration of[Co（dmgH）₂（4-Me-py）Cl]（1） to the photocathode,suggesting 1 could accept electrons from photoexcited CdS for water reduction and NiO could move the holes in the valence band of CdS to anode for water oxidation.     

Redox Communication within Multinuclear Iron–Sulfur Complexes Related to Electronic Interplay in the Active Site of [FeFe]Hydrogenase

The one‐electron oxidations of a Fe₂ complex lead to the formation of a persistent metal‐stabilized thiyl radical Fe₂ species, mixed‐valent Fe₄, and Fe₈ complexes. The unpaired spin in the Fe₂ radical species delocalizes over the Fe₂ and the aromatic dithiolate, mostly on the terminal sulfur. The subsequent dimerization of the singly oxidized Fe₂ to the Fe₄ retains the partial thiyl radical character. For an analogue with less steric hindrance, the π–π stacking interaction between the dithiolato aromatic rings induces generation of the Fe₈, in which process electronic structures of the species are modulated through reducing the thiyl radical to the thiolate. Electronic reorganization repeats when the Fe₈ is converted to Fe₄. Electronic interplay in the complexes decreases the energy gap of frontier MOs and buffers electronic impacts upon redox events. Easier accessible redox potentials and increased stability of the species are facilitated. The results demonstrate that electronic versatility of the benzenedithiolate exerts pronounced influences on electronic and coordination structure of the metal complexes.     

Synthesis of self‐healing polyurethane urea‐based supramolecular materials

Supramolecular polyurethane ureas are expected to have superior mechanical properties primarily due to the reversible, noncovalent interactions such as hydrogen bonding interactions. We synthesized polyurethane prepolymers from small molecular weight of poly(tetramethylene ether)glycol and isophorone diisocyanates, which were end capped with propylamine to synthesize polyurethane ureas with high contents of urea and urethane groups for hydrogen‐bonding formations to facilitate self‐healing. The effects of polyurethane urea molecular weight (3000 ≤ M_n ≤ 9000), crosslinking, and cutting direction were studied in terms of thermal, mechanical, and morphological properties with an emphasis on the self‐healing efficiency. It was found that the thermal self‐healability was more pronounced as the molecular weight of polyurethane urea decreased, showing a maximum of more than 96% with 3000 M_n when the sample was cut along the stretch direction. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 468–474     

Zinc polyoxometalate on activated carbon: an efficient catalyst for selective oxidation of alcohols with hydrogen peroxide

[PW₁₁ZnO₃₉]^5? was immobilized on activated carbon and characterized using Fourier transform infrared, X‐ray diffraction, Brunauer–Emmett–Teller and elemental analysis techniques. Effective oxidation of various alcohols with hydrogen peroxide was performed in the presence of this catalyst. Easy separation of the catalyst from the reaction mixture, cheapness, high activity and selectivity, stability as well as retained activity in subsequent catalytic cycles make this supported catalyst suitable for small‐scale synthesis. Copyright © 2015 John Wiley & Sons, Ltd.