A short comment on the effect of a shear layer on nonlinear water waves

In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with depth.We extend the study of Cheng,Cang and Liao(2009) by introducing a second parameter which measures the depth of the shear current.A high-order convergent analytical series solution is obtained by the homotopy analysis method(HAM).A detailed analysis of the impact of the depth parameter is given.We find that increasing this parameter so that the shear current is thinner re...     

On the simultaneous tridiagonalization of two symmetric matrices

We discuss congruence transformations aimed at simultaneously reducing a pair of symmetric matrices to tridiagonal–tridiagonal form under the very mild assumption that the matrix pencil is regular. We outline the general principles and propose a unified framework for the problem. This allows us to gain new insights, leading to an economical approach that only uses Gauss transformations and orthogonal Householder transformations. Numerical experiments show that the approach is numerically robust and competitive.     

The circumcentered-reflection method achieves better rates than alternating projections

Computational Optimization and Applications - We study the convergence rate of the Circumcentered-Reflection Method (CRM) for solving the convex feasibility problem and compare it with the Method...     

Electron-Deficient Borinic Acid Polymers: Synthesis,Supramolecular Assembly,and Examination as Catalysts in Amide Bond Formation

The Lewis acidic character of borinic-acid-functionalized polymers suggests broad potential applications in supramolecular materials, chemo- and biosensors, as well as supported catalysts. Two highly electron-deficient borinic acid copolymers ( 3 a and 3 b ) with variable steric hindrance at the boron center were prepared by reaction of aryldibromoboranes ArBBr₂ ( 2 , Ar=2,4-Cl₂Ph, 3,5-Cl₂Ph) with a 10 % stannylated polystyrene random copolymer, followed by conversion to the desired PS-B(Ar)OH functionalities. The supramolecular assembly of these polymers through Lewis acid–Lewis base interactions and reversible covalent B−O−B bond formation was investigated. Exposure of a polymer solution of 3 a to pyridine triggered spontaneous gelation, whereas 3 b only gelled upon addition of molecular sieves to favor formation of boroxane crosslinks. The crosslinking process was readily reversed by addition of small amounts of water or wet solvent. The dynamic processes were studied in detail by variable-temperature (VT) NMR by using molecular model compounds. The polymers and their corresponding model compounds were also examined as catalysts in the amide bond formation reaction between phenylacetic acid and benzylamine. The 3,5-dichlorophenyl borinic acid derivatives proved to be the more effective catalysts. Mechanistic studies suggested that the borane Lewis acid-catalyzed coupling involves initial acid-induced protodeboronation to release the dichlorophenyl boronic acid as the active catalyst.     

MPI+X: task-based parallelisation and dynamic load balance of finite element assembly

The main computing phases of numerical methods for solving partial differential equations are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. The matrix assembly consists of a loop over the elements, faces, edges or nodes of the MPI partitions to compute element matrices and vectors and then of their assemblies. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP, with different techniques to avoid the race condition, but presenting efficiency or implementation drawbacks. We propose an alternative, based on task parallelism using some extensions to the OpenMP programming model. In addition, dynamic load balance will be applied, especially efficient in the presence of hybrid meshes. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores.     

Radiological chronometry of uranium metal samples

Radiological chronometry is an important tool in nuclear forensics that uses several methods to determine the length of time that has elapsed since a material was last purified. One of the chronometers used in determining the age of metallic uranium involves measuring the fractional ingrowth of ²³⁰Th from its parent ²³⁴U with the assumption that the uranium metal contained no impurities, especially thorium, when it was purified. The affects of different etching procedures were evaluated for the removal of surface oxidation with three different types of uranium metal samples to determine whether the etching procedure affects the radiological age. The sample treated with a rigorous etching procedure had exhibited the most reliable radiological age while less rigorous etching yields a radiological age from 15 years to hundreds of years older than the known age. Any excess thorium on the surface of a uranium metal sample presents a bias in age determination and the sample will appear older than the true age. Although this research demonstrates the need for rigorous surface etching, a bias in the radiological age could have arisen if the uranium in the metal was heterogeneously distributed.     

Hydrophilic PET surfaces by aminolysis and glycopolymer brushes chemistry

Poly(ethylene terephthalate) (PET) is a semiaromatic thermoplastic polyester used in many fields. For specific applications, controlled of the surface wettability (hydrophily/hydrophoby) could be a great challenge. Aminolysis of PET surfaces with branched polyethylenimine gives amino functional groups on the surface with high grafting density. Then, in a second step, atom transfer radical polymerization (ATRP) initiator was grafted by reaction with 2‐bromoisobutyryl bromide. Surface initiated ATRP of 2‐lactobionamidoethyl methacrylate (LAMA) was performed in solution in the presence of a sacrificial initiator or an appropriate amount of Cu(II) species that act as deactivator. The efficiency of all reactions was confirmed by X‐ray photoelectron spectroscopy. Wetting properties and surface energy were found to vary systematically depending to the type of functionalization and grafting. The quantity of grafted carbohydrate was determined by phenol/sulfuric acid colorimetric titration. The sugar graft density was observed to vary according to the ratio (monomer)/(free initiator). High graft density could be obtained yielding to superhydrophilic polymer brushes. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2689–2697