A critical investigation of smoothed particle hydrodynamics applied to problems with free‐surfaces

In this paper, an in‐depth study of SPH method, in its original weakly compressible version, is achieved on dedicated 2D and 3D free‐surface flow test cases. These rather critical prototype problems shall constitute suitable test cases to get through when building a free‐surface SPH model. The present work aims at investigating various numerical aspects of this method, often little mentioned in literature. In particular, a great care is paid to the dynamic part of the solution, which is critical to the local hydrodynamic load prediction. The role of numerical errors in the development of acoustic frequencies in the pressure signals is discussed, as well as the influence of the choice of the sound velocity. On the shown test problems, it is also evidenced that some numerical tools are crucial to ensure the robustness and accuracy of the standard SPH method. The convergence of our model is heuristically proved on these nonlinear prototype tests, showing at the same time the very satisfactory level of accuracy reached. Through these tests, some other numerical specificities of the SPH method are discussed, such as the self‐redistribution of the particles occurring during the Lagrangian evolution. A higher order model is also proposed, and its advantages and drawbacks are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Integral mixed unit interval graphs

We characterize graphs that have intersection representations using unit intervals with open or closed ends such that all ends of the intervals are integral in terms of infinitely many minimal forbidden induced subgraphs. Furthermore, we provide a linear-time algorithm that decides if a given interval graph admits such an intersection representation.     

Combinatorial Identities Related to Eigen-Function Decompositions of Hill operators: Open Questions

We formulate three open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.     

Development of novel backwash cleaning technique for reverse osmosis in reclamation of secondary effluent

The objective of the study was to further develop a novel cleaning technique for reverse osmosis in reclamation of municipal secondary effluent. This technique is a new backwash method via direct osmosis (DO) by intermittent injection of the high salinity (HS) solution without stopping of high pressure pump and it is environment and membrane friendly technique. In the study, DO-HS trials were carried out with a UF-RO pilot system which was operated on site with the secondary treated effluent as the raw feed. Different operating conditions for DO-HS treatment in the actual process were investigated. It was found that the operation for implementation of the DO-HS cleaning technique developed was easy. For the first time, the actual profiles of HS concentration, DO backwash flow rate, brine flow rate and permeate pressure during DO-HS treatment have been demonstrated. It was observed that turbidity of the brine stream during DO-HS treatment at 3 NTU was 5 times higher than that before DO-HS treatment. The results from this study have confirmed the previous hypothesis with DO-HS treatment that there would be a strong driving force for DO backwash to lift and sweep the foulants from the membrane surface which would be carried over to the brine. The optimal plant operating conditions in terms of RO feed flow rate, HS concentration and HS injection time are ready for the DO-HS method to be adopted and validated in a long-term continuous plant operation.     

Ionothermal synthesis and crystal structures of metal phosphate chains

We have prepared isostructural aluminium and gallium phosphate chains by ionothermal reactions in 1-ethyl-3-methylimidazolium bromide and 1-ethylpyridinium bromide under a variety of conditions. The chains can be prepared as pure phases or along with three dimensional framework phases. The chains are favoured at shorter heating times and the crystallinity can be improved by addition of transition metal acetates and amines which are not included in the final structure. The chain can be prepared with or without the presence of hydrofluoric acid.     

Hydrophilic functionalization of syndiotactic polystyrene via a combination of electrophilic bromination and Suzuki–Miyaura reaction

Postfunctionalization of high‐molecular‐weight syndiotactic polystyrene (sPS) was achieved via combination of electrophilic bromination at the para‐position of the polymer aromatic ring and subsequent Suzuki–Miyaura cross‐coupling reactions with functionalized phenylboronic acids. The concentration of brominated styrene repeating unit in sPS was conveniently controlled by changing the ratio of added bromine relative to the polymer repeating unit. Brominated sPS (8.5 mol %) was converted quantitatively to other polar functional groups via Suzuki–Miyaura cross‐coupling reactions with various functional group‐substituted phenylboronic acids. The surface properties of functionalized sPS were studied by measuring water contact angles. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4335–4343, 2010     

Decomposition method in correction problems for inconsistent systems of linear inequalities with partitioned matrices

Correction problems for inconsistent systems of linear inequalities with partitioned matrices are examined. The criteria used are based on the minimum of the sum of squares and the minimax weighted Euclidean norm of a block in the correction matrix.     

Vortex structure in FeTeSe single crystals

Vortex structure in FeTe_0.66Se_0.44 and FeTe_0.6Se_0.4 single crystals with T _c ∼ 11.7 and 14.5 K, respectively, has been studied using the decoration technique. It has been found that in single crystals with the simplest crystalline structure of 11-family iron-containing superconductors (without interlayers), no regular vortex lattice is observed, similar to the case of the previously studied 122 and 1111 families. Using transmission electron microscopy, the dislocation structure with a density of ∼10⁹ cm⁻² has been observed. The problem of pinning in iron-containing superconductor single crystals is discussed.