A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Morphological reorganization and mechanical enhancement in multilayered polyethylene/polypropylene films by layer multiplication or mild annealing

Shortly after processing, Polyethylene/Polypropylene (PE/PP) multilayer films demonstrate an increase in tensile modulus and other mechanical properties when the individual layer thickness is below 0.5 µm. Subsequent annealing at 60 °C for 16 h brings the properties of all other samples to similar values. WAXD characterization of the layered films identified a prevalence of mesophase in the thicker PP layers. In samples with increased layer numerosity or subjected to annealing, WAXD detected its conversion to α crystalline phase that correlates with improved mechanical properties. SSNMR and DSC detailed the defective nature of α iPP crystallites. Comonomers, detected by NMR in the commercial polymers used for the films, are the source of “tunable disorder” that dictates the formation of the PP mesophase and the low temperature of conversion to the mechanically stronger defective α phase. Soft intrafilm layer interfaces instead enable nucleation and localized polymer chain rearrangement even without annealing. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 520–531     

���з������������ǿ��������

In this paper, we mainly studied the limit properties for the countable nonhomogeneous Markov chains. We established some limit properties for the functions of the countable nonhomogeneous Markov chains with variables under the convergence in the sense, which extended the similar conclusions for the functions with two variables. At last, as a corollary, we given the similar result in the homogeneous Markov stock market.     

Site‐Resolved Two‐Step Relaxation Process in an Asymmetric Dy2 Single‐Molecule Magnet

Elaborate chemical design is of utmost importance in order to slow down the relaxation dynamics in single‐molecule magnets (SMMs) and hence improve their potential applications. Much interest was devoted to the study of distinct relaxation processes related to the different crystal fields of crystallographically independent lanthanide ions. However, the assignment of the relaxation processes to specific metal sites remains a challenging task. To address this challenge, a new asymmetric Dy₂ SMM displaying a well‐separated two‐step relaxation process with the anisotropic centers in fine‐tuned local environments was elaborately designed. For the first time a one‐to‐one relationship between the metal sites and the relaxation processes was evidenced. This work sheds light on complex multiple relaxation and may direct the rational design of lanthanide SMMs with enhanced magnetic properties.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆(picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃](C₃H₅N₂)₃ ⋅ 3H₂O series (Ln=Ce–Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.