Efficient Synthesis of Cyclic Block Copolymers by Rotaxane Protocol by Linear/Cyclic Topology Transformation

High‐yielding synthesis of cyclic block copolymer (CBC) using the rotaxane protocol by linear‐cyclic polymer topology transformation was first demonstrated. Initial complexation of OH‐terminated sec‐ammonium salt and a crown ether was followed by the successive living ring‐opening polymerizations of two lactones to a linear block copolymer having a rotaxane structure by the final capping of the propagation end. CBC was obtained in a high yield by an exploitation of the mechanical linkage through the translational movement of the rotaxane component to transform polymer structure from linear to cyclic. Furthermore, the change of the polymer topology was translated into a macroscopic change in crystallinity of the block copolymer.     

Solid‐state drawing of β‐nucleated polypropylene: Effect of additives on drawability and mechanical properties

Isotactic polypropylene (i‐PP) can crystallize in different crystal modifications. In this article, the effect of sepiolite (one‐dimensional) and carbon black (three‐dimensional) fillers on the solid‐state drawability of i‐PP is discussed. The cross‐hatched structure of thermodynamically most stable α‐crystal phase in i‐PP does not allow for perfect chain alignment during solid‐state drawing. The β‐phase i‐PP, obtained by addition of specific nucleating agents, crystallizes in a non‐cross‐hatched spherulitic structure and allows more easy drawing. Depending on the filler type, β–α transformation takes place at different draw ratios, as was observed by in situ wide‐angle X‐ray diffraction measurements. It was observed that β‐nucleated i‐PP has a lower yield stress and can be drawn further than i‐PP crystallized in the α‐crystal phase. If added in the right amount, both carbon black and sepiolite have a reinforcing effect on PP tapes. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1071–1082     

An improved exponential transformation for nearly singular boundary element integrals in elasticity problems

This paper presents an improved exponential transformation for nearly singular boundary element integrals in elasticity problems. The new transformation is less sensitive to the position of the projection point compared with the original transformation. In our work, the conventional distance function is modified into a new form in the polar coordinate system. Based on the refined distance function, an improved exponential transformation is proposed in the polar coordinate system. Moreover, to perform integrations on irregular elements, an adaptive integration scheme considering both the element shape and the projection point associated with the improved transformation is proposed. Furthermore, when the projection point is located outside the integration element, another nearest point is introduced to subdivide the integration elements into triangular or quadrilateral patches of fine shapes. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method.     

“Painlevé 34” equation: Equivalence test

We give the complete solution of the Equivalence Problem for “Painlevé 34” equation.     

Solitons and Bäcklund transformation for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Bilinear form and Bäcklund transformation are derived by virtue of the Bell polynomials. Besides, the one- and two-soliton solutions are constructed via the Hirota method.     

Kinetics of the Coordination Transformation for Preparation of Nanosized ZnS in a PVA Film

Abstract

This study was focused on the pervasion process of sulfion in a PVA–Zn²⁺ complex film. A diffusion equation for this process, based on the Fick first diffusion law, is suggested, which was in good agreement with the experimental results. The diffusion constant was 9.92 × 10^?6 cm²/sec, calculated by combining the model and the experimental results.     

A study on the phase transformation behaviour of Cu-20wt.Sn alloy produced using powder metallurgy method: Experimental and molecular dynamics modelling

In this study, Cu-20wt.Sn alloy was produced by powder metallurgy (PM) method by using high purity element powders. The phases in the microstructure of the produced alloy were determined by XRD study. The phase transformation behaviour of the alloy was investigated by DSC and modelling method. Moreover, the Cu-20wt.Sn alloy system was modelled with molecular dynamics (MD) simulation based on modified Embedded Atom Method (MEAM). The radial distribution function (RDF) was calculated to determine the structural properties of system during the phase transformations. The experimental results showed that the transformation ($\alpha +\delta$) → ($\alpha +\gamma$) occur at temperature above 500°C. The simulation results showed that the phase transformation $\alpha +\delta \to \alpha +\gamma$ occurs at 550°C temperature. Our simulation results are in reasonable agreement with the experimental data.     

A 1D Roe decomposition of a system of equations governing wave height transformation

A Roe‐type decomposition for a system of equations governing onshore/offshore wave transformation in coastal waters is derived. The equation set approximated pertains to coastal waters prior to wave breaking, and is based on depth‐averaging and time‐averaging of the Euler equations. The equations are those used in many commercial codes for simulation of wave height and wave‐averaged currents. This novel approach uses a combination of some standard Roe averages, together with physical reasoning and power series expansions to derive a Roe‐averaged Jacobian (with real, linearly independent eigenvectors) and ensures conservation, and thereby effects the decomposition. It is shown that the resulting derived Roe‐averaged quantities are accurate to a high degree, by comparing them with their analytical equivalents for a wide range of nondimensional water depths and slopes likely to be encountered in coastal problems. Numerical tests of time‐invariant wave height transformation and wave group propagation are undertaken; these indicate good performance of the scheme in practice. Copyright © 2011 John Wiley & Sons, Ltd.