Application of topological degree theory to semi-definite complementarity problem

The topological degree theory is applied to study the problem of existence of solutions to the semi-definite complementarity problem (SDCP). A notion of an exceptional family of matrices is introduced, and assertions of a non-strict alternative type are obtained. Namely, for a continuous mapping, there exists at least one of the following two items: either a solution to the SDCP, or an exceptional family of matrices. Hence, if there is no exceptional family, then at least one solution exists     

Cu(II) immobilized on Fe3O4–diethylenetriamine: A new magnetically recoverable catalyst for the synthesis of 2,3‐dihydroquinazolin‐4(1H)‐ones and oxidative coupling of thiols

Cu(II) immobilized on Fe₃O₄–diethylenetriamine was designed as a new, inexpensive and efficient heterogeneous catalyst for the synthesis of 2,3‐dihydroquinazolin‐4(1H )‐ones and the oxidative coupling of thiols. The structure of the nanomagnetic catalyst was comprehensively characterized using Fourier transform infrared spectroscopy, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, vibrating sample magnetometry, thermogravimetric analysis, X‐ray diffraction and atomic absorption spectroscopy. Simple preparation of the catalyst from commercially available materials, high catalytic activity, simple operation, high yields, use of green solvents, easy magnetic separation and reusability of the catalyst with unaltered activity make our protocol a green and feasible synthetic strategy.     

Morphological,Thermal, and Electrical Characterization of Syndiotactic Polypropylene/Multiwalled Carbon Nanotube Composites

In this work, syndiotactic polypropylene/multiwalled carbon nanotubes (MWCNT) nanocomposites, in various concentrations, were produced using melt mixing. The influence of the addition of MWCNT on the morphology, crystalline form, and the thermal and electrical properties of the polymer matrix was studied. To that aim, scanning electron microscopy, Raman spectroscopy, X-ray diffraction, differential scanning calorimetry, and dielectric relaxation spectroscopy were employed. Significant alterations of both the crystallization behavior and the thermal properties of the matrix were found on addition of the carbon nanotubes: conversion of the disordered crystalline form I to the ordered one, increase of the crystallization temperature and the degree of crystallinity, and decrease of the glass transition temperature and the heat capacity jump. Finally, the electrical percolation threshold was found between 2.5–3.0 wt.% MWCNT. For comparison purposes, the results of the system studied here are also correlated with the findings from a previous work on the isotactic polypropylene/MWCNT system.     

An operator splitting strategy for fluid–structure interaction problems with thin elastic structures in an incompressible Newtonian flow

We present a computational framework based on the use of the Newton and level set methods to model fluid–structure interaction problems involving elastic membranes freely suspended in an incompressible Newtonian flow. The Mooney–Rivlin constitutive model is used to model the structure. We consider an extension to a more general case of the method described in Laadhari (2017) to model the elasticity of the membrane. We develop a predictor–corrector finite element method where an operator splitting scheme separates different physical phenomena. The method features an affordable computational burden with respect to the fully implicit methods. An exact Newton method is described to solve the problem, and the quadratic convergence is numerically achieved. Sample numerical examples are reported and illustrate the accuracy and robustness of the method.     

The relation between structure changes and thermal expansion in liquid indium

The structure of liquid indium in a wide temperature range has been investigated by means of X-ray diffraction and reverse Monte Carlo methods. Analysis of temperature dependence of the interatomic distances and coordination numbers allowed us to determine the existence of structural transformation in a liquid state. Moreover, it was found that at a temperature of 640 K thermal expansion coefficients, estimated from temperature dependence of interatomic distances, change its sign from negative to positive confirming the transformations in structure of liquid indium which are observed by temperature variations.     

针对连续变化法测定络合物稳定常数实验中可能出现的设计缺陷的讨论

连续变化法测定络合物组成和稳定常数是大学化学中的经典学生实验。但针对1：2和1：3的络合反应，实验教科书的设计中可能出现数据点过少也就是溶液配制过少的问题。如果按照要求配制溶液，由于没有完全反应的混合溶液，而其他混合溶液给出的数据又都呈良好的线性，就缺少了用来估算曲线的数据点，结果是，将没有足够的数据对稳定常数进行估算。对这种可能出现的数据点过少的实验设计的原因、结果和解决方法进行了探讨。     

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.