高波数问题的超收敛性

 本文考虑求解Helmholtz方程的有限元方法的超逼近性质以及基于PPR后处理方法的超收敛性质.我们首先给出了矩形网格上的p-次元在收敛条件k（kh）^2p+1≤C₀下的有限元解和基于Lobatto点的有限元插值之间的超逼近以及重构的有限元梯度和精确解之间的超收敛分析.然后我们给出了四边形网格上的线性有限元方法的分析.这些估计都给出了与波数k和网格尺寸h的依赖关系.同时我们回顾了三角形网格上的线性有限元的超收敛结果.最后我们给出了数值实验并且结合Richardson外推进一步减少了误差.     

A Modified Polynomial Preserving Recovery and Its Applications to A Posteriori Error Estimates

<正>A modified polynomial preserving gradient recovery technique is proposed. Unlike the polynomial preserving gradient recovery technique,the gradient recovered with the modified polynomial preserving recovery(MPPR) is constructed element-wise, and it is discontinuous across the interior edges.One advantage of the MPPR technique is that the implementation is easier when adaptive meshes are involved.Superconvergence results of the gradient recovered with MPPR are proved for finite element methods for elliptic boundary problems and eigenvalue problems under adaptive meshes. The MPPR is applied to adaptive finite element methods to construct asymptotic exact a posteriori error estimates.Numerical tests are provided to examine the theoretical results and the effectiveness of the adaptive finite element algorithms.     

Effects of toughening propylene/ethylene graft copolymer on the crystallization behavior and mechanical properties of polypropylene random-copolymerized with a small amount of ethylene

Linear low-density polyethylene (LLDPE) was grafted onto the backbone chains of isotactic polypropylene (iPP) during reactive melt-extrusion to produce a novel toughening modifier, propylene/ethylene graft copolymer (PEGC), to improve the properties of iPP random(-copolymerized with a small amount of ethylene) (PPR). The crystallization behavior as well as the non-isothermal crystallization kinetics of the PEGC modified PPRs were investigated via differential scanning calorimetry (DSC), polarized optical microscopy (POM) and wide-angle X-ray diffraction (WAXD). The fractured surface topography was characterized using scanning electron microscopy (SEM), and the mechanical properties through notched impact and tensile testing as well as dynamic mechanical thermal analysis (DMTA). The results show that, at a PEGC content of 8 wt%, notched impact strength of the PEGC modified PPR increased by 30.6% at low temperature (−25 °C). As regards crystalline morphology, the PEGC, as an effective heterogeneous nucleating agent, fostered nucleation of the PPR to elevate its crystallization temperature as well as rate of crystallization, thus refining the PPR (iPP) spherulites and improving the interfacial structure between iPP spherulites. The Jeziorny approach was unsatisfactory for simulation of the non-isothermal crystallization process of the PEGC modified PPRs; however, the Mo method described consistently the crystallization kinetics over the entire isothermal process.     

Design of super-tough and antibacterial PPR/nano-ZnO composites based on the excellent dispersion of ZnO particles

Herein, polyvinyl pyrrolidone (PVP) dispersants are used to disperse and isolate zinc oxide (ZnO) particles. A high-pressure spray device is used to dry the dispersed nano-fillers quickly to achieve the structure of PVP chains wrapping and isolating ZnO particles. Scanning electron microscopy shows that most of the size of the agglomerated ZnO nanoparticles in polypropylene random (PPR, obtained by random copolymerization of propylene and ethylene) is maintained below 100 nm, and only a small amount of large agglomerates with a particle size less than 400 nm. An excellent dispersion of nano-ZnO fillers prepared by this method can greatly improve the toughness of PPR and endow it with good antibacterial properties. When the content of the ZnO nanoparticles is 3 wt%, the notched impact strength of PVZ3 increases to 48.85 kJ m⁻² (unbroken), which is 3.6 times than that of pure PPR. In addition, 3 phr ZnO nanoparticles give PPR excellent antibacterial properties, with an antibacterial rate of 99.9% (Escherichia coli and Staphylococcus aureus). The value of antibacterial activity (E. coli) of PVZ3 reached more than 6.0, which is nearly three times that of PZ.     

Enhanced ultraviolet resistance of polypropylene random copolymer filled by ZnO-supported mesoporous zeolite

To enhance the ultraviolet resistance of ZnO based polymer materials, ZnO-supported mesoporous zeolite(M-ZnO) was prepared and characterized by atomic absorption spectroscopy and scanning electron microscopy. The ultraviolet resistance, crystallization behavior and melting characteristics of ZnO and M-ZnO filled PPR composites were compared by FTIR spectra and differential scanning calorimetry. The ultraviolet resistance of M-ZnO filled PPR composites is higher than that of ZnO filled PPR composites, indicating higher ultraviolet resistance of M-ZnO than that of ZnO. The crystallization temperatures of mesoporous zeolite filled PPR were higher than those of M-ZnO and decreased with increasing UV-irradiation time. But the crystallization temperatures of M-ZnO filled PPR composites were not influenced by UV-irradiation time. The ZnO supported on the surface of zeolite is effective in enhancing the ultraviolet resistance of ZnO based polymer materials.     

一种高强度准聚轮烷水凝胶的制备及性能研究

通过点击化学在聚乙二醇单甲醚(MPEG)端基分别修饰了葡萄糖(Glc)、甘露糖(Man)和半乳糖(Gal),制备了一系列端基为糖的聚乙二醇单甲醚(MPEG-Glc、MPEG-Man和MPEG-Gal),此类端基为糖的MPEG和α-环糊精(α-CD)混合后能够形成稳定的准聚轮烷(PPR)水凝胶,而端基没有修饰糖的MPEG和α-CD只能形成黏度较大的溶液而无法形成稳定存在的凝胶.通过流变仪测试可知水凝胶的弹性模量高达1.0×105 Pa,远大于文献中通过黏土等增强的PPR水凝胶的强度,我们认为该MPEG端基的糖之间能够形成新的"糖交联"点从而有效提高了凝胶的强度.通过向水凝胶中加入和MPEG端基的糖具有相互作用的苯硼酸半酯聚合物(PNIPAM-co-PBOB)或刀豆蛋白(Con A),发现在凝胶中加入PNIPAM-co-PBOB或Con A后可明显降低PPR水凝胶的强度.通过扫描电镜(SEM)和X射线衍射(XRD)对水凝胶的形貌以及微观结构进行表征分析,发现此凝胶的微观结构和文献中报道的PPR水凝胶基本一致,进一步证明了上述结论.