A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Nanocomposite hydrogel consisting of Na‐montmorillonite with enhanced mechanical properties

A new kind of nanocomposite (NC) hydrogel with Na‐montmorillonite (MMT) is presented in this article. The NC hydrogels were synthesized by free radical copolymerization of acrylamide and (3‐acrylamidopropyl) trimethylammonium chloride (ATC) in the presence of MMT and N,N′‐methylene‐bis‐acrylamide used as chemical cross‐linker. Due to the cation‐exchange reaction between MMT and ATC (cationic monomer) during the synthesis of NC hydrogels, MMT platelets were considered chemical “plane” cross‐linkers, different from “point” cross‐linkers. With increasing amount of MMT, the crosslinking degree enhanced, causing a decrease of the swelling degree at equilibrium. Investigations of mechanical properties indicated that NC hydrogels exhibited enhanced strength and toughness, which resulted from chemical interaction between exfoliated MMT platelets and polymer chains in hydrogels. Dynamic shear measurements showed that both storage modulus and loss modulus increased with increasing MMT content. The idea described here provided a new route to prepare hydrogels with high mechanical properties by using alternative natural Na‐MMT. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1020–1026     

Preparation and gas sensing activity of La and Y co-doped titania nanoparticles

Journal of Sol-Gel Science and Technology - A novel gas sensing material, La–Y co-doped TiO2 nanoparticles, was synthesized by sol–gel method and applied to detect organic pollutants...     

Unsymmetrical Pyrene‐Fused Phthalocyanine Derivatives: Synthesis,Structure, and Properties

Novel pyrene‐fused unsymmetrical phthalocyanine derivatives 2,3,9,10,16,17‐hexakis(2,6‐dimethylphenoxy)‐22,25‐diaza(2,7‐di‐tert‐butylpyrene)[4,5]phthalocyaninato zinc complex Zn[Pc(Pz‐pyrene)(OC₈H₉)₆] ( 1 ) and 2,3,9,10‐tra(2,6‐dimethylphenoxy)‐15,18,22,25‐traza(2,7‐di‐tert‐butylpyrene)[4,5]phthalocyaninato zinc compound Zn[Pc(Pz‐pyrene)₂(OC₈H₉)₄] ( 2 ) were isolated for the first time. These unsymmetrical pyrene‐fused phthalocyanine derivatives have been characterized by a wide range of spectroscopic and electrochemical methods. In particular, the pyrene‐fused phthalocyanine structure was unambiguously revealed on the basis of single crystal X‐ray diffraction analysis of 1 , representing the first structurally characterized phthalocyanine derivative fused with an aromatic moiety larger than benzene.