Wave front shape for a constrained cylindrically anisotropic elastic solid

The two-dimensional wave front shape caused by a point impulse excitation in a cylindrically anisotropic elastic solid is considered. The elastic parameters of the solid are constrained such that E = G This constraint allows the parametric equations of the wave front to be expressed exactly in terms of elementary transcendental functions. The precise location of double and cusp points on the front is treated in detail. Time histories of several wave front patterns are presented and an interesting feature of the front is generalized to the unconstrained solid.     

Classification of Material <Emphasis Type="Italic">G</Emphasis>-Structures

A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained.     

金属有机框架材料UTSA-74高效去除水溶液中的砷

利用水热法合成金属有机框架材料UTSA-74,并用它同时去除水中的As(Ⅴ)和As(Ⅲ)。 批次实验结果表明,在低质量浓度情况下(~1 mg/L),UTSA-74对As(Ⅴ)的去除率高达95%。 对As(Ⅲ)的去除率达85%。 经拟合,本实验符合拟二级动力学及Freundlich等温吸附模型。 本文还探究了共存离子(如Cl^-、NO₃^-、PO₄^3-)干扰影响,结果表明PO₄^3-的存在会抑制吸附的进行,可能是由于竞争吸附位点所致。 此外,本文对吸附后的材料进行洗脱(0.1 mol/L NaOH),将洗脱后的UTSA-74材料再次进行吸附探究,反复3次,其去除率仍可达70%左右。 为探究其中机理,本文通过X射线衍射(XRD)、扫描电子显微镜(SEM)、红外光谱(IR)对吸附前后材料进行表征,结果表明吸附过程中可能形成了Zn—O—As,以此促进吸附反应的进行。 综上所述,UTSA-74可以作为一种处理砷的新型吸附剂,具有一定的实用价值。     

C74(BN)2的UV和IR 光谱研究

Equilibrium geometries of 16 possible isomers for C74（BN）2 were studied by INDO series of methods, to indicate that the most stable three geometries are those where boron and nitrogen atoms substitute carbon atoms located at the same hexagon near the longest axis of C78 （C2v） to form B-N-B-N unit. Electronic spectra of C74（BN）2 were investigated with INDO/CIS method. The reason for the red shift of UV absorptions for C74（BN）2 compared with those of C78 （C2v） was discussed. IR spectra for 9,8,28,29-C74（BN）2 and 28,29,30,31-C74（BN）2 were calculated on the basis of AM1 geometries.     

Automated flow-based anion-exchange method for high-throughput isolation and real-time monitoring of RuBisCO in plant extracts

In this work, a miniaturized, completely enclosed multisyringe-flow system is proposed for high-throughput purification of RuBisCO from Triticum aestivum extracts. The automated method capitalizes on the uptake of the target protein at 4 °C onto Q-Sepharose Fast Flow strong anion-exchanger packed in a cylindrical microcolumn (105 × 4 mm) followed by a stepwise ionic-strength gradient elution (0-0.8 mol/L NaCl) to eliminate concomitant extract components and retrieve highly purified RuBisCO. The manifold is furnished downstream with a flow-through diode-array UV/vis spectrophotometer for real-time monitoring of the column effluent at the protein-specific wavelength of 280 nm to detect the elution of RuBisCO. Quantitation of RuBisCO and total soluble proteins in the eluate fractions were undertaken using polyacrylamide gel electrophoresis (PAGE) and the spectrophotometric Bradford assay, respectively. A comprehensive investigation of the effect of distinct concentration gradients on the isolation of RuBisCO and experimental conditions (namely, type of resin, column dimensions and mobile-phase flow rate) upon column capacity and analyte breakthrough was effected. The assembled set-up was aimed to critically ascertain the efficiency of preliminary batchwise pre-treatments of crude plant extracts (viz., polyethylenglycol (PEG) precipitation, ammonium sulphate precipitation and sucrose gradient centrifugation) in terms of RuBisCO purification and absolute recovery prior to automated anion-exchange column separation. Under the optimum physical and chemical conditions, the flow-through column system is able to admit crude plant extracts and gives rise to RuBisCO purification yields better than 75%, which might be increased up to 96 ± 9% with a prior PEG fractionation followed by sucrose gradient step.     

Automated in-syringe single-drop head-space micro-extraction applied to the determination of ethanol in wine samples

A novel approach of head-space single-drop micro-extraction applied to the determination of ethanol in wine is presented. For the first time, the syringe of an automated syringe pump was used as an extraction chamber of adaptable size for a volatile analyte. This approach enabled to apply negative pressure during the enrichment step, which favored the evaporation of the analyte. Placing a slowly spinning magnetic stirring bar inside the syringe, effective syringe cleaning as well as mixing of the sample with buffer solution to suppress the interference of acetic acid was achieved.     

Adaptive finite element methods for Cahn–Hilliard equations

We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn–Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space–time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach.     

Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics

In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.     

Four applications of majorization to convexity in the calculus of variations

The resemblance between the Horn-Thompson theorem and a recent theorem by Dacorogna-Marcellini-Tanteri indicates that Schur-convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity, such as rank one convexity or quasiconvexity. In Theorem 6.6, we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant.Majorization is used in order to give a very short proof of a theorem of Thompson and Freede [R.C. Thompson, L.J. Freede, Eigenvalues of sums of Hermitian matrices III, J. Res. Nat. Bur. Standards B 75B (1971) 115-120], Ball [J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, in: R.J. Knops (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. 1, Res. Notes Math., 17, Pitman, 1977, pp. 187-241], or Le Dret [H. Le Dret, Sur les fonctions de matrices convexes et isotropes, CR Acad. Sci. Paris, Série I 310 (1990) 617-620], concerning the convexity of a class of isotropic functions which appear in nonlinear elasticity.Next we prove (Theorem 7.3) a lower semicontinuity result for functionals with the form _∫Ωw(D?(x))dx, with w(F)=h(lnV_F). Here F=R_FU_F=V_FR_F is the usual polar decomposition of F∈gl(n,R), and lnV_F is Hencky’s logarithmic strain.We close this paper with a compact proof of Dacorogna-Marcellini-Tanteri theorem, based only on classical results about majorization. The mentioned resemblance of this theorem with the Horn-Thompson theorem is thus explained.     

A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally we compare this solution with the one obtained with global minimization.