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In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We first prove that the discrete maximum principle holds under reasonable constraints on time step size and coefficient of stabilized term. Secondly, we analyze the maximum-norm error. Thirdly, we can see that the proposed scheme is unconditionally energy-stable by defining the modified energy and selecting the appropriate parameters. Finally, two numerical examples are presented to verify the theoretical results.

This paper aims to construct a two-grid scheme for distributed optimal control governed by semilinear elliptic equations. The state and co-state are approximated by the P_0^2-P_1 pair and the control variable is approximated by piecewise constant functions. First, a priori error estimates for the control variable, the state variables and the co-state variables are obtained. Second, a two-grid P_0^2-P_1 mixed finite element scheme is presented and the corresponding error is analyzed. Finally, a numerical example demonstrating our theoretical results is also presented in this paper.

In this paper, a two-grid finite element scheme for semilinear parabolic integro-differential equations is proposed. In the two-grid scheme, continuous linear element is used for spatial discretization, while Crank-Nicolson scheme and Leap-Frog scheme are ultilized for temporal discretization. Based on the combination of the interpolation and Ritz projection technique, some superclose estimates between the interpolation and the numerical solution in the \begin{document}$ H^1 $\end{document} -norm are derived. Notice that we only need to solve nonlinear problem once in the two-grid scheme, namely, the first time step on the coarse-grid space. A numerical example is presented to verify the effectiveness of the proposed two-grid scheme.

In this paper, we consider a system of two coupled quasilinear viscoelastic equations in canonical form with Dirichlet boundary condition. By using the perturbed energy method, the property of blow-up in finite time of solution of energy is given with strong enough the dissipation of the viscoelastic term. Which extends some existing results for a single equation to the case of a coupled system.

RNA interference (RNAi), based on hairpin RNA (hpRNA) expression, plays an important role in functional analysis of plant genes. Traditional methods for making RNAi constructs usually involve multiple time-consuming cloning steps. We have developed a Gateway-compatible binary vector for RNAi-mediated gene knockdown in plants from pCAMBIA2301 and pHANNIBAL vectors. The new plant RNAi binary vector, named pCAMBIA2301-GW-RNAi, has two inverted repeated Gateway cassettes driven by the cauliflower mosaic virus 35S (CaMV 35S) promoter. This enables site-specific recombination at two sites by one Gateway LR reaction without restriction enzymes and ligases. The pCAMBIA2301-GW-RNAi vector's effectiveness was evaluated by Agrobacterium-mediated transient co-expression assays of overexpression and silencing constructs of HvCEBiP in Nicotiana benthamiana followed by western blot analysis. Obtained results show that the developed RNAi vector successfully knocked down 35S-driven expression of HvCEBiP, as expression levels of the encoded HvCEBiP protein were significantly reduced.

Biodegradable poly(3-hydroxybutyrate) (PHB)/functionalized multi-walled carbon nanotubes (f-MWNTs) nanocomposite was prepared in this work by solution casting method at 2 wt% f-MWNTs loading. Scanning electron microscopy and transmission electron microscopy observations indicate a homogeneous distribution of f-MWNTs in the PHB matrix. Nonisothermal melt crystallization, overall isothermal melt crystallization kinetics, and crystalline morphology of neat PHB and the PHB/f-MWNTs nanocomposite were studied in detail. It is found that the presence of f-MWNTs enhances the crystallization of PHB during nonisothermal and isothermal melt crystallization processes in the nanocomposite due to the heterogeneous nucleation effect of f-MWNTs. Moreover, the incorporation of a small quantity of f-MWNTs apparently improves the thermal stability of the PHB/f-MWNTs nanocomposite with respect to neat PHB. Two methods are employed to study the activation energies of thermal degradation for both the neat PHB and the PHB/f-MWNTs nanocomposite. The activation energy of thermal degradation of the PHB/f-MWNTs nanocomposite is higher than that of neat PHB. Copyright © 2009 John Wiley & Sons, Ltd.

In this work, nonisothermal melt crystallization and subsequent melting behavior of poly(hydroxybutyrate) (PHB) and its nanocomposites at different multiwalled carbon nanotubes (MWCNTs) loadings were investigated. Increasing the MWCNTs loadings has enhanced the nonisothermal melt crystallization of PHB significantly in the nanocomposites when compared with that of the neat PHB; furthermore, increasing the cooling rates shift the crystallization exotherms to low temperature range for both neat PHB and its nanocomposites. Double melting behavior is found for both neat PHB and its nanocomposites crystallized nonisothermally from the melt, which is explained by the melting, recrystallization, and remelting model. Effects of the MWCNTs loadings, cooling rates, and heating rates on the subsequent melting behavior of PHB were studied in detail. It is found that increasing the MWCNTs loadings, decreasing the cooling rates, and increasing the heating rates would restrict the occurrence of the recrystallization of PHB in the nanocomposites. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2238–2246, 2009

Isothermal Melt Crystallization Kinetics Study of Biodegradable Poly(3-hydroxybutyrate)/Multiwalled Carbon Nanotubes Nanocomposites

By using the mathematical uniform design, a new agglomerated flux for high speed and multi-arc submerged arc welding (SAW) has been developed in this paper, which performs excellently in welding process, and the effects of flux composition on the welding characteristics is analyzed as well. The mechanical tests show that the weld metal obtained in SAW with this flux exhibits high toughness at low temperature, and the other mechanical properties of the weld metal also satisfy the technical specifications for the West to East Pipeline Project in China. The microstructures of the weld metal are also examined. Both optical and TEM microphotoes demonstrate that the weld consists mainly of small-sized and uniformly distributed acicular ferrite. These microstructures can effectively prevent the initiation and propagation of micro cracks, resulting in high notch toughness of the weld metal at low temperature.

Biodegradable poly(epsilon-caprolactone) (PCL)/multi-walled carbon nanotubes containing carboxylic groups (f-MWNTs) nanocomposites were prepared via simple melt compounding at low f-MWNTs loading in this work. Scanning and transmission electron microscopy observations indicate a homogeneous and fine distribution of f-MWNTs throughout the PCL matrix. The effect of low f-MWNTs loading on the crystallization, mechanical properties, and controlled enzymatic degradation of PCL in the nanocomposites were studied in detail with various techniques. The experimental results indicate that the incorporation of f-MWNTs enhances both the nonisothermal crystallization peak temperature and the overall isothermal crystallization rate of PCL in the PCL/f-MWNTs nanocomposites relative to neat PCL; moreover, the incorporation of a small quantity of f-MWNTs has improved apparently the mechanical properties of the PCL/MWNTs nanocomposites compared to neat PCL. The enzymatic degradation of neat PCL and the PCL/f-MWNTs nanocomposites at low f-MWNTs loading was studied in detail. The variation of weight loss with enzymatic degradation time, the surface morphology change, the reduced film thickness, the appearance of f-MWNTs on the surface of the films, and the almost unchanged molecular weight after enzymatic degradation suggest that the enzymatic degradation of neat PCL and the PCL/f-MWNTs nanocomposites may proceed via surface erosion mechanism. The presence of f-MWNTs reduces the enzymatic degradation rate of the PCL matrix in the nanocomposites compared with that of the pure PCL film.

In this paper, the influence of aging treatment on microstructures evolution and shear strength in Sn-3.0Ag-0.5Cu, Sn-4.0Ag-0.5Cu and Sn-3.5Ag lead-free solders were investigated. For comparison, the specimens as-soldered and after aging at temperature of 100degC were respectively put up observation for IMC and shear test. Morphology, micro structure and component at interface of solder joint were observed and analyzed. The results show that morphology and microstructure of intermetallic compound change form long needle-like to scallop-like, and the thickness and quantity of intermetallic compound increases with increasing aging time. Shear load of the lead-free solder joint decreases at constant strain rate with increasing aging. At the identical work condition, the shear load of solder joint with different lead-free alloy had not significantly change. Sn-3.5Ag presents the better shear property than the others.

The growth behavior and the morphology of IMCs at the Sn-3.0Ag-0.5Cu/Cu interface were investigated firstly. Then the effect of reflow time on IMCs during reflow soldering was also studied in detail. The reflow time was 15s, 30s, 60s, 120s, 240s and 360s respectively. The scanning electron microscope (SEM) was utilized to observe the microstructure of solder joint and the alloy layer in interface of solder and Cu substrate. In order to survey component and distribution of IMCs, the X-ray energy dispersion spectrometer (EDS) was employed to do qualitative analysis and quantitative analysis of observed IMCs. The results show that, in all different reflow times, the obvious IMCs was observed at interface and the various morphology IMCs were also found in solder joint. With increasing of the reflow time, the morphology of IMCs changed gradually from long needle-like to scallop-like, and the quantity and the thickness of IMCs were always increasing. The effect of the reflow time on the serrated height of IMCs was not monotonous, that was from high to low then to high again, but the mean thickness of IMC layer was elevating at all times. In addition, it was observed that the great deal of kirkedall voiding existed at the interface between Cu substrate and Sn-Ag-Cn solder. The qualitative analysis and quantitative analysis by EDS show that there was a layer of Cu-Sn alloy in which the concentration of Cu lower from the Cu substrate to the solder. The study on the formation of IMC and voiding will also be discussed in the future