Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

容量矩阵法在涡方法中的应用

本文将容量矩阵技术与快速Fourier变换相结合求解非矩形域的Poisson方程,再与格子涡方法相结合,发展了一套求解复杂外形的快速涡方法。作为算例,计算了有厚度平板和楔形体的分离流动,得到了满意的结果。特别是在垂直平板绕流中,模拟出了由于剪切层不稳定性引起的小涡结构。     

快速镍刷镀层在含磨粒的油润滑条件下的摩擦磨损性能研究

作者在含磨粒的油润滑条件下对快速镍刷镀层的摩擦磨损性能与45~#钢(淬火+低温回火)的进行了对比试验研究。结果表明,镍刷镀层不仅磨损量和摩擦系数始终都比45~#钢的小,而且它的稳定磨损阶段也长而未出现45~#钢那样明显加剧的磨损。作者指出,这主要是由于镍刷渡层组织所含微孔既可吸附和储存润滑油而起辅助润滑作用,又能使磨粒镶嵌于其中而减少磨粒磨损的缘故,而且随着摩擦温升其塑性也得到改善,因而快速镍刷镀层的摩擦磨损性能都比质地致密且硬度更高的45~#钢的好。     

Synthesis of polyamidoamine dendrimer (PAMAM/CuS/AA) nanocomposite and its application in the removal of Isma acid fast yellow G Dye

The adsorption of Isma acid fast yellow G dye was studied using polyamidoamine (PAMAM)/Copper sulfide (CuS)/AA nanocomposite containing different amounts of CuS by batch technique. PAMAM dendrimer/CuS/AA nanocomposites were synthesized via gamma irradiation cross‐linking method with the aid of sonication. The nanocomposites were characterized by Fourier‐transform infrared, X‐ray diffraction, transmission electron microscope, energy dispersive spectroscopy X‐ray, thermal gravimetric analysis, ultraviolet‐visible, and fluorescence spectroscopy. The size of the CuS nanoparticles was formed in the range of 12–19 nm. The adsorption capacity of the nanocomposites was evaluated as a function of initial dye concentration, pH, adsorbent dosage, and time. It was verified that the adsorption rate fits a pseudo‐second‐order kinetics for initial Isma acid fast yellow G dye concentrations. Results indicated that the adsorption of Isma acid fast yellow G dye fitted well to the Langmuir model. Our results demonstrate that the PAMAM dendrimer/CuS/AA nanocomposite is very promising for removing organic dyes from wastewater. Copyright © 2015 John Wiley & Sons, Ltd.     

Low‐memory iterative density fitting

A new low‐memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix‐vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15‐fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12‐core CPU workstation. © 2015 Wiley Periodicals, Inc.     

Quantification of fatty acids in erythrocytes and plasma by fast gas chromatography

As a result of the heterogeneous nature of lipid classes in complex biological matrices such as plasma and erythrocytes, it is imperative to have a robust and validated methodology for fatty acid quantification. The effective method presented here combines available methodology of fast gas chromatography and an improvement of the sample preparation methodology before injection into the gas chromatograph. This methodology ensures complete transesterification and quantification of total and individual fatty acids (and not only in relative amounts) by addition of internal standards. We considered sample preparation key, and we established the use of lysis buffer and ethanol for erythrocytes and plasma sample preparation, respectively. Fatty acid profile was determined by acid methylation and fast gas chromatography equipped with a flame ionization detector. The triacylglycerol 13:0, phosphatidylcholine 23:0, and methyl esters 21:0 were used as internal standards. Within the linearity of the calibration, the ratio of the peak area of each fatty acid over the peak area of the internal standard was constant (coefficient of variation ≤ 2.5). Satisfactory repeatability <15% and intermediate reproducibility < 15% were observed. Finally, this validated method was applied to a pre‐clinical trial that investigated the impact of dietary fats on accretion of specific fatty acids in plasma and erythrocytes.     

Protein C recognition by ion‐coordinated imprinted monolithic cryogels

The protein C imprinted monolithic cryogel was synthesized using 2‐hydroxyethyl methacrylate by redox cryo‐polymerization method. The prepared monolithic cryogel was characterized by Fourier transform infrared spectroscopy, swelling test, surface area measurements, and scanning electron microscopy. The nonimprinted cryogel was prepared as well for control. Adsorption of protein C from aqueous solutions was investigated in a continuous mode and several parameters affecting adsorption performance were optimized. The maximum protein C adsorption amount was 30.4 mg/g. The selectivity studies were performed by monolithic column studies and fast protein liquid chromatography, using hemoglobin and human serum albumin as competing proteins. The relative selectivity coefficients were 2.37 and 8.89 for hemoglobin and human serum albumin, respectively. Reusability was tested for ten consecutive adsorption–desorption cycles, and no significant change in adsorption capacity was recorded. A pseudo‐second‐order model was suitable to interpret kinetic data, and the Langmuir model suited the adsorption isotherms well.     

Directly‐coupled‐column ultra‐fast liquid chromatography with diode array detection method for the rapid quantification of allergenic disperse dyes in water preconcentrated by magnetic solid‐phase extraction

A directly‐coupled‐column ultra‐fast liquid chromatography coupled with diode array detection method for the determination of 12 allergenic disperse dyes in river water at sub‐ppb levels has been developed and successfully validated. The analytical method is based on the use of two different reversed‐phased columns connected through a two‐position switching valve. A baseline separation was achieved by proper selection of stationary phases, mobile phases, and the use of a gradient elution in both dimensions. Furthermore, an easy‐to‐handle magnetic solid‐phase extraction procedure was developed for the preconcentration of 12 allergenic disperse dyes from river water. An enrichment factor of 100 times was obtained. The results showed excellent performance in terms of trueness (76.8–99.0%), precision (intraday: 2.2–8.0%, interday: 3.3–8.2%), and sensitivity (limits of determination, 0.027–1.46 μg/L). Twenty real samples collected from the outfalls in the Yaojiang, Yongjiang and Fenghuajiang estuary were analyzed, and three of the studied compounds were found in one collected sample (12.6 μg/L for disperse blue 7, 11.6 μg/L for disperse blue 106, and 0.22 μg/L for disperse blue 3).     

A fast discontinuous finite element discretization for the space‐time fractional diffusion‐wave equation

In this article, we study fast discontinuous Galerkin finite element methods to solve a space‐time fractional diffusion‐wave equation. We introduce a piecewise‐constant discontinuous finite element method for solving this problem and derive optimal error estimates. Importantly, a fast solution technique to accelerate Toeplitz matrix‐vector multiplications which arise from discontinuous Galerkin finite element discretization is developed. This fast solution technique is based on fast Fourier transform and it depends on the special structure of coefficient matrices. In each temporal step, it helps to reduce the computational work from required by the traditional methods to log , where is the size of the coefficient matrices (number of spatial grid points). Moreover, the applicability and accuracy of the method are verified by numerical experiments including both continuous and discontinuous examples to support our theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2043–2061, 2017     

Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions

A fast multipole method (FMM) is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems. In this paper, a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach. Generalized minimum residual method (GMRES) is used as an iterative solver to solve the equation system formed by BEM iteratively. The numerical results show that the scheme presented is applicable to certain large scale problems. The project supported by the National Nature Science Foundation of China (10172053) and the Ministry of Education