三维多物质欧拉界面处理的并行算法研究

针对现有的算法无法对爆炸冲击进行有效的研究这一问题,在改进了Youngs界面技术的基础上设计了三维多物质Euler界面处理的并行算法。然后采用MPI标准进行了算法的程序设计并对程序进行了并行性能测试和不同分区的算例测试,测试结果表明并行算法对加速比有较大的提高,而不同分区对并行算法的计算结果并没有影响。最后应用所编写的程序对空中爆炸和聚能射流进行了仿真,结果表明程序的模拟结果与前人的研究数据是符合的,说明了程序的有效性。     

Nonlinear transformation methods for accelerating the convergence of Coulomb integrals over exponential type functions

It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of Coulomb integrals are the most frequently encountered. As the molecular system gets larger, computation of these integrals becomes one of the most laborious and time consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. The atomic orbital basis functions chosen in the present work are Slater type functions. These functions can be expressed as finite linear combinations of B functions which are suitable to apply the Fourier transform method. The difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of highly oscillatory semi-infinite integrals. In this work, we present a generalized algorithm based on the nonlinear transformation of Sidi, for a precise and fast numerical evaluation of molecular integrals over Slater type functions and over B functions. Numerical results obtained for the three-center two-electron Coulomb and hybrid integrals over B functions and over Slater type functions. Comparisons with numerical results obtained using alternatives approaches and an existing code are listed.     

Optimisation of a matrix solid-phase dispersion method for the determination of organophosphate compounds in dust samples

A fast and inexpensive sample preparation procedure based on the matrix solid-phase dispersion (MSPD) technique is proposed for the isolation of several organophosphate esters (mainly employed as flame retardants and plasticizers) from indoor dust samples. Extraction and clean-up were carried out in a single step and target compounds were determined by gas chromatography (GC) with nitrogen-phosphorus detection (NPD). The main parameters affecting extraction yield and selectivity, such as type and amount of dispersant material, clean-up co-sorbent and extraction solvent, were evaluated and optimised. Under final conditions, 0.5 g of dust were dispersed with equal amounts of anhydrous sodium sulphate and Florisil, and loaded on the top of a polypropylene cartridge containing 0.5 g of alumina. The dispersed sample was washed with 2 mL of n-hexane to remove the least polar interferences and analytes were eluted with 3 mL of acetone. Recoveries of the proposed method for spiked samples ranged from 80 to 116%, and the day-to-day variability remained between 5 and 10%. Data on levels of organophosphate species in dust from private houses and vehicle cabins are provided. In both cases, the lowest concentrations corresponded to the short chain, non-chlorinated, alkyl organophosphates, whereas mean values above 1 μg g⁻¹ were measured for the rest of analytes.     

Modeling of nucleic acid adsorption on 3D prisms in microchannels

Understanding nucleic acid adsorption in microchannels is critical to improve the efficiency of purifying and extracting nucleic acid (NA) from sample solutions by microfluidic technologies. Using a microchannel with 3D prismatic silica elements on the wall can dramatically increase the surface area-to-volume ratio, and hence facilitate the nucleic acid adsorption on the wall. In this study a theoretical model for modeling adsorption in a microchannel with a designed 3D surface structure was developed, and five dimensionless numbers were found to be the key parameters in the adsorption process. Extensive numerical simulations were conducted. Two flow modes, the electroosmotic flow (EOF) and pressure-driven flow (PDF), were investigated for their effect on the adsorption. It was found that the EOF is more desirable than PDF. The 3D prismatic elements can increases the NA molecule adsorption not only by providing more surface areas, but also by the induced pressure resisting the central bulk electroosmotic flow. Finally, the effects of adsorption kinetic parameters (i.e., the kinetic association/dissociation constants, the diffusion coefficient, the total site density, the loading concentration, and the channel height), on the adsorption process were discussed in detail.     

Computation of exact inertia and inclusions of eigenvalues (singular values) of tridiagonal (bidiagonal) matrices

This report may be considered as a non-trivial extension of an unpublished report by William Kahan (Accurate Eigenvalues of a symmetric tri-diagonal matrix, Technical Report CS 41, Computer Science Department, Stanford University, 1966). His interplay between matrix theory and computer arithmetic led to the development of algorithms for computing accurate eigenvalues and singular values. His report is generally considered as the precursor for the development of IEEE standard 754 for binary arithmetic. This standard has been universally adopted by virtually all PC, workstation and midrange hardware manufactures and tens of billions of such machines have been produced. Now we use the features in this standard to improve the original algorithm.In this paper, we describe an algorithm in floating-point arithmetic to compute the exact inertia of a real symmetric (shifted) tridiagonal matrix. The inertia, denoted by the integer triplet (π, ν, ζ), is defined as the number of positive, negative and zero eigenvalues of a real symmetric (or complex Hermitian) matrix and the adjective exact refers to the eigenvalues computed in exact arithmetic. This requires the floating-point computation of the diagonal matrix D of the LDL^t factorization of the shifted tridiagonal matrix T − τI with +∞ and −∞ rounding modes defined in IEEE 754 standard. We are not aware of any other algorithm which gives the exact answer to a numerical problem when implemented in floating-point arithmetic in standard working precisions. The guaranteed intervals for eigenvalues are obtained by bisection or multisection with this exact inertia information. Similarly, using the Golub-Kahan form, guaranteed intervals for singular values of bidiagonal matrices can be computed. The diameter of the eigenvalue (singular value) intervals depends on the number of shifts with inconsistent inertia in two rounding modes. Our algorithm not only guarantees the accuracy of the solutions but is also consistent across different IEEE 754 standard compliant architectures. The unprecedented accuracy provided by our algorithms could be also used to debug and validate standard floating-point algorithms for computation of eigenvalues (singular values). Accurate eigenvalues (singular values) are also required by certain algorithms to compute accurate eigenvectors (singular vectors).We demonstrate the accuracy of our algorithms by using standard matrix examples. For the Wilkinson matrix, the eigenvalues (in IEEE double precision) are very accurate with an (open) interval diameter of 6 ulps (units of the last place held of the mantissa) for one of the eigenvalues and lesser (down to 2 ulps) for others. These results are consistent across many architectures including Intel, AMD, SGI and DEC Alpha. However, by enabling IEEE double extended precision arithmetic in Intel/AMD 32-bit architectures at no extra computational cost, the (open) interval diameters were reduced to one ulp, which is the best possible solution for this problem. We have also computed the eigenvalues of a tridiagonal matrix which manifests in Gauss-Laguerre quadrature and the results are extremely good in double extended precision but less so in double precision. To demonstrate the accuracy of computed singular values, we have also computed the eigenvalues of the Kac₃₀ matrix, which is the Golub-Kahan form of a bidiagonal matrix. The tridiagonal matrix has known integer eigenvalues. The bidiagonal Cholesky factor of the Gauss-Laguerre tridiagonal is also included in the singular value study.     

Numerical methods for inverse problems in electrooptics of polydisperse colloids

In this paper we propose a new method for the determination of the distribution of electrical and geometrical particle parameters based on electrooptical experimental data. The electrooptical method leads to the solution of inverse ill-posed problems. The main equations for the determination of the distribution of particles on these parameters are presented. To find out the distribution functions from the electrooptical experimental data one has to solve the first-kind Fredholm integral equation corresponding to the problem under study. The proposed method of its solution is based on the penalty functions method. The results of modelling that let us compare the various numerical methods are presented.     

Determination of aflatoxins in olive oil by liquid chromatography-tandem mass spectrometry

A liquid chromatography-tandem mass spectrometric with electrospray ionization (LC/ESI-MS/MS) method for determining the four naturally occurring aflatoxins (AFs) B1, B2, G1, and G2 in olive oil is proposed. AFs were extracted from oil sample by means of matrix solid phase dispersion (MSPDE), utilizing C18 as dispersing material. No further purification step, such as lipid removal, was performed. Aflatoxin M1, the hepatic metabolite of AFB1, was employed as internal standard. Olive oil extract was analyzed by LC/ESI-MS/MS in positive ionization mode, with multireaction monitoring acquisition. Due to a signal suppression ranging between 4 and 23%, quantitation was performed by matrix-matched calibration curves. The regression line coefficients of determination were above 0.9991. Sample recoveries ranged from 92 to 107%, with relative standard deviations below 13% for spiking levels between 0.5 and 5 ng g⁻¹; method quantification limits ranged between 0.04 and 0.12 ng g⁻¹. The developed LC/ESI-MS/MS method, although not as sensitive as LC coupled to fluorescence detection, is rapid, selective, accurate and precise, thus it can be used as confirmatory assay. The MSPDE appears suitable for application to other oleaginous matrices and for multiresidue investigation.     

三腔渡越管振荡器高频结构的解析研究

 从圆柱坐标系下Borgnis位函数的齐次标量Helmholtz方程出发,引入慢波驻波概念及其场表达式,利用Borgnis位函数的边界条件及相邻子区公共界面上的场匹配条件,导出了三腔渡越管振荡器内角向均匀TM模的色散关系及场分布的解析表达式。运用该解析法求得三腔渡越管振荡器的谐振频率与实验中测得的微波频率一致,求得的场分布与数值法得到的场分布十分吻合。     

回旋行波管动力学分析及数值计算

 以小回旋电子注、均匀截面光滑壁圆柱波导为例,对回旋行波管动力学色散方程作了解析分析和讨论;数值计算和分析了注波互作用耦合系数与电子注参数的相互关系,为优化选择电子注参数,提高注波互作用效率获得了依据。     

八信道WDM色散补偿的实验研究

研制了一种啁啾的多波长光纤Bragg光栅 ,波长、波长间隔符合ITU T标准 ,利用这种多波长啁啾光栅可以同时对多信道波长进行色散补偿 ,这种啁啾的多波长光纤Bragg光栅能滤除反射峰之间未用波长范围内的放大器的自发辐射噪声 (ASE) ,并进行了 8× 10Gb/s 10 2km色散补偿实验 ,各信道补偿一致性很好。