Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method

An efficient numerical inverse radiation analysis based on the backward Monte Carlo (BMC) method is presented to determine the three-dimensional (3-D) temperature distribution in a large rectangular enclosure containing the participating medium, using radiative intensities in the visible range received by charge-coupled device (CCD) cameras. For large radiative sources and small detectors, when the radiation onto a small spot and onto a small direction cone is desired, the BMC method is more efficient than the forward Monte Carlo (FMC) method. Because the temperature reconstruction from the measured radiative intensities is an ill-posed inverse problem, least-square QR decomposition (LSQR) method is introduced to determine the meaningful temperature distribution. In order to gain insight into the effects on the accuracy of temperature distribution reconstruction, the detailed analyses are made using numerical simulations. The results show that the temperature distribution can be reconstructed accurately for the exact and noisy data.     

Geometrically nonlinear analysis with a 4-node membrane element formulated by the quadrilateral area coordinate method

Recently, a 4-node quadrilateral membrane element AGQ6-I, has been successfully developed for analysis of linear plane problems. Since this model is formulated by the quadrilateral area coordinate method (QACM), a new natural coordinate system for developing quadrilateral finite element models, it is much less sensitive to mesh distortion than other 4-node isoparametric elements and free of various locking problems that arise from irregular mesh geometries. In order to extend these advantages of QACM to nonlinear applications, the total Lagrangian (TL) formulations of element AGQ6-I was established in this paper, which is also the first time that a plane QACM element being applied in the implicit geometrically nonlinear analysis. Numerical examples of geometrically nonlinear analysis show that the presented formulations can prevent loss of accuracy in severely distorted meshes, and therefore, are superior to those of other 4-node isoparametric elements. The efficiency of QACM for developing simple, effective and reliable serendipity plane membrane elements in geometrically nonlinear analysis is demonstrated clearly.     

A second-order difference scheme for a parameterized singular perturbation problem

In this paper we consider a singularly perturbed quasilinear boundary value problem depending on a parameter. The problem is discretized using a hybrid difference scheme on Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independent of singular perturbation parameter. Numerical experiments support these theoretical results.     

[Cu(DPPZ)(L-Ser)]+与DNA的相互作用及其分析应用研究

研究了DNA与铜(Ⅱ)-L丝氨酸-二吡啶并[3,2-a:2',3'-c]吩嗪配合物[Cu(DPPZ)(L-Ser)-]+相互作用的共振光散射光谱和紫外可见吸收光谱,通过研究体系与溴化乙啶相互作用的荧光光谱特征,证明其作用方式为插入作用.在pH 7.2的缓冲溶液中,[Cu(DPPZ)(L-Ser)]+由于插入作用而在DNA表面聚集,使体系的共振光散射强度增强,最大敞射峰在400 nm处.在最佳实验条件下,共振光散射增强的强度与浓度在0.42～4.20 ng·mL1范围的DNA具有良好的线性关系.方法的检出限为0.29 ng·mL-1.该法用于DNA样品的测定,回收率在97.8%～106.0%之间.     

线-板式脉冲电晕放电反应器的发射光谱研究

以发射光谱法为基础,检测了常压状态线-板式脉冲电晕放电过程OH自由基在反应器内的空间分布;研究了线电极直径,线线间距以及线板间距对生成OH自由基的影响;从而明确脉冲电晕放电反应器的性能。结果显示:OH自由基浓度沿线电极X轴方向逐渐降低,活化区域半径20mm左右,沿Y轴方向先升高后降低,活化区域半径大于30mm;线电极的直径小于2mm时,OH自由基的光谱强度基本不变,线电极直径继续增大,发射光谱强度随之迅速下降。线线间距逐渐增大,OH自由基的发射光谱强度随之增强。OH自由基的发射光谱强度随着线板间距的增大而降低。     

An almost second order uniformly convergent scheme for a singularly perturbed initial value problem

In this paper a nonlinear singularly perturbed initial problem is considered. The behavior of the exact solution and its derivatives is analyzed, and this leads to the construction of a Shishkin-type mesh. On this mesh a hybrid difference scheme is proposed, which is a combination of the second order difference schemes on the fine mesh and the midpoint upwind scheme on the coarse mesh. It is proved that the scheme is almost second-order convergent, in the discrete maximum norm, independently of singular perturbation parameter. Numerical experiment supports these theoretical results.     

Perturbation solution to heat conduction in melting or solidification with heat generation

The Stefan problem involving a source term is considered in this technical note. As an example, planar solidification with time-dependent heat generation in a semi-infinite plane is solved by use of a perturbation technique. The perturbation solution is validated by reducing the problem to the case without heat generation whose exact solution is available. An application to the case with constant heat generation is presented, for which a closed-form solution is obtained. The effects of heat generation and Stefan number on the evolution of solidification are examined using the perturbation solution.     

A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems

A system of coupled singularly perturbed initial value problems with two small parameters is considered. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solution of the system has boundary layers that overlap and interact. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh a hybrid finite difference scheme is proved to be almost second-order accurate, uniformly in both small parameters. Numerical results supporting the theory are presented.     

四阶奇异摄动边值问题在自适应网格上的一致收敛分析

we study a difference scheme for the fourth-order singular pertur-bation differential equation on the Bakhvalov-Shishkin grid by Green‘‘s function.The method is shown to be uniformly convergent with respect to the perturbation parameter,of order N^-2 in the maxmum norm on Bakhvalov-Shishkin meshes.Numerical results support our theoretical results.