带电粒子光学系统优化问题的研究

对带电粒子光学系统的优化过程进行了研究,提出将象差的优化与透镜场形的优化分离开来。在象差的优化中考虑含光学参数的隐式约束条件。该优化过程只需做简单的积分运算,因此不必花费时间计算电磁场。在透镜场形的优化中,其优化模型与一般电磁系统的优化完全一样,因而可以采用已经研究的很多的电磁场的优化方法来优化透镜的场形。计算了两个优化的实例。     

Free‐Radical Propagation Rate Coefficients via n‐Pulse Periodic Polymerization

Aspects of applying n‐pulse periodic initiation in pulsed laser polymerization/size‐exclusion chromatography (PLP/SEC) experiments are studied via simulation of molecular weight distributions (MWDs). In n‐pulse periodic PLP/SEC, sequences of n laser pulses at successive time intervals Δt₁ up to Δt_n are periodically applied. With the dark time intervals being suitably chosen, n‐modal MWDs with n well separated peaks occur. The n‐pulse periodic PLP/SEC method has the potential for providing accurate propagation rate coefficients, k_p. Among several measures for k_p, the differences in molecular weights at the MWD peak positions yield the best estimate of k_p under conditions of medium and high pulse laser‐induced free‐radical concentration. Deducing k_p from n dark time intervals (corresponding to n regions of free‐radical chain length) within one experiment at otherwise identical PLP/SEC conditions allows addressing in more detail a potential chain‐length dependence of k_p. Simulations are compared with experimental data for 2‐pulse periodic polymerization of methyl methacrylate.

Measured MWD (solid line) and associated first derivative curve (dotted line) for a 2‐pulse periodic bulk polymerization experiment of MMA at 20 °C.     

Octonionic Yang–Mills instanton on quaternionic line bundle of Spin(7) holonomy

The total space of the spinor bundle on the four-dimensional sphere S⁴ is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang–Mills instanton on this eight-dimensional gravitational instanton. This is a higher dimensional generalization of (anti-) self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang–Mills field and derive a system of non-linear ordinary differential equations. The solutions are classified according to the asymptotic behavior at infinity. We give a complete solution when the gauge group is reduced to a product of SU(2) subalgebras in Spin(7). The existence of more general Spin(7) valued solutions can be seen by making an asymptotic expansion.     

类镍金离子的双电子复合速率系数

 在自旋轨道劈裂阵模型下, 理论计算在0.02keV≤T≤10keV范围内,类镍金Au⁵¹⁺的3d⁹nln''l''(n''=4,5,6; l''=s,p,d,f)双电子复合速率系数,并分析了影响双电子复合速率系数的主要因素。     

Stress in transversely isotropic half-space with typical loads acting on its surface

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Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

A Two-Step Smoothing Method for Varying-Coefficient Models with Repeated Measurements

Datasets involving repeated measurements over time are common in medical trials and epidemiological cohort studies. The outcomes and covariates are usually observed from randomly selected subjects, each at a set of possibly unequally spaced time design points. One useful approach for evaluating the effects of covariates is to consider linear models at a specific time, but the coefficients are smooth curves over time. We show that kernel estimators of the coefficients that are based on ordinary local least squares may be subject to large biases when the covariates are time-dependent. As a modification, we propose a two-step kernel method that first centers the covariates and then estimates the curves based on some local least squares criteria and the centered covariates. The practical superiority of the two-step kernel method over the ordinary least squares kernel method is shown through a fetal growth study and simulations. Theoretical properties of both the two-step and ordinary least squares kernel estimators are developed through their large sample mean squared risks.     

Positron Emission Tomography and Random Coefficients Regression

We further explore the relation between random coefficients regression (RCR) and computerized tomography. Recently, Beran et al. (1996, Ann. Statist., 24, 2569–2592) explored this connection to derive an estimation method for the non-parametric RCR problem which is closely related to image reconstruction methods in X-ray computerized tomography. In this paper we emphasize the close connection of the RCR problem with positron emission tomography (PET). Specifically, we show that the RCR problem can be viewed as an idealized (continuous) version of a PET experiment, by demonstrating that the nonparametric likelihood of the RCR problem is equivalent to that of a specific PET experiment. Consequently, methods independently developed for either of the two problems can be adapted from one problem to the other. To demonstrate the close relation between the two problems we use the estimation method of Beran, Feuerverger and Hall for image reconstruction in PET.     

横观各向同性半无限空间表面典型荷载作用下的地基附加应力系数

在胡海昌和Lekhnitskii解的基础上,求得了地基表面作用竖直载荷时的附加应力系数的统一表达式,它可同时适用于各向同性和横观各向同性地基材料。详细讨论了5种典型载荷工况:圆形均布荷载、矩形均布荷载、矩形三角形分布荷载、均布线性和条形荷载。解的最终结果可由初等函数表示。文中同时也通过数值例子图示了材料各向异性对附加应力系数的影响。     

一类非线性变系数差分方程平衡点的全局吸引性

本利用相关的差分方程的全局吸引性研究了一类具时滞的非线性变系数差分方程ｘｎ＋１＝ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ１－ｃｘｎ－ｋ）的正平衡点ｘ＾－＝１的全局吸引性,获得了一个好的充分条件。