Some Aspects of the Implementation of Scaling Quantum Mechanical Molecular Force Fields

Some features of software implementation of the Pulay scaling procedure are considered. The advantages of the single value decomposition method for maintaining well-conditionality of the scale factor determination problem are demonstrated. The necessity of using a rational number of scale factors is shown. The possibility of obtaining transferable scale factors with the Pulay method and thus predict the vibrational spectra of related compounds is emphasized.     

Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

Strongly polynomial-time approximation for a class of bicriteria problems

Consider the following problem: given a ground set and two minimization objectives of the same type find a subset from a given subset-class that minimizes the first objective subject to a budget constraint on the second objective. Using Megiddo's parametric method we improve an earlier weakly polynomial time algorithm.     

非饱和土本构关系的混合物理论(Ⅱ)--线性本构方程和场方程

通过对非饱和土非线性本构方程和场方程的线性化，推导出了非饱和土的线性本构方程和场方程，把线性方程表示为与Biot饱和多孔介质方程相似的形式；证明了Darcy定律对非饱和土的适用性；说明了Biot饱和多孔介质方程是这些线性方程的特征。所有这些都表明用混合理论处理非饱和土本构问题的正确性。     

晶体微观结构的数值计算

晶体微观结构是晶体材料在特定物理条件下其多个能量极小平衔态在空间形成的某种微尺度的规则分布．几何非线性的连续介质力学理论可以用能量极小化原理来解释晶体微观结构的形成，并用Young测度来刻画平衡态各变体在空间的概率分布．定性的理解与定量地分析和计算晶体材料的微观结构对于发展和改进高级晶体功能材料，如形状记忆合金、铁电体、磁至伸缩材料等，有重要的意义．本文回顾了近年来晶体微观结构数值计算方面的最新进展．介绍了计算晶体微观结构的几种数值方法及有关的数值分析结果。     

基于粗糙集理论的知识约简及应用实例

在保持分类能力不变的前提下 ,通过利用粗糙集理论中的知识约简方法 ,在保护知识库分类不变的条件下 ,删除其中不相关或不重要的知识 ,从而导出问题的决策 .利用基于决策表的粗糙集模型算法 ,实例分析如何数字化表示决策表 ,并对其进行属性约简和属性值的约简 ,从而提取决策规则 .     

脉冲充磁的超导圆盘的电流密度和俘获场分布的研究

本从第一性原理出发，计算了充磁线圈产生的磁场，脉冲充磁的超导圆盘中的感应电流密度和俘获场分布．以超导体中的电流运动方程为基础，通过磁通动力学方程E=Ec(J/Jc)^n和物质方程B=μ0H表示超导圆盘的超导特性．计算表明第一个脉冲充磁电流的峰值和磁通蠕动指数对于超导圆盘中的感应电流分布非常重要．同时研究了充磁电流的宽度，波形，第二个充磁电流的峰值和充磁线圈的形状对于俘获场的影响．计算表明不断减小脉冲充磁电流峰值的反复充磁可以保持超导圆盘中的感应电流密度的平台在一确定水平．     

Electromagnetic energy flow near nanoparticles—I: single spheres

The electromagnetic (EM) energy flow near single spheres is investigated by applying Mie theory. From the patterns of the energy flow, the absorption and the scattering of light can be understood in the microscopic point of view. In the absorption profiles of metallic particles, most absorbed energy is consumed on the surface of the particles, which indicates that the resonance of surface plasmon is different from that of the bulk plasmon. Two mechanisms to enhanced local EM field are also distinguished. One is the surface plasmon resonance, and another one is the intensified energy flow.     

单调全局最优化问题的凸化外逼近算法

单调优化是指目标函数与约束函数均为单调函数的全局优化问题．本文提出一种新的凸化变换方法把单调函数化为凸函数，进而把单调优化问题化为等价的凸极大或凹极小问题，然后采用Hoffman的外逼近方法来求得问题的全局最优解．我们把这种凸化方法同Tuy的Polyblock外逼近方法作了比较，通过数值比较可以看出本文提出的凸化的方法在收敛速度上明显优于Polyblock方法．     

Single-electron charging spectra: from natural to artificial atoms

We present a theoretical study of the charging spectra in natural and artificial atoms. We apply a model electrostatic potential created by a homogenously charged sphere. This model potential allows for a continuous passage from the Coulomb potential of the nucleus to parabolic confinement potential of quantum dots. We consider electron systems with N=1,…,10 electrons with the use of the Hartree–Fock method. We discuss the qualitative similarities and differences between the chemical potential spectrum of electron systems bound to nucleus and confined in quantum dots.