电子系统的统计理论

本文用统计微扰理论的模拟法来计算热力学平衡电子系统的热力学量。利用Feynman图形的分析法及最发散图形求和的概念,计算了热平衡电子系统(包含有点电荷的不均匀情况)由于相互作用所引起的热力学势的改变和比热等。把所计算的结果用介电常数表示出来,并进行了一定的讨论。     

金等离子体中Au48+-Au52+平衡分布的统计热力学研究

基于全相对论多组态Dirac Fock理论 ,采用“多功能相对论原子结构程序 (GRASP2 )” ,考虑量子电动力学 (QED)效应和Breit修正 ,涉及实验谱中Au等离子体M带的几类重要跃迁 ,计算了Au4 8 —Au52 离子的能级结构和能级简并度 .用统计热力学方法计算各离子的配分函数 ,由配分函数计算等离子体内这五种离子的电离与复合平衡常数 ,根据同时反应的平衡理论研究电离与复合达到平衡时等离子体内各离子的相对分布基于全相对论多组态Dirac Fock理论 ,采用“多功能相对论原子结构程序 (GRASP2 )” ,考虑量子电动力学 (QED)效应和Breit修正 ,涉及实验谱中Au等离子体M带的几类重要跃迁 ,计算了Au4 8 —Au52 离子的能级结构和能级简并度 .用统计热力学方法计算各离子的配分函数 ,由配分函数计算等离子体内这五种离子的电离与复合平衡常数 ,根据同时反应的平衡理论研究电离与复合达到平衡时等离子体内各离子的相对分布     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

任意形状瞳孔的光学传递函数的计算及光学传函与价值函数之间的关系

本文提出了一种不用传统的表面平滑而计算光学传递函数的方法,用简单的求和来代替面积分.此外,用此方法,可将传递函数作为改善计算的价值函数.     

类氦铷、铌离子光电离截面的细致计算

采用ＨＦ加相对论修正的ＨＦＲ方法，考虑束缚组态间的相互作用，计算了类氦铷与类氦铌离子各能级间跃迁的光电截面，所包括的离子组态为１ｓｎｌ—１ｓεｌ±１（１≤ｎ≤６、０≤ｌ≤ｎ－１），取自由电子能量区间为０～１０倍的离化能，分析了系统计算误差与计算精度，给出了对未态求和及三次样条插值后的结果。     

电子枪与像管等真空电子束器件的辅助设计

本文应用差分迭代的数值方法和热电子发射的统计理论,编写了一个用于设计计算电子枪、静电透镜和各类像管的通用软件包,并能用CAD绘出各种图表。文中给出一些实例,其计算结果均与实测或资料给出的相符。文中还提出了最佳统计像曲的概念,以及等位线的追迹和电子束管中有关离子轨迹的追迹方法等。     

金等离子体中Au48+—Au52+平衡分布的统计热力学研究

基于全相对论多组态Dirac-Fock理论，采用“多功能相对论原子结构程序(GRASP2)”，考虑量子电动力学(QED)效应和Breit修正，涉及实验谱中Au等离子体M带的几类重要跃迁，计算了Au48+—Au52+离子的能级结构和能级简并度.用统计热力学方法计算 各离子的配分函数，由配分函数计算等离子体内这五种离子的电离与复合平衡常数，根据同 时反应的平衡理论研究电离与复合达到平衡时等离子体内各离子的相对分布. 关键词： 金等离子体 配分函数 平衡常数 离子丰度     

基态类Ne锗离子双电子复合的半相对论计算

采用半相对论多组态Ｈａｒｔｒｅｅ一Ｆｏｃｋ模型，计算了类Ｎｅ锗离子经过３ｌ３ｌ＇和４ｌ４ｌ＇双激发态到类Ｎａ离子单激发态的态对态双电子复合速率系数，同时给出了描写上述复合过程的参数Ｂ和。通过对求和而获得的部分双电子复合速率系数与其它理论计算结果进行了比较。     

类硼离子基态的精细结构(英文)

以多电子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,建立了类硼离子基态精细结构能量的解析表达式.完成了所有角向积分和自旋求和计算,使精细结构能量表示为若干个径向积分之和.在此基础上计算了类硼体系(Z=5~8)基态精细结构能量,计算结果与实验数据符合得较好.     

类氟离子基态的精细结构

以多电子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,建立了类氟离子基态精细结构能量的解析表达式.完成了所有角向积分和自旋求和计算,使精细结构能量表示为若干个径向积分之和.在此基础上对类氟体系(Z=9～13)基态的精细结构能量进行了具体计算,计算结果与实验数据符合得较好.     

离子组态效应对电子传导不透明度的影响

 基于相对论Hartree-Fock-Slater 自洽场原子结构模型, 考虑电子-离子间的弹性散射机制, 用分波法和扩展的Ziman 公式对电子传导不透明度作了计算。考虑到等离子体离子环境的影响, 不仅引进了等离子体的结构因子, 而且更细致地考虑了等离子体内离子类型 (组态) 对电子传导     

Entropic Formulation of Statistical Mechanics

We present an alternative formulation of Equilibrium Statistical Mechanics which follows the method based on the maximum statistical entropy principle in Information Theory combined with the use of Massieu–Planck functions. The different statistical ensembles are obtained by a suitable restriction of the whole set of available microstates. The main advantage is that all of the equations that relate the average values with derivatives of the partition function are formally identical in the different ensembles. Moreover, Einstein's fluctuation formula is also derived within the same framework. This provides a suitable starting point for the calculation of fluctuations of extensive and intensive variables in any statistical ensemble.     

An analysis of BCS solutions with realistic interactions

We adopt the principle that the BCS solution can be regarded as a generating function for ground states of neighbouring nuclei. A parametrisation of the binding energy in terms of the number of particles is assumed and the assumption tested. Using an ansatz from statistical mechanics, a formula for the distribution of the number of particles is developed and the formula is shown to give accurate answers. The concept of temperature is introduced and its interpretation in many-particle theory is clarified.     

Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in favor. Based upon the principle of evidence, it is shown how to measure and control these biases for both hypothesis assessment and estimation problems. Optimality results are established for the principle of evidence as the basis of the approach to these problems. A close relationship is established between measuring bias in Bayesian inferences and frequentist properties that hold for any proper prior. This leads to a possible resolution to an apparent conflict between these approaches to statistical reasoning. Frequentism is seen as establishing figures of merit for a statistical study, while Bayes determines the inferences based upon statistical evidence.     

Physical properties of voltage gated pores

Experiments on single ionic channels have contributed to a large extent to our current view on the function of cell membrane. In these experiments the main observables are the physical quantities: ionic concentration, membrane electrostatic potential and ionic fluxes, all of them presenting large fluctuations. The classical theory of Goldman–Hodking–Katz assumes that an open channel can be well described by a physical pore where ions follow statistical physics. Nevertheless real molecular channels are active pores with open and close dynamical states. By skipping the molecular complexity of real channels, here we present the internal structure and calibration of two active pore models. These models present a minimum set of degrees of freedom, specifically ion positions and gate states, which follow Langevin equations constructed from a unique potential energy functional and by using standard rules of statistical physics. Numerical simulations of both models are implemented and the results show that they have dynamical properties very close to those observed in experiments of Na and K molecular channels. In particular a significant effect of the external ion concentration on gating dynamics is predicted, which is consistent with previous experimental observations. This approach can be extended to other channel types with more specific phenomenology.     

Sensitivities of ionic explosives

ABSTRACT

We have investigated the relevance for ionic explosive sensitivity of three factors that have been demonstrated to be related to the sensitivities of molecular explosives. These are (1) the maximum available heat of detonation, (2) the amount of free space per molecule (or per formula unit) in the crystal lattice and (3) specific features of the electrostatic potential on the molecular or ionic surface. We find that for ionic explosives, just as for molecular ones, there is an overall tendency for impact sensitivity to increase as the maximum detonation heat release is greater. This means that the usual emphasis upon designing explosives with large heats of detonation needs to be tempered somewhat. We also show that a moderate detonation heat release does not preclude a high level of detonation performance for ionic explosives, as was already demonstrated for molecular ones. Relating the free space per formula unit to sensitivity may require a modified procedure for ionic explosives; this will continue to be investigated. Finally, an encouraging start has been made in linking impact sensitivities to the electrostatic potentials on ionic surfaces, although limited so far to ammonium salts.     

Theory of atomic spectral emission intensity

The theoretical derivation of a new spectral line intensity formula for atomic radiative emission is presented. The theory is based on first principles of quantum physics, electrodynamics, and statistical physics. Quantum rules lead to revision of the conventional principle of local thermal equilibrium of matter and radiation. Study of electrodynamics suggests absence of spectral emission from fractions of the numbers of atoms and ions in a plasma due to radiative inhibition caused by electromagnetic force fields. Statistical probability methods are extended by the statement: A macroscopic physical system develops in the most probable of all conceivable ways consistent with the constraining conditions for the system. The crucial role of statistical physics in transforming quantum logic into common sense logic is stressed. The theory is strongly supported by experimental evidence.     

基于畸变透镜孔衍射的激光束型转变

为了研究用畸变透镜孔产生的不同束型的精细激光束,先由基尔霍夫衍射公式得到高斯光束微圆孔衍射积分式,然后再经适当推理得到高斯光束通过畸变透镜孔的菲涅耳衍射的计算式,进而探讨了畸变透镜孔菲涅耳衍射对高斯光束进行束型转变的原理。用Matlab软件进行计算机模拟实验,表明了这种方法和技术是可行的。这种激光束整形技术可产生用于微细加工的不同束型的精细激光束。     

Simple variational approach to the thermal properties of ionic crystals

The thermal properties of ionic crystals are analysed using the variational principle of classical statistical mechanics. The Einstein and Debye pictures of the lattice vibrations are adopted as trial Hamiltonians. No explicit calculation of the lattice spectrum is needed. The variational result for the thermal expansion in the Einstein picture is identical to that recently derived by Narayan and Ramaseshan by a physically motivated thermal force picture. The agreement with experimental values in the alkali halide family of crystals is surprisingly good, the root mean square error being about 14%. The parameters in the interionic potential used are obtained from the lattice spacings and compressibilities of the crystals and not from anharmonic properties. The Debye picture gives about equally good results for the thermal expansion, but better results for the thermal vibration amplitudes of the ions. It differs from the Einstein picture in incorporating correlated vibrations of atoms and in having an explicit Coulomb contribution to the thermal properties. It is suggested that the theory given in this paper has a useful role to play in studies of thermal expansion and phase stability for large families of ionic crystals when combined with semi-empirical theories.     

天然裂缝储层压裂定向井稳态产量的蒙特卡洛计算

针对各向异性天然裂缝储层,蒙特卡洛随机模拟天然裂缝分布,从统计学角度表征天然裂缝参数,根据势叠加原理,把天然裂缝和人工裂缝当成独立的源进行势叠加,考虑天然裂缝和人工裂缝的耦合作用,建立压裂定向井稳态产量计算公式.计算结果表明,基于蒙特卡洛的天然裂缝模拟能从统计学角度反映产量变化趋势,能快速分析压裂定向井稳态产能.