分片光滑物态方程的能量方程非线性迭代解法

实际应用中的物态方程由分片光滑曲面拼接而成,拼接处存在间断.隐式求解相应的能量方程时,经常出现迭代收敛慢的情况和非物理解.本文通过构造对应的新的非线性问题,提出一种非线性迭代算法.该算法适用于求解有间断的分片光滑物态方程的非线性能量方程,其中引入一个度量能量变化的参数用于自动判断跳段是否发生,在求解时无需事先知道物态方程间断的位置,且能精确计算物态方程间断带来的能量盈亏,用于评估物态方程间断对能量的影响.典型算例验证了新算法具有稳定的收敛性,并给出符合物理规律的解.     

d2,8电子体系共价效应对光谱的影响

在含过渡金属离子的半磁半导体的光学和磁学性质研究中,由于体系的共价性较强,d轨道不再是纯d轨道,而是混合轨道t2g或eg。相应地,需要引入两个共价因子Nt和Ne。建立在混合轨道上的含有共价因子的能量矩阵称为广义能量矩阵。建立了d2,8电子体系的(45×45)阶广义能量矩阵。在广义能量矩阵中,拉卡(Racah)参量A不再是相加常量,同时,d8电子体系不能简单地视为互补的d2空穴体系,因为它们的能量矩阵形式不同。Nt和Ne虽然是属于两个不同轨道的不同的共价因子,但在数值上不能有大的差别,因为考虑进共价效应后,拉卡静电参量A对能级计算有极大的影响。这意味着在通常的光谱拟合中所采用的BCΔ方案是好的近似。以上结论被应用于ZnS∶Ni2 的d-d跃迁谱,计算结果与实验符合。     

Diatomic gasdynamic lasing molecules as quantum quasi-harmonic oscillators

We investigate the role played by the molecules as quantum oscillators in a diatomic gasdynamic laser by considering quasi-harmonic behaviour within the context of one-dimensional quantum anharmonic oscillators. Vibrational energy levels depending upon a parameter relative to anharmonicity are discussed in terms of the values taken on by this parameter and the values taken on by the vibrational quantum number.     

Bulk and boundary effects in a one-dimensional water-like fluid

Sites of a one-dimensional lattice may be either vacant or occupied by molecules with two orientational states, a ‘monomer’ state taking up one site and a ‘dimer’ state taking up two sites. There is a nearest-neighbour energy — ε for all molecules and an additional bonding energy — ω for adjacent dimers. Hence low temperatures and pressures favour an open structure with molecules predominantly in the dimer state. Bulk behaviour is investigated by both matrix and combinatorial methods and maxima in density isobars and minima in isothermal compressibility curves are found at certain parameter values. These are anomalous properties similar to those occurring in fluid water.

Boundary effects in a chain with end sites are calculated by matrix methods for several types of boundary condition. The effect on the open structure is measured by the change in the number of dimer-dimer bonds due to the presence of the boundary. For a ‘structure-breaking’ boundary, which forces the adjacent molecule into the monomer state, occupation probabilities near the boundary are compared with bulk values. It is concluded that boundary effects in the fluid are confined to the first few layers of molecules.     

Quantum groups of motion and rotational spectra of heavy nuclei

A simple model of rotator based on the q-Poincaré energy mass relation describes the rotational levels of even-even nuclei. Owing to the presence of the q-deformation, although the rotational velocities result is of the order of 10⁻³ c, the behaviour is completely different from the usual rigid rotator. The quantum deformation parameter introduces a time scale that is of the order of the characteristic time of the strong interaction. The second free parameter, the radius of the nucleus, gives the right nuclear dimensions. The two-parameter energy fit is very good, even in comparison with the su_q(2) based model. Although describing only single band effects, the model gives the correct experimental values where backbending or upbending occur.     

Properties of ordering alloys ofβ-brass type in a model incorporating correlation and the order dependence of lattice parameters

The statistical theory is applied to ordering in a B2 superlattice (CuZn alloy) with allowance for correlation and the distance dependence of the pair-interaction energy. The theoretical temperature dependence for the long-range-order parameter agrees quite well with that observed, as does the lattice parameter, the configuration specific heat, and the specific-heat discontinuity at the order-disorder transition for CuZn.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 9, pp. 7–11, September, 1971.The authors are indebted to L. E. Popov for useful discussion.     

A simple molecular statistical treatment of a model for cholesterics

The cholesteric state is discussed in terms of a model consisting of the Maier-Saupe and a twist interaction. The model can be easily solved in the mean field approximation. In the practical case of a large pitch analytical expressions are obtained for relevant quantities like the order parameters and the free energy. Then it appears that the pitch is temperature independent, which is a general result, and does not influence the discontinuity of the main (nematic) order parameter at the isotropic-cholesteric transition. Interactions giving rise to a temperature-dependent pitch are discussed briefly.     

Strain incompatibility and its influence on grain coarsening during cyclic deformation of ARB copper

It is well known that the characteristic length scale in ultra-fine grained and nanocrystalline metals has a significant effect on the mechanical behaviour. The inhibited ability to accommodate imposed strain with conventional dislocation mechanism has led to the activation of unconventional deformation mechanisms. For one, grain coarsening at shear bands has been observed to occur within metals with sub-micron grain size upon cyclic deformation. Such grain coarsening is often linked to the observed cyclic softening behaviour. The purpose of this study was to investigate the relationship between strain localisation associated with shear banding and the observed deformation-induced grain coarsening in ultra-fine grained metals. The investigation was carried out using ultra-fine grained, oxygen-free high conductivity copper processed by accumulative roll-bonding. A close relationship between strain localisation and deformation-induced grain coarsening was revealed. As strain localisation is not only found at shear bands, but also at other places whereby heterogeneous microstructure or geometric discontinuity is present, hence the present study bears a general significance. Such strain localisation sites may also include a hard constituent embedded in a relatively ductile matrix, micro-crack tips and artificial notches. The stress concentration at these sites provides a high input of strain energy for grain boundary motion leading to grain coarsening. Furthermore, when the grain size is very small, the stress gradient leading away from the stress concentration sites is also believed to increase the driving force for grain boundary migration within the affected regions.     

Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges

For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion determinant. For the parameter dependent Gaussian and Laguerre ensembles the matrix elements of the determinant are expressed in terms of corresponding skew-orthogonal polynomials, and their limiting value for infinite matrix dimension are computed in the vicinity of the soft and hard edges respectively. A connection formula relating the distributions at the hard and soft edge is obtained, and a universal asymptotic behaviour of the two point correlation is identified.     

Frenkel type defects and the melting of silver halide crystals

The author assumes that the melting of the crystals is connected with the passage of ions into interstitial positions. He introduces the assumption about the dependence of the energy of the crystal on the degree of order and from the above by the method of statistical thermodynamics he calculates the free energy of the crystal as a function of the temperature and a parameter characterizing the degree of order. By a discussion of the isotherms of the free energy he then obtains the melting temperature at which the degree of order changes suddenly. From this discontinuity the latent heat and the entropy can be determined. The calculated values are in good agreement with experiment.     

Regularizing a vortex sheet near a separation point

Current methods for computing vortex sheet separation use a regularization parameter which is discontinuous from the body to the vortex sheet. We propose two methods for reducing the errors associated with the discontinuity and improving convergence with respect to the regularization parameter. The “velocity smoothing” method is the simpler of the two, and removes the discontinuity in regularization from one of the two equations where it occurs. The “tapered smoothing” method removes the discontinuity from both equations. In a model problem, both methods are found to converge much more rapidly (with exponents 3/2 and 2 versus 1/2 for the standard method) as the regularization parameter tends to zero. Unsteady algorithms are proposed for evolving the free sheet using the two methods, and are tested in a benchmark problem. Accuracy is significantly improved for similar computational expense.     

衍折射设计用于均匀照明的衍射光学器件

 在工艺上衍射光学元件是通过相位板来实现的,由于其多台阶化产生的不连续性,会对目标光场产生sinc调制,产生高级次衍射斑,损失了15%或者更多能量。通过对设计衍射光学器件的传统的IO迭代算法进行了研究,提出了一种与衍折射相结合的设计方法,在衍射光学器件的部分区域形成一块连续相位区域,减少了相位片台阶化区域的光强和衍射斑的强度。通过逐步变化连续相位对输出光强情况的影响的研究,可以优化相位参数,使入射到输出面的光束保证一定匀滑性的前提下,提高目标光场区域的衍射效率达到90%以上,能够满足均匀照明的要求。     

高能中性束注入加热

本文仔细地研究了高能中性束注入加热的有关问题,利用多束模型计算了中性束注入加热。本文的主要特点是在捕获快离子与本底离子和电子能量交换表示式中,直接用误差函数积分进行计算,而不像以前的计算中作大参量和小参量展开近似。当快离子能量比较低时,大参量展开不再适用,因此本文的计算更为精确,更为有用。给出了多束注入加热的计算结果及其结果的讨论。本计算方法可与输运方程联立求解,数值模拟等离子体行为。     

Theoretical study of spin-singlet contributions to zero-field splitting of a 3d6 ion in a trigonal ligand field and applications to Fe2+ in FeSiF6 · 6H2O and FeCO3

The complete energy matrix (210 × 210) for d⁶(d⁴) configuration ions in a trigonal ligand field is constructed. The energy levels and zero-field splitting parameters in ferrous fluosilicate and ferrous carbonate are studied. The contributions of spin singlets to zero-field splitting parameters in a trigonal ligand field are investigated for the first time. The calculation results indicate that the spin-singlet contribution to second-order zero-field splitting parameter D is negligible, but the contributions to fourth-order zero-field splitting parameter a ? F cannot be neglected. Moreover, it is found that the stronger the trigonal ligand field, the larger are the spin-singlet contributions to the zero-field splitting parameters.     

Elliptic behaviour in the sawtooth standard map

This paper examines the standard map with sawtooth nonlinearity when the eigenvalues of the Jacobian lie on the unit circle. This is an area-preserving map of the torus to itself that is linear except on a line on which it is discontinuous. We discuss the closure of the set of images of the discontinuity and present numerical evidence that its Lebesgue measure is positive. Moreover, we present evidence that the measure of the closure of images of the discontinuity changes continuously with the parameter k. This means that the sawtooth standard map may exhibit coexistence of two positive measure subsets on which the dynamics is respectively regular and irregular in a certain sense. In the appendix we show that this map is equivalent to a map studied by electronics engineers as a model for the quiescent behaviour of a linear lossless digital filter with “two's complement” overflow.     

Interfaces in metal matrix composites

The interface region in a given composite has a great deal of importance in determining the ultimate properties of the composite. An interface is, by definition, a bidimensional region through which there occurs a discontinuity in one or more material parameters. In practice, there is always some volume associated with the interface region over which a gradual transition in material parameter(s) occurs. The importance of the interface region in composites stems from two main reasons: (i) the interface occupies a very large area in composites, and (ii) in general, the reinforcement and the metal matrix will form a system that is not in thermodynamic equilibrium. One can discuss the interface in a composite at various levels. An optimum one should be neither so simple that it covers only a few special cases nor so complex that it is not useful in designing composites from processing and applications points of view. In this paper, my objective is to give examples of interface microstructure in different metal matrix composite systems and suggest some ways of controlling the interface characteristics in order to control the properties of the composite. I shall give examples of the interface microstructure in different metal matrix composites (particle and fiber reinforced as well as laminates) and discuss some of the important implications on various aspects of metal matrix composites, from the processing stage to ultimate performance of the composite.     

低能轻离子输运的单参数描述

低能离子输运的一个重要特点是它有可能被一个简单的参数所确定，我们发现离子的标度输运截面即是具有这种重要性质的参数。这种单值对应关系反映了不同能量的不同靶一离子的组合在输运上的内在相似性。本文给出了标度输运截面的定义，讨论了此标度参数标定离子输运行为的理论依据。同时通过应用离子输运双群模型所作的大量计算检验了单参数标定离子输运行为这一结论。最后给出以标度输运截面为自变量的离子反射系数和平均投影射程的经验公式。 关键词：     

Effect of solute atoms on fracture toughness in dilute magnesium alloys

The effect of alloying elements on the toughness and the fracture behaviour was investigated on seven kinds of Mg-0.3?at.% X (X?=?Ag, Al, Ca, Pb, Sn, Y and Zn) alloys with a grain size of 3–5?μm. The fracture toughness and fracture behaviour in magnesium alloys were closely related to the segregation energy. The Mg–Al and –Zn alloys that had small segregation energy showed high toughness and ductile fracture in most regions, while the Mg–Ca alloy with large segregation energy exhibited low toughness and intergranular fracture. These different tendencies resulted from solute segregation at grain boundaries (GBs). The change in the lattice parameter ratio was the influential material parameter regardless of whether the GB embrittlement was for enhancement or suppression.     

Extended Taylor series and interpolation of physically meaningful functions

An extension of the concept of the Taylor series to arbitrary functions that are physically meaningful is presented. The series is obtained using a matrix to describe the behaviour of the function at any position of discontinuity while performing the Taylor series expansion in the rest of the considered domain. The matrix is derived from the continuity conditions that are inherent to a particular physical problem. This allows an introduction of function classes that are relevant from the physical problem point of view. Several illustrative examples of physically meaningful function classes are derived. It is then demonstrated that using the derived function classes and the concept of the extended Taylor series one can obtain the interpolation formulae fitted for a particular class of physically meaningful functions. The application of the interpolation formulae based on these novel concepts shows clear advantages over the standard approach. Finally, it is also shown that the developed concept of the extended Taylor series and classes of physically meaningful functions can be used for the extrapolation and an elegant derivation of finite difference approximations for physical problems.