Efficient computer implementation of the renormalized coupled-cluster methods: The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) approaches

The recently proposed renormalized (R) and completely renormalized (CR) coupled-cluster (CC) methods of the CCSD[T] and CCSD(T) types have been implemented using recursively generated intermediates and fast matrix multiplication routines. The details of this implementation, including the complete set of equations that have been used in writing efficient computer codes, memory requirements, and typical CPU timings, are discussed. The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) computer codes and similar codes for the standard CC methods, including the LCCD, CCD, CCSD, CCSD[T], and CCSD(T) approaches, have been incorporated into the gamess package. Information about the main features of this new set of CC programs is provided.     

PIII treatment of Ti alloys and NiTi for medical applications

PIII is a powerful method to obtain hard and wear resistant surface on Ti alloys and NiTi by oxygen or nitrogen implantation. By adjusting the temperature, treatment time and heating regime, different phase compositions and layer thickness can be obtained. Depending on the specific system, a strong influence of the resulting microstructure on the wear and fatigue properties was observed. By considering these restrictions, successful animal tests can be designed and executed, as shown in this review article.     

累积正态分布函数的逼近函数综述

Fisher z变换是一个显式的初等函数,用来逼近累积正态分布函数（标准正态分布的累积分布函数）。介绍了累积正态分布函数逼近函数的评价标准,对有代表性的逼近函数表达式及相应的最大距离误差值进行归纳总结。     

Behavior of residual carbon in Sm(Co, Fe, Cu, Zr)z permanent magnets

When sintered Sm(Co, Fe, Cu, Zr)_z permanent magnets are prepared by metal injection molding, some organic binders are added in alloy powder, which leads to much residual carbon in the magnets. The residual carbon decreases magnetic properties and destroys the microstructure of the magnets. In this paper, the behavior of carbon in Sm(Co, Fe, Cu, Zr)_z permanent magnets has been studied. The results indicate that Sm(Co, Fe, Cu, Zr)_z magnets can keep excellent magnetic properties when the carbon content is below 0.1 wt.%: Br ≥ 10 kGs, H_cj ≥ 22 kOe, BH_max ≥ 25 MGOe. When the carbon content is above 0.1 wt.%, Br, H_cj and BH_max decrease with increasing carbon content evidently. Carbon consumes Zr content and forms ZrC, which reduces the volume fraction of the lamella and Sm(Co, Cu)₅ phases. Thus, the cell size increases and the cellular microstructure deteriorates. When the carbon content reaches 0.43 wt.%, there is not enough Sm(Co, Cu)₅ phase to form a uniform cellular microstructure. Br, H_cj and BH_max are approximate to zero. Since carbon has little influence on the content of Sm₂(Co, Fe)₁₇ phase, Ms can keep a high value (≥100 emu/g). ZrC has high melting point (3420 °C) and acts as dispersion particle in the magnets, which prevents the grains of SEM structure growing and reduces the liquid content of green compacts during sintering. Therefore, the density of the magnets decreases.     

Maple procedures for the coupling of angular momenta. An up-date of the Racah module

An up-date of the Racah module is presented, adopted to Maple 11 and 12, which supports both, algebraic manipulations of expressions from Racah's algebra as well as numerical computations of many functions and symbols from the theory of angular momentum. The functions that are known to the program include the Wigner rotation matrices and n-j symbols, Clebsch-Gordan and Gaunt coefficients, spherical harmonics of various kinds as well as several others.

Program summary

Program title:RacahCatalogue identifier: ADFV_v10_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFV_v10_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 30 436No. of bytes in distributed program, including test data, etc.: 544 866Distribution format: tar.gzProgramming language: Maple 11 and 12Computer: All computers with a license for the computer algebra package Maple [1]Operating system: Suse Linux 10.2+ and Ubuntu 8.10Classification: 4.1, 5Catalogue identifier of previous version: ADFV_v9_0Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 616Does the new version supersede the previous version?: YesNature of problem: The theories of angular momentum and spherical tensor operators, sometimes known also as Racah's algebra, provide a powerful calculus for studying spin networks and (quantum) many-particle systems. For an efficient use of these theories, however, one requires not only a reliable handling of a large number of algebraic transformations and rules but, more often than not, also a fast access to their standard quantities, such as the Wigner n-j symbols, Clebsch-Gordan coefficients, spherical harmonics of various kinds, the rotation matrices, and many others.Solution method: A set of Maple procedures has been developed and maintained during the last decade which supports both, algebraic manipulations as well as fast computations of the standard expressions and symbols from the theory of angular momentum [2,3]. These procedures are based on a sizeable set of group-theoretical (and often rather sophisticated) relations which has been discussed and proven in the literature; see the monograph by Varshalovich et al. [4] for a comprehensive compilation. In particular the algebraic manipulation of complex (Racah) expressions may result in considerable simplifications, thus reducing the ‘numerical costs’, and often help obtain further insight into the behaviour of physical systems.Reasons for new version: A revision of the Racah module became necessary for mainly three reasons: (i) Since the last extension of the Racah procedures [5], which was developed within the framework of Maple 8, several updates of Maple were distributed by the vendors (currently Maple 13) and required a number of adaptations to the source code; (ii) the increasing size and program structure of the Racah module made it advisible to separate the (procedures for the treatment of the) atomic shell model from the manipulation and computation of Racah expressions. Therefore, the computation of angular coefficients for different coupling schemes, (grand) coefficients of fractional parentage as well as the matrix elements (of various irreducible tensors from the shell model) is to be maintained from now on independently within the Jucys module; (iii) a number of bugs and inconsistencies have been reported to us and corrected in the present version.Summary of revisions: In more detail, the following changes have been made:

1.

Since recent versions of Maple now support the automatic type checking of all incoming arguments and the definition of user-defined types; we have adapted most of the code to take advantage of these features, and especially those commands that are accessible by the user.

2.

In the computation of the Wigner n-j symbols and Clebsch-Gordan coefficients, we now return a ‘0’ in all cases in which the triangular rules are not fulfilled, for example, if δ(a,b,c)=0 for or . This change in the program saves the user making these tests on the quantum numbers explicitly everytime (in the summation over more complex expressions) that such a symbol or coefficient is invoked. The program still terminates with an error message if the (half-integer and integer) angular momentum quantum numbers appear in an inproper combination.

3.

While a recursive generation of the Wigner 3-j and 6-j symbols [6] may reduce the costs of some computations (and has thus been utilized in the past), it also makes the program rather sophisticated, especially if an algebraic evaluation or computations with a high number of Digits need to be supported by the same generic commands. The following procedures are therefore no longer supported by the Racah module:Racah_compute_w3j_jrange(), Racah_compute_w3j_mrange(),Racah_compute_w3j_recursive(), Racah_compute_w6j_range(), andRacah_compute_w6j_recursive().On most PCs, a sequential computation of all requested symbols is carried out within the same time basically.

4.

Because the module Jucys has grown to a size of about 35,000 lines of code and data, it appears helpful and necessary to maintain it independently. The procedures from the Jucys modules were designed to facilitate the computation of matrix elements of the unit tensors, the coefficients of fractional parentage (of various types) as well as transformation matrices between different coupling schemes [7] and are, thus, independent of the Racah module (although they typically require that the Racah code is available). The Jucys module is no longer distributed together with the present code.

5.

Apart from the Wigner n-j symbols (see above), some minor bugs have been reported and corrected in Racah_expand() and Racah_set().

6.

To facilitate the test of the installation and as a first tutorial on the module, we now provide the Maple worksheet Racah-tests-2009-maple12.mw in the Racah2009 root directory. This worksheet contains the examples and test cases from the previous versions. For the test of the installation, it is recommended that a ‘copy’ of this worksheet is saved and compared to the results from the re-run. It can be used also as a helpful source to define new examples in interactive work with the Racah module.

The Racah module is distributed in a tar file ADFV_v10_0.tar.gz from which the RACAH2009 root directory is (re-)generated by the command tar -zxvf ADFV_v10_0.tar.gz. This directory contains the source code libraries (tested for Maple 11 and 12), a Read.me for the installation of the program, the worksheet Racah-tests-2009-maple12.mw as well as the document Racah-commands-2009.pdf. This .pdf document serves as a Short Reference Manual and provides the definition of all the data structures of the Racah program together with an alphabetic list of all user relevant (and exported) commands. Although emphasis was placed on preserving the compatibility of the program with earlier releases of Maple, this cannot always be guaranteed due to changes in the Maple syntax. The Racah2009 root also contains an example of a .mapleinit file that can be modified and incorporated into the user's home directory to make the Racah module accessible like any other module of Maple. As mentioned above, the worksheet Racah-tests-2009-maple12.mw, help test the installation and may serve as a first tutorial.Restrictions: The (Racah) program is based on the concept of Racah expressions [cf. Fig. 1 in Ref. [4]] which, in principle, may contain any number of Wigner n-j symbols (n?9), Clebsch-Gordan coefficients, spherical harmonics and/or rotation matrices. In practise, of course, the required time and the success of an evaluation procedure depends on the complexity of the expressions and on the storage available, sometimes also on Maple's internal garbage treatment. In some cases, it is advisable to attempt first a simplification of the magnetic quantum numbers for a given expression before the summation over further 6-j and 9-j symbols should be taken into account. For all other quantities (that are compiled in Ref. [8], Tables 1 and 2, and explained in more detail in the Short Reference Manual, Racah-commands-2009.pdf), we currently just facilitate fast numerical computations by exploiting, as far as possible, Maple's hardware floating-point model. The program also supports simplifications on the Wigner rotation matrices. In integrals over the rotation matrices, products of up to three Wigner D-functions or reduced matrices (with the same angular arguments) are recognized; for the integration over a solid angle, however, the domain of integration must be specified explicitly for the Euler angles α and γ in order to force Maple to generate a constant of integration. In the course of the evaluation of Racah expressions, it is, in practice, often difficult to check internally whether all substructures of an expression are defined properly. Therefore, the user must ensure that all angular momenta (if given explicitly) must finally evaluate to integer and half-integer values and that they satisfy proper coupling conditions.Unusual features: The Racah program is designed for interactive use and for providing a quick and algebraic evaluation of (complex) expressions from Racah's algebra. In the evaluation, it exploits a large set of sum rules which are known from Racah's algebra and which may include (multiple) summations over dummy indices; see Varshalovich et al. [5] for a more detailed account of the theory. One strength of the program is that it recognizes automatically the symmetries of the symbols and functions, and that it applies also (some of) the graphical rules due to Yutsis and coworkers [9]. As before, the result of the evaluation process will be provided as Racah expressions, if a further simplification could be achieved, and may hence be used for further derivations and calculations within the given framework. In dealing with recoupling coefficients, these coefficients can be entered simply as a string of angular momenta (variables), separated by commas, and very similar to how they appear in mathematical texts. This is a crucial advantage of the program, compared with previous developments, for which the angular momenta and coupling coefficients had often to be given in a very detailed format. A Short Reference Manual to all procedures of the Racah program is provided by this distribution; it also contains the worksheet Racah-tests-2009-maple12.mw that contains the examples from all previous versions and may help test the installation. This worksheet can serve as a first tutorial to the Racah procedures. In the past, the Racah program has been utilized extensively in a number of applications including angular and polarization studies of heavy ions [10], angular distributions and correlation functions following photon-induced excitation processes [11], entanglement studies [12], in application of point-group symmetries and several others.Running time: The worksheet supplied with the distribution takes about 1 minute to run.References:

[1] Maple is a registered trademark of Waterloo Maple Inc.

[2] S. Fritzsche, Comp. Phys. Commun. 103 (1997) 51.

[3] S. Fritzsche, S. Varga, D. Geschke, B. Fricke, Comp. Phys. Commun. 111 (1998) 167;

T. Ingho, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 139 (2001) 297;

S. Fritzsche, T. Ingho, T. Bastug, M. Tomaselli, Comp. Phys. Commun. 139 (2001) 314.

[4] D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore a.o., 1988.

[5] J. Pagaran, S. Fritzsche, G. Gaigalas, Comp. Phys. Commun. 174 (2006) 616.

[6] K. Schulten, R.G. Gordon, Comp. Phys. Commun. 11 (1976) 269.

[7] G. Gaigalas, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 135 (2001) 219;

G. Gaigalas, S. Fritzsche, Comp. Phys. Commun. 149 (2002) 39;

G. Gaigalas, O. Scharf, S. Fritzsche, Comp. Phys. Commun. 166 (2005) 141.

[8] S. Fritzsche, T. Ingho, M. Tomaselli, Comp. Phys. Commun. 153 (2003) 424.

[9] A.P. Yutsis, I.B. Levinson, V.V. Vanagas, The Theory of Angular Momentum, Israel Program for Scientific Translation, Jerusalem, 1962.

[10] S. Fritzsche, P. Indelicato, T. Stöhlker, J. Phys. B 38 (2005) S707.

[11] M. Kitajima, M. Okamoto, M. Hoshino, et al., J. Phys. B 35 (2002) 3327;

N.M. Kabachnik, S. Fritzsche, A.N. Grum-Grzhimailo, et al., Phys. Reports 451 (2007) 155;

S. Fritzsche, A.N. Grum-Grzhimailo, E.V. Gryzlova, N.M. Kabachnik, J. Phys. B 41 (2008) 165601;

T. Radtke, et al., Phys. Rev. A 77 (2008) 022507.

[12] T. Radtke, S. Fritzsche, Comp. Phys. Commun. 175 (2006) 145.

     

Solid state reaction in sandwich-type Al/Cu thin films

Al/Cu/Al and Cu/Al/Cu triple layers with approximately 10 nm single layer thickness deposited on tungsten substrates were analyzed in the early stages of reactive interdiffusion by means of atom probe tomography. The first reaction product is found after 5 min thermal treatment at 110 degrees C and identified by direct chemical analysis to be Al2Cu. Surprisingly, we found a significant asymmetry in the reaction rate of the new phase with the stacking sequence: the thickness of the product grown at the interfaces, at which Cu is deposited on top of the Al layer, is approximately 1.5-2 times thicker than the other one at the interfaces at which Al is deposited onto a Cu layer. On the other hand, at both interfaces the thickness of the product layer depends parabolically on time. No precursory interdiffusion and no distinct nucleation process of the product are observed.     

Precise Coulomb wave functions for a wide range of complex ?, η and z

A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the Schrödinger equation in order to provide very stable calculations, even for large values of |η| or |ℑ(?)|. Moreover, a simple analytic continuation for is introduced, so that this zone of the complex z-plane does not pose any problem. This code is particularly well suited for low-energy calculations and the calculation of resonances with extremely small widths. Numerical instabilities appear, however, when both |η| and |ℑ(?)| are large and comparable or smaller than |ℑ(?)|.

Program summary

Title of program: cwfcomplexCatalogue number:ADYO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYO_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputers on which the program has been tested: DELL GX400Operating systems: Linux, WindowsProgramming language used: C++No. of bits in a word: 64No. of processors used: 1Has the code been vectorized?: noNo. of bytes in distributed program, including test data, etc.: 33 092No. of lines in distributed program, including test data, etc.: 3210Distribution format:tar.gzNature of physical problem: The calculation of Coulomb wave functions with all of their arguments complex is revisited. The new methods introduced allow to greatly augment the range of accessible ?, η, and z.Method of solution: Power/asymptotic series and continued fractions are supplemented with direct integrations of the Coulomb Schrödinger equation. Analytic continuation for is also precisely computed using linear combinations of the functions provided by standard methods, which do not follow the branch cut requirements demanded for Coulomb wave functions.Typical running time: N/AUnusual features of the program: none     

基于(w，z)参数轴对称3D刚体摆姿态PD控制

基于(w,z)参数化轴对称Three Dimensions(3D)摆的姿态控制问题研究,提出(w,z)参数描述姿态描述方法。该方法通过2次绕正交轴旋转,引入复变量,将球面上的点向复平面投影。提出Proportion Differentiation(pd)控制对轴对称3D摆的姿态控制方法。首先列出轴对称3D摆的动力学方程,以(w,z)参数表示轴对称3D摆的姿态运动学方程及推导过程。利用(w,z)参数设计出PD控制器,使得轴对称3D刚体摆在其倒立位置渐近稳定。仿真实验验证了控制器对轴称3D摆姿态控制的有效。     

Work function variations of incandescent filaments during self-cooling in vacuum

A novel method of dynamic measurement of work function (WF) variations of hot metal filaments is described. It is essential in this method that electron emission current (I_e) is recorded during filament self-cooling when no heating power is supplied, thereby I_e is not disturbed by the potential gradient along the filament. WF shift due to the presence of a low-pressure gas, where the main active compounds are O₂ and H₂O, is calculated from an equation derived on the basis of the Richardson formula. The relative increase of WF found by this method was 5 times larger for tungsten than that for tantalum over the entire temperature range from 900 to 1800 K. Our method may be used in research studies of adsorption-related phenomena on metallic surfaces at high temperatures.     

用多元有理函数矩阵研究系统的结构性质

本文着重介绍了各种结构化矩阵，经比较，说明多元有理函数矩阵（ＲＦＭ）能起初地描述线性物理系统，通过对多元有理函数域Ｆ（ｚ）上的能控制能观性的讨论，说明ＲＦＭ是研究与系统结构相关性质的有力工具，也说明了研究Ｆ（ｚ）上能控制观性的必要性。