PHON: A program to calculate phonons using the small displacement method

The program phon calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like the Helmholtz free energy, the entropy, the specific heat and the internal energy of the harmonic crystal. The procedure is based on the small displacement method, and can be used in combination with any program capable to calculate forces on the atoms of the crystal. In order to examine the usability of the method, I present here two examples: metallic Al and insulating MgO. The phonons of these two materials are calculated using density functional theory. The small displacement method results are compared with those obtained using the linear response method. In the case of Al the method provides accurate phonon frequencies everywhere in the Brillouin Zone (BZ). In the case of MgO the longitudinal branch of the optical phonons near the centre of the BZ is incorrectly described as degenerate with the two transverse branches, because the non-analytical part of the dynamical matrix is ignored here; however, thermodynamic properties like the Helmholtz free are essentially unaffected.

Program summary

Program title: PHONCatalogue identifier: AEDP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDP_v1_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.: 19 580No. of bytes in distributed program, including test data, etc.: 612 193Distribution format: tar.gzProgramming language: Fortran 90Computer: Any Unix, LinuxOperating system: UnixRAM: Depends on super-cell size, but usually negligibleClassification: 7.8External routines: Subprograms ZHEEV and DSYEV (Lapack); needs BLAS. A tutorial is provided with the distribution which requires the installation of the quantum-espresso package (http://www.quantum-espresso.org)Nature of problem: Stable crystals at low temperature can be well described by expanding the potential energy around the atomic equilibrium positions. The movements of the atoms around their equilibrium positions can then be described using harmonic theory, and is characterised by global vibrations called phonons, which can be identified by vectors in the Brillouin zone of the crystal, and there are 3 phonon branches for each atom in the primitive cell. The problem is to calculate the frequencies of these phonons for any arbitrary choice of q-vector in the Brillouin zone.Solution method: The small displacement method: each atom in the primitive cell is displaced by a small amount, and the forces induced on all the other atoms in the crystal are calculated and used to construct the force constant matrix. Supercells of ∼100 atoms are usually large enough to describe the force constant matrix up to the range where its elements have fallen to negligibly small values. The force constant matrix is then used to compute the dynamical matrix at any chosen q-vector in the Brillouin zone, and the diagonalisation of the dynamical matrix provides the squares of the phonon frequencies. The PHON code needs external programs to calculate these forces, and it can be used with any program capable of calculating forces in crystals. The most useful applications are obtained with codes based on density functional theory, but there is no restriction on what can be used.Running time: Negligible, typically a few seconds (or at most a few minutes) on a PC. It can take longer if very dense meshes of q-points are needed, for example, to compute very accurate phonon density of states.     

GFCUBHEX: Program to calculate elastic Green's functions and displacement fields for applications in atomistic simulations of defects in cubic and HCP crystals

GFCUBHEX is a program that calculates Green's tensor function and displacement fields for a point force in cubic and hexagonal crystals based on an exact single integral solution (Synge, 1957). Linear interpolation between grid points is used to speed up calculations of the orientation-dependent part of the Green's function. The program can be used to calculate the Green's function and the displacement field in atomistic simulations with an arbitrary choice of orthogonal coordinate system.     

特殊平面应力状态下应变法求解主应力公式综述

以应力测定中的几个关键问题为研究对象,综述了线性应变和平面应变状态下应变测量及应力计算方法。主要对平面应力状态下应变测试和应力求解技巧、电阻应变仪选择和测试点及应变片布置问题进行讨论,并归纳了几种应变花法计算主应力的通用公式,可为工程结构设计和实验验证提供参考。     

A computer program for the geometrically nonlinear analysis of plane slender bars and frames

A computer program, developed for the analysis of the geometrically nonlinear behavior of plane frames, is described. The mathematical solution employs the Newton Raphson iterative procedure for simultaneous nonlinear algebraic equations, derived from a discrete (finite difference) solution of a complete set of nonlinear equilibrium equations for the in-plane finite deflections of bars. Multiple-unknown problems are treated.     

A BASIC program to calculate the temperature variation of mineral-growth rates

A BASIC program is presented for the calculation of the complete temperature variation of mineral-growth rates based on partial data. The algorithm is derived from a corresponding states equation for crystal growth, together with a compensation relationship in the standard Arrhenius equation of growth rate vs temperature.     

A general program to calculate moments of the electron density distribution and multipolar interactions

A new program which utilizes the formalism of tensors of moments of the electron density distribution to calculate multipolar interactions is presented. It enables the possibility of inclusion of higher order moments into calculations (limited by the numerical stability of the results) combined with the multicenter multipole expansion.     

Using an HP-1000 computer to calculate the conformational energy of molecules by body's algorithm

A program for determining the conformation of minimum potential energy of molecules from empirical valence-force potentials, using the method of Boyd, is described. This version of the program is written for an HP-1000/F Computer (Hewlett-Packard) with RTE-IVB Operating System.The principal features of the program are low memory requirements (38 kbytes) and short execution time.     

MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test

Insulin sensitivity and pancreatic responsivity are the two main factors controlling glucose tolerance. We have proposed a method for measuring these two factors, using computer analysis of a frequently-sampled intravenous glucose tolerance test (FSIGT). This 'minimal modelling approach' fits two mathematical models with FSIGT glucose and insulin data: one of glucose disappearance and one of insulin kinetics. MINMOD is the computer program which identifies the model parameters for each individual. A nonlinear least squares estimation technique is used, employing a gradient-type of estimation algorithm, and the first derivatives (not known analytically) are computed according to the 'sensitivity approach'. The program yields the parameter estimates and the precision of their estimation. From the model parameters, it is possible to extract four indices: SG, the ability of glucose per se to enhance its own disappearance at basal insulin, SI, the tissue insulin sensitivity index, phi 1, first phase pancreatic responsivity, and phi 2, second phase pancreatic responsivity. These four characteristic parameters have been shown to represent an integrated metabolic portrait of a single individual.     

BUFMAKE: a computer program to calculate the compositions of buffers of defined buffer capacity and ionic strength for ultra-violet spectrophotometry

A versatile computer program, BUFMAKE, was developed to calculate the composition of buffer solution for a given pH value with the ability to optimize the buffer capacity and ionic strength. The software was exemplified using a five-component buffer recipe which consists of boric acid, citric acid, ethylenediamine, potassium dihydrogen orthophosphate and trishydroxymethylaminomethane. It has been demonstrated that the proposed buffer solution with the composition calculated by the BUFMAKE program is suitable for use in ultra-violet spectrophotometry over a broad range of pH (2–12), buffer capacity (0.01–0.05) and ionic strength (0.1–0.3).     

A MATLAB program to calculate translational and rotational diffusion coefficients of a single particle

We developed a graphical user interface, MATLAB based program to calculate the translational diffusion coefficients in three dimensions for a single diffusing particle, suspended inside a fluid. When the particles are not spherical, in addition to their translational motion also a rotational freedom is considered for them and in addition to the previous translational diffusion coefficients a planar rotational diffusion coefficient can be calculated in this program. Time averaging and ensemble averaging over the particle displacements are taken to calculate the mean square displacement variations in time and so the diffusion coefficients. To monitor the random motion of non-spherical particles a reference frame is used that the particle just have translational motion in it. We call it the body frame that is just like the particle rotates about the z-axis of the lab frame.Some statistical analysis, such as velocity autocorrelation function and histogram of displacements for the particle either in the lab or body frames, are available in the program. Program also calculates theoretical values of the diffusion coefficients for particles of some basic geometrical shapes; sphere, spheroid and cylinder, when other diffusion parameters like temperature and fluid viscosity coefficient can be adjusted.

Program summary

Program title: KOJACatalogue identifier: AEHK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHK_v1_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.: 48 021No. of bytes in distributed program, including test data, etc.: 1 310 320Distribution format: tar.gzProgramming language: MatLab (MathWorks Inc.) version 7.6 or higher. Statistics Toolbox and Curve Fitting Toolbox required.Computer: Tested on windows and linux, but generally it would work on any computer running MatLab (MathWorks Inc.). There is a bug in windows 7, if the user is not the administrator sometimes the program was not able to overwrite some internal files.Operating system: Any supporting MatLab (MathWorks Inc.) v7.6 or higher.RAM: About eight times that of loaded dataClassification: 12Nature of problem: In many areas of physics, knowing diffusion coefficients is vital and gives useful information about the physical properties of diffusive particles and the environment. In many cases a diffusive particle is not a sphere and has rotation during its movements. In these cases information about a particle's trajectory both in lab and body frame would be useful. Also some statistical analysis is needed to obtain more information about a particle's motion.Solution method: This program tries to gather all required tools to analyse raw data from the Brownian motion of a diffusing particle. Ability to switch between different methods of calculation of mean square displacement to find diffusion coefficients depends on the correlations between data points. There are three methods in the program: time average, ensemble average and their combinations. A linear fit is done to measure Diffusion Coefficient (D), the weight and fraction of data points is controllable. Given physical properties of the system, the program can calculates D theoretically for some basic geometrical shapes; sphere, spheroid and cylinder. In the case of non-spherical particles if data of rotation is available, the code can calculate trajectory and diffusion also in body frame. There are more statistical tools available in the program, such as histogram and autocorrelation function to obtain more information e.g. relaxation time to ideal diffusion motion. Code uses log–log diagram of mean square displacement (MSD) to calculate the amount of deviation from normal diffusion to sub- or super-diffusion.Running time: It is dependent on the input data, but for typical data in the order of mega bytes, it would take tens of minutes.     

A novel formulation and solution of the plane elastostatic displacement problem

The displacement problem of elastostatics in two dimensions is formulated in terms of integral equations via the Airy stress function. The integral equations are solved numerically using piecewise constant approximations to the unknown functions. The validity of the formulation is demonstrated by its application to a simple problem with a known solution.     

A computer program to perform transformations of gravimetric and aeromagnetic surveys

In this paper, we present the main equations concerned with the transformations of potential field data distributed on a regular grid. The grid does not need to be filled entirely with data, and the grid mesh may be rectangular. Accurate procedures of convolution and data interpolation and extrapolation are described. A FORTRAN IV computer program, termed TRSMAP, is described and a detailed listing is given.     

BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.

Program summary

Program title: BOKASUNCatalogue identifier: AECG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_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.: 9404No. of bytes in distributed program, including test data, etc.: 104 123Distribution format: tar.gzProgramming language: FORTRAN77Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUXOperating system: LINUXRAM: 120 kbytesClassification: 4.4Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum.Solution method: The integrals depend on three internal masses and the external momentum squared p². The method is a combination of an accelerated expansion in 1/p² in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations.Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending on the required accuracy and the values of the physical parameters).