Motion4D - A library for lightrays and timelike worldlines in the theory of relativity

The Motion4D-library solves the geodesic equation as well as the parallel- and Fermi-Walker-transport in four-dimensional Lorentzian spacetimes numerically. Initial conditions are given with respect to natural local tetrads which are adapted to the symmetries or the coordinates of the spacetime. Beside some already implemented metrics like the Schwarzschild and Kerr metric, the object oriented structure of the library permits to implement other metrics or integrators in a straight forward manner.

Program summary

Program title: Motion4D-libraryCatalogue identifier: AEEX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEX_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.: 150 425No. of bytes in distributed program, including test data, etc.: 5 139 407Distribution format: tar.gzProgramming language: C++Computer: All platforms with a C++ compilerOperating system: Linux, Unix, WindowsRAM: 39 MBytesClassification: 1.5External routines: Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/)Nature of problem: Solve geodesic equation, parallel and Fermi-Walker transport in four-dimensional Lorentzian spacetimes.Solution method: Integration of ordinary differential equationsRunning time: The test runs provided with the distribution require only a few seconds to run.     

The Invar tensor package

The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing tensor products of up to seven Riemann tensors within seconds. It has been implemented both in Mathematica and Maple algebraic systems.

Program summary

Program title:Invar Tensor PackageCatalogue identifier:ADZK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_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.: 136 240No. of bytes in distributed program, including test data, etc.:2 711 923Distribution format:tar.gzProgramming language:Mathematica and MapleComputer:Any computer running Mathematica versions 5.0 to 5.2 or Maple versions 9 and 10Operating system:Linux, Unix, Windows XPRAM:30 MbWord size:64 or 32 bitsClassification:5External routines:The Mathematica version requires the xTensor and xPerm packages. These are freely available at http://metric.iem.csic.es/Martin-Garcia/xActNature of problem:Manipulation and simplification of tensor expressions. Special attention on simplifying scalar polynomial expressions formed from the Riemann tensor on a four-dimensional metric-compatible manifold.Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor.Restrictions:The present versions do not fully address the problem of reducing differential invariants or monomials of the Riemann tensor with free indices.Running time:Less than a second to fully reduce a monomial of the Riemann tensor of degree 7 in terms of independent invariants.     

A completely open source based computing system for computer generation of Fourier holograms

Computer generated holograms are usually generated using commercial software like MATLAB, MATHCAD, Mathematica, etc. This work is an approach in doing the same using freely distributed open source packages and Operating System. A Fourier hologram is generated using this method and tested for simulated and optical reconstruction. The reconstructed images are in good agreement with the objects chosen. The significance of using such a system is also discussed.

Program summary

Program title: FHOLOCatalogue identifier: AEDS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDS_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.: 176 336No. of bytes in distributed program, including test data, etc.: 4 294 872Distribution format: tar.gzProgramming language: C++Computer: any X86 micro computerOperating system: Linux (Debian Etch)RAM: 512 MBClassification: 18Nature of problem: To generate a Fourier Hologram in micro computer only by using open source operating system and packages.Running time: Depends on the matrix size. 10 sec for a matrix of size 256×256.     

Monte Carlo event generator for black hole production and decay in proton-proton collisions - QBH version 1.02

We describe the Monte Carlo event generator for black hole production and decay in proton-proton collisions - QBH version 1.02. The generator implements a model for quantum black hole production and decay based on the conservation of local gauge symmetries and democratic decays. The code in written entirely in C++ and interfaces to the PYTHIA 8 Monte Carlo code for fragmentation and decays.

Program summary

Program title: QBHCatalogue identifier: AEGU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGU_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.: 10 048No. of bytes in distributed program, including test data, etc.: 118 420Distribution format: tar.gzProgramming language: C++Computer: x86Operating system: Scientific Linux, Mac OS XRAM: 1 GBClassification: 11.6External routines: PYTHIA 8130 (http://home.thep.lu.se/~torbjorn/pythiaaux/present.html) and LHAPDF (http://projects.hepforge.org/lhapdf/)Nature of problem: Simulate black hole production and decay in proton-proton collision.Solution method: Monte Carlo simulation using importance sampling.Running time: Eight events per second.     

Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems.Program summaryProgram title: NAPACatalogue identifier: AEJZ_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJZ_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.: 4060No. of bytes in distributed program, including test data, etc.: 113 498Distribution format: tar.gzProgramming language: MAPLE R13Computer: PCOperating system: Windows XP/7RAM: 2 GbytesClassification: 4.3Nature of problem: Solve nonlinear differential equations with initial conditions.Solution method: Adomian decomposition method and Padé technique.Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.     

PArthENoPE: Public algorithm evaluating the nucleosynthesis of primordial elements

We describe a program for computing the abundances of light elements produced during Big Bang Nucleosynthesis which is publicly available at http://parthenope.na.infn.it/. Starting from nuclear statistical equilibrium conditions the program solves the set of coupled ordinary differential equations, follows the departure from chemical equilibrium of nuclear species, and determines their asymptotic abundances as function of several input cosmological parameters as the baryon density, the number of effective neutrino, the value of cosmological constant and the neutrino chemical potential. The program requires commercial NAG library routines.

Program summary

Program title: PArthENoPECatalogue identifier: AEAV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAV_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.: 10 033No. of bytes in distributed program, including test data, etc.: 46 002Distribution format: tar.gzProgramming language: Fortran 77Computer: PC-compatible running Fortran on Unix, MS Windows or LinuxOperating system: Windows 2000, Windows XP, LinuxClassification: 1.2, 1.9, 17.8External routines: NAG LibrariesNature of problem: Computation of yields of light elements synthesized in the primordial universe.Solution method: BDF method for the integration of the ODEs, implemented in a NAG routine.Running time: 90 sec with default parameters on a Dual Xeon Processor 2.4 GHz with 2 GB RAM.     

Real-time Java simulations of multiple interference dielectric filters

An interactive Java applet for real-time simulation and visualization of the transmittance properties of multiple interference dielectric filters is presented. The most commonly used interference filters as well as the state-of-the-art ones are embedded in this platform-independent applet which can serve research and education purposes. The Transmittance applet can be freely downloaded from the site http://cpc.cs.qub.ac.uk.

Program summary

Program title: TransmittanceCatalogue identifier: AEBQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBQ_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.: 5778No. of bytes in distributed program, including test data, etc.: 90 474Distribution format: tar.gzProgramming language: JavaComputer: Developed on PC-Pentium platformOperating system: Any Java-enabled OS. Applet was tested on Windows ME, XP, Sun Solaris, Mac OSRAM: VariableClassification: 18Nature of problem: Sophisticated wavelength selective multiple interference filters can include some tens or even hundreds of dielectric layers. The spectral response of such a stack is not obvious. On the other hand, there is a strong demand from application designers and students to get a quick insight into the properties of a given filter.Solution method: A Java applet was developed for the computation and the visualization of the transmittance of multilayer interference filters. It is simple to use and the embedded filter library can serve educational purposes. Also, its ability to handle complex structures will be appreciated as a useful research and development tool.Running time: Real-time simulations     

Visual tool for estimating the fractal dimension of images

This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from “noise”, we considered also the family of all band-pass filters with the same band-width (specified as parameter). The fractal dimension can be thus represented as a function of the pixel color code. The program was used for the study of paintings cracks, as an additional tool which can help the critic to decide if an artistic work is original or not.

Program summary

Program title: Fractal Analysis v01Catalogue identifier: AEEG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_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.: 29 690No. of bytes in distributed program, including test data, etc.: 4 967 319Distribution format: tar.gzProgramming language: MS Visual Basic 6.0Computer: PCOperating system: MS Windows 98 or laterRAM: 30MClassification: 14Nature of problem: Estimating the fractal dimension of images.Solution method: Optimized implementation of the box-counting algorithm. Use of a band-pass filter for separating the real information from “noise”. User friendly graphical interface.Restrictions: Although various file-types can be used, the application was mainly conceived for the 8-bit grayscale, windows bitmap file format.Running time: In a first approximation, the algorithm is linear.     

xPerm: fast index canonicalization for tensor computer algebra

We present a very fast implementation of the Butler-Portugal algorithm for index canonicalization with respect to permutation symmetries. It is called xPerm, and has been written as a combination of a Mathematica package and a C subroutine. The latter performs the most demanding parts of the computations and can be linked from any other program or computer algebra system. We demonstrate with tests and timings the effectively polynomial performance of the Butler-Portugal algorithm with respect to the number of indices, though we also show a case in which it is exponential. Our implementation handles generic tensorial expressions with several dozen indices in hundredths of a second, or one hundred indices in a few seconds, clearly outperforming all other current canonicalizers. The code has been already under intensive testing for several years and has been essential in recent investigations in large-scale tensor computer algebra.

Program summary

Program title: xPermCatalogue identifier: AEBH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBH_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.: 93 582No. of bytes in distributed program, including test data, etc.: 1 537 832Distribution format: tar.gzProgramming language: C and Mathematica (version 5.0 or higher)Computer: Any computer running C and Mathematica (version 5.0 or higher)Operating system: Linux, Unix, Windows XP, MacOSRAM:: 20 MbyteWord size: 64 or 32 bitsClassification: 1.5, 5Nature of problem: Canonicalization of indexed expressions with respect to permutation symmetries.Solution method: The Butler-Portugal algorithm.Restrictions: Multiterm symmetries are not considered.Running time: A few seconds with generic expressions of up to 100 indices. The xPermDoc.nb notebook supplied with the distribution takes approximately one and a half hours to execute in full.     

LanHEP—a package for the automatic generation of Feynman rules in field theory. Version 3.0

The LanHEP program version 3.0 for Feynman rules generation from the Lagrangian is described. It reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric theories can be described using the superpotential formalism and the 2-component fermion notation. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as LaTeX table. One-loop counterterms can be generated in FeynArts format.

Program summary

Program title: LanHEPCatalogue identifier: ADZV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECH_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.: 83 041No. of bytes in distributed program, including test data, etc.: 1 090 931Distribution format: tar.gzProgramming language: CComputer: PCOperating system: LinuxRAM: 2 MB (SM), 12 MB (MSSM), 120 MB (MSSM with counterterms)Classification: 4.4Nature of problem: Deriving Feynman rules from the LagrangianSolution method: The program reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Tools for checking the correctness of the model, and for simplifying the output expressions are provided. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alternatively, Feynman rules can be generated in FeynArts format or as a LaTeX table.Running time: 1 sec (SM), 8 sec (MSSM), 8 min (MSSM with counterterms)     

Algorithmic derivation of Dyson-Schwinger equations

We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE¹ which provides such an implementation. It derives the Dyson-Schwinger equations graphically once the interactions of the theory are specified. A few examples for the application of both the algorithm and the DoDSE package are provided.

Program summary

Program title: DoDSECatalogue identifier: AECT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECT_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.: 105 874No. of bytes in distributed program, including test data, etc.: 262 446Distribution format: tar.gzProgramming language: Mathematica 6 and higherComputer: all on which Mathematica is availableOperating system: all on which Mathematica is availableClassification: 11.1, 11.4, 11.5, 11.6Nature of problem: Derivation of Dyson-Schwinger equations for a theory with given interactions.Solution method: Implementation of an algorithm for the derivation of Dyson-Schwinger equations.Unusual features: The results can be plotted as Feynman diagrams in Mathematica.Running time: Less than a second to minutes for Dyson-Schwinger equations of higher vertex functions.     

Generating and using truly random quantum states in Mathematica

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.Program summaryProgram title: TRQSCatalogue identifier: AEKA_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKA_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.: 7924No. of bytes in distributed program, including test data, etc.: 88 651Distribution format: tar.gzProgramming language: Mathematica, CComputer: Requires a Quantis quantum random number generator (QRNG, http://www.idquantique.com/true-random-number-generator/products-overview.html) and supporting a recent version of MathematicaOperating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit)RAM: Case dependentClassification: 4.15Nature of problem: Generation of random density matrices.Solution method: Use of a physical quantum random number generator.Running time: Generating 100 random numbers takes about 1 second, generating 1000 random density matrices takes more than a minute.     

TiReX: Replica-exchange molecular dynamics using Tinker

We present a driver program for performing replica-exchange molecular dynamics simulations with the Tinker package. Parallelization is based on the Message Passing Interface, with every replica assigned to a separate process. The algorithm is not communication intensive, which makes the program suitable for running even on loosely coupled cluster systems. Particular attention is paid to the practical aspects of analyzing the program output.

Program summary

Program title: TiReXCatalogue identifier: AEEK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEK_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.: 43 385No. of bytes in distributed program, including test data, etc.: 502 262Distribution format: tar.gzProgramming language: Fortran 90/95Computer: Most UNIX machinesOperating system: LinuxHas the code been vectorized or parallelized?: parallelized with MPIClassification: 16.13External routines: TINKER version 4.2 or 5.0, built as a libraryNature of problem: Replica-exchange molecular dynamics.Solution method: Each replica is assigned to a separate process; temperatures are swapped between replicas at regular time intervals.Running time: The sample run may take up to a few minutes.     

HRMC: Hybrid Reverse Monte Carlo method with silicon and carbon potentials

Fortran 77 code is presented for a hybrid method of the Metropolis Monte Carlo (MMC) and Reverse Monte Carlo (RMC) for the simulation of amorphous silicon and carbon structures. In additional to the usual constraints of the pair correlation functions and average coordination, the code also incorporates an optional energy constraint. This energy constraint is in the form of either the Environment Dependent Interatomic Potential (applicable to silicon and carbon) and the original and modified Stillinger-Weber potentials (applicable to silicon). The code also allows porous systems to be modeled via a constraint on porosity and internal surface area using a novel restriction on the available simulation volume.

Program summary

Program title: HRMC version 1.0Catalogue identifier: AEAO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAO_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.: 200 894No. of bytes in distributed program, including test data, etc.: 907 557Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Any computer capable of running executables produced by the g77 Fortran compilerOperating system: Unix, WindowsRAM: Depends on the type of empirical potential use, number of atoms and which constraints are employedClassification: 7.7Nature of problem: Atomic modeling using empirical potentials and experimental dataSolution method: Monte CarloAdditional comments: The code is not standard FORTRAN 77 but includes some additional features and therefore generates errors when compiled using the Nag95 compiler. It does compile successfully with the GNU g77 compiler (http://www.gnu.org/software/fortran/fortran.html).Running time: Depends on the type of empirical potential use, number of atoms and which constraints are employed. The test included in the distribution took 37 minutes on a DEC Alpha PC.     

FracMAP: A user-interactive package for performing simulation and orientation-specific morphology analysis of fractal-like solid nano-agglomerates

Computer simulation techniques have found extensive use in establishing empirical relationships between three-dimensional (3d) and two-dimensional (2d) projected properties of particles produced by the process of growth through the agglomeration of smaller particles (monomers). In this paper, we describe a package, FracMAP, that has been written to simulate 3d quasi-fractal agglomerates and create their 2d pixelated projection images by restricting them to stable orientations as commonly encountered for quasi-fractal agglomerates collected on filter media for electron microscopy. Resulting 2d images are analyzed for their projected morphological properties.

Program summary

Program title: FracMAPCatalogue identifier: AEDD_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDD_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.: 4722No. of bytes in distributed program, including test data, etc.: 27 229Distribution format: tar.gzProgramming language: C++Computer: PCOperating system: Windows, LinuxRAM: 2.0 MegabytesClassification: 7.7Nature of problem: Solving for a suitable fractal agglomerate construction under constraints of typical morphological parameters.Solution method: Monte Carlo approximation.Restrictions: Problem complexity is not representative of run-time, since Monte Carlo iterations are of a constant complexity.Additional comments: The distribution file contains two versions of the FracMAP code, one for Windows and one for Linux.Running time: 1 hour for a fractal agglomerate of size 25 on a single processor.     

Generating relativistic pseudo-potentials with explicit incorporation of semi-core states using APE, the Atomic Pseudo-potentials Engine

We present a computer package designed to generate and test norm-conserving pseudo-potentials within Density Functional Theory. The generated pseudo-potentials can be either non-relativistic, scalar relativistic or fully relativistic and can explicitly include semi-core states. A wide range of exchange-correlation functionals is included.

Program summary

Program title: Atomic Pseudo-potentials Engine (APE)Catalogue identifier: AEAC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAC_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.: 88 287No. of bytes in distributed program, including test data, etc.: 649 959Distribution format: tar.gzProgramming language: Fortran 90, CComputer: any computer architecture, running any flavor of UNIXOperating system: GNU/LinuxRAM: <5 MbClassification: 7.3External routines: GSL (http://www.gnu.org/software/gsl/)Nature of problem: Determination of atomic eigenvalues and wave-functions using relativistic and nonrelativistic Density-Functional Theory. Construction of pseudo-potentials for use in ab-initio simulations.Solution method: Grid-based integration of the Kohn-Sham equations.Restrictions: Relativistic spin-polarized calculations are not possible. The set of exchange-correlation functionals implemented in the code does not include orbital-dependent functionals.Unusual features: The program creates pseudo-potential files suitable for the most widely used ab-initio packages and, besides the standard non-relativistic Hamann and Troullier-Martins potentials, it can generate pseudo-potentials using the relativistic and semi-core extensions to the Troullier-Martins scheme. APE also has a very sophisticated and user-friendly input system.Running time: The example given in this paper (Si) takes 10 s to run on a Pentium IV machine clocked at 2 GHz.     

Code C# for chaos analysis of relativistic many-body systems

This work presents a new Microsoft Visual C# .NET code library, conceived as a general object oriented solution for chaos analysis of three-dimensional, relativistic many-body systems. In this context, we implemented the Lyapunov exponent and the “fragmentation level” (defined using the graph theory and the Shannon entropy). Inspired by existing studies on billiard nuclear models and clusters of galaxies, we tried to apply the virial theorem for a simplified many-body system composed by nucleons. A possible application of the “virial coefficient” to the stability analysis of chaotic systems is also discussed.

Program summary

Program title: Chaos Many-Body Engine v01Catalogue identifier: AEGH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_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.: 30 053No. of bytes in distributed program, including test data, etc.: 801 258Distribution format: tar.gzProgramming language: Visual C# .NET 2005Computer: PCOperating system: .Net Framework 2.0 running on MS WindowsHas the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution threadRAM: 128 MegabytesClassification: 6.2, 6.5External routines: .Net Framework 2.0 LibraryNature of problem: Chaos analysis of three-dimensional, relativistic many-body systems.Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, and energy conservation precision test.Additional comments: Easy copy/paste based deployment method.Running time: Quadratic complexity.