RELCI: A program for relativistic configuration interaction calculations

The set-up and diagonalization of (large) Hamiltonian matrices are two key elements in studying the structure and properties of many-electron atoms and ions. The efficiency in dealing with these tasks eventually determines for which atomic systems useful ab initio predictions can be made today and how accurate these predictions are. To facilitate further structure calculations, in particular for open-shell atoms and ions, here we present a new configuration interaction program in the framework of the Ratip package which help incorporate different approximations to the electron-electron interaction in the Hamiltonian matrix and, thus, into the representation of the wave functions. Our new program also supports several computational modes to allow for a flexible choice between particular time and storage requirements of the user. Care has been taken to provide a modern and user-friendly component of the Ratip package which carefully applies the concepts of Fortran 90/95.     

Order statistics and selection methods of evolutionary algorithms

Selection methods are essential components of evolutionary algorithms (EAs). This paper reviews five popular selection methods used in EAs. The algorithms are examined using the cumulants of the fitness distribution of the selected individuals. The cumulants are calculated using order statistics. The method presented here considers finite populations of arbitrary size. The results show important differences among the selection methods considered, even when they are configured to have the same selection intensity.     

GFACTOR2001: A program for relativistic atomic g-factor calculations

We describe a program for the computation of Landé g factor. Approximate atomic wavefunctions are assumed to be linear combinations of configuration state functions, in turn, constructed from four-component spin-orbitals to be many particle eigenfunctions of the parity and angular momentum operators.     

octopus: a first-principles tool for excited electron-ion dynamics

We present a computer package aimed at the simulation of the electron-ion dynamics of finite systems, both in one and three dimensions, under the influence of time-dependent electromagnetic fields. The electronic degrees of freedom are treated quantum mechanically within the time-dependent Kohn-Sham formalism, while the ions are handled classically. All quantities are expanded in a regular mesh in real space, and the simulations are performed in real time. Although not optimized for that purpose, the program is also able to obtain static properties like ground-state geometries, or static polarizabilities. The method employed proved quite reliable and general, and has been successfully used to calculate linear and non-linear absorption spectra, harmonic spectra, laser induced fragmentation, etc. of a variety of systems, from small clusters to medium sized quantum dots.     

numer, a code for Numerov integrations of Coulomb functions

The code numer is used for numerical integrations of Coulomb radial wave functions using the Numerov method. The input specifies a function and its derivative to start integrations, an integration range and an accuracy parameter ac such that the accumulated error is no larger than ac. Alternative input is initial function, integration step, and function after first step. For positive energies, options exist to use either the atomic-physics variables (?,r) or the nuclear-physics variables (η,ρ).     

Optimization and parallelization of a force field for silicon using OpenMP

The force field by Lenosky and coworkers is the latest force field for silicon which is one of the most studied materials. It has turned out to be highly accurate in a large range of test cases. The optimization and parallelization of this force field using OpenMp and Fortran90 is described here. The optimized program allows us to handle a very large number of silicon atoms in large scale simulations. Since all the parallelization is hidden in a single subroutine that returns the total energies and forces, this subroutine can be called from within a serial program in an user friendly way.     

fgh, a code for the calculation of Coulomb radial wave functions from series expansions

The code fgh is an up-dated version of a code coulfg (see [Seaton, Comput. Phys. Comm. 25 (1982) 87]), used for the calculation of the Coulomb functions f and g, analytic in the energy, for attractive potentials. The new code works for attractive and repulsive potentials and also gives the functions h which have simple asymptotic forms. There is an option to use either the variables (?,r) customary in atomic physics, or (for positive energies) (η,ρ) customary in nuclear physics. When (η,ρ) are used, the code also gives the functions F_?(η,ρ) and G_?(η,ρ).Use of series solutions can lead to loss of accuracy due to cancellation effects. fgh provides an indication of the number of significant figures lost due to cancellations.     

A combinatorial algorithm for max csp

We consider the problem max csp over multi-valued domains with variables ranging over sets of size s_i?s and constraints involving k_j?k variables. We study two algorithms with approximation ratios A and B, respectively, so we obtain a solution with approximation ratio max(A,B).The first algorithm is based on the linear programming algorithm of Serna, Trevisan, and Xhafa [Proc. 15th Annual Symp. on Theoret. Aspects of Comput. Sci., 1998, pp. 488-498] and gives ratio A which is bounded below by s^1−k. For k=2, our bound in terms of the individual set sizes is the minimum over all constraints involving two variables of , where s₁ and s₂ are the set sizes for the two variables.We then give a simple combinatorial algorithm which has approximation ratio B, with B>A/e. The bound is greater than s^1−k/e in general, and greater than s^1−k(1−(s−1)/2(k−1)) for s?k−1, thus close to the s^1−k linear programming bound for large k. For k=2, the bound is if s=2, 1/2(s−1) if s?3, and in general greater than the minimum of 1/4s₁+1/4s₂ over constraints with set sizes s₁ and s₂, thus within a factor of two of the linear programming bound.For the case of k=2 and s=2 we prove an integrality gap of . This shows that our analysis is tight for any method that uses the linear programming upper bound.     

A skew-symmetric property of rigid-body systems

The configuration space for the attitude of a vehicle can be modeled as SO(3), namely the rotation matrix group. This work investigates the globally valid dynamics of natural Lagrangian systems and gyroscopic systems with configuration space including SO(3). The dynamics is derived by using the global representations of jet bundles of SO(3). A skew-symmetric property associated with the systems can be then established. Such property can be used in many applications such as the adaptive controller design.     

The Monte Carlo Event Generator AcerMC version 1.0 with interfaces to PYTHIA 6.2 and HERWIG 6.3

The AcerMC Monte Carlo Event Generator is dedicated for the generation of Standard Model background processes at pp LHC collisions. The program itself provides a library of the massive matrix elements and phase space modules for generation of a set of selected processes: , , , , and complete electroweak process. The hard process event, generated with one of these modules, can be completed by the initial and final state radiation, hadronization and decays, simulated with either PYTHIA or HERWIG Monte Carlo event generator. Interfaces to both of these generators are provided in the distribution version. The matrix element codes have been derived with the help of the MADGRAPH package. The phase-space generation is based on the multi-channel self-optimizing approach as proposed in NEXTCALIBUR event generator. Eventually, additional smoothing of the phase space was obtained by using a modified ac-VEGAS routine in order to improve the generation efficiency.     

A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method

The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.     

A combinatorial property on angular orders of plane point sets

We study the following combinatorial property of point sets in the plane: For a set S of n points in general position and a point p∈S consider the points of S−p in their angular order around p. This gives a star-shaped polygon (or a polygonal path) with p in its kernel. Define c(p) as the number of convex angles in this star-shaped polygon around p, and c(S) as the sum of all c(p), for p∈S. We show that for every point set S, c(S) is always at least . This bound is shown to be almost tight. Consequently, every set of n points admits a star-shaped polygonization with at least convex angles.     

Switching through singularities

Asymptotic tracking is studied for systems which are not regular, that is, the relative degree is not well defined. For these systems, the input–output linearizing control law has singularities. We propose a tracking control law which switches between an approximate tracking law (Hauser et al., IEEE Trans. Automat. Control 37 (3) (1992) 392–398) close to the singularities, and an exact tracking law away from the singularities, and we study the applicability of this law based on the behavior of the system’s zero dynamics at the switching boundary. As in Hauser et al. (IEEE Trans. Automat. Control 37 (3) (1992) 392–398), the ball and beam example is used to motivate the study.     

Continuous time-varying linear systems

We discuss implicit systems of ordinary linear differential equations with (time-) variable coefficients, their solutions in the signal space of hyperfunctions according to Sato and their solution spaces, called time-varying linear systems or behaviours, from the system theoretic point of view. The basic result, inspired by an analogous one for multidimensional constant linear systems, is a duality theorem which establishes a categorical one–one correspondence between time-varying linear systems or behaviours and finitely generated modules over a suitable skew-polynomial ring of differential operators. This theorem is false for the signal spaces of infinitely often differentiable functions or of meromorphic (hyper-)functions or of distributions on . It is used to obtain various results on key notions of linear system theory. Several new algorithms for modules over rings of differential operators and, in particular, new Gröbner basis algorithms due to Insa and Pauer make the system theoretic results effective.     

Measuring texture classification algorithms

The texture analysis literature lacks a widely accepted method for comparing algorithms. This paper proposes a framework for comparing texture classification algorithms. The framework consists of several suites of texture classification problems, a standard functionality for algorithms, and a method for computing a score for each algorithm. We use the framework to demonstrate the peaking phenomenon in texture classification algorithms. The framework is publicly available on the Internet.     

Summative evaluation of the SINCGARS Tutor

In an earlier set of studies with a different Intelligently Coached Simulation (Orey, M.A., Fan, H., Park, J., Tzeng, S., & Gustafson, K. (1995). Evaluation of Device operator in a context of a coached simulation environment), we found a retention and a transfer problem. We tried to solve these problems while building a new Intelligently Coached Simulation (the SINCGARS Tutor). The solutions to the two problems were to use an interactive conceptual model for the retention problem and we used photographs of the equipment as the visuals of the simulation. We then tested this new tutor with a group of 22 officers who were not only required to know how to operate the SINCGARS radio, but would be responsible for teaching others in their unit when their training was complete. We had one group of officers train on the real equipment, in pairs, with one instructor available for guidance. The other group of 11 learned via the SINCGARS Tutor. The post test was to put an actual radio into operation while being observed by a trained observer. Results indicate that not only did the transfer problem go away, but officers trained on the computer performed the task more accurately both initially on the immediate post test and again on a surprise four-week delayed post test. The SINCGARS Tutor was found to be a very good training solution.     

Continuity properties of balanced realizations

In this paper topological and geometrical properties of pre-balanced and balanced realizations are considered. It is shown that analytic pre-balancing coordinate transformations do exist and that the set of pre-balanced realizations forms an analytic submanifold. Explicit formulas for the tangent spaces and their dimension are derived. Continuity properties of balanced realizations are studied. For systems with more than two inputs and two outputs explicit points of discontinuity of balancing coordinate transformations are described. A certain class of balancing coordinate transformations is shown to be discontinuous, even for distinct and fixed singular values.