A fast method for choosing the optimum extrapolation parameter for an e.a.d.i. scheme

This paper describes a fast method for choosing the optimum extrapolation parameter ω in an Extrapolated Alternating Direction Implicit (E.A.D.I.) Scheme, for the numerical solution of elliptic partial differential equations. An analysis is presented to show that in the case that the acceleration parameter r is varied, a set of values for the extrapolation parameter ω could be defined. The optimum value of ω is easily obtained from this set. A numerical example demonstrates the applicability of the proposed method.     

基于CompactLogix和现场总线的过程控制系统

对过程控制中的集散控制系统DCS与现场总线控制系统FCS进行了比较,详细阐述了基于Rockwell Automation的现场总线技术DeviceNet的网络控制方法,并通过PID算法编程与监控软件开发,实现了基于CompactLogix控制器与DeviceNet现场总线的过程控制系统。     

Implementing peridynamics within a molecular dynamics code

Peridynamics (PD) is a continuum theory that employs a nonlocal model to describe material properties. In this context, nonlocal means that continuum points separated by a finite distance may exert force upon each other. A meshless method results when PD is discretized with material behavior approximated as a collection of interacting particles. This paper describes how PD can be implemented within a molecular dynamics (MD) framework, and provides details of an efficient implementation. This adds a computational mechanics capability to an MD code, enabling simulations at mesoscopic or even macroscopic length and time scales.     

Classification and Uncertainty Visualization of Dendritic Spines from Optical Microscopy Imaging

Neuronal dendrites and their spines affect the connectivity of neural networks, and play a significant role in many neurological conditions. Neuronal function is observed to be closely correlated with the appearance, disappearance and morphology of the spines. Automatic 3‐D reconstruction of neurons from light microscopy images, followed by the identification, classification and visualization of dendritic spines is therefore essential for studying neuronal physiology and biophysical properties. In this paper, we present a method to reconstruct dendrites using a surface representation of the dendrite. The 1‐D skeleton of the dendritic surface is then extracted by a medial geodesic function that is robust and topologically correct. This is followed by a Bayesian identification and classification of the spines. The dendrite and spines are visualized in a manner that displays the spines' types and the inherent uncertainty in identification and classification. We also describe a user study conducted to validate the accuracy of the classification and the efficacy of the visualization.     

Filter diagonalization: Filtering and postprocessing with prolates

A detailed account is given of a recent modification of the Filter Diagonalization technique that serves to analyze a signal spectrum within a selected energy range. Our approach employs for filtering the eigenfunctions of the Finite Fourier Transform, or prolates, which are superior to other filters due to their special properties. In particular, prolates are simultaneously band-limited and highly concentrated at a finite time-interval, producing filters with optimal accuracy. In addition both features are acquired by the convolution of a band-limited function with a prolate, that permits the latter to be interpolated via the Walter and Shen sampling formula, which essentially simplifies the supplementary computations. Rigorous filtering error estimates are obtained. Test calculations illustrate the facilities of the presented modification.     

Dynamics of the deconfinement transition of quarks and gluons in a finite volume

We employ finite elements methods for the approximation of solutions of the Ginzburg-Landau equations describing the deconfinement transition in quantum chromodynamics. These methods seem appropriate for situations where the deconfining transition occurs over a finite volume as in relativistic heavy ion collisions, where in addition expansion of the system and flow of matter are important. Simulation results employing finite elements are presented for a Ginzburg-Landau equation based on a model free energy describing the deconfining transition in pure gauge SU(2) theory. Results for finite and infinite system are compared.     

Stochastic optimization for modeling physiological time series: application to the heart rate response to exercise

Stochastic optimization is applied to the problem of optimizing the fit of a model to the time series of raw physiological (heart rate) data. The physiological response to exercise has been recently modeled as a dynamical system. Fitting the model to a set of raw physiological time series data is, however, not a trivial task. For this reason and in order to calculate the optimal values of the parameters of the model, the present study implements the powerful stochastic optimization method ALOPEX IV, an algorithm that has been proven to be fast, effective and easy to implement. The optimal parameters of the model, calculated by the optimization method for the particular athlete, are very important as they characterize the athlete's current condition. The present study applies the ALOPEX IV stochastic optimization to the modeling of a set of heart rate time series data corresponding to different exercises of constant intensity. An analysis of the optimization algorithm, together with an analytic proof of its convergence (in the absence of noise), is also presented.     

A parallel code for the analysis of light curves of close binary stars with surface inhomogeneities through the Astrocomp-grid portal

We present a parallel code for the analysis of sequences of light curves of magnetically active close binaries with brightness inhomogeneities on the surfaces of their component stars. The procedure allows us to search for the best values of the photometric parameters of the binary system as well as to obtain maps of the brightness inhomogeneities regularized by means of the Maximum Entropy and Tikhonov methods. The large amount of computational work is managed by means of a parallel application based on MPI. The code has been made available through the web-based portal Astrocomp (http://www.astrocomp.it) that allows a registered remote user to run it on a set of high-performance computing resources in a completely transparent manner.     

Efficient parallel implementation of Bose Hubbard model: Exact numerical ground states and dynamics of gaseous Bose-Einstein condensates

We present a parallel implementation of the Bose Hubbard model, using imaginary time propagation to find the lowest quantum eigenstate and real time propagation for simulation of quantum dynamics. Scaling issues, performance of sparse matrix-vector multiplication, and a parallel algorithm for determining nonzero matrix elements are described. Implementation of imaginary time propagation yields an O(N) linear convergence on a single processor and slightly better than ideal performance on up to 160 processors for a particular problem size. The determination of the nonzero matrix elements is intractable using sequential non-optimized techniques for large problem sizes. Thus, we discuss a parallel algorithm that takes advantage of the intrinsic structural characteristics of the Fock-space matrix representation of the Bose Hubbard Hamiltonian and utilizes a parallel implementation of a Fock state look up table to make this task solvable within reasonable timeframes. Our parallel algorithm demonstrates near ideal scaling on thousand of processors. We include results for a matrix 22.6 million square, with 202 million nonzero elements, utilizing 2048 processors.     

Fast LP method for the Schrödinger equation

The LP and CP methods are two versions of the piecewise perturbation methods to solve the Schrödinger equation. On each step the potential function is approximated by a constant (for CP) or by a linear function (for LP) and the deviation of the true potential from this approximation is treated by the perturbation theory.This paper is based on the idea that an LP algorithm can be made faster if expressed in a CP-like form. We obtain a version of order 12 whose two main ingredients are a new set of formulae for the computation of the zeroth-order solution which replaces the use of the Airy functions, and a convenient way of expressing the formulae for the perturbation corrections. Tests on a set of eigenvalue problems with a very big number of eigenvalues show that the proposed algorithm competes very well with a CP version of the same order and is by one order of magnitude faster than the LP algorithms existing in the literature. We also formulate a new technique for the step width adjustment and bring some new elements for a better understanding of the energy dependence of the error for the piecewise perturbation methods.     

Sewing algorithm

We present a procedure that in many cases enables the Monte Carlo sampling of states of a large system from the sampling of states of a smaller system. We illustrate this procedure, which we call the sewing algorithm, for sampling states from the transfer matrix of the two-dimensional Ising model.     

Scheduling optimization in coupling independent services as a Grid transaction

Due to the dynamic properties of autonomous resource providers, the coupling of independent services as a Grid transaction may abort with inconsistency. In many situations people would resort to compensation actions to regain consistency; consequently there comes the issue of compensation-cost. To handle such an issue, for the first time we set up a costing model for the all-or-nothing transaction of Grid services, and introduce the ECC metric to evaluate related service scheduling. The analysis of ECC estimation is based on the so-called CC-PreC commit pattern, which is an abstract of a category of common use cases of commit handling. Our analysis theoretically illustrates the high degree of computational complexity of scheduling optimization with respect to the cost labeling, timing and order of requests. Under certain typical conditions we prove that infinite possible schemes of scheduling can be reduced down to a finite set of candidates of scheduling. Especially based on the ECC metric, the caution scheduling is thoroughly investigated, which as a basic policy could be employed in certain common scenarios, and under which the intuitive product-first or cost-first schemes are justified in several typical situations.     

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials.

Program summary

Program title: KANTBPCatalogue identifier: ADZH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_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.: 4224No. of bytes in distributed program, including test data, etc.: 31 232Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IVOperating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XPRAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MBClassification: 2.1, 2.4External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986]Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations.Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns (E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A−EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDLT factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system.Restrictions: The computer memory requirements depend on:

•

(a) the number of differential equations;

•

(b) the number and order of finite-elements;

•

(c) the total number of hyperradial points; and

•

(d) the number of eigensolutions required.

Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively.Running time: The running time depends critically upon:

•

(a) the number of differential equations;

•

(b) the number and order of finite-elements;

•

(c) the total number of hyperradial points on interval [0,ρmax]; and

•

(d) the number of eigensolutions required.

The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.     

Using a generalized molecular dynamics force model for random microstructure generation of different aspect-ratios and orientation for use in the optical design of an LED edge-lit backlight

We propose a method for the pattern generation on the base of a light guide for application in an edge-lit backlight. This method uses the molecular dynamics method of a generalized force model as a generation scheme to produce a microstructure with a pattern combining a variable aspect ratio and a variable microstructure orientation. This generation scheme can accommodate the needs of the subsequent optical design phase, and allows for easier optical optimization to reach the equal luminance condition. The scheme is incorporated into several new schemes to meet these needs, the most important of which is the cell division technique, which allows the adjustment of the microstructure density in each sub-domain, or cell. In addition, the boundary treatments allow the precise control of the microstructure density in each cell and the ability to smooth the microstructure distribution across the cell boundary. Finally, we present an example of a backlight with one light emitting diode showing the integration of the generation scheme and the optical design phase in order to assess the validation of the proposed scheme.     

MJK: A program to calculate observable quantities in electron-atom collisions

We describe a code which utilizes partial-wave amplitudes to calculate a variety of physical quantities studied in electron-atom scattering. For elastic scattering and excitation of atoms with arbitrary angular momenta in collisions with spin-polarized and unpolarized electrons, the program can calculate angle-integrated and angle-differential cross sections, the spin polarization of scattered electrons, the spin left-right (up-down) asymmetry, generalized STU parameters, and the statistical tensors of the final atomic state, which determine polarization and correlation parameters in radiative and nonradiative decays of these states. In addition, the program transforms partial-wave scattering amplitudes into a representation of projections of the angular momenta in the natural and collision coordinate frames, thereby providing the possibility for a user to conveniently calculate any observable not explicitly included in the code. The program can be used directly as a final module after running the Belfast R-matrix codes in the Breit-Pauli mode.     

GenMin: An enhanced genetic algorithm for global optimization

A new method that employs grammatical evolution and a stopping rule for finding the global minimum of a continuous multidimensional, multimodal function is considered. The genetic algorithm used is a hybrid genetic algorithm in conjunction with a local search procedure. We list results from numerical experiments with a series of test functions and we compare with other established global optimization methods. The accompanying software accepts objective functions coded either in Fortran 77 or in C++.

Program summary

Program title: GenMinCatalogue identifier: AEAR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAR_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.: 35 810No. of bytes in distributed program, including test data, etc.: 436 613Distribution format: tar.gzProgramming language: GNU-C++, GNU-C, GNU Fortran 77Computer: The tool is designed to be portable in all systems running the GNU C++ compilerOperating system: The tool is designed to be portable in all systems running the GNU C++ compilerRAM: 200 KBWord size: 32 bitsClassification: 4.9Nature of problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques are frequently trapped in local minima. Global optimization is hence the appropriate tool. For example, solving a nonlinear system of equations via optimization, employing a least squares type of objective, one may encounter many local minima that do not correspond to solutions (i.e. they are far from zero).Solution method: Grammatical evolution and a stopping rule.Running time: Depending on the objective function. The test example given takes only a few seconds to run.     

Genetically controlled random search: a global optimization method for continuous multidimensional functions

A new stochastic method for locating the global minimum of a multidimensional function inside a rectangular hyperbox is presented. A sampling technique is employed that makes use of the procedure known as grammatical evolution. The method can be considered as a “genetic” modification of the Controlled Random Search procedure due to Price. The user may code the objective function either in C++ or in Fortran 77. We offer a comparison of the new method with others of similar structure, by presenting results of computational experiments on a set of test functions.

Program summary

Title of program: GenPriceCatalogue identifier:ADWPProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWPProgram available from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: the tool is designed to be portable in all systems running the GNU C++ compilerInstallation: University of Ioannina, GreeceProgramming language used: GNU-C++, GNU-C, GNU Fortran-77Memory required to execute with typical data: 200 KBNo. of bits in a word: 32No. of processors used: 1Has the code been vectorized or parallelized?: noNo. of lines in distributed program, including test data, etc.:13 135No. of bytes in distributed program, including test data, etc.: 78 512Distribution format: tar. gzNature of physical problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques are frequently trapped in local minima. Global optimization is hence the appropriate tool. For example, solving a nonlinear system of equations via optimization, employing a “least squares” type of objective, one may encounter many local minima that do not correspond to solutions, i.e. minima with values far from zero.Method of solution: Grammatical Evolution is used to accelerate the process of finding the global minimum of a multidimensional, multimodal function, in the framework of the original “Controlled Random Search” algorithm.Typical running time: Depending on the objective function.     

Cross section calculations in Glauber model: I. Core plus one-nucleon case

This paper presents a Fortran program to calculate cross sections for various reactions between composite particles in the framework of Glauber theory. The projectile nucleus is described as a core plus one valence-nucleon system. The input data needed for the calculation are the core and target densities and the nucleon-nucleon profile function. The single-particle wave function of the valence nucleon may be provided by a user or generated by the code if appropriate quantum numbers of the wave function are specified. Multiple integrations involving the valence-nucleon wave function are performed by a Monte Carlo technique with Metropolis algorithm. The program gives the total reaction cross section, the one-nucleon removal cross section, the elastic differential cross section, and the longitudinal momentum distribution of the core fragment. Sample calculations include the reactions of ^13,19C+¹²C, ¹¹Be+¹²C, ¹¹Be+⁹Be, and ⁸B+¹²C systems.