Computer Subroutines Research Articles

IR-spectroscopic studies of hydrogen-bonding solutions: Lineshape analysis of ethanol + hexane system

IR (infrared) line shapes of OH stretching bands in hydrogen-bonding states of ethanol–hexane solutions have been examined using a theoretically rigorous Voigt function, instead of the commonly used empirical Lorentz–Gauss equation. An efficient and numerically-stable computer code with the Voigt function has been developed in order to analyze hydrogen-bonding effects in IR absorption spectra. Although the Voigt function is not an analytically-closed form, a numerical computer subroutine, with only three adjustable parameters for each IR band (or peak), provides a unique solution in a least-squares analysis of the line shapes. On the other hand, the Lorentz–Gauss equation is an analytical function with four adjustable parameters for each IR peak. However, this function makes non-linear least-squares analyses almost impossible due to the existence of strong correlations among the parameters. Example analyses, using the ethanol–hexane system, are given. The degree of hydrogen-bonding associations of ethanol and an effective IR-absorbance coefficient for hydrogen-bonded clusters have been estimated, and results are quite reasonable, compared with those in the literature.

Surface‐enhanced hyper‐Raman and surface‐enhanced Raman scattering from molecules adsorbed on nanoparticles‐on‐smooth‐electrode (NOSE) substrate I. Pyridine, pyrazine and benzene

AbstractMetal nanoparticles‐on‐smooth‐electrode (NOSE) was used as the substrate in a potential‐dependent surface‐enhanced hyper‐Raman(SEHRS), hyper‐Rayleigh(SEHRyS) and Raman (SERS) study of adsorbed molecules of pyridine, pyrazine and benzene. The three molecules are chosen because they are known to adsorb in different orientations on an Ag surface, thus allowing us to examine the sensitivity of SEHRS and SERS signals to the orientation of adsorbed molecules on the NOSE substrate. A computational subroutine is developed and interfaced with Gaussian‐98 to calculate the numeric infrared, Raman and hyper‐Raman intensities, as well as their projections along any molecular‐fixed orientation axis at the level of finite perturbation theory. In this study, we tried to make four types of systematic comparisons. First, we compared the performance of Agn|Ag NOSE substrate with that of traditional substrates such as a randomly roughened Ag electrode or a randomly aggregated Ag sol in SEHRS and SERS. Secondly, we tried to compare between infrared, Raman and hyper‐Raman spectra, which represent the parity‐differentiated one‐photon, two‐photon and three‐photon processes, respectively, with the aim of examining the complementarity between SEHRS and SERS as well as between SEHRS and infrared absorption. Thirdly, we compared isotropic normal spectra with surface‐enhanced spectra (SEHRS and SERS), with the aim of examining the effect of surface adsorption on the selectivity and enhancement. Lastly, we made a systematic comparison between the observed and calculated spectra for both isotropic and surface spectra, which allowed us to assign and interpret the observed data and to infer the most likely orientation of the adsorbed molecules. The NOSE method can be generalized easily to other metal nanoparticles dispersed on a smooth inert metal electrode. The rapid development in the synthesis of metal nanoparticles of various sizes, shapes and crystalline states makes the NOSE method a much more flexible and versatile substrate in the study and applications of SERS and SEHRS techniques. Copyright © 2005 John Wiley & Sons, Ltd.

Parametrization of nuclear parton distributions

Optimum nuclear parton distributions are obtained by analysing available experimental data on electron and muon deep inelastic scattering (DIS). The distributions are given at Q 2=1 GeV2 with a number of parameters, which are determined by a X 2 analysis of the data. Valencequark distributions are relatively well determined at medium x, but they are slightly dependent on the assumed parametrization form particularly at small x. Although antiquark distributions are shadowed at small x, their behavior is not obvious at medium x from the F 2 data. The gluon distributions could not be restricted well by the inclusive DIS data; however, the analysis tends to support the gluon shadowing at small x. We provide analytical expressions and computer subroutines for calculating the nuclear parton distributions, so that other researchers could use them for applications to other high-energy nuclear reactions.

Determination of nuclear parton distributions

Parametrization of nuclear parton distributions is investigated in the leading order of ${\ensuremath{\alpha}}_{s}.$ The parton distributions are provided at ${Q}^{2}=1 {\mathrm{GeV}}^{2}$ with a number of parameters, which are determined by a ${\ensuremath{\chi}}^{2}$ analysis of the data on nuclear structure functions. A quadratic or cubic functional form is assumed for the initial distributions. Although valence quark distributions in the medium x region are relatively well determined, the small x distributions depend slightly on the assumed functional form. It is difficult to determine the antiquark distributions at medium x and gluon distributions. From the analysis, we propose parton distributions at ${Q}^{2}=1 {\mathrm{GeV}}^{2}$ for nuclei from deuteron to heavy ones with a mass number $A\ensuremath{\sim}208.$ They are provided either analytical expressions or computer subroutines for practical usage. Our studies should be important for understanding the physics mechanism of the nuclear modification and also for applications to heavy-ion reactions. This kind of nuclear parametrization should also affect existing parametrization studies in the nucleon because ``nuclear'' data are partially used for obtaining the optimum distributions in the ``nucleon.''

Processing of Composites: Simulations of the Draping of Fabrics with Updated Material Behaviour Law

In the processing of composites, fibre reinforcement is draped over complex three dimensional geometries, yielding local variations in the fibre volume fraction and fibre orientation with subsequent effects on the permeability of the reinforcement during resin infiltration and on the properties of the composite product. This study presents computer simulations of the draping of fabrics by following a mechanical, finite element approach. The fabric is considered as a solid continuum with mechanical properties and friction properties at interfaces. The problem is solved by applying an explicit dynamic finite element analysis. In order to incorporate the large shear deformation of fabric during draping, an updated material behaviour law was formulated on the basis of changing fibre directions. The model was implemented in a user computer subroutine and tested first in case-studies of simple in-plane shear where the predictions were also compared with experimental data from a picture frame type of shear test. Thereafter, numerical simulations focused on the draping of a fabric in a “hat” shaped mould, comprising a hemispherical cup with a wide flat rim. The predictions were compared with predictions from similar simulations without the updated material behaviour law, experimental data and predictions from a “fishnet” algorithm.

Processing of Composites: Simulations of the Draping of Fabrics with Updated Material Behaviour Law

In the processing of composites, fibre reinforcement is draped over complex three dimensional geometries, yielding local variations in the fibre volume fraction and fibre orientation with subsequent effects on the permeability of the reinforcement during resin infiltration and on the properties of the composite product. This study presents computer simulations of the draping of fabrics by following a mechanical, finite element approach. The fabric is considered as a solid continuum with mechanical properties and friction properties at interfaces. The problem is solved by applying an explicit dynamic finite element analysis. In order to incorporate the large shear deformation of fabric during draping, an updated material behaviour law was formulated on the basis of changing fibre directions. The model was implemented in a user computer subroutine and tested first in case-studies of simple in-plane shear where the predictions were also compared with experimental data from a picture frame type of shear test. Thereafter, numerical simulations focused on the draping of a fabric in a “hat” shaped mould, comprising a hemispherical cup with a wide flat rim. The predictions were compared with predictions from similar simulations without the updated material behaviour law, experimental data and predictions from a “fishnet” algorithm.

Algorithm 804

Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The routines can handle a large range of the order n and the parameter h . Sample test results and graphs are given.

Effect of material nonlinearity in unidirectional composites on the behavior of beam structures

The present study is made to investigate the effect of material nonlinearity in unidirectional composites on the behavior of beams, where the fiber orientation is considered. The effect of these two factors on deflection, bending moment and external reactions is investigated. In order to achieve these objectives, a computer subroutine based on secant mechanical property is incorporated in a main computer program for beam and frame analysis. The program can solve structures made of unidirectional composite materials which exhibit general material nonlinearity. Several numerical examples including various beam structures having different fiber orientations are presented, for both linear and nonlinear analysis.

Analysis of draw–redraw processes

An analytical model is developed to analyze the draw–redraw processes. Thickening of the flange is modeled using a complete pure radial drawing analysis which takes into account interfacial friction and radial thickness variation. A plastic bending analysis is used to calculate thinning in all forming radii. Material properties, tooling geometry, and process parameters are included in the model. The derivation is then developed into computer subroutines. By arranging the subroutines into the deforming sequence, draw–redraw process can be simulated. The predicted wall thickness profiles agree very well with the experimental measurements. Characterization of wall thickness profile is also discussed.

MODELING SIMULATION AND CONTROL OF THE WOOD DRYING PROCESS Part 3. Programming and Computer Solutions

In this paper, the programming and computer subroutines of wood drying process (WDP) are studied. This WDP is represented by the set of non-linear partial differential equations which are decomposed into fast and slow subsystems. Moreover, a few procedures have been used to estimate piecewise linear parameters and to reconstruct the real parameter distributions along the drying kiln. Several aspects including estimating stepsize, tuning sensitivity of the operating functions, and general solutions of the internal model (M) are discussed and illustrated

Algorithm 746: PCOMP—a Fortran code for automatic differentiation

Automatic differentiation is an interesting and important tool for all numerical algorithms that require derivatives, e.g., in nonlinear programming, optimal control, parameter estimation, and differential equations. The basic idea is to avoid not only numerical approximations, which are expensive with respect to CPU time and contain round-off errors, but also hand-coded differentiation. This article introduces the forward and backward accumulation methods and describes the numerical implementation of a computer code with the name PCOMP. The main intention of the approach used is to provide a flexible and portable Fortran code for practical applications. The underlying language is described in terms of a formal grammar and is a subset of Fortran with a few extensions. Besides a parser that generates an intermediate code and that can be executed independently from the evaluation routines, there are other subroutines for the direct computation of function and gradient values, which can be called directly from a user program. On the other hand, it is possible to generate a Fortran code for function and gradient evaluation that can be compiled and linked separately.

Inversion of chord-integrated data from noncircular tokamak plasmas (abstract)a)

The superior performance of diverted and elongated plasmas in tokamaks motivates improvements of inversion techniques for chord integrated data (from interferometry, spectroscopy, bolometry, etc.) from such noncircular plasmas. We present a technique planned for TEXT-U. First, flux-surface contours are calculated using EFIT or a filament code. A computer subroutine is provided which then computes, for a given chord, the length of the chord segment enclosed within the flux surface ψ, as a function of ψ from the tangent surface ψtan outward. Using the length functions, the inversions may be performed using the technique of Park or by least-squares fitting. Inversions of FIR interferometer data are presented.

Bessel functions Jn( z) and Yn( z) of integer order and complex argument

This paper describes computer subroutines which were developed to compute Bessel functions of the first and second kind ( J n ( z) and Y n ( z), respectively) for a complex argument z and a range of integer orders. A novel way of determ ining the starting point of backward recurrence is used, and the algorithm for Y n ( z) improves on previous algorithms in terms of accuracy and restrictions on the range of orders.

Boundary Formulations for Sensitivity Analysis Without Matrix Derivatives

A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

Statistical Intervals: A Guide for Practitioners

Presents a detailed exposition of statistical intervals and emphasizes applications in industry. The discussion differentiates at an elementary level among different kinds of statistical intervals and gives instruction with numerous examples and simple math on how to construct such intervals from sample data. This includes confidence intervals to contain a population percentile, confidence intervals on probability of meeting specified threshold value, and prediction intervals to include observation in a future sample. Also has an appendix containing computer subroutines for nonparametric statistical intervals.

Fire-Plume-Generated Ceiling Jet Characteristics and Convective Heat Transfer to Ceiling and Wall Surfaces in a Two-Layer Fire Environment: Uniform Temperature Geiling and Walls

This work presents a model to predict the instantaneous rate of convective heat transfer from fire plume gases to the overhead ceiling surface in a room of fire origin. The room is assumed to be a rectangular parallelepiped and, at times of interest, ceiling temperatures are simulated as being uniform. Also presented is an estimate of the convective heat transfer, due to ceiling-jet-driven wall flows, to both the upper and lower portions of the walls. The effect on the heat transfer of the location of the fire within the room is taken into account. Finally presented is a model of the velocity and temperature distributions in the ceiling jet.The model equations were used to develop an algorithm and associated modular computer subroutine to carry out the indicated heat transfer calculations. The subroutine is written in FORTRAN 77 and called CEILHT. The algorithm and subroutine are suitable for use in two-layer zone-type compartment fire model computer codes. The subroutine was tested for a variety of fire environments involving a 107 W fire in a 8m × 8m × 4m high enclosure. While the calculated results were plausible, it is important to point out that CEILHT simulations have not been exprerimentally validated.

Three-dimensional scalar beam diffraction by a half plane

The complex source point technique greatly simplifies the inclusion of source directivity in scattering and diffraction solutions. By replacing its coordinates by appropriate complex coordinates, an omnidirectional source becomes a beam source. Any diffraction solution for the source becomes the corresponding solution for beam diffraction. Geometrical diffraction theory solutions for local beam sources can be most easily obtained in this way. Here the complex source point technique is applied to a canonical solution in geometrical diffraction theory: three-dimensional scalar beam diffraction by a half plane. First, a general three-dimensional solution for a scalar point source and its evolution to a beam source is reviewed. An exact uniform asymptotic solution for point and beam source diffraction by a rigid or soft half plane is then given for arbitrary incidence in three dimensions. A method for numerical evaluation of the diffraction integrals is shown. In this method the Fresnel integrals with complex arguments are converted to complementary error functions with complex arguments, for which efficient computer subroutines are available. The procedure is illustrated by a numerical example and three-dimensional numerical plots are presented. Electromagnetic (vector) field three-dimensional beam diffraction by half planes will yield to the same approach. So also will three-dimensional beam diffraction by wedges using the uniform geometrical theory of diffraction but the resulting expressions are more complicated.

Calculation of vector potentials from scalar potentials for 3D finite difference solutions

The authors describe a method for solving 3-D magnetostatic problems by which the vector potential is calculated from the scalar potential. The proposed method has been realized by a computer subroutine which is now part of the program system PROFI. As an example the distribution of the normal component of the magnetic flux density was calculated at the boundary of a symmetric iron piece.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computer-assisted design of surface coils used in magnetic resonance imaging. I. The calculation of the magnetic field

For a number of reasons, it is desirable to fabricate coils which, for a known current, shall produce predetermined values of the magnetic field intensity at a number of points within a nuclear magnetic resonance imager. The calculation of the magnetic field intensity at a set of points involves the integration of the Biot-Savart equation for all components of the segments of conductor which make up the coil. This process in itself is a rather formidable task. When this process is parameterized in terms of coil diameter, coil spacing, etc. the problem is to determine the values of these parameters to match values of magnetic field intensities which are desired. The problem thereby increases in complexity to the point where, by ordinary methods, the problem becomes intractable. This note describes an algorithm and offers a computer subroutine to calculate magnetic fields for coils of arbitrary shape and complexity for fixed currents.

Modular molecular mechanics programs and transportable force fields—a partly implemented proposal

Abstract This is a proposal for development of modular molecular mechanics and molecular dynamics programs and for standardization of the format of force fields and of the format of molecular descriptions. This capability will require standardization of certain arrays and variables so that an MM/MD “engine” can be designed to use packages of logic subroutines and computational subroutines. The objective is to facilitate the widespread participation of many groups in the development of better force fields and better programs so that we have the capability of working reliably with a variety of force fields.