Accuracy Of Numerical Calculations Research Articles

Highly accurate bound state calculations of the two-center molecular ions by using the universal variational expansion for three-body systems

The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. Three-body universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in arbitrary three-body systems, including Coulomb three-body systems with arbitrary particle masses and electric charges. Our main interest is related to the adiabatic three-body systems which contain one bound electron and two heavy nuclei of hydrogen isotopes: the protium $p$, deuterium $d$ and tritium $t$. We also consider the analogous (model) hydrogen ion ${}^{\infty}$H$^{+}_2$ with the two infinitely heavy nuclei. PACS number(s): 36.10.-k and 36.10.Dr

A new framework for the complex system’s simulation and analysis

Statistics (or probabilistic theory) and machine learning are currently the main methods of complex system researching. In order to solve the problems of the statistics and machine learning the CUP algorithm in this paper is proposed. The paper gave the basic definition and the measure of the CUP meanwhile it provided the theoretical support for application. Fitting algorithm based on CUP system was introduced. The algorithm can output more information from the fitting process. Contract of fitting to Lorenz system between CUP algorithm and artificial neural net was displayed in the following part. The different fitting effect by different candidate coefficient set is discussed. A typical example of realistic social application and other usages are put up. The CUP algorithm provides the probability and numerical fitting conclusion CUP algorithm the same time while numerical calculation accuracy is optional for different problems.

On accurate high-order numerical derivatives computations for quantum chemistry purposes

Various molecular parameters in quantum chemistry could be computed as derivatives of energy over different arguments. Unfortunately, it is quite complicated to obtain analytical expression for characteristics that are of interest in the framework of methods that account electron correlation. Especially it relates to the coupled cluster (CC) theory. In such cases, numerical differentiation comes to rescue. This approach, like any other numerical method has empirical parameters and restrictions that require investigation. Current work is called to clarify the details of Finite-Field method usage for high-order derivatives calculation in CC approaches. General approach to the parameter choice and corresponding recommendations about numerical steadiness verification are proposed. As an example of Finite-Field approach implementation characterization of optical properties of fullerene passing process through the aperture of carbon nanotorus is given.

Numerical program optimisation by automatic improvement of the accuracy of computations

Over the last decade, guaranteeing the accuracy of computations relying on the IEEE754 floating-point arithmetic has become increasingly complex. Failures, caused by small or large perturbations due to round-off errors, have been registered. To cope with this issue, we have developed a tool which corrects these errors by automatically transforming programs in a source to source manner. Our transformation, relying on static analysis by abstract abstraction, operates on pieces of code with assignments, conditionals and loops. By transforming programs, we can significantly optimise the numerical accuracy of computations by minimising the error relatively to the exact result. In this article, we present two important desirable side-effects of our transformation. Firstly, we show that our transformed programs, executed in single precision, may compete with not transformed codes executed in double precision. Secondly, we show that optimising the numerical accuracy of programs accelerates the convergence of numerical iterative methods. Both of these properties of our transformation are of great interest for numerical software.

Analysis of optical characteristics of holey photonic crystal devices with the extended coupled-mode formalism

Presented here is a new approach for analysis of the so-called holey photonic crystals—a class of electro-optical components, in which periodicity of air holes in dielectric media is used for confinement of light. This class includes several kinds of microstructured fibers, semiconductor lasers etc. Accurate evaluation of optical characteristics of those devices is usually a complicated problem due to the large dimensions and the fine structure of their refractive index distribution. Furthermore, usually, only numerical solutions for this class of optical components are available. The overwhelming majority of the physical models, suitable for analysis of holey photonic devices, proceed from the “natural” assumption: the devices are considered as arrays of air holes, surrounded by dielectric material. In this work we propose another model. Namely, we treat them as arrays of dielectric spots (waveguides), embedded in the air (cladding material). This model allows utilization of the extended coupled-mode theory (a relatively new approach designed for analysis of infinite arrays of coupled waveguides and previously considered inapplicable to holey optical components) for calculations of the latter. In this sense, we present a new method for analysis of holey photonic crystals. On the one hand, our method allows analytical evaluation of some optical characteristics of holey optical components (such as the number of photonic bands and bandwidth). On the other hand, accurate numerical computation of the photonic band structure of the holey photonic devices, incorporating a large number of holes, can be done with this technique on a timescale of several minutes.

An accurate discontinuous Galerkin method for solving point-source Eikonal equation in 2-D heterogeneous anisotropic media

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications.

Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems

ABSTRACTAn analysis was performed in this paper to study the problem of magnetohydrodynamic squeezing flow of nanofluid between parallel disks. This paper also proposed a reproducing kernel method for solving fourth-order four-point boundary value problems. In order to eliminate the singularity of the equation, a transform was used. Convergence analysis and error estimation for the present method in -space were also discussed. The exact solution was represented in the form of series in the reproducing kernel Hilbert space which proved higher accuracy in numerical computation. The algorithm derived from this approach can be easily implemented. The ideas and techniques presented in this paper will be useful for solving many other problems.

Study of Multiphase Flow in Wellbore under the Condition of Sour Gas Invasion

The deep marine carbonate formation is one of the key areas of oil and gas resource exploration and development for the future, and the basic characters of these resources are HTHP, high content of sour gas and narrow mud density window. Sour gases (H2S or CO2) are prone to invade into wellbore, leading to serious drilling accidents such as kick and blowout. Considering the sour gas solubility, phase transition and effects of temperature and pressure on the physical parameters of drilling fluid, a multiphase flow model for sour gas invasion is established, and a transient heat transfer and pressure coupling solving method is proposed to ensure the accuracy of numerical calculation. The results indicate that the annulus circulating temperature with H2S invasion is the highest, temperature with CO2 comes second and CH4 is the least. As gas solubility decreases and its phase transition near the wellhead, the volume of gas is expanded sharply and the gas phase volume fraction changes dramatically, which may lead to kick and blowout accidents instantly. When gas solubility is considered, a larger annular pressure could be got, and H2S has a larger influence on the annular pressure than CO2. Furthermore, the dissolved gas and annular pressure varying with different content of H2S or CO2 in sour gas are calculated and analyzed. The research results may provide valuable theoretical guidance for the deep sour gas reservoir exploration and development.

Three-component Parallel and Synchronous Seismic Data Acquisition Based on Time-division Sampling System

To economize power dissipation and volume of the three-component parallel and synchronous seismic data acquisition system, under the inspiration of sampling rate conversion theory in the digital signal processing, a project of three-component parallel and synchronous seismic data acquisition method is proposed based on time-division sampling system, in which triple interpolation is implemented in the three sets of data acquired by time-division sampling. Then another interpolation or decimation is carried out to aim at converting sampling rate of the system into the target value. Results of the error analysis show that the accuracy of numerical calculation in this conversion process is superior to the resolution ratio of hardware system. the prominent dominant of this project is that power dissipation and volume of parallel and synchronous acquisition system applied to band-limited signal are optimized and performance of the whole system is improved.

On Traveling Wave Fronts in a Degenerate Nonlinear Parabolic System Modeling Bacterial Pattern Formation

In this paper we consider a degenerate nonlinear parabolic system which models spatio-temporal patterns generated by bacterial colonies. A three-dimensional phase space analysis of wave fronts in this model system is performed. The existence of a sharp wave front for a minimum speed in addition to smooth wave fronts for large speeds is shown. Further, an accurate numerical computation of such wave front solutions is presented.

Evaluation and Analysis of Curvature-Corrected Filter-based Turbulent Model

AbstractPrediction of the characteristics of turbulent flow with streamline curvature is of great importance in engineering applications. In this paper, a curvature-corrected filter-based turbulent model is suggested by applying the Spalart-Shur correction term. This new version of the model (FBM-CC) has been tested and verified through two canonical benchmarks with strong streamline curvature: the flow in a two-dimensional U-duct and the free shear flow past NACA0012 airfoil with a round tip. Predictions of the FBM-CC model are compared with available experimental data and the corresponding results of the original FBM model. The numerical results show that the FBM-CC model significantly improves the sensitivity to the effect of streamline curvature and the numerical calculation accuracy, in relatively good agreement with the experimental data, which suggests that this proposed model may be employed to simulate the turbulent curved flow in engineering applications.

Numerical Study of MHD Viscoelastic Fluid Flow with Binary Chemical Reaction and Arrhenius Activation Energy

Abstract Here we address the influence of heat/mass transfer on MHD axisymmetric viscoelastic fluid flow developed by an elastic sheet stretching linearly in the radial direction. Constitutive relations of Maxwell fluid model are utilized in mathematical formulation of the problem. Non-linear radiation heat flux is factored in the model which accounts for both small and large temperature differences. Chemical reaction effects with modified Arrhenius energy function are analyzed which are not yet explored for viscoelastic fluid flows. Highly accurate numerical computations are performed. Our computations show S-shaped profiles of temperature function in case of sufficiently large temperature differences. Species concentration increases when activation energy for chemical reaction is increased. However, both chemical reaction rate and temperature gradient tend to reduce the solute concentration.

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent properties in two-electron atoms/ions which include the negatively charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively charged, helium-like ions from Li$^{+}$ to Ni$^{26+}$. All these ions are considered in their ground $1^{1}S-$state(s). The slowly convergent properties selected in this study include the electron-nulceus $\langle r^{2 k}_{eN} \rangle$ and electron-electron $\langle r^{2 k}_{ee} \rangle$ expectation values for $k$ = 2, 3, 4 and 5.

MIMO FSO communication using subcarrier intensity modulation over double generalized gamma fading

Atmospheric turbulence-induced fading is known to have a serious detrimental effect on the performance of free-space optical (FSO) communication. The involvement of multiple lasers and photodetectors in FSO systems offers an effective way to overcome fading. Very recently, a new generic fading model, called double-generalized gamma (double GG), is developed for accurately describing irradiance fading over a wide range of turbulence conditions. Therefore, for a general and exact study of the multiple-input multiple-output (MIMO) FSO system, the double GG fading model is adopted in this paper. We investigate the MIMO FSO systems using subcarrier intensity modulation. Two typical transmit diversity schemes, repetition code (RC) and orthogonal space-time block code (OSTBC), are considered. We first propose a new power series expression for the probability density function of the double GG fading. Then we derive the average error rate expressions for both schemes in terms of double power series. The truncated forms of the derived power series enable the rapid and accurate numerical computation of the error rates. Furthermore, we present the asymptotic error rate analyses at high electrical signal-to-noise ratio (SNR) for both schemes. Closed-form diversity order and coding gain for both schemes are also obtained. Our numerical results, verified by simulation, confirm that RC outperforms OSTBC for MIMO FSO systems with subcarrier intensity modulation in double GG fading. The asymptotic coding gain of the RC scheme over the OSTBC scheme is analytically quantified for varying degrees of the fading strength.

Calculation of the effective stiffnesses of corrugated plates by solving the problem on the plate cross-section

It is shown that for corrugated, in particular, multilayer plates, the tree-dimensional cell problem of averaging can be reduced to the two-dimensional problem on the cross section of the periodicity cell of the plate. This significantly increases the accuracy of numerical calculation of the effective stiffnesses of corrugated plates. Numerical calculations of the stiffnesses of a plate with a sinusoidal corrugation are performed, and the results are compared with available data.

Editorial: Quantitative Biology: Dynamics of Living Systems.

Editorial: Quantitative Biology: Dynamics of Living Systems.

Influence of Void Transposition Structure on the Leakage Magnetic Field and Circulating Current Loss of Stator Bars in Water-Cooled Turbo-Generators

In the design of stator bar structure, void transposition is an important way of reducing circulating current loss in water-cooled turbo-generators. The different void transposition structures have a great influence on circulating current loss. However, the influences of void transposition structure on the leakage magnetic field and circulating current loss are not definite. A 600-MW water-cooled turbo-generator is taken as an example. A three-dimensional (3-D) physical model of transposition bars in a single slot is established, and the field-circuit coupling method is used in 3-D numerical calculation of the leakage magnetic field and circulating current loss. The influences of segment number and length of the void transposition on the slot leakage magnetic field, current, and circulating current loss are obtained. The relationship between the slot leakage magnetic field distribution along the axial direction and circulating current loss based on different void transposition structures is clarified. The numerical calculation accuracy is validated with the current test experiment. New strategies and theoretical basis will be provided for the optimal design and technology of the transposition bars.

Scaling law and general expression for transport ac loss of a rectangular thin strip with power-law E(J) relation

Transport ac loss Q of a superconducting rectangular thin strip obeying a power-law relation E∝Jn as a function of current amplitude Im may be, following Norris, expressed by normalized quantities as q(im). A scaling law is deduced that if Icf, Ic and f being the critical current and frequency, is multiplied by a positive constant C, then im and qm are multiplied by C1/(n−1)and C2/(n−1),respectively. Based on this scaling law and the well-known Norris formula, the general function of q(im, n, f) is obtained graphically or analytically for any practical purpose, after accurate numerical computations on a set of q(im) at several values of n and a fixed value of f.

Use of Weno Schemes for Simulation of the Reflected Shock Wave–Boundary Layer Interaction

Numerical simulation of the shock wave–laminar boundary layer interaction is carried out on the basis of the model problem at different Reynolds numbers. The use of WENO schemes of high order of accuracy is demonstrated. The calculated shock-wave structure of the fl ow is compared with the data available in the literature and with the data obtained from TVD schemes. Criteria of accuracy of numerical calculations that are related to the position of shock-wave structures, and also the time of solution of the problem with various difference schemes, are discussed. Recommendations on practical use of difference schemes of high order of accuracy are given.

Design Calculation for Wedge Cam of Small Roller Centering Three-Jaw Jig

As wedge cam contour’s conventional equation of small roller centering three-jaw jig calculated by classic method is complex and difficult to be used for processing directly, a numerical calculation method for the wedge cam contour is proposed. Firstly, structure and working principle of centering small roller jig is introduced. Secondly, a new numerical calculation method sampling for wedge cam contour using equal step is presented, which can be obtained sampling points expression by numerical calculation model. Then,these samples points assignment will be fitting and interpolation in accordance with quadratic polynomial curve. The equation of quadratic polynomial interpolation on these sampling points these sampling will be obtained, which can be directly applied to NC programming. At last, through comparing fitted quadratic polynomial curve calculated by the numerical method with the theoretical curve calculated by classic method, it is found that the comparison tolerance is much smaller than conventional processing tolerance which is produced by using the theoretical curve for processing. The comparison tolerance is analyzed, refining the sampling step length and using piecewise fitting and interpolation loop calculation method is proposed,which can further improve numerical calculation accuracy to satisfy the requirement of higher and higher positioning. Therefore, it can be concluded that the numerical calculation method can effectively solve the difficult processing problem of wedge cam contour, which will produce better economic benefits.