Approximation of the exponential integral (well function) using sampling methods
Baalousha, Husam Musa
2015-04-01
Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.
Approximation of the Doppler broadening function by Frobenius method
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C.
2005-01-01
An analytical approximation of the Doppler broadening function ψ(x,ξ) is proposed. This approximation is based on the solution of the differential equation for ψ(x,ξ) using the methods of Frobenius and the parameters variation. The analytical form derived for ψ(x,ξ) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)
Approximation methods for the partition functions of anharmonic systems
International Nuclear Information System (INIS)
Lew, P.; Ishida, T.
1979-07-01
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations
Quantal density functional theory II. Approximation methods and applications
International Nuclear Information System (INIS)
Sahni, Viraht
2010-01-01
This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)
Multi-level methods and approximating distribution functions
International Nuclear Information System (INIS)
Wilson, D.; Baker, R. E.
2016-01-01
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Multi-level methods and approximating distribution functions
Energy Technology Data Exchange (ETDEWEB)
Wilson, D., E-mail: daniel.wilson@dtc.ox.ac.uk; Baker, R. E. [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom)
2016-07-15
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Directory of Open Access Journals (Sweden)
Jie Shen
2015-01-01
Full Text Available We describe an extension of the redistributed technique form classical proximal bundle method to the inexact situation for minimizing nonsmooth nonconvex functions. The cutting-planes model we construct is not the approximation to the whole nonconvex function, but to the local convexification of the approximate objective function, and this kind of local convexification is modified dynamically in order to always yield nonnegative linearization errors. Since we only employ the approximate function values and approximate subgradients, theoretical convergence analysis shows that an approximate stationary point or some double approximate stationary point can be obtained under some mild conditions.
An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
Directory of Open Access Journals (Sweden)
Wei Wang
2014-01-01
Full Text Available We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.
International Nuclear Information System (INIS)
Gaj, E.V.; Badikov, S.A.; Gusejnov, M.A.; Rabotnov, N.S.
1988-01-01
Possible applications of rational functions in the analysis of neutron cross sections, angular distributions and neutron constants generation are described. Results of investigations made in this direction, which have been obtained after the preceding conference in Kiev, are presented: the method of simultaneous treatment of several cross sections for one compound nucleus in the resonance range; the use of the Pade approximation for elastically scattered neutron angular distribution approximation; obtaining of subgroup constants on the basis of rational approximation of cross section functional dependence on dilution cross section; the first experience in function approximation by two variables
Rational function approximation method for discrete ordinates problems in slab geometry
International Nuclear Information System (INIS)
Leal, Andre Luiz do C.; Barros, Ricardo C.
2009-01-01
In this work we use rational function approaches to obtain the transfer functions that appear in the spectral Green's function (SGF) auxiliary equations for one-speed isotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use the computation of the Pade approximants to compare the results with the standard SGF method's applied to deep penetration problems in homogeneous domains. This work is a preliminary investigation of a new proposal for handling leakage terms that appear in the two transverse integrated one-dimensional SN equations in the exponential SGF method (SGF-ExpN). Numerical results are presented to illustrate the rational function approximation accuracy. (author)
Approximated calculation of the vacuum wave function and vacuum energy of the LGT with RPA method
International Nuclear Information System (INIS)
Hui Ping
2004-01-01
The coupled cluster method is improved with the random phase approximation (RPA) to calculate vacuum wave function and vacuum energy of 2 + 1 - D SU(2) lattice gauge theory. In this calculating, the trial wave function composes of single-hollow graphs. The calculated results of vacuum wave functions show very good scaling behaviors at weak coupling region l/g 2 >1.2 from the third order to the sixth order, and the vacuum energy obtained with RPA method is lower than the vacuum energy obtained without RPA method, which means that this method is a more efficient one
APPROX, 1-D and 2-D Function Approximation by Polynomials, Splines, Finite Elements Method
International Nuclear Information System (INIS)
Tollander, Bengt
1975-01-01
1 - Nature of physical problem solved: Approximates one- and two- dimensional functions using different forms of the approximating function, as polynomials, rational functions, Splines and (or) the finite element method. Different kinds of transformations of the dependent and (or) the independent variables can easily be made by data cards using a FORTRAN-like language. 2 - Method of solution: Approximations by polynomials, Splines and (or) the finite element method are made in L2 norm using the least square method by which the answer is directly given. For rational functions in one dimension the result given in L(infinite) norm is achieved by iterations moving the zero points of the error curve. For rational functions in two dimensions, the norm is L2 and the result is achieved by iteratively changing the coefficients of the denominator and then solving the coefficients of the numerator by the least square method. The transformation of the dependent and (or) independent variables is made by compiling the given transform data card(s) to an array of integers from which the transformation can be made
Zeng, Lang; He, Yu; Povolotskyi, Michael; Liu, XiaoYan; Klimeck, Gerhard; Kubis, Tillmann
2013-06-01
In this work, the low rank approximation concept is extended to the non-equilibrium Green's function (NEGF) method to achieve a very efficient approximated algorithm for coherent and incoherent electron transport. This new method is applied to inelastic transport in various semiconductor nanodevices. Detailed benchmarks with exact NEGF solutions show (1) a very good agreement between approximated and exact NEGF results, (2) a significant reduction of the required memory, and (3) a large reduction of the computational time (a factor of speed up as high as 150 times is observed). A non-recursive solution of the inelastic NEGF transport equations of a 1000 nm long resistor on standard hardware illustrates nicely the capability of this new method.
International Nuclear Information System (INIS)
Huh, Jae Sung; Kwak, Byung Man
2011-01-01
Robust optimization or reliability-based design optimization are some of the methodologies that are employed to take into account the uncertainties of a system at the design stage. For applying such methodologies to solve industrial problems, accurate and efficient methods for estimating statistical moments and failure probability are required, and further, the results of sensitivity analysis, which is needed for searching direction during the optimization process, should also be accurate. The aim of this study is to employ the function approximation moment method into the sensitivity analysis formulation, which is expressed as an integral form, to verify the accuracy of the sensitivity results, and to solve a typical problem of reliability-based design optimization. These results are compared with those of other moment methods, and the feasibility of the function approximation moment method is verified. The sensitivity analysis formula with integral form is the efficient formulation for evaluating sensitivity because any additional function calculation is not needed provided the failure probability or statistical moments are calculated
A point-value enhanced finite volume method based on approximate delta functions
Xuan, Li-Jun; Majdalani, Joseph
2018-02-01
We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.
Bisetti, Fabrizio
2012-01-01
with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix
International Nuclear Information System (INIS)
Song Lina; Wang Weiguo
2010-01-01
In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
A Method of Approximating Expectations of Functions of Sums of Independent Random Variables
Klass, Michael J.
1981-01-01
Let $X_1, X_2, \\cdots$ be a sequence of independent random variables with $S_n = \\sum^n_{i = 1} X_i$. Fix $\\alpha > 0$. Let $\\Phi(\\cdot)$ be a continuous, strictly increasing function on $\\lbrack 0, \\infty)$ such that $\\Phi(0) = 0$ and $\\Phi(cx) \\leq c^\\alpha\\Phi(x)$ for all $x > 0$ and all $c \\geq 2$. Suppose $a$ is a real number and $J$ is a finite nonempty subset of the positive integers. In this paper we are interested in approximating $E \\max_{j \\in J} \\Phi(|a + S_j|)$. We construct a nu...
Directory of Open Access Journals (Sweden)
Cristinel Mortici
2015-01-01
Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.
Methods of approximation theory
National Research Council Canada - National Science Library
Stepane︠t︡s, A. I
2005-01-01
.... Korneichuk, Α. V. Efimov, S. A. Telyakovskii, etc. In the same years, the concept of (φ, β) -derivative defined for a given function / by a given sequence of numbers ψ = ψ (k), k = 1 , 2 , . . . , and numbers β was formed. The ordinary rth derivative, r = 1 , 2 , . . . , of a periodic function is a particular case of the (φ, /3)-derivative for y(k...
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as 1996......, due to this difference, it is possible to provide arguments favoring the method of Longstaff and Schwartz. Finally, we compare the methods in a realistic numerical setting and show that practitioners would do well to choose the method of Longstaff and Schwartz instead of the methods of Carriere...
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [Centro Federal de Educacao Tecnologica de Quimica de Nilopolis/RJ (CEFET), RJ (Brazil)]. E-mail: dpalma@cefeteq.br; Martinez, Aquilino S.; Silva, Fernando C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br; fernando@lmn.con.ufrj.br
2005-07-01
An analytical approximation of the Doppler broadening function {psi}(x,{xi}) is proposed. This approximation is based on the solution of the differential equation for {psi}(x,{xi}) using the methods of Frobenius and the parameters variation. The analytical form derived for {psi}(x,{xi}) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)
Rosolen, A.; Peco, C.; Arroyo, M.
2013-01-01
We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp i...
Energy Technology Data Exchange (ETDEWEB)
Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp [Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Champagne, Benoît; Botek, Edith [Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur (Belgium)
2015-01-22
We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.
Fujiwara, Takeo; Nishino, Shinya; Yamamoto, Susumu; Suzuki, Takashi; Ikeda, Minoru; Ohtani, Yasuaki
2018-06-01
A novel tight-binding method is developed, based on the extended Hückel approximation and charge self-consistency, with referring the band structure and the total energy of the local density approximation of the density functional theory. The parameters are so adjusted by computer that the result reproduces the band structure and the total energy, and the algorithm for determining parameters is established. The set of determined parameters is applicable to a variety of crystalline compounds and change of lattice constants, and, in other words, it is transferable. Examples are demonstrated for Si crystals of several crystalline structures varying lattice constants. Since the set of parameters is transferable, the present tight-binding method may be applicable also to molecular dynamics simulations of large-scale systems and long-time dynamical processes.
International Nuclear Information System (INIS)
Dalmasse, Kevin; Nychka, Douglas W.; Gibson, Sarah E.; Fan, Yuhong; Flyer, Natasha
2016-01-01
The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal polarimetric measurements using the Fe XIII 10747 and 10798 lines, which are sensitive to the coronal magnetic field. However, inverting such polarimetric measurements into magnetic field data is a difficult task because the corona is optically thin at these wavelengths and the observed signal is therefore the integrated emission of all the plasma along the line of sight. To overcome this difficulty, we take on a new approach that combines a parameterized 3D magnetic field model with forward modeling of the polarization signal. For that purpose, we develop a new, fast and efficient, optimization method for model-data fitting: the Radial-basis-functions Optimization Approximation Method (ROAM). Model-data fitting is achieved by optimizing a user-specified log-likelihood function that quantifies the differences between the observed polarization signal and its synthetic/predicted analog. Speed and efficiency are obtained by combining sparse evaluation of the magnetic model with radial-basis-function (RBF) decomposition of the log-likelihood function. The RBF decomposition provides an analytical expression for the log-likelihood function that is used to inexpensively estimate the set of parameter values optimizing it. We test and validate ROAM on a synthetic test bed of a coronal magnetic flux rope and show that it performs well with a significantly sparse sample of the parameter space. We conclude that our optimization method is well-suited for fast and efficient model-data fitting and can be exploited for converting coronal polarimetric measurements, such as the ones provided by CoMP, into coronal magnetic field data.
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
International Nuclear Information System (INIS)
Bricka, M.
1962-03-01
This report addresses the problem of determination of neutron spectrum by using a set of detectors. The spectrum approximation method based on a polygonal function is more particularly studied. The author shows that the coefficients of the usual mathematical model can be simply formulated and assessed. The study of spectra approximation by a polygonal function shows that dose can be expressed by a linear function of the activity of the different detectors [fr
Measure Fields for Function Approximation
1993-06-01
intelligence research is provided by ONR contract N00014-91-J-4038 J.L. Marroquin was supported in part by a grant from the Consejo Nacional de Ciencia y ... Tecnologia , Mexico. _ 93-28011 9-3 -- -" nnuM IInu 4 0 0 0 1 Introduction imating functions are always discontinuous, and the dis- continuities are...capacity and generalization capabili- is present panel (a) of figure 1 shows a function z(z, y ) ties. that is equal to a tilted plane inside an L
Reliable Function Approximation and Estimation
2016-08-16
compressed sensing results to a wide class of infinite -dimensional problems. We discuss four key application domains for the methods developed in this... infinite -dimensional problems. We discuss four key findings arising from this project, as related to uncertainty quantification, image processing, matrix...compressed sensing results to a wide class of infinite -dimensional problems. We discuss four key application domains for the methods developed in this project
Discovery of functional and approximate functional dependencies in relational databases
Directory of Open Access Journals (Sweden)
Ronald S. King
2003-01-01
Full Text Available This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.
Tutu, Hiroki
2011-06-01
Stochastic resonance (SR) enhanced by time-delayed feedback control is studied. The system in the absence of control is described by a Langevin equation for a bistable system, and possesses a usual SR response. The control with the feedback loop, the delay time of which equals to one-half of the period (2π/Ω) of the input signal, gives rise to a noise-induced oscillatory switching cycle between two states in the output time series, while its average frequency is just smaller than Ω in a small noise regime. As the noise intensity D approaches an appropriate level, the noise constructively works to adapt the frequency of the switching cycle to Ω, and this changes the dynamics into a state wherein the phase of the output signal is entrained to that of the input signal from its phase slipped state. The behavior is characterized by power loss of the external signal or response function. This paper deals with the response function based on a dichotomic model. A method of delay-coordinate series expansion, which reduces a non-Markovian transition probability flux to a series of memory fluxes on a discrete delay-coordinate system, is proposed. Its primitive implementation suggests that the method can be a potential tool for a systematic analysis of SR phenomenon with delayed feedback loop. We show that a D-dependent behavior of poles of a finite Laplace transform of the response function qualitatively characterizes the structure of the power loss, and we also show analytical results for the correlation function and the power spectral density.
Nonlinear Ritz approximation for Fredholm functionals
Directory of Open Access Journals (Sweden)
Mudhir A. Abdul Hussain
2015-11-01
Full Text Available In this article we use the modify Lyapunov-Schmidt reduction to find nonlinear Ritz approximation for a Fredholm functional. This functional corresponds to a nonlinear Fredholm operator defined by a nonlinear fourth-order differential equation.
Polynomial approximation of functions in Sobolev spaces
International Nuclear Information System (INIS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces
A partition function approximation using elementary symmetric functions.
Directory of Open Access Journals (Sweden)
Ramu Anandakrishnan
Full Text Available In statistical mechanics, the canonical partition function [Formula: see text] can be used to compute equilibrium properties of a physical system. Calculating [Formula: see text] however, is in general computationally intractable, since the computation scales exponentially with the number of particles [Formula: see text] in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm - the direct interaction algorithm (DIA - for approximating the canonical partition function [Formula: see text] in [Formula: see text] operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs, which can be computed in [Formula: see text] operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.
DEFF Research Database (Denmark)
Senjean, Bruno; Knecht, Stefan; Jensen, Hans Jørgen Aa
2015-01-01
Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is, in principle, very attractive but has been hard to use in practice. A practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The model relies on two modifications of GOK-DFT: use...... promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semilocal functionals. Even at the Kohn-Sham ensemble DFT level, which is recovered when the range-separation parameter is set to 0, LIM performs better than...
An inductive algorithm for smooth approximation of functions
International Nuclear Information System (INIS)
Kupenova, T.N.
2011-01-01
An inductive algorithm is presented for smooth approximation of functions, based on the Tikhonov regularization method and applied to a specific kind of the Tikhonov parametric functional. The discrepancy principle is used for estimation of the regularization parameter. The principle of heuristic self-organization is applied for assessment of some parameters of the approximating function
RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.
Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the
Smooth function approximation using neural networks.
Ferrari, Silvia; Stengel, Robert F
2005-01-01
An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.
Quasi-fractional approximation to the Bessel functions
International Nuclear Information System (INIS)
Guerrero, P.M.L.
1989-01-01
In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
Multidimensional stochastic approximation using locally contractive functions
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Legendre-tau approximations for functional differential equations
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
On approximation of functions by product operators
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Hare Krishna Nigam
2013-12-01
Full Text Available In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r, 1≤ r <∞ and the weighted class W(Lr,ξ(t, 1≤ r <∞ by (C,2(E,1 product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
Function approximation of tasks by neural networks
International Nuclear Information System (INIS)
Gougam, L.A.; Chikhi, A.; Mekideche-Chafa, F.
2008-01-01
For several years now, neural network models have enjoyed wide popularity, being applied to problems of regression, classification and time series analysis. Neural networks have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. The latter is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. In a previous contribution, we have used a well known simplified architecture to show that it provides a reasonably efficient, practical and robust, multi-frequency analysis. We have investigated the universal approximation theory of neural networks whose transfer functions are: sigmoid (because of biological relevance), Gaussian and two specified families of wavelets. The latter have been found to be more appropriate to use. The aim of the present contribution is therefore to use a m exican hat wavelet a s transfer function to approximate different tasks relevant and inherent to various applications in physics. The results complement and provide new insights into previously published results on this problem
Saddlepoint approximation methods in financial engineering
Kwok, Yue Kuen
2018-01-01
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...
Approximate solution methods in engineering mechanics
International Nuclear Information System (INIS)
Boresi, A.P.; Cong, K.P.
1991-01-01
This is a short book of 147 pages including references and sometimes bibliographies at the end of each chapter, and subject and author indices at the end of the book. The test includes an introduction of 3 pages, 29 pages explaining approximate analysis, 41 pages on finite differences, 36 pages on finite elements, and 17 pages on specialized methods
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
Discontinuous approximate molecular electronic wave-functions
International Nuclear Information System (INIS)
Stuebing, E.W.; Weare, J.H.; Parr, R.G.
1977-01-01
Following Kohn, Schlosser and Marcus and Weare and Parr an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh--Ritz method in the replacement of the usual kinetic energy operators circumflex T(μ) with operators circumflex T'(μ) = circumflex T(μ) + circumflex I(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the nabla PSI . nabla PSI way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of nabla PSI and the change of PSI across surfaces of discontinuity. Various calculations are carried out for the hydrogen molecule-ion and the hydrogen molecule. It is shown that ab initio calculations on molecules can be carried out quite generally with a basis of atomic orbitals exactly obeying the zero-differential overlap (ZDO) condition, and a firm basis is thereby provided for theories of molecular electronic structure invoking the ZDO aoproximation. It is demonstrated that a valence bond theory employing orbitals exactly obeying ZDO can provide an adequate account of chemical bonding, and several suggestions are made regarding molecular orbital methods
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
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Soon-Mo Jung
2011-01-01
Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
Sequential function approximation on arbitrarily distributed point sets
Wu, Kailiang; Xiu, Dongbin
2018-02-01
We present a randomized iterative method for approximating unknown function sequentially on arbitrary point set. The method is based on a recently developed sequential approximation (SA) method, which approximates a target function using one data point at each step and avoids matrix operations. The focus of this paper is on data sets with highly irregular distribution of the points. We present a nearest neighbor replacement (NNR) algorithm, which allows one to sample the irregular data sets in a near optimal manner. We provide mathematical justification and error estimates for the NNR algorithm. Extensive numerical examples are also presented to demonstrate that the NNR algorithm can deliver satisfactory convergence for the SA method on data sets with high irregularity in their point distributions.
An approximation to the interference term using Frobenius Method
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mail: aquilino@lmp.ufrj.br
2007-07-01
An analytical approximation of the interference term {chi}(x,{xi}) is proposed. The approximation is based on the differential equation to {chi}(x,{xi}) using the Frobenius method and the parameter variation. The analytical expression of the {chi}(x,{xi}) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U{sup 238} isotope for different energies and temperature ranges. (author)
An approximation to the interference term using Frobenius Method
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da
2007-01-01
An analytical approximation of the interference term χ(x,ξ) is proposed. The approximation is based on the differential equation to χ(x,ξ) using the Frobenius method and the parameter variation. The analytical expression of the χ(x,ξ) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U 238 isotope for different energies and temperature ranges. (author)
Mathieu functions and its useful approximation for elliptical waveguides
Pillay, Shamini; Kumar, Deepak
2017-11-01
The standard form of the Mathieu differential equation is where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.
Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method
Madureira, Alexandre L.; Sarkis, Marcus
2017-01-01
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\\infty$ coefficients. The methods are of Galerkin type and follows the Variational Multiscale and Localized Orthogonal Decomposition--LOD approaches in the sense that it decouples spaces into multiscale and fine subspaces. In a first method, the multiscale basis functions are obtained by mapping coarse basis functions, based...
A cluster approximation for the transfer-matrix method
International Nuclear Information System (INIS)
Surda, A.
1990-08-01
A cluster approximation for the transfer-method is formulated. The calculation of the partition function of lattice models is transformed to a nonlinear mapping problem. The method yields the free energy, correlation functions and the phase diagrams for a large class of lattice models. The high accuracy of the method is exemplified by the calculation of the critical temperature of the Ising model. (author). 14 refs, 2 figs, 1 tab
Using function approximation to determine neural network accuracy
International Nuclear Information System (INIS)
Wichman, R.F.; Alexander, J.
2013-01-01
Many, if not most, control processes demonstrate nonlinear behavior in some portion of their operating range and the ability of neural networks to model non-linear dynamics makes them very appealing for control. Control of high reliability safety systems, and autonomous control in process or robotic applications, however, require accurate and consistent control and neural networks are only approximators of various functions so their degree of approximation becomes important. In this paper, the factors affecting the ability of a feed-forward back-propagation neural network to accurately approximate a non-linear function are explored. Compared to pattern recognition using a neural network for function approximation provides an easy and accurate method for determining the network's accuracy. In contrast to other techniques, we show that errors arising in function approximation or curve fitting are caused by the neural network itself rather than scatter in the data. A method is proposed that provides improvements in the accuracy achieved during training and resulting ability of the network to generalize after training. Binary input vectors provided a more accurate model than with scalar inputs and retraining using a small number of the outlier x,y pairs improved generalization. (author)
Approximate convex hull of affine iterated function system attractors
International Nuclear Information System (INIS)
Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry
2012-01-01
Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.
Applications exponential approximation by integer shifts of Gaussian functions
Directory of Open Access Journals (Sweden)
S. M. Sitnik
2013-01-01
Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
On Approximate Solutions of Functional Equations in Vector Lattices
Directory of Open Access Journals (Sweden)
Bogdan Batko
2014-01-01
Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.
Function approximation with polynomial regression slines
International Nuclear Information System (INIS)
Urbanski, P.
1996-01-01
Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author)
International Nuclear Information System (INIS)
Yuste, Santos Bravo; Abad, Enrique
2011-01-01
We present an iterative method to obtain approximations to Bessel functions of the first kind J p (x) (p > -1) via the repeated application of an integral operator to an initial seed function f 0 (x). The class of seed functions f 0 (x) leading to sets of increasingly accurate approximations f n (x) is considerably large and includes any polynomial. When the operator is applied once to a polynomial of degree s, it yields a polynomial of degree s + 2, and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree. We focus on the set of polynomial approximations generated from the seed function f 0 (x) = 1. This set of polynomials is useful not only for the computation of J p (x) but also from a physical point of view, as it describes the long-time decay modes of certain fractional diffusion and diffusion-wave problems.
Space-angle approximations in the variational nodal method
International Nuclear Information System (INIS)
Lewis, E. E.; Palmiotti, G.; Taiwo, T.
1999-01-01
The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared
On the approximation of the limit cycles function
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L. Cherkas
2007-11-01
Full Text Available We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x$, which is based on the Newton scheme applied to the Poincaré function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Liénard system.
Numerical approximations of difference functional equations and applications
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Zdzisław Kamont
2005-01-01
Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Local Approximation and Hierarchical Methods for Stochastic Optimization
Cheng, Bolong
In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the
Shape theory categorical methods of approximation
Cordier, J M
2008-01-01
This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and
Augmenting Ordinal Methods of Attribute Weight Approximation
DEFF Research Database (Denmark)
Daneilson, Mats; Ekenberg, Love; He, Ying
2014-01-01
of the obstacles and methods for introducing so-called surrogate weights have proliferated in the form of ordinal ranking methods for criteria weights. Considering the decision quality, one main problem is that the input information allowed in ordinal methods is sometimes too restricted. At the same time, decision...... makers often possess more background information, for example, regarding the relative strengths of the criteria, and might want to use that. We propose combined methods for facilitating the elicitation process and show how this provides a way to use partial information from the strength of preference...
Approximate methods for derivation of covariance data
International Nuclear Information System (INIS)
Tagesen, S.
1992-01-01
Several approaches for the derivation of covariance information for evaluated nuclear data files (EFF2 and ENDF/B-VI) have been developed and used at IRK and ORNL respectively. Considerations, governing the choice of a distinct method depending on the quantity and quality of available data are presented, advantages/disadvantages are discussed and examples of results are given
Comparison of four support-vector based function approximators
de Kruif, B.J.; de Vries, Theodorus J.A.
2004-01-01
One of the uses of the support vector machine (SVM), as introduced in V.N. Vapnik (2000), is as a function approximator. The SVM and approximators based on it, approximate a relation in data by applying interpolation between so-called support vectors, being a limited number of samples that have been
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
Approximated Function Based Spectral Gradient Algorithm for Sparse Signal Recovery
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-02-01
Full Text Available Numerical algorithms for the l0-norm regularized non-smooth non-convex minimization problems have recently became a topic of great interest within signal processing, compressive sensing, statistics, and machine learning. Nevertheless, the l0-norm makes the problem combinatorial and generally computationally intractable. In this paper, we construct a new surrogate function to approximate l0-norm regularization, and subsequently make the discrete optimization problem continuous and smooth. Then we use the well-known spectral gradient algorithm to solve the resulting smooth optimization problem. Experiments are provided which illustrate this method is very promising.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
On root mean square approximation by exponential functions
Sharipov, Ruslan
2014-01-01
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.
Function approximation using combined unsupervised and supervised learning.
Andras, Peter
2014-03-01
Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.
Precise analytic approximations for the Bessel function J1 (x)
Maass, Fernando; Martin, Pablo
2018-03-01
Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.
Approximate formulas for elasticity of the Tornquist functions and some their advantages
Issin, Meyram
2017-09-01
In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Efficient approximation of black-box functions and Pareto sets
Rennen, G.
2009-01-01
In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the
A simple approximation method for dilute Ising systems
International Nuclear Information System (INIS)
Saber, M.
1996-10-01
We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs
Directory of Open Access Journals (Sweden)
Yunfeng Wu
2014-01-01
Full Text Available This paper presents a novel adaptive linear and normalized combination (ALNC method that can be used to combine the component radial basis function networks (RBFNs to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error and the better fidelity (characterized by normalized correlation coefficient of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.
Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio
2015-04-21
We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.
DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers
Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro
2016-10-01
This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.
Longitudinal functional principal component modelling via Stochastic Approximation Monte Carlo
Martinez, Josue G.
2010-06-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
Reducing Approximation Error in the Fourier Flexible Functional Form
Directory of Open Access Journals (Sweden)
Tristan D. Skolrud
2017-12-01
Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
Directory of Open Access Journals (Sweden)
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
On approximation and energy estimates for delta 6-convex functions.
Saleem, Muhammad Shoaib; Pečarić, Josip; Rehman, Nasir; Khan, Muhammad Wahab; Zahoor, Muhammad Sajid
2018-01-01
The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.
On approximation and energy estimates for delta 6-convex functions
Directory of Open Access Journals (Sweden)
Muhammad Shoaib Saleem
2018-02-01
Full Text Available Abstract The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted L2 $L^{2}$-norm.
Cheap contouring of costly functions: the Pilot Approximation Trajectory algorithm
International Nuclear Information System (INIS)
Huttunen, Janne M J; Stark, Philip B
2012-01-01
The Pilot Approximation Trajectory (PAT) contour algorithm can find the contour of a function accurately when it is not practical to evaluate the function on a grid dense enough to use a standard contour algorithm, for instance, when evaluating the function involves conducting a physical experiment or a computationally intensive simulation. PAT relies on an inexpensive pilot approximation to the function, such as interpolating from a sparse grid of inexact values, or solving a partial differential equation (PDE) numerically using a coarse discretization. For each level of interest, the location and ‘trajectory’ of an approximate contour of this pilot function are used to decide where to evaluate the original function to find points on its contour. Those points are joined by line segments to form the PAT approximation of the contour of the original function. Approximating a contour numerically amounts to estimating a lower level set of the function, the set of points on which the function does not exceed the contour level. The area of the symmetric difference between the true lower level set and the estimated lower level set measures the accuracy of the contour. PAT measures its own accuracy by finding an upper confidence bound for this area. In examples, PAT can estimate a contour more accurately than standard algorithms, using far fewer function evaluations than standard algorithms require. We illustrate PAT by constructing a confidence set for viscosity and thermal conductivity of a flowing gas from simulated noisy temperature measurements, a problem in which each evaluation of the function to be contoured requires solving a different set of coupled nonlinear PDEs. (paper)
Complexity of Gaussian-Radial-Basis Networks Approximating Smooth Functions
Czech Academy of Sciences Publication Activity Database
Kainen, P.C.; Kůrková, Věra; Sanguineti, M.
2009-01-01
Roč. 25, č. 1 (2009), s. 63-74 ISSN 0885-064X R&D Projects: GA ČR GA201/08/1744 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gaussian-radial-basis-function networks * rates of approximation * model complexity * variation norms * Bessel and Sobolev norms * tractability of approximation Subject RIV: IN - Informatics, Computer Science Impact factor: 1.227, year: 2009
Analytical approximations to seawater optical phase functions of scattering
Haltrin, Vladimir I.
2004-11-01
This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.
Approximate analytical methods for solving ordinary differential equations
Radhika, TSL; Rani, T Raja
2015-01-01
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti
Variational, projection methods and Pade approximants in scattering theory
International Nuclear Information System (INIS)
Turchetti, G.
1980-12-01
Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt
Design of A Cyclone Separator Using Approximation Method
Sin, Bong-Su; Choi, Ji-Won; Lee, Kwon-Hee
2017-12-01
A Separator is a device installed in industrial applications to separate mixed objects. The separator of interest in this research is a cyclone type, which is used to separate a steam-brine mixture in a geothermal plant. The most important performance of the cyclone separator is the collection efficiency. The collection efficiency in this study is predicted by performing the CFD (Computational Fluid Dynamics) analysis. This research defines six shape design variables to maximize the collection efficiency. Thus, the collection efficiency is set up as the objective function in optimization process. Since the CFD analysis requires a lot of calculation time, it is impossible to obtain the optimal solution by linking the gradient-based optimization algorithm. Thus, two approximation methods are introduced to obtain an optimum design. In this process, an L18 orthogonal array is adopted as a DOE method, and kriging interpolation method is adopted to generate the metamodel for the collection efficiency. Based on the 18 analysis results, the relative importance of each variable to the collection efficiency is obtained through the ANOVA (analysis of variance). The final design is suggested considering the results obtained from two optimization methods. The fluid flow analysis of the cyclone separator is conducted by using the commercial CFD software, ANSYS-CFX.
Directory of Open Access Journals (Sweden)
V. A. Baturin
2017-03-01
Full Text Available An optimal control problem for discrete systems is considered. A method of successive improvements along with its modernization based on the expansion of the main structures of the core algorithm about the parameter is suggested. The idea of the method is based on local approximation of attainability set, which is described by the zeros of the Bellman function in the special problem of optimal control. The essence of the problem is as follows: from the end point of the phase is required to find a path that minimizes functional deviations of the norm from the initial state. If the initial point belongs to the attainability set of the original controlled system, the value of the Bellman function equal to zero, otherwise the value of the Bellman function is greater than zero. For this special task Bellman equation is considered. The support approximation and Bellman equation are selected. The Bellman function is approximated by quadratic terms. Along the allowable trajectory, this approximation gives nothing, because Bellman function and its expansion coefficients are zero. We used a special trick: an additional variable is introduced, which characterizes the degree of deviation of the system from the initial state, thus it is obtained expanded original chain. For the new variable initial nonzero conditions is selected, thus obtained trajectory is lying outside attainability set and relevant Bellman function is greater than zero, which allows it to hold a non-trivial approximation. As a result of these procedures algorithms of successive improvements is designed. Conditions for relaxation algorithms and conditions for the necessary conditions of optimality are also obtained.
Tau method approximation of the Hubbell rectangular source integral
International Nuclear Information System (INIS)
Kalla, S.L.; Khajah, H.G.
2000-01-01
The Tau method is applied to obtain expansions, in terms of Chebyshev polynomials, which approximate the Hubbell rectangular source integral:I(a,b)=∫ b 0 (1/(√(1+x 2 )) arctan(a/(√(1+x 2 )))) This integral corresponds to the response of an omni-directional radiation detector situated over a corner of a plane isotropic rectangular source. A discussion of the error in the Tau method approximation follows
Improvement of Tone's method with two-term rational approximation
International Nuclear Information System (INIS)
Yamamoto, Akio; Endo, Tomohiro; Chiba, Go
2011-01-01
An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method. (author)
Integral approximants for functions of higher monodromic dimension
Energy Technology Data Exchange (ETDEWEB)
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
Pade approximants for entire functions with regularly decreasing Taylor coefficients
International Nuclear Information System (INIS)
Rusak, V N; Starovoitov, A P
2002-01-01
For a class of entire functions the asymptotic behaviour of the Hadamard determinants D n,m as 0≤m≤m(n)→∞ and n→∞ is described. This enables one to study the behaviour of parabolic sequences from Pade and Chebyshev tables for many individual entire functions. The central result of the paper is as follows: for some sequences {(n,m(n))} in certain classes of entire functions (with regular Taylor coefficients) the Pade approximants {π n,m(n) }, which provide the locally best possible rational approximations, converge to the given function uniformly on the compact set D={z:|z|≤1} with asymptotically best rate
Approximation solutions for indifference pricing under general utility functions
Chen, An; Pelsser, Antoon; Vellekoop, M.H.
2008-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners
Animating Nested Taylor Polynomials to Approximate a Function
Mazzone, Eric F.; Piper, Bruce R.
2010-01-01
The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…
Approximate Solutions for Indifference Pricing under General Utility Functions
Chen, A.; Pelsser, A.; Vellekoop, M.
2007-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners
Are there approximate relations among transverse momentum dependent distribution functions?
Energy Technology Data Exchange (ETDEWEB)
Harutyun AVAKIAN; Anatoli Efremov; Klaus Goeke; Andreas Metz; Peter Schweitzer; Tobias Teckentrup
2007-10-11
Certain {\\sl exact} relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into {\\sl approximate} ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting $h_{1L}^{\\perp(1)a}(x)$ to $h_L^a(x)$, and discuss how it can be further tested by future CLAS and COMPASS data.
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos; Paul, Thierry; Pezzotti, Federica; Pulvirenti, Mario
2011-01-01
We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.
Singlet structure function F_1 in double-logarithmic approximation
Ermolaev, B. I.; Troyan, S. I.
2018-03-01
The conventional ways to calculate the perturbative component of the DIS singlet structure function F_1 involve approaches based on BFKL which account for the single-logarithmic contributions accompanying the Born factor 1 / x. In contrast, we account for the double-logarithmic (DL) contributions unrelated to 1 / x and because of that they were disregarded as negligibly small. We calculate the singlet F_1 in the double-logarithmic approximation (DLA) and account at the same time for the running α _s effects. We start with a total resummation of both quark and gluon DL contributions and obtain the explicit expression for F_1 in DLA. Then, applying the saddle-point method, we calculate the small- x asymptotics of F_1, which proves to be of the Regge form with the leading singularity ω _0 = 1.066. Its large value compensates for the lack of the factor 1 / x in the DLA contributions. Therefore, this Reggeon can be identified as a new Pomeron, which can be quite important for the description of all QCD processes involving the vacuum (Pomeron) exchanges at very high energies. We prove that the expression for the small- x asymptotics of F_1 scales: it depends on a single variable Q^2/x^2 only instead of x and Q^2 separately. Finally, we show that the small- x asymptotics reliably represent F_1 at x ≤ 10^{-6}.
Approximate models for the analysis of laser velocimetry correlation functions
International Nuclear Information System (INIS)
Robinson, D.P.
1981-01-01
Velocity distributions in the subchannels of an eleven pin test section representing a slice through a Fast Reactor sub-assembly were measured with a dual beam laser velocimeter system using a Malvern K 7023 digital photon correlator for signal processing. Two techniques were used for data reduction of the correlation function to obtain velocity and turbulence values. Whilst both techniques were in excellent agreement on the velocity, marked discrepancies were apparent in the turbulence levels. As a consequence of this the turbulence data were not reported. Subsequent investigation has shown that the approximate technique used as the basis of Malvern's Data Processor 7023V is restricted in its range of application. In this note alternative approximate models are described and evaluated. The objective of this investigation was to develop an approximate model which could be used for on-line determination of the turbulence level. (author)
Approximate solution fuzzy pantograph equation by using homotopy perturbation method
Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.
2017-09-01
In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
An outer approximation method for the road network design problem.
Asadi Bagloee, Saeed; Sarvi, Majid
2018-01-01
Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.
International Nuclear Information System (INIS)
Cafiero, Mauricio; Gonzalez, Carlos
2005-01-01
We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...... to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations....
An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation
Hao, Q.
2017-05-26
We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.
An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation
Hao, Q.; Alkhalifah, Tariq Ali
2017-01-01
We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.
Analytical Evaluation of Beam Deformation Problem Using Approximate Methods
DEFF Research Database (Denmark)
Barari, Amin; Kimiaeifar, A.; Domairry, G.
2010-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified......, and this process produces noise in the obtained answers. This paper deals with the solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Perturbation, Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Variational...... Iteration Method (VIM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate for systems of non-linear differential equation....
Efficient solution of parabolic equations by Krylov approximation methods
Gallopoulos, E.; Saad, Y.
1990-01-01
Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.
Analytical models approximating individual processes: a validation method.
Favier, C; Degallier, N; Menkès, C E
2010-12-01
Upscaling population models from fine to coarse resolutions, in space, time and/or level of description, allows the derivation of fast and tractable models based on a thorough knowledge of individual processes. The validity of such approximations is generally tested only on a limited range of parameter sets. A more general validation test, over a range of parameters, is proposed; this would estimate the error induced by the approximation, using the original model's stochastic variability as a reference. This method is illustrated by three examples taken from the field of epidemics transmitted by vectors that bite in a temporally cyclical pattern, that illustrate the use of the method: to estimate if an approximation over- or under-fits the original model; to invalidate an approximation; to rank possible approximations for their qualities. As a result, the application of the validation method to this field emphasizes the need to account for the vectors' biology in epidemic prediction models and to validate these against finer scale models. Copyright © 2010 Elsevier Inc. All rights reserved.
The generalized approximation method and nonlinear heat transfer equations
Directory of Open Access Journals (Sweden)
Rahmat Khan
2009-01-01
Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.
An approximation method for nonlinear integral equations of Hammerstein type
International Nuclear Information System (INIS)
Chidume, C.E.; Moore, C.
1989-05-01
The solution of a nonlinear integral equation of Hammerstein type in Hilbert spaces is approximated by means of a fixed point iteration method. Explicit error estimates are given and, in some cases, convergence is shown to be at least as fast as a geometric progression. (author). 25 refs
Calculating Resonance Positions and Widths Using the Siegert Approximation Method
Rapedius, Kevin
2011-01-01
Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…
Deconvolution of EPR spectral lines with an approximate method
International Nuclear Information System (INIS)
Jimenez D, H.; Cabral P, A.
1990-10-01
A recently reported approximation expression to deconvolution Lorentzian-Gaussian spectral lines. with small Gaussian contribution, is applied to study an EPR line shape. The potassium-ammonium solution line reported in the literature by other authors was used and the results are compared with those obtained by employing a precise method. (Author)
On quasiclassical approximation in the inverse scattering method
International Nuclear Information System (INIS)
Geogdzhaev, V.V.
1985-01-01
Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem
Approximating methods for intractable probabilistic models: Applications in neuroscience
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro
2002-01-01
This thesis investigates various methods for carrying out approximate inference in intractable probabilistic models. By capturing the relationships between random variables, the framework of graphical models hints at which sets of random variables pose a problem to the inferential step. The appro...
Directory of Open Access Journals (Sweden)
W. Łenski
2015-01-01
Full Text Available The results generalizing some theorems on N, pnE, γ summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated.
An Approximate Method for Pitch-Damping Prediction
National Research Council Canada - National Science Library
Danberg, James
2003-01-01
...) method for predicting the pitch-damping coefficients has been employed. The CFD method provides important details necessary to derive the correlation functions that are unavailable from the current experimental database...
Approximate inference for spatial functional data on massively parallel processors
DEFF Research Database (Denmark)
Raket, Lars Lau; Markussen, Bo
2014-01-01
With continually increasing data sizes, the relevance of the big n problem of classical likelihood approaches is greater than ever. The functional mixed-effects model is a well established class of models for analyzing functional data. Spatial functional data in a mixed-effects setting...... in linear time. An extremely efficient GPU implementation is presented, and the proposed methods are illustrated by conducting a classical statistical analysis of 2D chromatography data consisting of more than 140 million spatially correlated observation points....
The complex variable boundary element method: Applications in determining approximative boundaries
Hromadka, T.V.
1984-01-01
The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.
Approximation methods for efficient learning of Bayesian networks
Riggelsen, C
2008-01-01
This publication offers and investigates efficient Monte Carlo simulation methods in order to realize a Bayesian approach to approximate learning of Bayesian networks from both complete and incomplete data. For large amounts of incomplete data when Monte Carlo methods are inefficient, approximations are implemented, such that learning remains feasible, albeit non-Bayesian. The topics discussed are: basic concepts about probabilities, graph theory and conditional independence; Bayesian network learning from data; Monte Carlo simulation techniques; and, the concept of incomplete data. In order to provide a coherent treatment of matters, thereby helping the reader to gain a thorough understanding of the whole concept of learning Bayesian networks from (in)complete data, this publication combines in a clarifying way all the issues presented in the papers with previously unpublished work.
Introduction to methods of approximation in physics and astronomy
van Putten, Maurice H P M
2017-01-01
This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis. The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal dete...
Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function
Durmus, Aysen
2018-03-01
The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.
An approximate methods approach to probabilistic structural analysis
Mcclung, R. C.; Millwater, H. R.; Wu, Y.-T.; Thacker, B. H.; Burnside, O. H.
1989-01-01
A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks
International Nuclear Information System (INIS)
Phillips, C.K.; Perkins, F.W.; Hwang, D.Q.
1985-07-01
Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are ignored by ray tracing mthods, are included self-consistently using the parabolic method since continuous representations for the wave electromagnetic fields are computed directly. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters
Optimization in engineering sciences approximate and metaheuristic methods
Stefanoiu, Dan; Popescu, Dumitru; Filip, Florin Gheorghe; El Kamel, Abdelkader
2014-01-01
The purpose of this book is to present the main metaheuristics and approximate and stochastic methods for optimization of complex systems in Engineering Sciences. It has been written within the framework of the European Union project ERRIC (Empowering Romanian Research on Intelligent Information Technologies), which is funded by the EU's FP7 Research Potential program and has been developed in co-operation between French and Romanian teaching researchers. Through the principles of various proposed algorithms (with additional references) this book allows the reader to explore various methods o
Simple Methods to Approximate CPC Shape to Preserve Collection Efficiency
Directory of Open Access Journals (Sweden)
David Jafrancesco
2012-01-01
Full Text Available The compound parabolic concentrator (CPC is the most efficient reflective geometry to collect light to an exit port. Anyway, to allow its actual use in solar plants or photovoltaic concentration systems, a tradeoff between system efficiency and cost reduction, the two key issues for sunlight exploitation, must be found. In this work, we analyze various methods to model an approximated CPC aimed to be simpler and more cost-effective than the ideal one, as well as to preserve the system efficiency. The manufacturing easiness arises from the use of truncated conic surfaces only, which can be realized by cheap machining techniques. We compare different configurations on the basis of their collection efficiency, evaluated by means of nonsequential ray-tracing software. Moreover, due to the fact that some configurations are beam dependent and for a closer approximation of a real case, the input beam is simulated as nonsymmetric, with a nonconstant irradiance on the CPC internal surface.
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Physical Applications of a Simple Approximation of Bessel Functions of Integer Order
Barsan, V.; Cojocaru, S.
2007-01-01
Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…
Topological approximation methods for evolutionary problem of nonlinear hydrodynamics
Zvyagin, Victor
2008-01-01
The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji
2016-12-01
Free-energy based reinforcement learning (FERL) was proposed for learning in high-dimensional state and action spaces. However, the FERL method does only really work well with binary, or close to binary, state input, where the number of active states is fewer than the number of non-active states. In the FERL method, the value function is approximated by the negative free energy of a restricted Boltzmann machine (RBM). In our earlier study, we demonstrated that the performance and the robustness of the FERL method can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that RBM function approximation can be further improved by approximating the value function by the negative expected energy (EERL), instead of the negative free energy, as well as being able to handle continuous state input. We validate our proposed method by demonstrating that EERL: (1) outperforms FERL, as well as standard neural network and linear function approximation, for three versions of a gridworld task with high-dimensional image state input; (2) achieves new state-of-the-art results in stochastic SZ-Tetris in both model-free and model-based learning settings; and (3) significantly outperforms FERL and standard neural network function approximation for a robot navigation task with raw and noisy RGB images as state input and a large number of actions. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.
Big geo data surface approximation using radial basis functions: A comparative study
Majdisova, Zuzana; Skala, Vaclav
2017-12-01
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.
H4: A challenging system for natural orbital functional approximations
International Nuclear Information System (INIS)
Ramos-Cordoba, Eloy; Lopez, Xabier; Piris, Mario; Matito, Eduard
2015-01-01
The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D 2h to D 4h symmetry in H 4 molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H 4 D 4h /D 2h potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D 2h –D 4h transition of H 4 has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H 4 PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices
H4: A challenging system for natural orbital functional approximations
Ramos-Cordoba, Eloy; Lopez, Xabier; Piris, Mario; Matito, Eduard
2015-10-01
The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D2h to D4h symmetry in H4 molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H4 D4h/D2h potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D2h-D4h transition of H4 has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H4 PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.
Linear source approximation scheme for method of characteristics
International Nuclear Information System (INIS)
Tang Chuntao
2011-01-01
Method of characteristics (MOC) for solving neutron transport equation based on unstructured mesh has already become one of the fundamental methods for lattice calculation of nuclear design code system. However, most of MOC codes are developed with flat source approximation called step characteristics (SC) scheme, which is another basic assumption for MOC. A linear source (LS) characteristics scheme and its corresponding modification for negative source distribution were proposed. The OECD/NEA C5G7-MOX 2D benchmark and a self-defined BWR mini-core problem were employed to validate the new LS module of PEACH code. Numerical results indicate that the proposed LS scheme employs less memory and computational time compared with SC scheme at the same accuracy. (authors)
Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before...... passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response....... outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first...
Perturbation methods and closure approximations in nonlinear systems
International Nuclear Information System (INIS)
Dubin, D.H.E.
1984-01-01
In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed
On rational approximation methods for inverse source problems
Rundell, William
2011-02-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace\\'s equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
On rational approximation methods for inverse source problems
Rundell, William; Hanke, Martin
2011-01-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
Efficient Method to Approximately Solve Retrial Systems with Impatience
Directory of Open Access Journals (Sweden)
Jose Manuel Gimenez-Guzman
2012-01-01
Full Text Available We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady-state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.
International Nuclear Information System (INIS)
Haeggblom, H.
1968-08-01
The method of calculating the resonance interaction effect by series expansions has been studied. Starting from the assumption that the neutron flux in a homogeneous mixture is inversely proportional to the total cross section, the expression for the flux can be simplified by series expansions. Two types of expansions are investigated and it is shown that only one of them is generally applicable. It is also shown that this expansion gives sufficient accuracy if the approximate resonance line shape function is reasonably representative. An investigation is made of the approximation of the resonance shape function with a Gaussian function which in some cases has been used to calculate the interaction effect. It is shown that this approximation is not sufficiently accurate in all cases which can occur in practice. Then, a rational approximation is introduced which in the first order approximation gives the same order of accuracy as a practically exact shape function. The integrations can be made analytically in the complex plane and the method is therefore very fast compared to purely numerical integrations. The method can be applied both to statistically correlated and uncorrelated resonances
Energy Technology Data Exchange (ETDEWEB)
Haeggblom, H
1968-08-15
The method of calculating the resonance interaction effect by series expansions has been studied. Starting from the assumption that the neutron flux in a homogeneous mixture is inversely proportional to the total cross section, the expression for the flux can be simplified by series expansions. Two types of expansions are investigated and it is shown that only one of them is generally applicable. It is also shown that this expansion gives sufficient accuracy if the approximate resonance line shape function is reasonably representative. An investigation is made of the approximation of the resonance shape function with a Gaussian function which in some cases has been used to calculate the interaction effect. It is shown that this approximation is not sufficiently accurate in all cases which can occur in practice. Then, a rational approximation is introduced which in the first order approximation gives the same order of accuracy as a practically exact shape function. The integrations can be made analytically in the complex plane and the method is therefore very fast compared to purely numerical integrations. The method can be applied both to statistically correlated and uncorrelated resonances.
Introduction to Methods of Approximation in Physics and Astronomy
van Putten, Maurice H. P. M.
2017-04-01
Modern astronomy reveals an evolving Universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data analysis. In realizing the full discovery potential of these multimessenger approaches, the latter increasingly involves high-performance supercomputing. These lecture notes developed out of lectures on mathematical-physics in astronomy to advanced undergraduate and beginning graduate students. They are organised to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. In the applications, considerable emphasis is put on fluid dynamical problems associated with accretion flows, as these are responsible for a wealth of high energy emission phenomena in astronomy. The topics chosen are largely aimed at phenomenological approaches, to capture main features of interest by effective methods of approximation at a desired level of accuracy and resolution. Formulated in terms of a system of algebraic, ordinary or partial differential equations, this may be pursued by perturbation theory through expansions in a small parameter or by direct numerical computation. Successful application of these methods requires a robust understanding of asymptotic behavior, errors and convergence. In some cases, the number of degrees of freedom may be reduced, e.g., for the purpose of (numerical) continuation or to identify
Balancing Exchange Mixing in Density-Functional Approximations for Iron Porphyrin.
Berryman, Victoria E J; Boyd, Russell J; Johnson, Erin R
2015-07-14
Predicting the correct ground-state multiplicity for iron(II) porphyrin, a high-spin quintet, remains a significant challenge for electronic-structure methods, including commonly employed density functionals. An even greater challenge for these methods is correctly predicting favorable binding of O2 to iron(II) porphyrin, due to the open-shell singlet character of the adduct. In this work, the performance of a modest set of contemporary density-functional approximations is assessed and the results interpreted using Bader delocalization indices. It is found that inclusion of greater proportions of Hartree-Fock exchange, in hybrid or range-separated hybrid functionals, has opposing effects; it improves the ability of the functional to identify the ground state but is detrimental to predicting favorable dioxygen binding. Because of the uncomplementary nature of these properties, accurate prediction of both the relative spin-state energies and the O2 binding enthalpy eludes conventional density-functional approximations.
Local Gaussian approximation in the generator coordinate method
International Nuclear Information System (INIS)
Onishi, Naoki; Une, Tsutomu.
1975-01-01
A transformation from a non-orthogonal representation to an orthogonal representation of wave functions is studied in the generator coordinate method. A differential equation can be obtained by the transformation for a case that the eigenvalue equation of the overlap kernel is solvable. By assuming local Gaussian overlap, we derive a Schroedinger-type equation for the collective motion from the Hill-Wheeler integral equation. (auth.)
Local Gaussian approximation in the generator coordinate method
Energy Technology Data Exchange (ETDEWEB)
Onishi, N [Tokyo Univ. (Japan). Coll. of General Education; Une, Tsutomu
1975-02-01
A transformation from a non-orthogonal representation to an orthogonal representation of wave functions is studied in the generator coordinate method. A differential equation can be obtained by the transformation for a case that the eigenvalue equation of the overlap kernel is solvable. By assuming local Gaussian overlap, we derive a Schroedinger-type equation for the collective motion from the Hill-Wheeler integral equation.
FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation
International Nuclear Information System (INIS)
Cody, W.J.; Garbow, Burton S.
1975-01-01
1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations
International Nuclear Information System (INIS)
Lee, M.W.; Bigeleisen, J.
1978-01-01
The MINIMAX finite polynomial approximation to an arbitrary function has been generalized to include a weighting function (WINIMAX). It is suggested that an exponential is a reasonable weighting function for the logarithm of the reduced partition function of a harmonic oscillator. Comparison of the error function for finite orthogonal polynomial (FOP), MINIMAX, and WINIMAX expansions of the logarithm of the reduced vibrational partition function show WINIMAX to be the best of the three approximations. A condensed table of WINIMAX coefficients is presented. The FOP, MINIMAX, and WINIMAX approximations are compared with exact calculations of the logarithm of the reduced partition function ratios for isotopic substitution in H 2 O, CH 4 , CH 2 O, C 2 H 4 , and C 2 H 6 at 300 0 K. Both deuterium and heavy atom isotope substitution are studied. Except for a third order expansion involving deuterium substitution, the WINIMAX method is superior to FOP and MINIMAX. At the level of a second order expansion WINIMAX approximations to ln(s/s')f are good to 2.5% and 6.5% for deuterium and heavy atom substitution, respectively
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
International Nuclear Information System (INIS)
Green, T.A.
1978-10-01
For one-electron heteropolar systems, the wave-theoretic Lagrangian of Paper I 2 is simplified in two distinct approximations. The first is semiclassical; the second is quantal, for velocities below those for which the semiclassical treatment is reliable. For each approximation, unitarity and detailed balancing are discussed. Then, the variational method as described by Demkov is used to determine the coupled equations for the radial functions and the Euler-Lagrange equations for the translational factors which are part of the theory. Specific semiclassical formulae for the translational factors are given in a many-state approximation. Low-velocity quantal formulae are obtained in a one-state approximation. The one-state results of both approximations agree with an earlier determination by Riley. 14 references
Born approximation to a perturbative numerical method for the solution of the Schrodinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-05-01
A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)
Baryons with functional methods
International Nuclear Information System (INIS)
Fischer, Christian S.
2017-01-01
We summarise recent results on the spectrum of ground-state and excited baryons and their form factors in the framework of functional methods. As an improvement upon similar approaches we explicitly take into account the underlying momentum-dependent dynamics of the quark-gluon interaction that leads to dynamical chiral symmetry breaking. For light octet and decuplet baryons we find a spectrum in very good agreement with experiment, including the level ordering between the positive- and negative-parity nucleon states. Comparing the three-body framework with the quark-diquark approximation, we do not find significant differences in the spectrum for those states that have been calculated in both frameworks. This situation is different in the electromagnetic form factor of the Δ, which may serve to distinguish both pictures by comparison with experiment and lattice QCD.
Wavelet series approximation using wavelet function with compactly ...
African Journals Online (AJOL)
The Wavelets generated by Scaling Function with Compactly Support are useful in various applications especially for reconstruction of functions. Generally, the computational process will be faster if Scaling Function support descends, so computational errors are summarized from one level to another level. In this article, the ...
Two site spin correlation function in Bethe-Peierls approximation for Ising model
Energy Technology Data Exchange (ETDEWEB)
Kumar, D [Roorkee Univ. (India). Dept. of Physics
1976-07-01
Two site spin correlation function for an Ising model above Curie temperature has been calculated by generalising Bethe-Peierls approximation. The results derived by a graphical method due to Englert are essentially the same as those obtained earlier by Elliott and Marshall, and Oguchi and Ono. The earlier results were obtained by a direct generalisation of the cluster method of Bethe, while these results are derived by retaining that class of diagrams , which is exact on Bethe lattice.
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.; Shidkov, E.P.
1987-01-01
The method for numerical evaluation of path integrals in Eucledean quantum mechanics without lattice discretization is elaborated. The method is based on the representation of these integrals in the form of functional integrals with respect to the conditional Wiener measure and on the use of the derived approximate exact on a class of polynomial functionals of a given degree. By the computations of non-perturbative characteristics, concerned the topological structure of vacuum, the advantages of this method versus lattice Monte-Carlo calculations are demonstrated
Approximate Dual Averaging Method for Multiagent Saddle-Point Problems with Stochastic Subgradients
Directory of Open Access Journals (Sweden)
Deming Yuan
2014-01-01
Full Text Available This paper considers the problem of solving the saddle-point problem over a network, which consists of multiple interacting agents. The global objective function of the problem is a combination of local convex-concave functions, each of which is only available to one agent. Our main focus is on the case where the projection steps are calculated approximately and the subgradients are corrupted by some stochastic noises. We propose an approximate version of the standard dual averaging method and show that the standard convergence rate is preserved, provided that the projection errors decrease at some appropriate rate and the noises are zero-mean and have bounded variance.
International Nuclear Information System (INIS)
Sin, M. W.; Kim, M. H.
2002-01-01
To calculate total dose effect on semi-conductor devices in satellite for a period of space mission effectively, two approximate calculation models for a comic radiation shielding were proposed. They are a sectoring method and a chord-length distribution method. When an approximate method was applied in this study, complex structure of satellite was described into multiple 1-dimensional slabs, structural materials were converted to reference material(aluminum), and the pre-calculated dose-depth conversion function was introduced to simplify the calculation process. Verification calculation was performed for orbit location and structure geometry of KITSAT-1 and compared with detailed 3-dimensional calculation results and experimental values. The calculation results from approximate method were estimated conservatively with acceptable error. However, results for satellite mission simulation were underestimated in total dose rate compared with experimental values
Energy Technology Data Exchange (ETDEWEB)
Sin, M. W.; Kim, M. H. [Kyunghee Univ., Yongin (Korea, Republic of)
2002-10-01
To calculate total dose effect on semi-conductor devices in satellite for a period of space mission effectively, two approximate calculation models for a comic radiation shielding were proposed. They are a sectoring method and a chord-length distribution method. When an approximate method was applied in this study, complex structure of satellite was described into multiple 1-dimensional slabs, structural materials were converted to reference material(aluminum), and the pre-calculated dose-depth conversion function was introduced to simplify the calculation process. Verification calculation was performed for orbit location and structure geometry of KITSAT-1 and compared with detailed 3-dimensional calculation results and experimental values. The calculation results from approximate method were estimated conservatively with acceptable error. However, results for satellite mission simulation were underestimated in total dose rate compared with experimental values.
An approximation method for diffusion based leaching models
International Nuclear Information System (INIS)
Shukla, B.S.; Dignam, M.J.
1987-01-01
In connection with the fixation of nuclear waste in a glassy matrix equations have been derived for leaching models based on a uniform concentration gradient approximation, and hence a uniform flux, therefore requiring the use of only Fick's first law. In this paper we improve on the uniform flux approximation, developing and justifying the approach. The resulting set of equations are solved to a satisfactory approximation for a matrix dissolving at a constant rate in a finite volume of leachant to give analytical expressions for the time dependence of the thickness of the leached layer, the diffusional and dissolutional contribution to the flux, and the leachant composition. Families of curves are presented which cover the full range of all the physical parameters for this system. The same procedure can be readily extended to more complex systems. (author)
The approximation function of bridge deck vibration derived from the measured eigenmodes
Directory of Open Access Journals (Sweden)
Sokol Milan
2017-12-01
Full Text Available This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approximate the displacement vibration function by a sum of sine functions whose periodicity is determined by spectral analysis adapted for non-uniformly sampled data and where the parameters of scale and phase are estimated as usual by the least-squares method. Moreover, this periodic component is supplemented by a cubic regression spline (fitted on its residuals that captures individual displacements between piers. The statistical evaluation of the stiffness parameter is performed using more vertical modes obtained from experimental results. The previous method (Sokol and Flesch, 2005, which was derived for near the pier areas, has been enhanced to the whole length of the bridge. The experimental data describing the mode shapes are not appropriate for direct use. Especially the higher derivatives calculated from these data are very sensitive to data precision.
The Pade approximate method for solving problems in plasma kinetic theory
International Nuclear Information System (INIS)
Jasperse, J.R.; Basu, B.
1992-01-01
The method of Pade Approximates has been a powerful tool in solving for the time dependent propagator (Green function) in model quantum field theories. We have developed a modified Pade method which we feel has promise for solving linearized collisional and weakly nonlinear problems in plasma kinetic theory. In order to illustrate the general applicability of the method, in this paper we discuss Pade solutions for the linearized collisional propagator and the collisional dielectric function for a model collisional problem. (author) 3 refs., 2 tabs
Approximate scattering wave functions for few-particle continua
International Nuclear Information System (INIS)
Briggs, J.S.
1990-01-01
An operator identity which allows the wave operator for N particles interacting pairwise to be expanded as products of operators in which fewer than N particles interact is given. This identity is used to derive appproximate scattering wave functions for N-particle continua that avoid certain difficulties associated with Faddeev-type expansions. For example, a derivation is given of a scattering wave function used successfully recently to describe the three-particle continuum occurring in the electron impact ionization of the hydrogen atom
Multiuser detection and channel estimation: Exact and approximate methods
DEFF Research Database (Denmark)
Fabricius, Thomas
2003-01-01
subtractive interference cancellation with hyperbolic tangent tentative decision device, in statistical mechanics and machine learning called the naive mean field approach. The differences between the proposed algorithms lie in how the bias is estimated/approximated. We propose approaches based on a second...... propose here to use accurate approximations borrowed from statistical mechanics and machine learning. These give us various algorithms that all can be formulated in a subtractive interference cancellation formalism. The suggested algorithms can e ectively be seen as bias corrections to standard...... of the Junction Tree Algorithm, which is a generalisation of Pearl's Belief Propagation, the BCJR, sum product, min/max sum, and Viterbi's algorithm. Although efficient algoithms, they have an inherent exponential complexity in the number of users when applied to CDMA multiuser detection. For this reason we...
Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC
Directory of Open Access Journals (Sweden)
Morten Hovd
2010-04-01
Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.
Single image super-resolution based on approximated Heaviside functions and iterative refinement
Wang, Xin-Yu; Huang, Ting-Zhu; Deng, Liang-Jian
2018-01-01
One method of solving the single-image super-resolution problem is to use Heaviside functions. This has been done previously by making a binary classification of image components as “smooth” and “non-smooth”, describing these with approximated Heaviside functions (AHFs), and iteration including l1 regularization. We now introduce a new method in which the binary classification of image components is extended to different degrees of smoothness and non-smoothness, these components being represented by various classes of AHFs. Taking into account the sparsity of the non-smooth components, their coefficients are l1 regularized. In addition, to pick up more image details, the new method uses an iterative refinement for the residuals between the original low-resolution input and the downsampled resulting image. Experimental results showed that the new method is superior to the original AHF method and to four other published methods. PMID:29329298
Hermite-distributed approximating functional-based formulation of ...
Indian Academy of Sciences (India)
2016-07-29
Jul 29, 2016 ... number of quantum mechanical methods are currently available in literature for handling a wide variety of dynamical problems [3,4]. In all cases ..... For the characterization of tunnelling time in two dimensions, we have ...
convergent methods for calculating thermodynamic Green functions
Bowen, S. P.; Williams, C. D.; Mancini, J. D.
1984-01-01
A convergent method of approximating thermodynamic Green functions is outlined briefly. The method constructs a sequence of approximants which converges independently of the strength of the Hamiltonian's coupling constants. Two new concepts associated with the approximants are introduced: the resolving power of the approximation, and conditional creation (annihilation) operators. These ideas are illustrated on an exactly soluble model and a numerical example. A convergent expression for the s...
Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon
2017-12-01
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.
On Approximation of Hyper-geometric Function Values of a Special Class
Directory of Open Access Journals (Sweden)
P. L. Ivankov
2017-01-01
Full Text Available Investigations of arithmetic properties of the hyper-geometric function values make it possible to single out two trends, namely, Siegel’s method and methods based on the effective construction of a linear approximating form. There are also methods combining both approaches mentioned. The Siegel’s method allows obtaining the most general results concerning the abovementioned problems. In many cases it was used to establish the algebraic independence of the values of corresponding functions. Although the effective methods do not allow obtaining propositions of such generality they have nevertheless some advantages. Among these advantages one can distinguish at least two: a higher precision of the quantitative results obtained by effective methods and a possibility to study the hyper-geometric functions with irrational parameters.In this paper we apply the effective construction to estimate a measure of the linear independence of the hyper-geometric function values over the imaginary quadratic field. The functions themselves were chosen by a special way so that it could be possible to demonstrate a new approach to the effective construction of a linear approximating form. This approach makes it possible also to extend the well-known effective construction methods of the linear approximating forms for poly-logarithms to the functions of more general type.To obtain the arithmetic result we had to establish a linear independence of the functions under consideration over the field of rational functions. It is apparently impossible to apply directly known theorems containing sufficient (and in some cases needful and sufficient conditions for the system of functions appearing in the theorems mentioned. For this reason, a special technique has been developed to solve this problem.The paper presents the obtained arithmetic results concerning the values of integral functions, but, with appropriate alterations, the theorems proved can be adapted to
Approximate solution of the transport equation by methods of Galerkin type
International Nuclear Information System (INIS)
Pitkaranta, J.
1977-01-01
Questions of the existence, uniqueness, and convergence of approximate solutions of transport equations by methods of the Galerkin type (where trial and weighting functions are the same) are discussed. The results presented do not exclude the infinite-dimensional case. Two strategies can be followed in the variational approximation of the transport operator: one proceeds from the original form of the transport equation, while the other is based on the partially symmetrized equation. Both principles are discussed in this paper. The transport equation is assumed in a discretized multigroup form
Bayesian Parameter Estimation via Filtering and Functional Approximations
Matthies, Hermann G.
2016-11-25
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
Bayesian Parameter Estimation via Filtering and Functional Approximations
Matthies, Hermann G.; Litvinenko, Alexander; Rosic, Bojana V.; Zander, Elmar
2016-01-01
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
Approximating Smooth Step Functions Using Partial Fourier Series Sums
2012-09-01
interp1(xt(ii), smoothstepbez( t(ii), min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); ii = find( abs(t - tau/2) <= epi ); iii = t(ii...interp1( xt(ii), smoothstepbez( rt, min(rt), max(rt), ’y’), t(ii), ’linear’, ’ extrap ’ ); % stepm(ii) = 1 - interp1(xt(ii), smoothstepbez( t(ii...min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); In this case, because x is also defined as a function of the independent parameter
Approximate relativistic corrections to atomic radial wave functions
International Nuclear Information System (INIS)
Cowan, R.D.; Griffin, D.C.
1976-01-01
The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of r/sub m/ is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Spherical Bessel transform via exponential sum approximation of spherical Bessel function
Ikeno, Hidekazu
2018-02-01
A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.
Variation Iteration Method for The Approximate Solution of Nonlinear ...
African Journals Online (AJOL)
In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...
Analytic approximation for the modified Bessel function I -2/3(x)
Martin, Pablo; Olivares, Jorge; Maass, Fernando
2017-12-01
In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.
A method for the approximate solutions of the unsteady boundary layer equations
International Nuclear Information System (INIS)
Abdus Sattar, Md.
1990-12-01
The approximate integral method proposed by Bianchini et al. to solve the unsteady boundary layer equations is considered here with a simple modification to the scale function for the similarity variable. This is done by introducing a time dependent length scale. The closed form solutions, thus obtained, give satisfactory results for the velocity profile and the skin friction to a limiting case in comparison with the results of the past investigators. (author). 7 refs, 2 figs
Born approximation to a perturbative numerical method for the solution of the Schroedinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-01-01
A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Approximation methods for the stability analysis of complete synchronization on duplex networks
Han, Wenchen; Yang, Junzhong
2018-01-01
Recently, the synchronization on multi-layer networks has drawn a lot of attention. In this work, we study the stability of the complete synchronization on duplex networks. We investigate effects of coupling function on the complete synchronization on duplex networks. We propose two approximation methods to deal with the stability of the complete synchronization on duplex networks. In the first method, we introduce a modified master stability function and, in the second method, we only take into consideration the contributions of a few most unstable transverse modes to the stability of the complete synchronization. We find that both methods work well for predicting the stability of the complete synchronization for small networks. For large networks, the second method still works pretty well.
An approximate moving boundary method for American option pricing
Chockalingam, A.; Muthuraman, K.
2015-01-01
We present a method to solve the free-boundary problem that arises in the pricing of classical American options. Such free-boundary problems arise when one attempts to solve optimal-stopping problems set in continuous time. American option pricing is one of the most popular optimal-stopping problems
Approximate methods and working rules for peak stress effects
International Nuclear Information System (INIS)
Jobson, D.A.
1983-01-01
In order to assess stress concentration effects and associated strain intensification at notches, Neuber's work on this subject is used frequently. Neuber refers to a particular nonlinear stress-strain relation which, he observed, led to the same deferential equation for the lateral displacements as that found by Chaplygin for the velocity potential of compressible flow. for a linearized adiabatic law. This finding has been examined by studying torsion problems, which Involve warping displacements. Although a deformation law of the type τ(γ) has been assumed, the shear strain components remain 'proportional' to the corresponding stress components for problems of the type considered. It has been found that the governing equations and boundary conditions for φ may be made completely analogous to those for the velocity potential of a corresponding compressible flow in a prismatic cylinder of the same shape as that of the solid bar, provided that the constitutive equation. for the solid and the gas correspond in a defined sense. This embodied Neuber's observation, which was restricted to a particular stress strain law, namely that which corresponded to a linear adiabatic gas relationship. The above finding also assimilates a well-known hydrodynamic analogy, to which it reduces for linearly elastic materials. Corresponding governing equations have further been established for the stress function and these have similarly been related to those for an analogous stream function, defined by reference to the flow density of the corresponding compressible fluid
Exact solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED
International Nuclear Information System (INIS)
Kernemann, A.; Stefanis, N.G.
1989-01-01
A set of new closed-form solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED is presented. A manifestly covariant phase-space path-integral method is applied for calculating the n-fermion Green's function in a classical external field. In the case of one and two fermions, explicit expressions for the full Green's functions are analytically obtained, with renormalization carried out in the modified minimal subtraction scheme. The renormalization constants and the corresponding anomalous dimensions are determined. The mass-shell behavior of the two-fermion Green's function is investigated in detail. No assumptions are made concerning the structure of asymptotic states and no IR cutoff is used in the calculations
Gorban, A N; Mirkes, E M; Zinovyev, A
2016-12-01
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.
High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.
Andras, Peter
2018-02-01
Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.
Convergence of method of lines approximations to partial differential equations
International Nuclear Information System (INIS)
Verwer, J.G.; Sanz-Serna, J.M.
1984-01-01
Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL schemes. The main purpose is to set up a general framework for a convergence analysis applicable to nonlinear problems. The stability materials for this framework are taken from the field of nonlinear stiff ODEs. In this connection, important concepts are the logarithmic matrix norm and C-stability. A nonlinear parabolic equation and the cubic Schroedinger equation are used for illustrating the ideas. (Auth.)
SET: A Pupil Detection Method Using Sinusoidal Approximation
Directory of Open Access Journals (Sweden)
Amir-Homayoun eJavadi
2015-04-01
Full Text Available Mobile eye-tracking in external environments remains challenging, despite recent advances in eye-tracking software and hardware engineering. Many current methods fail to deal with the vast range of outdoor lighting conditions and the speed at which these can change. This confines experiments to artificial environments where conditions must be tightly controlled. Additionally, the emergence of low-cost eye tracking devices calls for the development of analysis tools that enable non-technical researchers to process the output of their images. We have developed a fast and accurate method (known as ‘SET’ that is suitable even for natural environments with uncontrolled, dynamic and even extreme lighting conditions. We compared the performance of SET with that of two open-source alternatives by processing two collections of eye images: images of natural outdoor scenes with extreme lighting variations (‘Natural’; and images of less challenging indoor scenes (‘CASIA-Iris-Thousand’. We show that SET excelled in outdoor conditions and was faster, without significant loss of accuracy, indoors. SET offers a low cost eye-tracking solution, delivering high performance even in challenging outdoor environments. It is offered through an open-source MATLAB toolkit as well as a dynamic-link library (‘DLL’, which can be imported into many programming languages including C# and Visual Basic in Windows OS (www.eyegoeyetracker.co.uk.
International Nuclear Information System (INIS)
Sato, M.
1991-01-01
The Saha equation for a plasma in thermodynamic equilibrium (TE) is approximately solved to give the temperature as an explicit function of population densities. It is shown that the derived expressions for the Saha temperature are valid approximations to the exact solution. An application of the approximate temperature to the calculation of TE plasma parameters is also described. (orig.)
International Nuclear Information System (INIS)
Palma, Daniel A.; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C.
2008-01-01
The activation technique allows much more precise measurements of neutron intensity, relative or absolute. The technique requires the knowledge of the Doppler broadening function ψ(x,ξ) to determine the resonance self-shielding factors in the epithermal range G epi (τ,ξ). Two new analytical approximations for the Doppler broadening function ψ(x,ξ) are proposed. The approximations proposed are compared with other methods found in literature for the calculation of the ψ(x,ξ) function, that is, the 4-pole Pade method and the Frobenius method, when applied to the calculation of G epi (τ,ξ). The results obtained provided satisfactory accuracy. (authors)
Application of the N-quantum approximation method to bound state problems
International Nuclear Information System (INIS)
Raychaudhuri, A.
1977-01-01
The N-quantum approximation (NQA) method is examined in the light of its application to bound state problems. Bound state wave functions are obtained as expansion coefficients in a truncated Haag expansion. From the equations of motion for the Heisenberg field and the NQA expansion, an equation satisfied by the wave function is derived. Two different bound state systems are considered. In one case, the bound state problem of two identical scalars by scalar exchange is analyzed using the NQA. An integral equation satisfied by the wave function is derived. In the nonrelativistic limit, the equation is shown to reduce to the Schroedinger equation. The equation is solved numerically, and the results compared with those obtained for this system by other methods. The NQA method is also applied to the bound state of two spin 1/2 particles with electromagnetic interaction. The integral equation for the wave function is shown to agree with the corresponding Bethe Salpeter equation in the nonrelativistic limit. Using the Dirac (4 x 4) matrices the wave function is expanded in terms of structure functions and the equation for the wave function is reduced to two disjoint sets of coupled equation for the structure functions
Energy Technology Data Exchange (ETDEWEB)
Rudolph, E [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)
1975-01-01
As a model for gravitational radiation damping of a planet the electromagnetic radiation damping of an extended charged body moving in an external gravitational field is calculated in harmonic coordinates using a weak field, slowing-motion approximation. Special attention is paid to the case where this gravitational field is a weak Schwarzschild field. Using Green's function methods for this purpose it is shown that in a slow-motion approximation there is a strange connection between the tail part and the sharp part: radiation reaction terms of the tail part can cancel corresponding terms of the sharp part. Due to this cancelling mechanism the lowest order electromagnetic radiation damping force in an external gravitational field in harmonic coordinates remains the flat space Abraham Lorentz force. It is demonstrated in this simplified model that a naive slow-motion approximation may easily lead to divergent higher order terms. It is shown that this difficulty does not arise up to the considered order.
Efficient approximation of the incomplete gamma function for use in cloud model applications
Directory of Open Access Journals (Sweden)
U. Blahak
2010-07-01
Full Text Available This paper describes an approximation to the lower incomplete gamma function γ_{l}(a,x which has been obtained by nonlinear curve fitting. It comprises a fixed number of terms and yields moderate accuracy (the absolute approximation error of the corresponding normalized incomplete gamma function P is smaller than 0.02 in the range 0.9 ≤ a ≤ 45 and x≥0. Monotonicity and asymptotic behaviour of the original incomplete gamma function is preserved.
While providing a slight to moderate performance gain on scalar machines (depending on whether a stays the same for subsequent function evaluations or not compared to established and more accurate methods based on series- or continued fraction expansions with a variable number of terms, a big advantage over these more accurate methods is the applicability on vector CPUs. Here the fixed number of terms enables proper and efficient vectorization. The fixed number of terms might be also beneficial on massively parallel machines to avoid load imbalances, caused by a possibly vastly different number of terms in series expansions to reach convergence at different grid points. For many cloud microphysical applications, the provided moderate accuracy should be enough. However, on scalar machines and if a is the same for subsequent function evaluations, the most efficient method to evaluate incomplete gamma functions is perhaps interpolation of pre-computed regular lookup tables (most simple example: equidistant tables.
Chardon, Gilles; Daudet, Laurent
2013-11-01
This paper extends the method of particular solutions (MPS) to the computation of eigenfrequencies and eigenmodes of thin plates, in the framework of the Kirchhoff-Love plate theory. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the finite element method, at reduced complexity, and with large flexibility in the implementation choices.
Exact and approximate interior corner problem in neutron diffusion by integral transform methods
International Nuclear Information System (INIS)
Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.
1976-09-01
The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem
Fall with linear drag and Wien's displacement law: approximate solution and Lambert function
International Nuclear Information System (INIS)
Vial, Alexandre
2012-01-01
We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms. (paper)
Energy Technology Data Exchange (ETDEWEB)
Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)
1996-12-31
There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.
Evaluation of Fresnel's corrections to the eikonal approximation by the separabilization method
International Nuclear Information System (INIS)
Musakhanov, M.M.; Zubarev, A.L.
1975-01-01
Method of separabilization of potential over the Schroedinger approximate solutions, leading to Schwinger's variational principle for scattering amplitude, is suggested. The results are applied to calculation of the Fresnel corrections to the Glauber approximation
Arrival-time picking method based on approximate negentropy for microseismic data
Li, Yue; Ni, Zhuo; Tian, Yanan
2018-05-01
Accurate and dependable picking of the first arrival time for microseismic data is an important part in microseismic monitoring, which directly affects analysis results of post-processing. This paper presents a new method based on approximate negentropy (AN) theory for microseismic arrival time picking in condition of much lower signal-to-noise ratio (SNR). According to the differences in information characteristics between microseismic data and random noise, an appropriate approximation of negentropy function is selected to minimize the effect of SNR. At the same time, a weighted function of the differences between maximum and minimum value of AN spectrum curve is designed to obtain a proper threshold function. In this way, the region of signal and noise is distinguished to pick the first arrival time accurately. To demonstrate the effectiveness of AN method, we make many experiments on a series of synthetic data with different SNR from -1 dB to -12 dB and compare it with previously published Akaike information criterion (AIC) and short/long time average ratio (STA/LTA) methods. Experimental results indicate that these three methods can achieve well picking effect when SNR is from -1 dB to -8 dB. However, when SNR is as low as -8 dB to -12 dB, the proposed AN method yields more accurate and stable picking result than AIC and STA/LTA methods. Furthermore, the application results of real three-component microseismic data also show that the new method is superior to the other two methods in accuracy and stability.
Garza, Alejandro J.
Perhaps the most important approximations to the electronic structure problem in quantum chemistry are those based on coupled cluster and density functional theories. Coupled cluster theory has been called the ``gold standard'' of quantum chemistry due to the high accuracy that it achieves for weakly correlated systems. Kohn-Sham density functionals based on semilocal approximations are, without a doubt, the most widely used methods in chemistry and material science because of their high accuracy/cost ratio. The root of the success of coupled cluster and density functionals is their ability to efficiently describe the dynamic part of the electron correlation. However, both traditional coupled cluster and density functional approximations may fail catastrophically when substantial static correlation is present. This severely limits the applicability of these methods to a plethora of important chemical and physical problems such as, e.g., the description of bond breaking, transition states, transition metal-, lanthanide- and actinide-containing compounds, and superconductivity. In an attempt to tackle this problem, nonstandard (single-reference) coupled cluster-based techniques that aim to describe static correlation have been recently developed: pair coupled cluster doubles (pCCD) and singlet-paired coupled cluster doubles (CCD0). The ability to describe static correlation in pCCD and CCD0 comes, however, at the expense of important amounts of dynamic correlation so that the high accuracy of standard coupled cluster becomes unattainable. Thus, the reliable and efficient description of static and dynamic correlation in a simultaneous manner remains an open problem for quantum chemistry and many-body theory in general. In this thesis, different ways to combine pCCD and CCD0 with density functionals in order to describe static and dynamic correlation simultaneously (and efficiently) are explored. The combination of wavefunction and density functional methods has a long
Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference
Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah
1998-01-01
Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
Liang, Faming
2013-03-01
The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation. Since the proposed method makes use of only a small proportion of the data at each iteration, it avoids inverting large covariance matrices and thus is scalable to large datasets. The proposed method also leads to a general parameter estimation approach, maximum mean log-likelihood estimation, which includes the popular maximum (log)-likelihood estimation (MLE) approach as a special case and is expected to play an important role in analyzing large datasets. Under mild conditions, it is shown that the estimator resulting from the proposed method converges in probability to a set of parameter values of equivalent Gaussian probability measures, and that the estimator is asymptotically normally distributed. To the best of the authors\\' knowledge, the present study is the first one on asymptotic normality under infill asymptotics for general covariance functions. The proposed method is illustrated with large datasets, both simulated and real. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Introduction to functional methods
International Nuclear Information System (INIS)
Faddeev, L.D.
1976-01-01
The functional integral is considered in relation to Feynman diagrams and phase space. The holomorphic form of the functional integral is then discussed. The main problem of the lectures, viz. the construction of the S-matrix by means of the functional integral, is considered. The functional methods described explicitly take into account the Bose statistics of the fields involved. The different procedure used to treat fermions is discussed. An introduction to the problem of quantization of gauge fields is given. (B.R.H.)
International Nuclear Information System (INIS)
Lee, Yoon Hee; Cho, Nam Zin
2016-01-01
The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.
Energy Technology Data Exchange (ETDEWEB)
Lee, Yoon Hee; Cho, Nam Zin [KAERI, Daejeon (Korea, Republic of)
2016-05-15
The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.
International Nuclear Information System (INIS)
Gougam, L.A.; Taibi, H.; Chikhi, A.; Mekideche-Chafa, F.
2009-01-01
The problem of determining the analytical description for a set of data arises in numerous sciences and applications and can be referred to as data modeling or system identification. Neural networks are a convenient means of representation because they are known to be universal approximates that can learn data. The desired task is usually obtained by a learning procedure which consists in adjusting the s ynaptic weights . For this purpose, many learning algorithms have been proposed to update these weights. The convergence for these learning algorithms is a crucial criterion for neural networks to be useful in different applications. The aim of the present contribution is to use a training algorithm for feed forward wavelet networks used for function approximation. The training is based on the minimization of the least-square cost function. The minimization is performed by iterative second order gradient-based methods. We make use of the Levenberg-Marquardt algorithm to train the architecture of the chosen network and, then, the training procedure starts with a simple gradient method which is followed by a BFGS (Broyden, Fletcher, Glodfarb et Shanno) algorithm. The performances of the two algorithms are then compared. Our method is then applied to determine the energy of the ground state associated to a sextic potential. In fact, the Schrodinger equation does not always admit an exact solution and one has, generally, to solve it numerically. To this end, the sextic potential is, firstly, approximated with the above outlined wavelet network and, secondly, implemented into a numerical scheme. Our results are in good agreement with the ones found in the literature.
Directory of Open Access Journals (Sweden)
Stefan M. Stefanov
2014-01-01
Full Text Available We consider the data fitting problem, that is, the problem of approximating a function of several variables, given by tabulated data, and the corresponding problem for inconsistent (overdetermined systems of linear algebraic equations. Such problems, connected with measurement of physical quantities, arise, for example, in physics, engineering, and so forth. A traditional approach for solving these two problems is the discrete least squares data fitting method, which is based on discrete l2-norm. In this paper, an alternative approach is proposed: with each of these problems, we associate a nondifferentiable (nonsmooth unconstrained minimization problem with an objective function, based on discrete l1- and/or l∞-norm, respectively; that is, these two norms are used as proximity criteria. In other words, the problems under consideration are solved by minimizing the residual using these two norms. Respective subgradients are calculated, and a subgradient method is used for solving these two problems. The emphasis is on implementation of the proposed approach. Some computational results, obtained by an appropriate iterative method, are given at the end of the paper. These results are compared with the results, obtained by the iterative gradient method for the corresponding “differentiable” discrete least squares problems, that is, approximation problems based on discrete l2-norm.
International Nuclear Information System (INIS)
Kaschner, R.; Graefenstein, J.; Ziesche, P.
1988-12-01
From the local momentum balance using density functional theory an expression for the local quantum-mechanical stress tensor (or stress field) σ(r) of non-relativistic Coulomb systems is found out within the Thomas-Fermi approximation and its generalizations including gradient expansion method. As an illustration the stress field σ(r) is calculated for the jellium model of the interface K-Cs, containing especially the adhesive force between the two half-space jellia. (author). 23 refs, 1 fig
A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Mazhar Iqbal
2014-01-01
Full Text Available Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.
Wang, Yu; Chou, Chia-Chun
2018-05-01
The coupled complex quantum Hamilton-Jacobi equations for electronic nonadiabatic transitions are approximately solved by propagating individual quantum trajectories in real space. Equations of motion are derived through use of the derivative propagation method for the complex actions and their spatial derivatives for wave packets moving on each of the coupled electronic potential surfaces. These equations for two surfaces are converted into the moving frame with the same grid point velocities. Excellent wave functions can be obtained by making use of the superposition principle even when nodes develop in wave packet scattering.
International Nuclear Information System (INIS)
Marrero, S. I.; Turibus, S. N.; Assis, J. T. De; Monin, V. I.
2011-01-01
Data processing of the most of diffraction experiments is based on determination of diffraction line position and measurement of broadening of diffraction profile. High precision and digitalisation of these procedures can be resolved by approximation of experimental diffraction profiles by analytical functions. There are various functions for these purposes both simples, like Gauss function, but no suitable for wild range of experimental profiles and good approximating functions but complicated for practice using, like Vougt or PersonVII functions. Proposed analytical function is modified Cauchy function which uses two variable parameters allowing describing any experimental diffraction profile. In the presented paper modified function was applied for approximation of diffraction lines of steels after various physical and mechanical treatments and simulation of diffraction profiles applied for study of stress gradients and distortions of crystal structure. (Author)
Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava
Rassias, Michael
2014-01-01
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.
A domian Decomposition Method for Transient Neutron Transport with Pomrning-Eddington Approximation
International Nuclear Information System (INIS)
Hendi, A.A.; Abulwafa, E.E.
2008-01-01
The time-dependent neutron transport problem is approximated using the Pomraning-Eddington approximation. This approximation is two-flux approximation that expands the angular intensity in terms of the energy density and the net flux. This approximation converts the integro-differential Boltzmann equation into two first order differential equations. The A domian decomposition method that used to solve the linear or nonlinear differential equations is used to solve the resultant two differential equations to find the neutron energy density and net flux, which can be used to calculate the neutron angular intensity through the Pomraning-Eddington approximation
Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study
Directory of Open Access Journals (Sweden)
Dosch Mengia
2006-09-01
Full Text Available Abstract Background Developmental dyscalculia (DD is a specific learning disability affecting the acquisition of mathematical skills in children with otherwise normal general intelligence. The goal of the present study was to examine cerebral mechanisms underlying DD. Methods Eighteen children with DD aged 11.2 ± 1.3 years and twenty age-matched typically achieving schoolchildren were investigated using functional magnetic resonance imaging (fMRI during trials testing approximate and exact mathematical calculation, as well as magnitude comparison. Results Children with DD showed greater inter-individual variability and had weaker activation in almost the entire neuronal network for approximate calculation including the intraparietal sulcus, and the middle and inferior frontal gyrus of both hemispheres. In particular, the left intraparietal sulcus, the left inferior frontal gyrus and the right middle frontal gyrus seem to play crucial roles in correct approximate calculation, since brain activation correlated with accuracy rate in these regions. In contrast, no differences between groups could be found for exact calculation and magnitude comparison. In general, fMRI revealed similar parietal and prefrontal activation patterns in DD children compared to controls for all conditions. Conclusion In conclusion, there is evidence for a deficient recruitment of neural resources in children with DD when processing analog magnitudes of numbers.
A new way of obtaining analytic approximations of Chandrasekhar's H function
International Nuclear Information System (INIS)
Vukanic, J.; Arsenovic, D.; Davidovic, D.
2007-01-01
Applying the mean value theorem for definite integrals in the non-linear integral equation for Chandrasekhar's H function describing conservative isotropic scattering, we have derived a new, simple analytic approximation for it, with a maximal relative error below 2.5%. With this new function as a starting-point, after a single iteration in the corresponding integral equation, we have obtained a new, highly accurate analytic approximation for the H function. As its maximal relative error is below 0.07%, it significantly surpasses the accuracy of other analytic approximations
International Nuclear Information System (INIS)
Ramazanov, A.-R K
2005-01-01
Necessary and sufficient conditions for the best polynomial approximation with an arbitrary and, generally speaking, unbounded sign-sensitive weight to a continuous function are obtained; the components of the weight can also take infinite values, therefore the conditions obtained cover, in particular, approximation with interpolation at fixed points and one-sided approximation; in the case of the weight with components equal to 1 one arrives at Chebyshev's classical alternation theorem.
Delta-function Approximation SSC Model in 3C 273 S. J. Kang1 ...
Indian Academy of Sciences (India)
Abstract. We obtain an approximate analytical solution using δ approximate calculation on the traditional one-zone synchrotron self-. Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non- thermal photons are produced by both ...
Aarts, Ronald M; Janssen, Augustus J E M
2016-12-01
The Struve functions H n (z), n=0, 1, ... are approximated in a simple, accurate form that is valid for all z≥0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635-2637 (2003)]. The more general Struve functions occur when other acoustical quantities and/or non-rigid pistons are considered. The key step in the paper just cited is to express H 1 (z) as (2/π)-J 0 (z)+(2/π) I(z), where J 0 is the Bessel function of order zero and the first kind and I(z) is the Fourier cosine transform of [(1-t)/(1+t)] 1/2 , 0≤t≤1. The square-root function is optimally approximated by a linear function ĉt+d̂, 0≤t≤1, and the resulting approximated Fourier integral is readily computed explicitly in terms of sin z/z and (1-cos z)/z 2 . The same approach has been used by Maurel, Pagneux, Barra, and Lund [Phys. Rev. B 75, 224112 (2007)] to approximate H 0 (z) for all z≥0. In the present paper, the square-root function is optimally approximated by a piecewise linear function consisting of two linear functions supported by [0,t̂ 0 ] and [t̂ 0 ,1] with t̂ 0 the optimal take-over point. It is shown that the optimal two-piece linear function is actually continuous at the take-over point, causing a reduction of the additional complexity in the resulting approximations of H 0 and H 1 . Furthermore, this allows analytic computation of the optimal two-piece linear function. By using the two-piece instead of the one-piece linear approximation, the root mean square approximation error is reduced by roughly a factor of 3 while the maximum approximation error is reduced by a factor of 4.5 for H 0 and of 2.6 for H 1 . Recursion relations satisfied by Struve functions, initialized with the approximations of H 0 and H 1 , yield approximations for higher order Struve functions.
Approximation of functions in two variables by some linear positive operators
Directory of Open Access Journals (Sweden)
Mariola Skorupka
1995-12-01
Full Text Available We introduce some linear positive operators of the Szasz-Mirakjan type in the weighted spaces of continuous functions in two variables. We study the degree of the approximation of functions by these operators. The similar results for functions in one variable are given in [5]. Some operators of the Szasz-Mirakjan type are examined also in [3], [4].
National Research Council Canada - National Science Library
Franke, Richard
2001-01-01
.... It was found that for all levels the approximation of the covariance data for pressure height innovations by Legendre functions led to positive coefficients for up to 25 terms except at the some low and high levels...
International Nuclear Information System (INIS)
Capelle, K.; Gross, E.
1997-01-01
It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George
2016-01-01
The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766–1793 (1996); ibid. 56, 1794–1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.
Kushwaha, Jitendra Kumar
2013-01-01
Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction. PMID:24379744
Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems
International Nuclear Information System (INIS)
Stipanović, Dušan M.; Tomlin, Claire J.; Leitmann, George
2012-01-01
In this paper the problem of accomplishing multiple objectives by a number of agents represented as dynamic systems is considered. Each agent is assumed to have a goal which is to accomplish one or more objectives where each objective is mathematically formulated using an appropriate objective function. Sufficient conditions for accomplishing objectives are derived using particular convergent approximations of minimum and maximum functions depending on the formulation of the goals and objectives. These approximations are differentiable functions and they monotonically converge to the corresponding minimum or maximum function. Finally, an illustrative pursuit-evasion game example with two evaders and two pursuers is provided.
Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems
Energy Technology Data Exchange (ETDEWEB)
Stipanovic, Dusan M., E-mail: dusan@illinois.edu [University of Illinois at Urbana-Champaign, Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering (United States); Tomlin, Claire J., E-mail: tomlin@eecs.berkeley.edu [University of California at Berkeley, Department of Electrical Engineering and Computer Science (United States); Leitmann, George, E-mail: gleit@berkeley.edu [University of California at Berkeley, College of Engineering (United States)
2012-12-15
In this paper the problem of accomplishing multiple objectives by a number of agents represented as dynamic systems is considered. Each agent is assumed to have a goal which is to accomplish one or more objectives where each objective is mathematically formulated using an appropriate objective function. Sufficient conditions for accomplishing objectives are derived using particular convergent approximations of minimum and maximum functions depending on the formulation of the goals and objectives. These approximations are differentiable functions and they monotonically converge to the corresponding minimum or maximum function. Finally, an illustrative pursuit-evasion game example with two evaders and two pursuers is provided.
Jiang, Lijian
2009-10-02
The use of limited global information in multiscale simulations is needed when there is no scale separation. Previous approaches entail fine-scale simulations in the computation of the global information. The computation of the global information is expensive. In this paper, we propose the use of approximate global information based on partial upscaling. A requirement for partial homogenization is to capture long-range (non-local) effects present in the fine-scale solution, while homogenizing some of the smallest scales. The local information at these smallest scales is captured in the computation of basis functions. Thus, the proposed approach allows us to avoid the computations at the scales that can be homogenized. This results in coarser problems for the computation of global fields. We analyze the convergence of the proposed method. Mathematical formalism is introduced, which allows estimating the errors due to small scales that are homogenized. The proposed method is applied to simulate two-phase flows in heterogeneous porous media. Numerical results are presented for various permeability fields, including those generated using two-point correlation functions and channelized permeability fields from the SPE Comparative Project (Christie and Blunt, SPE Reserv Evalu Eng 4:308-317, 2001). We consider simple cases where one can identify the scales that can be homogenized. For more general cases, we suggest the use of upscaling on the coarse grid with the size smaller than the target coarse grid where multiscale basis functions are constructed. This intermediate coarse grid renders a partially upscaled solution that contains essential non-local information. Numerical examples demonstrate that the use of approximate global information provides better accuracy than purely local multiscale methods. © 2009 Springer Science+Business Media B.V.
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Solanko, Lukasz Michal; Nåbo, Lina J.
2014-01-01
2) wave function coupled to PCM, we introduce dynamical PCM solvent effects only in the Random Phase Approximation (RPA) part of the SOPPA response equations while the static solvent contribution is kept in both the RPA terms as well as in the higher order correlation matrix components of the SOPPA...... response equations. By dynamic terms, we refer to contributions that describe a change in environmental polarization which, in turn, reflects a change in the core molecular charge distribution upon an electronic excitation. This new combination of methods is termed PCM-SOPPA/RPA. We apply this newly...... defined method to the challenging cases of solvent effects on the lowest and intense electronic transitions in o-, m- and p-nitroaniline and o-, m- and p-nitrophenol and compare the performance of PCM-SOPPA/RPA with more conventional approaches. Compared to calculations based on time-dependent density...
Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges
Ismail-Beigi, Sohrab
2010-05-01
In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
Liang, Faming; Cheng, Yichen; Song, Qifan; Park, Jincheol; Yang, Ping
2013-01-01
large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the current estimate
Energy Technology Data Exchange (ETDEWEB)
Benoist, P; Kavenoky, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1968-01-15
In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation which involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expanding in orthogonal polynomials the angular flux of neutrons leaking from the medium and making no assumption about the angular flux within the medium, very good approximations to several classical plane geometry problems, i.e. the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method can be extended to other geometries. (authors) [French] On etablit une nouvelle methode d'approximation pour l'equation de Boltzmann en partant d'une forme particuliere de cette equation qui n'implique que le flux angulaire a la frontiere du milieu et ou les variables d'espace n'apparaissent pas explicitement. Par un developpement en polynomes orthogonaux du flux angulaire sortant du milieu et sans faire d'hypothese sur le flux angulaire a l'interieur du milieu, on obtient de tres bonnes approximations pour plusieurs problemes classiques en geometrie plane: l'albedo et le facteur de transmission des plaques, la longueur d'extrapolation du probleme de Milne, le spectre des neutrons reflechis par un milieu semi-infini ralentisseur. La methode se generalise a d'autres geometries. (auteurs)
Energy Technology Data Exchange (ETDEWEB)
Yoo, J.; Shin, H. S.; Song, T. Y.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
Energy Technology Data Exchange (ETDEWEB)
Yoo, J; Shin, H S; Song, T Y; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
Optimized implementations of rational approximations for the Voigt and complex error function
International Nuclear Information System (INIS)
Schreier, Franz
2011-01-01
Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued functions. For the complex error function w(x+iy), whose real part is the Voigt function K(x,y), code optimizations of rational approximations are investigated. An assessment of requirements for atmospheric radiative transfer modeling indicates a y range over many orders of magnitude and accuracy better than 10 -4 . Following a brief survey of complex error function algorithms in general and rational function approximations in particular the problems associated with subdivisions of the x, y plane (i.e., conditional branches in the code) are discussed and practical aspects of Fortran and Python implementations are considered. Benchmark tests of a variety of algorithms demonstrate that programming language, compiler choice, and implementation details influence computational speed and there is no unique ranking of algorithms. A new implementation, based on subdivision of the upper half-plane in only two regions, combining Weideman's rational approximation for small |x|+y<15 and Humlicek's rational approximation otherwise is shown to be efficient and accurate for all x, y.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation.
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-05-13
We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.
Agarwal, Mukul
2018-01-01
It is proved that the limit of the normalized rate-distortion functions of block independent approximations of an irreducible, aperiodic Markoff chain is independent of the initial distribution of the Markoff chain and thus, is also equal to the rate-distortion function of the Markoff chain.
Local density approximation for exchange in excited-state density functional theory
Harbola, Manoj K.; Samal, Prasanjit
2004-01-01
Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.
Bessel harmonic analysis and approximation of functions on the half-line
International Nuclear Information System (INIS)
Platonov, Sergei S
2007-01-01
We study problems of approximation of functions on [0,+∞) in the metric of L p with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the K-functional. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
Beck, Joakim; Tempone, Raul; Nobile, Fabio; Tamellini, Lorenzo
2012-01-01
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
Beck, Joakim
2012-09-01
In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.
International Nuclear Information System (INIS)
Wyatt, Robert E.; Kouri, Donald J.; Hoffman, David K.
2000-01-01
The quantum trajectory method (QTM) was recently developed to solve the hydrodynamic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for N fluid elements (particles) moving under the influence of both the force from the potential surface and from the quantum potential. In this study, distributed approximating functionals (DAFs) are used on a uniform grid to compute the necessary derivatives in the equations of motion. Transformations between the physical grid where the particle coordinates are defined and the uniform grid are handled through a Jacobian, which is also computed using DAFs. A difficult problem associated with computing derivatives on finite grids is the edge problem. This is handled effectively by using DAFs within a least squares approach to extrapolate from the known function region into the neighboring regions. The QTM-DAF is then applied to wave packet transmission through a one-dimensional Eckart potential. Emphasis is placed upon computation of the transmitted density and wave function. A problem that develops when part of the wave packet reflects back into the reactant region is avoided in this study by introducing a potential ramp to sweep the reflected particles away from the barrier region. (c) 2000 American Institute of Physics
International Nuclear Information System (INIS)
Ginsburg, C.A.
1980-01-01
In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)
Numerical analysis of different neural transfer functions used for best approximation
International Nuclear Information System (INIS)
Gougam, L.A.; Chikhi, A.; Biskri, S.; Chafa, F.
2006-01-01
It is widely recognised that the choice of transfer functions in neural networks is of en importance to their performance. In this paper, different neural transfer functions usec approximation are discussed. We begin with sigmoi'dal functions used most often by diffi authors . At a second step, we use Gaussian functions as previously suggested in refere Finally, we deal with a specified wavelet family. A comparison between the three cases < above is made exhibiting therefore the advantages of each transfer function. The approa< function improves as the dimension N of the elementary task basis increases
International Nuclear Information System (INIS)
Mukhtarova, M.I.
1988-01-01
Comparative analysis of approximations, used in the methods of Faddeev equations and hyperspherical harmonics (MHH) was conducted. The differences in solutions of these methods, related with introduction of approximation of sufficient partial states into the three-nucleon problem, is shown. MHH method is preferred. It is shown that MHH advantage can be manifested clearly when studying new classes of interactions: three-particle, Δ-isobar, nonlocal and other interactions
Numerical methods for hyperbolic differential functional problems
Directory of Open Access Journals (Sweden)
Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A. [CEFET QUIMICA de Nilopolis/RJ, Rio de Janeiro (Brazil); Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)
2008-07-01
The activation technique allows much more precise measurements of neutron intensity, relative or absolute. The technique requires the knowledge of the Doppler broadening function psi(x,xi) to determine the resonance self-shielding factors in the epithermal range G{sub epi} (tau,xi). Two new analytical approximations for the Doppler broadening function psi(x,xi) are proposed. The approximations proposed are compared with other methods found in literature for the calculation of the psi(x,xi) function, that is, the 4-pole Pade method and the Frobenius method, when applied to the calculation of G{sub epi} (tau,xi). The results obtained provided satisfactory accuracy. (authors)
International Nuclear Information System (INIS)
Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.
2008-01-01
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient
Directory of Open Access Journals (Sweden)
A. P. Karpenko
2015-01-01
Full Text Available We consider the relatively new and rapidly developing class of methods to solve a problem of multi-objective optimization, based on the preliminary built finite-dimensional approximation of the set, and thereby, the Pareto front of this problem as well. The work investigates the efficiency of several modifications of the method of adaptive weighted sum (AWS. This method proposed in the paper of Ryu and Kim Van (JH. Ryu, S. Kim, H. Wan is intended to build Pareto approximation of the multi-objective optimization problem.The AWS method uses quadratic approximation of the objective functions in the current sub-domain of the search space (the area of trust based on the gradient and Hessian matrix of the objective functions. To build the (quadratic meta objective functions this work uses methods of the experimental design theory, which involves calculating the values of these functions in the grid nodes covering the area of trust (a sensing method of the search domain. There are two groups of the sensing methods under consideration: hypercube- and hyper-sphere-based methods. For each of these groups, a number of test multi-objective optimization tasks has been used to study the efficiency of the following grids: "Latin Hypercube"; grid, which is uniformly random for each measurement; grid, based on the LP sequences.
An approximate method to estimate the minimum critical mass of fissile nuclides
International Nuclear Information System (INIS)
Wright, R.Q.; Jordan, W.C.
1999-01-01
When evaluating systems in criticality safety, it is important to approximate the answer before any analysis is performed. There is currently interest in establishing the minimum critical parameters for fissile actinides. The purpose is to describe the OB-1 method for estimating the minimum critical mass for thermal systems based on one-group calculations and 235 U spheres fully reflected by water. The observation is made that for water-moderated, well-thermalized systems, the transport and leakage from the system are dominated by water. Under these conditions two fissile mixtures will have nearly the same critical volume provided the infinite media multiplication factor (k ∞ ) for the two systems is the same. This observation allows for very simple estimates of critical concentration and mass as a function of the hydrogen-to-fissile (H/X) moderation ratio by comparison to the known 235 U system
Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid
International Nuclear Information System (INIS)
Zhou Shiqi
2008-01-01
In this work, a bridge density functional approximation (BDFA) (J. Chem. Phys. 112, 8079 (2000)) for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa (HCRY) fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail. (condensed matter: structure, thermal and mechanical properties)
Directory of Open Access Journals (Sweden)
Irina-Carmen ANDREI
2017-09-01
Full Text Available Following the demands of the design and performance analysis in case of liquid fuel propelled rocket engines, as well as the trajectory optimization, the development of efficient codes, which frequently need to call the Fuel Combustion Charts, became an important matter. This paper presents an efficient solution to the issue; the author has developed an original approach to determine the non-linear approximation function of two variables: the chamber pressure and the nozzle exit pressure ratio. The numerical algorithm based on this two variable approximation function is more efficient due to its simplicity, capability to providing numerical accuracy and prospects for an increased convergence rate of the optimization codes.
Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk
Directory of Open Access Journals (Sweden)
Devendra Kumar
2013-07-01
Full Text Available Pseudoanalytic functions (PAF are constructed as complex combination of real-valued analytic solutions to the Stokes-Betrami System. These solutions include the generalized biaxisymmetric potentials. McCoy [10] considered the approximation of pseudoanalytic functions on the disk. Kumar et al. [9] studied the generalized order and generalized type of PAF in terms of the Fourier coefficients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. The aim of this paper is to improve the results of McCoy [10] and Kumar et al. [9]. Our results apply satisfactorily for slow growth.
Approximation and inference methods for stochastic biochemical kinetics—a tutorial review
International Nuclear Information System (INIS)
Schnoerr, David; Grima, Ramon; Sanguinetti, Guido
2017-01-01
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics. (topical review)
Evaluation of the successive approximations method for acoustic streaming numerical simulations.
Catarino, S O; Minas, G; Miranda, J M
2016-05-01
This work evaluates the successive approximations method commonly used to predict acoustic streaming by comparing it with a direct method. The successive approximations method solves both the acoustic wave propagation and acoustic streaming by solving the first and second order Navier-Stokes equations, ignoring the first order convective effects. This method was applied to acoustic streaming in a 2D domain and the results were compared with results from the direct simulation of the Navier-Stokes equations. The velocity results showed qualitative agreement between both methods, which indicates that the successive approximations method can describe the formation of flows with recirculation. However, a large quantitative deviation was observed between the two methods. Further analysis showed that the successive approximation method solution is sensitive to the initial flow field. The direct method showed that the instantaneous flow field changes significantly due to reflections and wave interference. It was also found that convective effects contribute significantly to the wave propagation pattern. These effects must be taken into account when solving the acoustic streaming problems, since it affects the global flow. By adequately calculating the initial condition for first order step, the acoustic streaming prediction by the successive approximations method can be improved significantly.
Directory of Open Access Journals (Sweden)
V. E. Strizhius
2015-01-01
Full Text Available Methods of the approximate estimations of fatigue durability of composite airframe component typical elements which can be recommended for application at the stage of outline designing of the airplane are generated and presented.
An approximate method for lateral stability analysis of wall-frame ...
Indian Academy of Sciences (India)
Initially the stability differential equation of this equivalent sandwich beam is ... buckling loads of coupled shear-wall structures using continuous medium ... In this study, an approximate method based on continuum system model and transfer.
A full scale approximation of covariance functions for large spatial data sets
Sang, Huiyan
2011-10-10
Gaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.
A full scale approximation of covariance functions for large spatial data sets
Sang, Huiyan; Huang, Jianhua Z.
2011-01-01
Gaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.
Zhou, Chenyi; Guo, Hong
2017-01-01
We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.
International Nuclear Information System (INIS)
Shtromberger, N.L.
1989-01-01
To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs
CSIR Research Space (South Africa)
Kok, S
2012-07-01
Full Text Available continuously as the correlation function hyper-parameters approach zero. Since the global minimizer of the maximum likelihood function is an asymptote in this case, it is unclear if maximum likelihood estimation (MLE) remains valid. Numerical ill...
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman
2000-01-01
be obtained. This paper presents a new approach for system modelling under partial (global) information (or the so called Gray-box modelling) that seeks to perserve the benefits of the global as well as local methodologies sithin a unified framework. While the proposed technique relies on local approximations......Local function approximations concern fitting low order models to weighted data in neighbourhoods of the points where the approximations are desired. Despite their generality and convenience of use, local models typically suffer, among others, from difficulties arising in physical interpretation...... simultaneously with the (local estimates of) function values. The approach is applied to modelling of a linear time variant dynamic system under prior linear time invariant structure where local regression fails as a result of high dimensionality....
A new formulation for the Doppler broadening function relaxing the approximations of Beth–Plackzec
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Gonçalves, Alessandro C.; Martinez, Aquilino S.; Mesquita, Amir Z.
2016-01-01
Highlights: • One of the Beth–Placzek approximation were relaxed. • An additional term in the form of an integral is obtained. • A new mathematical formulation for the Doppler broadening function is proposed. - Abstract: In all nuclear reactors some neutrons can be absorbed in the resonance region and, in the design of these reactors, an accurate treatment of the resonant absorptions is essential. Apart from that, the resonant absorption varies with fuel temperature due to the Doppler broadening of the resonances. The thermal agitation movement in the reactor core is adequately represented in the microscopic cross-section of the neutron-core interaction through the Doppler broadening function. This function is calculated numerically in modern systems for the calculation of macro-group constants, necessary to determine the power distribution of a nuclear reactor. It can also be applied to the calculation of self-shielding factors to correct the measurements of the microscopic cross-sections through the activation technique and used for the approximate calculations of the resonance integrals in heterogeneous fuel cells. In these types of application we can point at the need to develop precise analytical approximations for the Doppler broadening function to be used in the calculation codes that calculate the values of this function. However, the Doppler broadening function is based on a series of approximations proposed by Beth–Plackzec. In this work a relaxation of these approximations is proposed, generating an additional term in the form of an integral. Analytical solutions of this additional term are discussed. The results obtained show that the new term is important for high temperatures.
On the functional integral approach in quantum statistics. 1. Some approximations
International Nuclear Information System (INIS)
Dai Xianxi.
1990-08-01
In this paper the susceptibility of a Kondo system in a fairly wide temperature region is calculated in the first harmonic approximation in a functional integral approach. The comparison with that of the renormalization group theory shows that in this region the two results agree quite well. The expansion of the partition function with infinite independent harmonics for the Anderson model is studied. Some symmetry relations are generalized. It is a challenging problem to develop a functional integral approach including diagram analysis, mixed mode effects and some exact relations in the Anderson system proved in the functional integral approach. These topics will be discussed in the next paper. (author). 22 refs, 1 fig
International Nuclear Information System (INIS)
Lublinsky, Michael
2004-01-01
A simple analytic expression for the nonsinglet structure function f NS is given. The expression is derived from the result of Ermolaev, Manaenkov, and Ryskin obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian
2018-05-08
An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.
Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations
Giraldi, Loic; Nouy, Anthony
2017-01-01
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.
Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations
Giraldi, Loic
2017-06-30
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.
Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)
2010-04-15
Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)
Badillo-Olvera, A.; Begovich, O.; Peréz-González, A.
2017-01-01
The present paper is motivated by the purpose of detection and isolation of a single leak considering the Fault Model Approach (FMA) focused on pipelines with changes in their geometry. These changes generate a different pressure drop that those produced by the friction, this phenomenon is a common scenario in real pipeline systems. The problem arises, since the dynamical model of the fluid in a pipeline only considers straight geometries without fittings. In order to address this situation, several papers work with a virtual model of a pipeline that generates a equivalent straight length, thus, friction produced by the fittings is taking into account. However, when this method is applied, the leak is isolated in a virtual length, which for practical reasons does not represent a complete solution. This research proposes as a solution to the problem of leak isolation in a virtual length, the use of a polynomial interpolation function in order to approximate the conversion of the virtual position to a real-coordinates value. Experimental results in a real prototype are shown, concluding that the proposed methodology has a good performance.
Ma, Yuan-Zhuo; Li, Hong-Shuang; Yao, Wei-Xing
2018-05-01
The evaluation of the probabilistic constraints in reliability-based design optimization (RBDO) problems has always been significant and challenging work, which strongly affects the performance of RBDO methods. This article deals with RBDO problems using a recently developed generalized subset simulation (GSS) method and a posterior approximation approach. The posterior approximation approach is used to transform all the probabilistic constraints into ordinary constraints as in deterministic optimization. The assessment of multiple failure probabilities required by the posterior approximation approach is achieved by GSS in a single run at all supporting points, which are selected by a proper experimental design scheme combining Sobol' sequences and Bucher's design. Sequentially, the transformed deterministic design optimization problem can be solved by optimization algorithms, for example, the sequential quadratic programming method. Three optimization problems are used to demonstrate the efficiency and accuracy of the proposed method.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method
Louaked, Mohammed; Seloula, Nour; Trabelsi, Saber
2017-01-01
In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
Directory of Open Access Journals (Sweden)
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method
Louaked, Mohammed
2017-07-20
In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017
Directory of Open Access Journals (Sweden)
Jiameng Wu
2018-01-01
Full Text Available The infinite depth free surface Green function (GF and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method.
Deep-inelastic structure functions in an approximation to the bag theory
International Nuclear Information System (INIS)
Jaffe, R.L.
1975-01-01
A cavity approximation to the bag theory developed earlier is extended to the treatment of forward virtual Compton scattering. In the Bjorken limit and for small values of ω (ω = vertical-bar2p center-dot q/q 2 vertical-bar) it is argued that the operator nature of the bag boundaries might be ignored. Structure functions are calculated in one and three dimensions. Bjorken scaling is obtained. The model provides a realization of light-cone current algebra and possesses a parton interpretation. The structure functions show a quasielastic peak. The spreading of the structure functions about the peak is associated with confinement. As expected, Regge behavior is not obtained for large ω. The ''momentum sum rule'' is saturated, indicating that the hadron's charged constituents carry all the momentum in this model. νW/subL/ is found to scale and is calculable. Application of the model to the calculation of spin-dependent and chiral-symmetry--violating structure functions is proposed. The nature of the intermediate states in this approximation is discussed. Problems associated with the cavity approximation are also discussed
An approximate method for nonlinear diffusion applied to enzyme inactivation during drying
Liou, J.K.
1982-01-01
An approximate model was developed for nonlinear diffusion with a power-function variation of the diffusion coefficient with concentration. This model may serve for the computation of desorption times and concentration profiles in non-shrinking or shrinking slabs, cylinders or spheres, under
An angularly refineable phase space finite element method with approximate sweeping procedure
International Nuclear Information System (INIS)
Kophazi, J.; Lathouwers, D.
2013-01-01
An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S n -like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S n scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S 2 sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)
A local adaptive method for the numerical approximation in seismic wave modelling
Directory of Open Access Journals (Sweden)
Galuzzi Bruno G.
2017-12-01
Full Text Available We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.
Comparison of approximate methods for multiple scattering in high-energy collisions. II
International Nuclear Information System (INIS)
Nolan, A.M.; Tobocman, W.; Werby, M.F.
1976-01-01
The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass
Laplace transform homotopy perturbation method for the approximation of variational problems.
Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R
2016-01-01
This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
Energy Technology Data Exchange (ETDEWEB)
Freeze, G.A.; Larson, K.W. [INTERA, Inc., Albuquerque, NM (United States); Davies, P.B. [Sandia National Labs., Albuquerque, NM (United States)
1995-10-01
Eight alternative methods for approximating salt creep and disposal room closure in a multiphase flow model of the Waste Isolation Pilot Plant (WIPP) were implemented and evaluated: Three fixed-room geometries three porosity functions and two fluid-phase-salt methods. The pressure-time-porosity line interpolation method is the method used in current WIPP Performance Assessment calculations. The room closure approximation methods were calibrated against a series of room closure simulations performed using a creep closure code, SANCHO. The fixed-room geometries did not incorporate a direct coupling between room void volume and room pressure. The two porosity function methods that utilized moles of gas as an independent parameter for closure coupling. The capillary backstress method was unable to accurately simulate conditions of re-closure of the room. Two methods were found to be accurate enough to approximate the effects of room closure; the boundary backstress method and pressure-time-porosity line interpolation. The boundary backstress method is a more reliable indicator of system behavior due to a theoretical basis for modeling salt deformation as a viscous process. It is a complex method and a detailed calibration process is required. The pressure lines method is thought to be less reliable because the results were skewed towards SANCHO results in simulations where the sequence of gas generation was significantly different from the SANCHO gas-generation rate histories used for closure calibration. This limitation in the pressure lines method is most pronounced at higher gas-generation rates and is relatively insignificant at lower gas-generation rates. Due to its relative simplicity, the pressure lines method is easier to implement in multiphase flow codes and simulations have a shorter execution time.
International Nuclear Information System (INIS)
Freeze, G.A.; Larson, K.W.; Davies, P.B.
1995-10-01
Eight alternative methods for approximating salt creep and disposal room closure in a multiphase flow model of the Waste Isolation Pilot Plant (WIPP) were implemented and evaluated: Three fixed-room geometries three porosity functions and two fluid-phase-salt methods. The pressure-time-porosity line interpolation method is the method used in current WIPP Performance Assessment calculations. The room closure approximation methods were calibrated against a series of room closure simulations performed using a creep closure code, SANCHO. The fixed-room geometries did not incorporate a direct coupling between room void volume and room pressure. The two porosity function methods that utilized moles of gas as an independent parameter for closure coupling. The capillary backstress method was unable to accurately simulate conditions of re-closure of the room. Two methods were found to be accurate enough to approximate the effects of room closure; the boundary backstress method and pressure-time-porosity line interpolation. The boundary backstress method is a more reliable indicator of system behavior due to a theoretical basis for modeling salt deformation as a viscous process. It is a complex method and a detailed calibration process is required. The pressure lines method is thought to be less reliable because the results were skewed towards SANCHO results in simulations where the sequence of gas generation was significantly different from the SANCHO gas-generation rate histories used for closure calibration. This limitation in the pressure lines method is most pronounced at higher gas-generation rates and is relatively insignificant at lower gas-generation rates. Due to its relative simplicity, the pressure lines method is easier to implement in multiphase flow codes and simulations have a shorter execution time
An approximate method to calculate ionization of LTE and non-LTE plasma
International Nuclear Information System (INIS)
Zhang Jun; Gu Peijun
1987-01-01
When matter, especially high Z element, is heated to high temperature, it will be ionized many times. The degree of ionization has a strong effect on many plasma properties. So an approximate method to calculate the mean ionization degree is needed for solving many practical problems. An analytical expression which is convenient for the approximate numerical calculation is given by fitting it to the scaling law and numerical results of the ionization potential of Thomas-Fermi statistical model. In LTE case, the ionization degree of Au calculated by using the approximate method is in agreement with that of the average ion model. By extending the approximate method to non-LTE case, the ionization degree of Au is similarly calculated according to Corona model and Collision-Radiatoin model(C-R). The results of Corona model agree with the published data quite well, while the results of C-R approach those of Corona model as the density is reduced and approach those of LTE as the density is increased. Finally, all approximately calculated results of ionization degree of Au and the comparision of them are given in figures and tables
International Nuclear Information System (INIS)
D’Amore, L; Campagna, R; Murli, A; Galletti, A; Marcellino, L
2012-01-01
The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has a finite set of data and one wants to recover an estimate of the inverse Laplace function from that. We propose a fitting model of data. More precisely, given a finite set of measurements on the real axis, arising from an unknown Laplace transform function, we construct a dth degree generalized polynomial smoothing spline, where d = 2m − 1, such that internally to the data interval it is a dth degree polynomial complete smoothing spline minimizing a regularization functional, and outside the data interval, it mimics the Laplace transform asymptotic behavior, i.e. it is a rational or an exponential function (the end behavior model), and at the boundaries of the data set it joins with regularity up to order m − 1, with the end behavior model. We analyze in detail the generalized polynomial smoothing spline of degree d = 3. This choice was motivated by the (ill)conditioning of the numerical computation which strongly depends on the degree of the complete spline. We prove existence and uniqueness of this spline. We derive the approximation error and give a priori and computable bounds of it on the whole real axis. In such a way, the generalized polynomial smoothing spline may be used in any real inversion algorithm to compute an approximation of the inverse Laplace function. Experimental results concerning Laplace transform approximation, numerical inversion of the generalized polynomial smoothing spline and comparisons with the exponential smoothing spline conclude the work. (paper)
Long-range-corrected Rung 3.5 density functional approximations
Janesko, Benjamin G.; Proynov, Emil; Scalmani, Giovanni; Frisch, Michael J.
2018-03-01
Rung 3.5 functionals are a new class of approximations for density functional theory. They provide a flexible intermediate between exact (Hartree-Fock, HF) exchange and semilocal approximations for exchange. Existing Rung 3.5 functionals inherit semilocal functionals' limitations in atomic cores and density tails. Here we address those limitations using range-separated admixture of HF exchange. We present three new functionals. LRC-ωΠLDA combines long-range HF exchange with short-range Rung 3.5 ΠLDA exchange. SLC-ΠLDA combines short- and long-range HF exchange with middle-range ΠLDA exchange. LRC-ωΠLDA-AC incorporates a combination of HF, semilocal, and Rung 3.5 exchange in the short range, based on an adiabatic connection. We test these in a new Rung 3.5 implementation including up to analytic fourth derivatives. LRC-ωΠLDA and SLC-ΠLDA improve atomization energies and reaction barriers by a factor of 8 compared to the full-range ΠLDA. LRC-ωΠLDA-AC brings further improvement approaching the accuracy of standard long-range corrected schemes LC-ωPBE and SLC-PBE. The new functionals yield highest occupied orbital energies closer to experimental ionization potentials and describe correctly the weak charge-transfer complex of ethylene and dichlorine and the hole-spin distribution created by an Al defect in quartz. This study provides a framework for more flexible range-separated Rung 3.5 approximations.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-01-01
We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...
Wang, S.; Zhang, X. N.; Gao, D. D.; Liu, H. X.; Ye, J.; Li, L. R.
2016-08-01
As the solar photovoltaic (PV) power is applied extensively, more attentions are paid to the maintenance and fault diagnosis of PV power plants. Based on analysis of the structure of PV power station, the global partitioned gradually approximation method is proposed as a fault diagnosis algorithm to determine and locate the fault of PV panels. The PV array is divided into 16x16 blocks and numbered. On the basis of modularly processing of the PV array, the current values of each block are analyzed. The mean current value of each block is used for calculating the fault weigh factor. The fault threshold is defined to determine the fault, and the shade is considered to reduce the probability of misjudgments. A fault diagnosis system is designed and implemented with LabVIEW. And it has some functions including the data realtime display, online check, statistics, real-time prediction and fault diagnosis. Through the data from PV plants, the algorithm is verified. The results show that the fault diagnosis results are accurate, and the system works well. The validity and the possibility of the system are verified by the results as well. The developed system will be benefit for the maintenance and management of large scale PV array.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A
2009-01-01
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour; Chá con-Rebollo, Tomas
2015-01-01
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour
2015-01-07
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
New finite volume methods for approximating partial differential equations on arbitrary meshes
International Nuclear Information System (INIS)
Hermeline, F.
2008-12-01
This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)
Combi, Carlo; Mantovani, Matteo; Sabaini, Alberto; Sala, Pietro; Amaddeo, Francesco; Moretti, Ugo; Pozzi, Giuseppe
2015-07-01
Functional dependencies (FDs) typically represent associations over facts stored by a database, such as "patients with the same symptom get the same therapy." In more recent years, some extensions have been introduced to represent both temporal constraints (temporal functional dependencies - TFDs), as "for any given month, patients with the same symptom must have the same therapy, but their therapy may change from one month to the next one," and approximate properties (approximate functional dependencies - AFDs), as "patients with the same symptomgenerallyhave the same therapy." An AFD holds most of the facts stored by the database, enabling some data to deviate from the defined property: the percentage of data which violate the given property is user-defined. According to this scenario, in this paper we introduce approximate temporal functional dependencies (ATFDs) and use them to mine clinical data. Specifically, we considered the need for deriving new knowledge from psychiatric and pharmacovigilance data. ATFDs may be defined and measured either on temporal granules (e.g.grouping data by day, week, month, year) or on sliding windows (e.g.a fixed-length time interval which moves over the time axis): in this regard, we propose and discuss some specific and efficient data mining techniques for ATFDs. We also developed two running prototypes and showed the feasibility of our proposal by mining two real-world clinical data sets. The clinical interest of the dependencies derived considering the psychiatry and pharmacovigilance domains confirms the soundness and the usefulness of the proposed techniques. Copyright © 2014 Elsevier Ltd. All rights reserved.
Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions
Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo
2007-01-01
We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.
International Nuclear Information System (INIS)
Manchev, B.; Marinova, B.; Nenkova, B.
2001-01-01
The method described on this report provides a set of simple, easily understood 'approximate' models applicable to a large class of system architectures. Constructing a Markov model of each redundant subsystem and its replacement after that by a pseudo-component develops the approximation models. Of equal importance, the models can be easily understood even of non-experts, including managers, high-level decision-makers and unsophisticated consumers. A necessary requirement for their application is the systems to be repairable and the mean time to repair to be much smaller than the mean time to failure. This ia a case most often met in the real practice. Results of the 'approximate' model application on a technological system of Kozloduy NPP are also presented. The results obtained can be compared quite favorably with the results obtained by using SAPHIRE software
Effect of flux discontinuity on spatial approximations for discrete ordinates methods
International Nuclear Information System (INIS)
Duo, J.I.; Azmy, Y.Y.
2005-01-01
This work presents advances on error analysis of the spatial approximation of the discrete ordinates method for solving the neutron transport equation. Error norms for different non-collided flux problems over a two dimensional pure absorber medium are evaluated using three numerical methods. The problems are characterized by the incoming flux boundary conditions to obtain solutions with different level of differentiability. The three methods considered are the Diamond Difference (DD) method, the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic type (AHOT-C). The last two methods are employed in constant, linear and quadratic orders of spatial approximation. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L 1 , L 2 , and L ∞ error norms are calculated. The results of this study demonstrate that the level of differentiability of the exact solution profoundly affects the rate of convergence of the numerical methods' solutions. Furthermore, in the case of discontinuous exact flux the methods fail to converge in the maximum error norm, or in the pointwise sense, in accordance with previous local error analysis. (authors)
Guliyev , Namig; Ismailov , Vugar
2016-01-01
The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studied in many papers. Such networks can approximate an arbitrary continuous function provided that an unlimited number of neurons in a hidden layer is permitted. In this paper, we consider constructive approximation on any finite interval of $\\mathbb{R}$ by neural networks with only one neuron in the hid...
Directory of Open Access Journals (Sweden)
L.L. Glazyrina
2016-12-01
Full Text Available In this paper, the initial-boundary problem for two nonlinear parabolic combined equations has been considered. One of the equations is set on the bounded domain Ω from R2, another equation is set along the curve lying in Ω. Both of the equations are parabolic equations with double degeneration. The degeneration can be present at the space operator. Furthermore, the nonlinear function which is under the sign of partial derivative with respect to the variable t, can be bound to zero. This problem has an applied character: such structure is needed to describe the process of surface and ground water combined movement. In this case, the desired function determines the level of water above the given impenetrable bottom, the section simulates the riverbed. The Bussinesk equation has been used for mathematical description of the groundwater filtration process in the domain Ω; a diffusion analogue of the Saint-Venant's system has been used on the section for description of the process of water level change in the open channel. Earlier, the authors proved the theorems of generalized solution existence and uniqueness for the considered problem from the functions classes which are called strengthened Sobolev spaces in the literature. To obtain these results, we used the technique which was created by the German mathematicians (H.W. Alt, S. Luckhaus, F. Otto to establish the correctness of the problems with a double degeneration. In this paper, we have proposed and investigated an approximate solution method for the above-stated problem. This method has been constructed using semidiscretization with respect to the variable t and the finite element method for space variables. Triangulation of the domain has been accomplished by triangles. The mesh has been set on the section line. On each segment of the line section lying between the nearby mesh points, on both side of this segment we have constructed the triangles with a common side which matches with
Mejia-Rodriguez, Daniel; Trickey, S. B.
2017-11-01
We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic-energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization, but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, Tao-Perdew-Staroverov-Scuseria, and strongly constrained and appropriately normed functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.
Short overview of PSA quantification methods, pitfalls on the road from approximate to exact results
International Nuclear Information System (INIS)
Banov, Reni; Simic, Zdenko; Sterc, Davor
2014-01-01
Over time the Probabilistic Safety Assessment (PSA) models have become an invaluable companion in the identification and understanding of key nuclear power plant (NPP) vulnerabilities. PSA is an effective tool for this purpose as it assists plant management to target resources where the largest benefit for plant safety can be obtained. PSA has quickly become an established technique to numerically quantify risk measures in nuclear power plants. As complexity of PSA models increases, the computational approaches become more or less feasible. The various computational approaches can be basically classified in two major groups: approximate and exact (BDD based) methods. In recent time modern commercially available PSA tools started to provide both methods for PSA model quantification. Besides availability of both methods in proven PSA tools the usage must still be taken carefully since there are many pitfalls which can drive to wrong conclusions and prevent efficient usage of PSA tool. For example, typical pitfalls involve the usage of higher precision approximation methods and getting a less precise result, or mixing minimal cuts and prime implicants in the exact computation method. The exact methods are sensitive to selected computational paths in which case a simple human assisted rearrangement may help and even switch from computationally non-feasible to feasible methods. Further improvements to exact method are possible and desirable which opens space for a new research. In this paper we will show how these pitfalls may be detected and how carefully actions must be done especially when working with large PSA models. (authors)
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Energy Technology Data Exchange (ETDEWEB)
Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be
2009-06-19
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -{alpha}r{sup {lambda}}exp(-{beta}r) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential.
International Nuclear Information System (INIS)
Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien
2009-01-01
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -αr λ exp(-βr) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential
Heßelmann, Andreas
2015-04-14
Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.
Directory of Open Access Journals (Sweden)
Wei Li
2012-01-01
Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.
Hinuma, Yoyo; Hayashi, Hiroyuki; Kumagai, Yu; Tanaka, Isao; Oba, Fumiyasu
2017-09-01
High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include C u2O , A g2O , MgO, ZnO, CdO, SnO, PbO, A l2O3 , G a2O3 , I n2O3 , L a2O3 , B i2O3 , Si O2 , Sn O2 , Pb O2 , Ti O2 , Zr O2 , Hf O2 , V2O5 , N b2O5 , T a2O5 , Mo O3 , and W O3 . Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and -0.04 eV, respectively, and root
Comparison of the methods for discrete approximation of the fractional-order operator
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Zborovjan Martin
2003-12-01
Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.
Székely, Balázs; Kania, Adam; Varga, Katalin; Heilmeier, Hermann
2017-04-01
Lacunarity, a measure of the spatial distribution of the empty space is found to be a useful descriptive quantity of the forest structure. Its calculation, based on laser-scanned point clouds, results in a four-dimensional data set. The evaluation of results needs sophisticated tools and visualization techniques. To simplify the evaluation, it is straightforward to use approximation functions fitted to the results. The lacunarity function L(r), being a measure of scale-independent structural properties, has a power-law character. Previous studies showed that log(log(L(r))) transformation is suitable for analysis of spatial patterns. Accordingly, transformed lacunarity functions can be approximated by appropriate functions either in the original or in the transformed domain. As input data we have used a number of laser-scanned point clouds of various forests. The lacunarity distribution has been calculated along a regular horizontal grid at various (relative) elevations. The lacunarity data cube then has been logarithm-transformed and the resulting values became the input of parameter estimation at each point (point of interest, POI). This way at each POI a parameter set is generated that is suitable for spatial analysis. The expectation is that the horizontal variation and vertical layering of the vegetation can be characterized by this procedure. The results show that the transformed L(r) functions can be typically approximated by exponentials individually, and the residual values remain low in most cases. However, (1) in most cases the residuals may vary considerably, and (2) neighbouring POIs often give rather differing estimates both in horizontal and in vertical directions, of them the vertical variation seems to be more characteristic. In the vertical sense, the distribution of estimates shows abrupt changes at places, presumably related to the vertical structure of the forest. In low relief areas horizontal similarity is more typical, in higher relief areas
Aft-body loading function for penetrators based on the spherical cavity-expansion approximation.
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Longcope, Donald B., Jr.; Warren, Thomas Lynn; Duong, Henry
2009-12-01
In this paper we develop an aft-body loading function for penetration simulations that is based on the spherical cavity-expansion approximation. This loading function assumes that there is a preexisting cavity of radius a{sub o} before the expansion occurs. This causes the radial stress on the cavity surface to be less than what is obtained if the cavity is opened from a zero initial radius. This in turn causes less resistance on the aft body as it penetrates the target which allows for greater rotation of the penetrator. Results from simulations are compared with experimental results for oblique penetration into a concrete target with an unconfined compressive strength of 23 MPa.
Random phase approximations for the screening function in high Tc superconductors
International Nuclear Information System (INIS)
Lopez-Aguilar, F.; Costa-Quintana, J.; Sanchez, A.; Puig, T.; Aurell, M.T.; Martinez, L.M.; Munoz, J.S.
1990-01-01
This paper reports on the electronic transferences from the CuO 2 sheets toward the CuO 3 linear chain, which locate electrons in the orbitals p y /p z of O4/O1 and d z 2 -y 2 of Cu1, and holes in the orbitals d x 2 -y 2 - P z /p y of Cu2 - P2/O3. These holes states present large interatomic overlapping. In this paper, we determine the screening function within the random phase approximation applied to the high-T c superconductors. This screening function is vanishing for determined values of the frequency which correspond to renormalized plasmon frequencies. These frequencies depends on the band parameters and their knowledge is essential for determining the self energy. This self energy is deduced and it contain independent terms for each of the channels for the localization
Global Approximations to Cost and Production Functions using Artificial Neural Networks
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Efthymios G. Tsionas
2009-06-01
Full Text Available The estimation of cost and production functions in economics relies on standard specifications which are less than satisfactory in numerous situations. However, instead of fitting the data with a pre-specified model, Artificial Neural Networks (ANNs let the data itself serve as evidence to support the modelrs estimation of the underlying process. In this context, the proposed approach combines the strengths of economics, statistics and machine learning research and the paper proposes a global approximation to arbitrary cost and production functions, respectively, given by ANNs. Suggestions on implementation are proposed and empirical application relies on standard techniques. All relevant measures such as Returns to Scale (RTS and Total Factor Productivity (TFP may be computed routinely.
Shiju, S.; Sumitra, S.
2017-12-01
In this paper, the multiple kernel learning (MKL) is formulated as a supervised classification problem. We dealt with binary classification data and hence the data modelling problem involves the computation of two decision boundaries of which one related with that of kernel learning and the other with that of input data. In our approach, they are found with the aid of a single cost function by constructing a global reproducing kernel Hilbert space (RKHS) as the direct sum of the RKHSs corresponding to the decision boundaries of kernel learning and input data and searching that function from the global RKHS, which can be represented as the direct sum of the decision boundaries under consideration. In our experimental analysis, the proposed model had shown superior performance in comparison with that of existing two stage function approximation formulation of MKL, where the decision functions of kernel learning and input data are found separately using two different cost functions. This is due to the fact that single stage representation helps the knowledge transfer between the computation procedures for finding the decision boundaries of kernel learning and input data, which inturn boosts the generalisation capacity of the model.
Negara, Ardiansyah
2013-01-01
Anisotropy of hydraulic properties of subsurface geologic formations is an essential feature that has been established as a consequence of the different geologic processes that they undergo during the longer geologic time scale. With respect to petroleum reservoirs, in many cases, anisotropy plays significant role in dictating the direction of flow that becomes no longer dependent only on the pressure gradient direction but also on the principal directions of anisotropy. Furthermore, in complex systems involving the flow of multiphase fluids in which the gravity and the capillarity play an important role, anisotropy can also have important influences. Therefore, there has been great deal of motivation to consider anisotropy when solving the governing conservation laws numerically. Unfortunately, the two-point flux approximation of finite difference approach is not capable of handling full tensor permeability fields. Lately, however, it has been possible to adapt the multipoint flux approximation that can handle anisotropy to the framework of finite difference schemes. In multipoint flux approximation method, the stencil of approximation is more involved, i.e., it requires the involvement of 9-point stencil for the 2-D model and 27-point stencil for the 3-D model. This is apparently challenging and cumbersome when making the global system of equations. In this work, we apply the equation-type approach, which is the experimenting pressure field approach that enables the solution of the global problem breaks into the solution of multitude of local problems that significantly reduce the complexity without affecting the accuracy of numerical solution. This approach also leads in reducing the computational cost during the simulation. We have applied this technique to a variety of anisotropy scenarios of 3-D subsurface flow problems and the numerical results demonstrate that the experimenting pressure field technique fits very well with the multipoint flux approximation
International Nuclear Information System (INIS)
Loginov, V.S.
1986-01-01
A technique for engineering design of two-dimensional stationary temperature field of rectangular cross section blending pile with inner heat release under nonsymmetrical cooling conditions is suggested. Area of its practical application is determined on the basis of experimental data known in literature. Different methods for calculating temperature distribution in betatron magnetic circuit are compared. Graph of maximum temperature calculation error on the basis of approximated expressions with respect to exact solution is given
International Nuclear Information System (INIS)
Galatolo, Stefano; Monge, Maurizio; Nisoli, Isaia
2016-01-01
We study the problem of the rigorous computation of the stationary measure and of the rate of convergence to equilibrium of an iterated function system described by a stochastic mixture of two or more dynamical systems that are either all uniformly expanding on the interval, either all contracting. In the expanding case, the associated transfer operators satisfy a Lasota–Yorke inequality, we show how to compute a rigorous approximations of the stationary measure in the L "1 norm and an estimate for the rate of convergence. The rigorous computation requires a computer-aided proof of the contraction of the transfer operators for the maps, and we show that this property propagates to the transfer operators of the IFS. In the contracting case we perform a rigorous approximation of the stationary measure in the Wasserstein–Kantorovich distance and rate of convergence, using the same functional analytic approach. We show that a finite computation can produce a realistic computation of all contraction rates for the whole parameter space. We conclude with a description of the implementation and numerical experiments. (paper)
Low rank approximation methods for MR fingerprinting with large scale dictionaries.
Yang, Mingrui; Ma, Dan; Jiang, Yun; Hamilton, Jesse; Seiberlich, Nicole; Griswold, Mark A; McGivney, Debra
2018-04-01
This work proposes new low rank approximation approaches with significant memory savings for large scale MR fingerprinting (MRF) problems. We introduce a compressed MRF with randomized singular value decomposition method to significantly reduce the memory requirement for calculating a low rank approximation of large sized MRF dictionaries. We further relax this requirement by exploiting the structures of MRF dictionaries in the randomized singular value decomposition space and fitting them to low-degree polynomials to generate high resolution MRF parameter maps. In vivo 1.5T and 3T brain scan data are used to validate the approaches. T 1 , T 2 , and off-resonance maps are in good agreement with that of the standard MRF approach. Moreover, the memory savings is up to 1000 times for the MRF-fast imaging with steady-state precession sequence and more than 15 times for the MRF-balanced, steady-state free precession sequence. The proposed compressed MRF with randomized singular value decomposition and dictionary fitting methods are memory efficient low rank approximation methods, which can benefit the usage of MRF in clinical settings. They also have great potentials in large scale MRF problems, such as problems considering multi-component MRF parameters or high resolution in the parameter space. Magn Reson Med 79:2392-2400, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Tamosiunaite, Minija; Asfour, Tamim; Wörgötter, Florentin
2009-03-01
Reinforcement learning methods can be used in robotics applications especially for specific target-oriented problems, for example the reward-based recalibration of goal directed actions. To this end still relatively large and continuous state-action spaces need to be efficiently handled. The goal of this paper is, thus, to develop a novel, rather simple method which uses reinforcement learning with function approximation in conjunction with different reward-strategies for solving such problems. For the testing of our method, we use a four degree-of-freedom reaching problem in 3D-space simulated by a two-joint robot arm system with two DOF each. Function approximation is based on 4D, overlapping kernels (receptive fields) and the state-action space contains about 10,000 of these. Different types of reward structures are being compared, for example, reward-on- touching-only against reward-on-approach. Furthermore, forbidden joint configurations are punished. A continuous action space is used. In spite of a rather large number of states and the continuous action space these reward/punishment strategies allow the system to find a good solution usually within about 20 trials. The efficiency of our method demonstrated in this test scenario suggests that it might be possible to use it on a real robot for problems where mixed rewards can be defined in situations where other types of learning might be difficult.
Approximating distributions from moments
Pawula, R. F.
1987-11-01
A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.
Reduced-rank approximations to the far-field transform in the gridded fast multipole method
Hesford, Andrew J.; Waag, Robert C.
2011-05-01
The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.
Density-functional expansion methods: Grand challenges.
Giese, Timothy J; York, Darrin M
2012-03-01
We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.
International Nuclear Information System (INIS)
Obradovic, D.
1970-04-01
In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)
Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng
2018-03-01
In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.
S-curve networks and an approximate method for estimating degree distributions of complex networks
International Nuclear Information System (INIS)
Guo Jin-Li
2010-01-01
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research. (general)
S-curve networks and an approximate method for estimating degree distributions of complex networks
Guo, Jin-Li
2010-12-01
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research.
A simple method to approximate liver size on cross-sectional images using living liver models
International Nuclear Information System (INIS)
Muggli, D.; Mueller, M.A.; Karlo, C.; Fornaro, J.; Marincek, B.; Frauenfelder, T.
2009-01-01
Aim: To assess whether a simple. diameter-based formula applicable to cross-sectional images can be used to calculate the total liver volume. Materials and methods: On 119 cross-sectional examinations (62 computed tomography and 57 magnetic resonance imaging) a simple, formula-based method to approximate the liver volume was evaluated. The total liver volume was approximated measuring the largest craniocaudal (cc), ventrodorsal (vd), and coronal (cor) diameters by two readers and implementing the equation: Vol estimated =ccxvdxcorx0.31. Inter-rater reliability, agreement, and correlation between liver volume calculation and virtual liver volumetry were analysed. Results: No significant disagreement between the two readers was found. The formula correlated significantly with the volumetric data (r > 0.85, p < 0.0001). In 81% of cases the error of the approximated volume was <10% and in 92% of cases <15% compared to the volumetric data. Conclusion: Total liver volume can be accurately estimated on cross-sectional images using a simple, diameter-based equation.
Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations
Directory of Open Access Journals (Sweden)
Ramon F. Álvarez-Estrada
2014-03-01
Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not
Energy Technology Data Exchange (ETDEWEB)
Haeggblom, H
1969-02-15
In order to investigate some aspects of the 'Intermediate Resonance Approximation' developed by Goldstein and Cohen, comparative calculations have been made using this method together with more accurate methods. The latter are as follows: a) For homogeneous materials the slowing down equation is solved in the fundamental mode approximation with the computer programme SPENG. All cross sections are given point by point. Because the spectrum can be calculated for at most 2000 energy points, the energy regions where the resonances are accurately described are limited. Isolated resonances in the region 100 to 240 eV are studied for {sup 238}U/Fe and {sup 238}U/Fe/Na mixtures. In the regions 161 to 251 eV and 701 to 1000 eV, mixtures of {sup 238}U and Na are investigated. {sup 239}Pu/Na and {sup 239}Pu/{sup 238}U/Na mixtures are studied in the region 161 to 251 eV. b) For heterogeneous compositions in slab geometry the integral transport equation is solved using the FLIS programme in 22 energy groups. Thus, only one resonance can be considered in each calculation. Two resonances are considered, namely those belonging to {sup 238}U at 190 and 937 eV. The compositions are lattices of {sup 238}U and Fe plates. The computer programme DORIX is used for the calculations using the Intermediate Resonance Approximation. Calculations of reaction rates and effective cross sections are made at 0, 300 and 1100 deg K for homogeneous media and at 300 deg K for heterogeneous media. The results are compared to those obtained by using the programmes SPENG and FLIS and using the narrow resonance approximation.
On function classes related pertaining to strong approximation of double Fourier series
Baituyakova, Zhuldyz
2015-09-01
The investigation of embedding of function classes began a long time ago. After Alexits [1], Leindler [2], and Gogoladze[3] investigated estimates of strong approximation by Fourier series in 1965, G. Freud[4] raised the corresponding saturation problem in 1969. The list of the authors dealing with embedding problems partly is also very long. It suffices to mention some names: V. G. Krotov, W. Lenski, S. M. Mazhar, J. Nemeth, E. M. Nikisin, K. I. Oskolkov, G. Sunouchi, J. Szabados, R. Taberski and V. Totik. Study on this topic has since been carried on over a decade, but it seems that most of the results obtained are limited to the case of one dimension. In this paper, embedding results are considered which arise in the strong approximation by double Fourier series. We prove theorem on the interrelation between the classes Wr1,r2HS,M ω and H(λ, p, r1, r2, ω(δ1, δ2)), in the one-dimensional case proved by L. Leindler.
Energy Technology Data Exchange (ETDEWEB)
Shu, Yu-Chen, E-mail: ycshu@mail.ncku.edu.tw [Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (China); Mathematics Division, National Center for Theoretical Sciences (South), Tainan 701, Taiwan (China); Chern, I-Liang, E-mail: chern@math.ntu.edu.tw [Department of Applied Mathematics, National Chiao Tung University, Hsin Chu 300, Taiwan (China); Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China); Mathematics Division, National Center for Theoretical Sciences (Taipei Office), Taipei 106, Taiwan (China); Chang, Chien C., E-mail: mechang@iam.ntu.edu.tw [Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan (China); Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China)
2014-10-15
Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms.
Directory of Open Access Journals (Sweden)
Shaofeng Xie
2017-01-01
Full Text Available Given the chaotic characteristics of the time series of landslides, a new method based on modified ensemble empirical mode decomposition (MEEMD, approximate entropy and the weighted least square support vector machine (WLS-SVM was proposed. The method mainly started from the chaotic sequence of time-frequency analysis and improved the model performance as follows: first a deformation time series was decomposed into a series of subsequences with significantly different complexity using MEEMD. Then the approximate entropy method was used to generate a new subsequence for the combination of subsequences with similar complexity, which could effectively concentrate the component feature information and reduce the computational scale. Finally the WLS-SVM prediction model was established for each new subsequence. At the same time, phase space reconstruction theory and the grid search method were used to select the input dimension and the optimal parameters of the model, and then the superposition of each predicted value was the final forecasting result. Taking the landslide deformation data of Danba as an example, the experiments were carried out and compared with wavelet neural network, support vector machine, least square support vector machine and various combination schemes. The experimental results show that the algorithm has high prediction accuracy. It can ensure a better prediction effect even in landslide deformation periods of rapid fluctuation, and it can also better control the residual value and effectively reduce the error interval.
Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar
2018-05-01
In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .
Novel diagrammatic method for computing transport coefficients - beyond the Boltzmann approximation
International Nuclear Information System (INIS)
Hidaka, Y.; Kunihiro, T.
2010-01-01
We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. Our method is based on a reformulation and extension of the diagrammatic method by Eliashberg given in the imaginary-time formalism to the relativistic quantum field theory in the real-time formalism, in which the cumbersome analytical continuation problem can be avoided. The transport coefficients are obtained from a two-point function via Kubo formula. It is know that naive perturbation theory breaks down owing to a so called pinch singularity, and hence a resummation is required for getting a finite and sensible result. As a novel resummation method, we first decompose the two point function into the singular part and the regular part, and then reconstruct the diagrams. We find that a self-consistent equation for the two-point function has the same structure as the linearized Boltzmann equation. It is known that the two-point function at the leading order is equivalent to the linearized Boltzmann equation. We find the higher order corrections are nicely summarized as a renormalization of the vertex function, spectral function, and collision term. We also discuss the critical behavior of the transport coefficients near a phase transition, applying our method. (author)
Fast generation of macro basis functions for LEGO through the adaptive cross approximation
Lancellotti, V.
2015-01-01
We present a method for the fast generation of macro basis functions in the context of the linear embedding via Green's operators approach (LEGO) which is a domain decomposition technique based on the combination of electromagnetic bricks in turn described by means of scattering operators. We show
Directory of Open Access Journals (Sweden)
Fernando Racimo
2014-11-01
Full Text Available Quantifying the proportion of polymorphic mutations that are deleterious or neutral is of fundamental importance to our understanding of evolution, disease genetics and the maintenance of variation genome-wide. Here, we develop an approximation to the distribution of fitness effects (DFE of segregating single-nucleotide mutations in humans. Unlike previous methods, we do not assume that synonymous mutations are neutral or not strongly selected, and we do not rely on fitting the DFE of all new nonsynonymous mutations to a single probability distribution, which is poorly motivated on a biological level. We rely on a previously developed method that utilizes a variety of published annotations (including conservation scores, protein deleteriousness estimates and regulatory data to score all mutations in the human genome based on how likely they are to be affected by negative selection, controlling for mutation rate. We map this and other conservation scores to a scale of fitness coefficients via maximum likelihood using diffusion theory and a Poisson random field model on SNP data. Our method serves to approximate the deleterious DFE of mutations that are segregating, regardless of their genomic consequence. We can then compare the proportion of mutations that are negatively selected or neutral across various categories, including different types of regulatory sites. We observe that the distribution of intergenic polymorphisms is highly peaked at neutrality, while the distribution of nonsynonymous polymorphisms has a second peak at [Formula: see text]. Other types of polymorphisms have shapes that fall roughly in between these two. We find that transcriptional start sites, strong CTCF-enriched elements and enhancers are the regulatory categories with the largest proportion of deleterious polymorphisms.
BLUES function method in computational physics
Indekeu, Joseph O.; Müller-Nedebock, Kristian K.
2018-04-01
We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.
Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation
Yokota, Rio
2018-01-03
There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.
Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation
Yokota, Rio; Ibeid, Huda; Keyes, David E.
2018-01-01
There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.
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Pierluigi Monaco
2016-10-01
Full Text Available Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from the late 1960s to early 1990s. Indeed, although the prospect of reaching sub-percent accuracy in the measurement of clustering poses a challenge even to full N-body simulations, an accurate estimation of the covariance matrix of clustering statistics, not to mention the sampling of parameter space, requires usage of a large number (hundreds in the most favourable cases of simulated (mock galaxy catalogs. Combination of few N-body simulations with a large number of realizations performed with approximate methods gives the most promising approach to solve these problems with a reasonable amount of resources. In this paper I review this topic, starting from the foundations of the methods, then going through the pioneering efforts of the 1990s, and finally presenting the latest extensions and a few codes that are now being used in present-generation surveys and thoroughly tested to assess their performance in the context of future surveys.
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Klin-eam Chakkrid
2009-01-01
Full Text Available Abstract A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.
Energy Technology Data Exchange (ETDEWEB)
Sato, Shunsuke A. [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Taniguchi, Yasutaka [Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan); Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435 (Japan); Shinohara, Yasushi [Max Planck Institute of Microstructure Physics, 06120 Halle (Germany); Yabana, Kazuhiro [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan)
2015-12-14
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-01
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
International Nuclear Information System (INIS)
Askar, S.S.; Alnowibet, K.
2016-01-01
Isoelastic demand function have been used in literature to study the dynamic features of systems constructed based on economic market structure. In this paper, we adopt the so-called Cobb–Douglas production function and study its impact on the steady state of an oligopolistic game that consists of four oligopolistic competitors or firms. Briefly, the paper handles three different scenarios. The first scenario introduces four oligopolistic firms who plays rational against each other in market. The firms use the myopic mechanism (or bounded rational) to update their production in the next time unit. The steady state of the obtained system in this scenario, which is the Nash equilibrium, is unique and its characteristics are investigated. Based on a local monopolistic approximation (LMA) strategy, one competitor prefers to play against the three rational firms and this is illustrated in the second scenario. The last scenario discusses the case when three competitors use the LMA strategy against a rational one. For all scenarios discrete dynamical systems are used to describe the game introduced in all scenarios. The stability analysis of the Nash equilibrium is investigated analytically and some numerical simulations are used to confirm the obtained analytical results.
Towards the Accuracy of Cybernetic Strategy Planning Models: Causal Proof and Function Approximation
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Christian A. Hillbrand
2003-04-01
Full Text Available All kind of strategic tasks within an enterprise require a deep understanding of its critical key success factors and their interrelations as well as an in-depth analysis of relevant environmental influences. Due to the openness of the underlying system, there seems to be an indefinite number of unknown variables influencing strategic goals. Cybernetic or systemic planning techniques try to overcome this intricacy by modeling the most important cause-and-effect relations within such a system. Although it seems to be obvious that there are specific influences between business variables, it is mostly impossible to identify the functional dependencies underlying such relations. Hence simulation or evaluation techniques based on such hypothetically assumed models deliver inaccurate results or fail completely. This paper addresses the need for accurate strategy planning models and proposes an approach to prove their cause-andeffect relations by empirical evidence. Based on this foundation an approach for the approximation of the underlying cause-andeffect function by the means of Artificial Neural Networks is developed.
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Ramon F. Alvarez-Estrada
2012-02-01
Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.
International Nuclear Information System (INIS)
Kutzler, F.W.; Painter, G.S.
1992-01-01
A fully self-consistent series of nonlocal (gradient) density-functional calculations has been carried out using the augmented-Gaussian-orbital method to determine the magnitude of gradient corrections to the potential-energy curves of the first-row diatomics, Li 2 through F 2 . Both the Langreth-Mehl-Hu and the Perdew-Wang gradient-density functionals were used in calculations of the binding energy, bond length, and vibrational frequency for each dimer. Comparison with results obtained in the local-spin-density approximation (LSDA) using the Vosko-Wilk-Nusair functional, and with experiment, reveals that bond lengths and vibrational frequencies are rather insensitive to details of the gradient functionals, including self-consistency effects, but the gradient corrections reduce the overbinding commonly observed in the LSDA calculations of first-row diatomics (with the exception of Li 2 , the gradient-functional binding-energy error is only 50--12 % of the LSDA error). The improved binding energies result from a large differential energy lowering, which occurs in open-shell atoms relative to the diatomics. The stabilization of the atom arises from the use of nonspherical charge and spin densities in the gradient-functional calculations. This stabilization is negligibly small in LSDA calculations performed with nonspherical densities
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Mustafa Bayram
2017-01-01
Full Text Available In this study, we have applied a generalized successive numerical technique to solve the elasticity problem of based on the elastic ground with variable coefficient. In the first stage, we have calculated the generalized successive approximation of being given BVP and in the second stage we have transformed it into Padé series. At the end of study a test problem has been given to clarify the method.
An improved corrective smoothed particle method approximation for second‐order derivatives
Korzilius, S.P.; Schilders, W.H.A.; Anthonissen, M.J.H.
2013-01-01
To solve (partial) differential equations it is necessary to have good numerical approximations. In SPH, most approximations suffer from the presence of boundaries. In this work a new approximation for the second-order derivative is derived and numerically compared with two other approximation
Approximate method for solving the velocity dependent transport equation in a slab lattice
International Nuclear Information System (INIS)
Ferrari, A.
1966-01-01
A method is described that is intended to provide an approximate solution of the transport equation in a medium simulating a water-moderated plate filled reactor core. This medium is constituted by a periodic array of water channels and absorbing plates. The velocity dependent transport equation in slab geometry is included. The computation is performed in a water channel: the absorbing plates are accounted for by the boundary conditions. The scattering of neutrons in water is assumed isotropic, which allows the use of a double Pn approximation to deal with the angular dependence. This method is able to represent the discontinuity of the angular distribution at the channel boundary. The set of equations thus obtained is dependent only on x and v and the coefficients are independent on x. This solution suggests to try solutions involving Legendre polynomials. This scheme leads to a set of equations v dependent only. To obtain an explicit solution, a thermalization model must now be chosen. Using the secondary model of Cadilhac a solution of this set is easy to get. The numerical computations were performed with a particular secondary model, the well-known model of Wigner and Wilkins. (author) [fr
Approximate k-NN delta test minimization method using genetic algorithms: Application to time series
Mateo, F; Gadea, Rafael; Sovilj, Dusan
2010-01-01
In many real world problems, the existence of irrelevant input variables (features) hinders the predictive quality of the models used to estimate the output variables. In particular, time series prediction often involves building large regressors of artificial variables that can contain irrelevant or misleading information. Many techniques have arisen to confront the problem of accurate variable selection, including both local and global search strategies. This paper presents a method based on genetic algorithms that intends to find a global optimum set of input variables that minimize the Delta Test criterion. The execution speed has been enhanced by substituting the exact nearest neighbor computation by its approximate version. The problems of scaling and projection of variables have been addressed. The developed method works in conjunction with MATLAB's Genetic Algorithm and Direct Search Toolbox. The goodness of the proposed methodology has been evaluated on several popular time series examples, and also ...
The spectral element method for static neutron transport in AN approximation. Part I
International Nuclear Information System (INIS)
Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.
2013-01-01
Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
26 CFR 1.985-3 - United States dollar approximate separate transactions method.
2010-04-01
...). For all purposes of subtitle A, this method of accounting must be used to compute the gross income... in section 989(a)) that has the dollar as its functional currency pursuant to § 1.985-1(b)(2). (2... currency (as defined in § 1.985-1(b)(2)(ii)(D)); (2) Making the adjustments necessary to conform such...
International Nuclear Information System (INIS)
Sanchez, Richard
1977-01-01
A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the Interface Current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding and water, or homogenized structural material. The cells are divided into zones which are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is made by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: the first uses a cylindrical cell model and one or three terms for the flux expansion; the second uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark pr
Nakayama, Hiromasa
2006-01-01
We give an algorithm to compute the local $b$ function. In this algorithm, we use the Mora division algorithm in the ring of differential operators and an approximate division algorithm in the ring of differential operators with power series coefficient.
Green's functions in quantum chemistry - I. The Σ perturbation method
International Nuclear Information System (INIS)
Sebastian, K.L.
1978-01-01
As an improvement over the Hartree-Fock approximation, a Green's Function method - the Σ perturbation method - is investigated for molecular calculations. The method is applied to the hydrogen molecule and to the π-electron system of ethylene under PPP approximation. It is found that when the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits. (K.B.)
A fast approximation method for reliability analysis of cold-standby systems
International Nuclear Information System (INIS)
Wang, Chaonan; Xing, Liudong; Amari, Suprasad V.
2012-01-01
Analyzing reliability of large cold-standby systems has been a complicated and time-consuming task, especially for systems with components having non-exponential time-to-failure distributions. In this paper, an approximation model, which is based on the central limit theorem, is presented for the reliability analysis of binary cold-standby systems. The proposed model can estimate the reliability of large cold-standby systems with binary-state components having arbitrary time-to-failure distributions in an efficient and easy way. The accuracy and efficiency of the proposed method are illustrated using several different types of distributions for both 1-out-of-n and k-out-of-n cold-standby systems.
On approximation of non-Newtonian fluid flow by the finite element method
Svácek, Petr
2008-08-01
In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.
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HU Qi-guo
2017-01-01
Full Text Available For reducing the vehicle compartment low frequency noise, the Optimal Latin hypercube sampling method was applied to perform experimental design for sampling in the factorial design space. The thickness parameters of the panels with larger acoustic contribution was considered as factors, as well as the vehicle mass, seventh rank modal frequency of body, peak sound pressure of test point and sound pressure root-mean-square value as responses. By using the RBF(radial basis function neuro-network method, an approximation model of four responses about six factors was established. Further more, error analysis of established approximation model was performed in this paper. To optimize the panel’s thickness parameter, the adaptive simulated annealing algorithm was im-plemented. Optimization results show that the peak sound pressure of driver’s head was reduced by 4.45dB and 5.47dB at frequency 158HZ and 134Hz respec-tively. The test point pressure were significantly reduced at other frequency as well. The results indicate that through the optimization the vehicle interior cavity noise was reduced effectively, and the acoustical comfort of the vehicle was im-proved significantly.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
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Danilo ePezo
2014-11-01
Full Text Available To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie’s method for Markov Chains (MC simulation is highly accurate, yet it becomes computationally intensive in the regime of high channel numbers. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA. Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties – such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Dangerfield et al., 2012; Linaro et al., 2011; Huang et al., 2013a; Orio and Soudry, 2012; Schmandt and Galán, 2012; Goldwyn et al., 2011; Güler, 2013, comparing all of them in a set of numerical simulations that asses numerical accuracy and computational efficiency on three different models: the original Hodgkin and Huxley model, a model with faster sodium channels, and a multi-compartmental model inspired in granular cells. We conclude that for low channel numbers (usually below 1000 per simulated compartment one should use MC – which is both the most accurate and fastest method. For higher channel numbers, we recommend using the method by Orio and Soudry (2012, possibly combined with the method by Schmandt and Galán (2012 for increased speed and slightly reduced accuracy. Consequently, MC modelling may be the best method for detailed multicompartment neuron models – in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
Pezo, Danilo; Soudry, Daniel; Orio, Patricio
2014-01-01
To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties—such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldwyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Orio and Soudry, 2012; Schmandt and Galán, 2012; Güler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC—which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models—in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels. PMID:25404914
Messica, A.
2016-10-01
The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.
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Hayashi Takeshi
2013-01-01
Full Text Available Abstract Background Genomic selection is an effective tool for animal and plant breeding, allowing effective individual selection without phenotypic records through the prediction of genomic breeding value (GBV. To date, genomic selection has focused on a single trait. However, actual breeding often targets multiple correlated traits, and, therefore, joint analysis taking into consideration the correlation between traits, which might result in more accurate GBV prediction than analyzing each trait separately, is suitable for multi-trait genomic selection. This would require an extension of the prediction model for single-trait GBV to multi-trait case. As the computational burden of multi-trait analysis is even higher than that of single-trait analysis, an effective computational method for constructing a multi-trait prediction model is also needed. Results We described a Bayesian regression model incorporating variable selection for jointly predicting GBVs of multiple traits and devised both an MCMC iteration and variational approximation for Bayesian estimation of parameters in this multi-trait model. The proposed Bayesian procedures with MCMC iteration and variational approximation were referred to as MCBayes and varBayes, respectively. Using simulated datasets of SNP genotypes and phenotypes for three traits with high and low heritabilities, we compared the accuracy in predicting GBVs between multi-trait and single-trait analyses as well as between MCBayes and varBayes. The results showed that, compared to single-trait analysis, multi-trait analysis enabled much more accurate GBV prediction for low-heritability traits correlated with high-heritability traits, by utilizing the correlation structure between traits, while the prediction accuracy for uncorrelated low-heritability traits was comparable or less with multi-trait analysis in comparison with single-trait analysis depending on the setting for prior probability that a SNP has zero
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Zwanziger, Ch.; Reinhold, J.
1980-02-01
The approximate LCAO MO method of Fenske and Hall has been extended to an all-election method allowing the calculation of inner-shell binding energies of molecules and their chemical shifts. Preliminary results are given.
Sparse approximation of multilinear problems with applications to kernel-based methods in UQ
Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren
2017-01-01
We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.
Sparse approximation of multilinear problems with applications to kernel-based methods in UQ
Nobile, Fabio
2017-11-16
We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak’s algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments.
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Mohammad Mehdi Rashidi
2010-01-01
Full Text Available The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method (DTM and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge–Kutta revealed that the DTM-Padé method is an excellent method for solving MHD boundary-layer equations.
Testing a Novel Method to Approximate Wood Specific Gravity of Trees
Michael C. Wiemann; G. Bruce. Williamson
2012-01-01
Wood specific gravity (SG) has long been used by foresters as an index for wood properties. More recently, SG has been widely used by ecologists as a plant functional trait and as a key variable in estimates of biomass. However, sampling wood to determine SG can be problematic; at present, the most common method is sampling with an increment borer to extract a bark-to-...
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
Guermond, J. L.
2010-09-17
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
Guermond, J. L.; Pasquetti, R.
2010-01-01
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.
The Boundary Function Method. Fundamentals
Kot, V. A.
2017-03-01
The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.
Gai, Litao; Bilige, Sudao; Jie, Yingmo
2016-01-01
In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.
Suboptimal control of pressurized water reactor power plant using approximate model-following method
International Nuclear Information System (INIS)
Tsuji, Masashi; Ogawa, Yuichi
1987-01-01
We attempted to develop an effective control system that can successfully manage the nuclear steam supply (NSS) system of a PWR power plant in an operational mode requiring relatively small variations of power. A procedure is proposed for synthesizing control system that is a simple, yet practiced, suboptimal control system. The suboptimal control system is designed in two steps; application of the optimal control theory, based on the linear state-feedback control and the use of an approximate model-following method. This procedure can appreciably reduce the complexity of the structure of the controller by accepting a slight deviation from the optimality and by the use of the output-feedback control. This eliminates the engineering difficulty caused by an incompletely state-feedback that is sometimes encountered in practical applications of the optimal state-feedback control theory to complex large-scale dynamical systems. Digital simulations and graphical studies based on the Bode-diagram demonstrate the effectiveness of the suboptimal control, and the applicability of the proposed design method as well. (author)
International Nuclear Information System (INIS)
Cartier, J.
2006-04-01
This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)
Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods
Pazner, Will; Persson, Per-Olof
2018-02-01
In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.
About the method of approximation of a simple closed plane curve with a sharp edge
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Zelenyy A.S.
2017-02-01
Full Text Available it was noted in the article, that initially the problem of interpolation of the simple plane curve arose in the problem of simulation of subsonic flow around a body with the subsequent calculation of the velocity potential using the vortex panel method. However, as it turned out, the practical importance of this method is much wider. This algorithm can be successfully applied in any task that requires a discrete set of points which describe an arbitrary curve: potential function method, flow around an airfoil with the trailing edge (airfoil, liquid drop, etc., analytic expression, which is very difficult to obtain, creation of the font and logo and in some tasks of architecture and garment industry.
On the trial functions in nested element method
International Nuclear Information System (INIS)
Altiparmakov, D.V.
1985-01-01
The R-function method is applied to the multidimensional steady-state neutron diffusion equation. Using a variational principle the nested element approximation is formulated. Trial functions taking into account the geometrical shape of material regions are constructed. The influence of both the surrounding regions and the corner singularities at the external boundary is incorporated into the approximate solution. Benchmark calculations show that such an approximation can yield satisfactory results. Moreover, in the case of complex geometry, the presented approach would result in a significant reduction of the number of unknowns compared to other methods
Based on Penalty Function Method
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Ishaq Baba
2015-01-01
Full Text Available The dual response surface for simultaneously optimizing the mean and variance models as separate functions suffers some deficiencies in handling the tradeoffs between bias and variance components of mean squared error (MSE. In this paper, the accuracy of the predicted response is given a serious attention in the determination of the optimum setting conditions. We consider four different objective functions for the dual response surface optimization approach. The essence of the proposed method is to reduce the influence of variance of the predicted response by minimizing the variability relative to the quality characteristics of interest and at the same time achieving the specific target output. The basic idea is to convert the constraint optimization function into an unconstraint problem by adding the constraint to the original objective function. Numerical examples and simulations study are carried out to compare performance of the proposed method with some existing procedures. Numerical results show that the performance of the proposed method is encouraging and has exhibited clear improvement over the existing approaches.
Bulk and interface dielectric functions: New results within the tight-binding approximation
International Nuclear Information System (INIS)
Elvira, V.D.; Duran, J.C.
1991-01-01
A tight-binding approach is used to analyze the dielectric behaviour of bulk semiconductors and semiconductor interfaces. This time interactions between second nearest neighbours are taken into account and several electrostatic models are proposed for the induced charge density around the atoms. The bulk dielectric function of different semiconductors (Si, Ge, GaAs and AlAs) are obtained and compared with other theoretical and experimental results. Finally, the energy band offset for GaAs-AlAs(1,0,0) interface is obtained and related to bulk properties of both semiconductors. The results presented in this paper show how the use of very simple but more realistic electrostatic models improve the analysis of the screening properties in semiconductors, giving a new support to the consistent tight-binding method for studying characteristics related to those properties. (Author)
An approximate method of short-term tsunami forecast and the hindcasting of some recent events
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Yu. P. Korolev
2011-11-01
Full Text Available The paper presents a method for a short-term tsunami forecast based on sea level data from remote sites. This method is based on Green's function for the wave equation possessing the fundamental property of symmetry. This property is well known in acoustics and seismology as the reciprocity principle. Some applications of this principle on tsunami research are considered in the current study. Simple relationships and estimated transfer functions enabled us to simulate tsunami waveforms for any selected oceanic point based only on the source location and sea level data from a remote reference site. The important advantage of this method is that it is irrespective of the actual source mechanism (seismic, submarine landslide or other phenomena. The method was successfully applied to hindcast several recent tsunamis observed in the Northwest Pacific. The locations of the earthquake epicenters and the tsunami records from one of the NOAA DART sites were used as inputs for the modelling, while tsunami observations at other DART sites were used to verify the model. Tsunami waveforms for the 2006, 2007 and 2009 earthquake events near Simushir Island were simulated and found to be in good agreement with the observations. The correlation coefficients between the predicted and observed tsunami waveforms were from 0.50 to 0.85. Thus, the proposed method can be effectively used to simulate tsunami waveforms for the entire ocean and also for both regional and local tsunami warning services, assuming that they have access to the real-time sea level data from DART stations.
Short-distance behavior of the Bethe--Salpeter wave function in the ladder approximation
International Nuclear Information System (INIS)
Guth, A.H.; Soper, D.E.
1975-01-01
We investigate the short-distance behavior of the (Wick-rotated) Bethe--Salpeter wave function for the two spin-1/2 quarks bound by the exchange of a massive vector meson. We use the ladder-model kernel, which has the same p -4 scaling behavior as the true kernel in a theory with a fixed point of the renormalization group at g not equal to 0. For a bound state with the quantum numbers of the pion, the leading asymptotic behavior is chi (q/sup μ/) approx. cq/sup -4 + epsilon(g)/γ 5 , where epsilon (g) =1- (1-g 2 /π 2 ) 1 / 2 . Our method also provides the full asymptotic series, although it should be noted that the nonleading terms will depend on the nonleading behavior of the ladder-model kernel. A general term has the form cq - /sup a/(lnq)/sup n/phi (q/sup μ/), where c is an unknown constant, a may be integral or nonintegral, n is an integer, and phi (q/sup μ/) is a representation function of the rotation group in four dimensions
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Tapas Kumar Biswas
2018-02-01
Full Text Available The mobility sector including all kinds of transportation systems are facing global challenges in re-spect of green environmental issues. There has been a paradigm shift in the concept of design and manufacturing of automotive vehicles keeping in mind the scarcity of fossil fuel and the impact of emission on environment due to burning of it. The addition of hybrid and electric vehicles in pas-senger car segment has got significant momentum to address the global challenges. This research investigates the performance of a group of hybrid vehicles from customers’ perspective. Among the different brands that are available in the hybrid vehicle market, smart customers have given pri-ority to vehicle cost, mileage, tail pipe emission, comfortness and high tank size volume for long drive. Considering these attributes, selection strategy for hybrid vehicles has been developed using entropy based multi-attributive border approximation area comparison (MABAC method. This research highlights the best hybrid vehicle which reduces air pollution in cities with other significant environmental benefits, reduces dependence on foreign energy imports and minimizes the annual fuel cost.
International Nuclear Information System (INIS)
Kopka, P; Wawrzynczak, A; Borysiewicz, M
2015-01-01
In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found. (paper)
Directory of Open Access Journals (Sweden)
Skorupski Krzysztof
2015-03-01
Full Text Available BC (Black Carbon, which can be found in the atmosphere, is characterized by a large value of the imaginary part of the complex refractive index and, therefore, might have an impact on the global warming effect. To study the interaction of BC with light often computer simulations are used. One of the methods, which are capable of performing light scattering simulations by any shape, is DDA (Discrete Dipole Approximation. In this work its accuracy was estimated in respect to BC structures using the latest stable version of the ADDA (vr. 1.2 algorithm. As the reference algorithm the GMM (Generalized Multiparticle Mie-Solution code was used. The study shows that the number of volume elements (dipoles is the main parameter that defines the quality of results. However, they can be improved by a proper polarizability expression. The most accurate, and least time consuming, simulations were observed for IGT_SO. When an aggregate consists of particles composed of ca. 750 volume elements (dipoles, the averaged relative extinction error should not exceed ca. 4.5%.
Foundation of the semiclassical approximation by means of path integral methods
International Nuclear Information System (INIS)
Krisztinkovics, F.
1984-01-01
The aim of our study is to find a technically unique semiclassical treatment to describe the collision processes between heavy ions. Thereby it shall be started from a complete quantum mechanical formulation of the collision process. This aim requires: 1. A completely quantum mechanical initial formulation for the whole system, 2. a unique and conceptually clear transition to semiclassics. In order to fulfil the requirements a method is offered which is in closest connection with the Feynman propagator respectively influence functional. (orig./HSI) [de
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Tibi, R.; Young, C. J.; Gonzales, A.; Ballard, S.; Encarnacao, A. V.
2016-12-01
The matched filtering technique involving the cross-correlation of a waveform of interest with archived signals from a template library has proven to be a powerful tool for detecting events in regions with repeating seismicity. However, waveform correlation is computationally expensive, and therefore impractical for large template sets unless dedicated distributed computing hardware and software are used. In this study, we introduce an Approximate Nearest Neighbor (ANN) approach that enables the use of very large template libraries for waveform correlation without requiring a complex distributed computing system. Our method begins with a projection into a reduced dimensionality space based on correlation with a randomized subset of the full template archive. Searching for a specified number of nearest neighbors is accomplished by using randomized K-dimensional trees. We used the approach to search for matches to each of 2700 analyst-reviewed signal detections reported for May 2010 for the IMS station MKAR. The template library in this case consists of a dataset of more than 200,000 analyst-reviewed signal detections for the same station from 2002-2014 (excluding May 2010). Of these signal detections, 60% are teleseismic first P, and 15% regional phases (Pn, Pg, Sn, and Lg). The analyses performed on a standard desktop computer shows that the proposed approach performs the search of the large template libraries about 20 times faster than the standard full linear search, while achieving recall rates greater than 80%, with the recall rate increasing for higher correlation values. To decide whether to confirm a match, we use a hybrid method involving a cluster approach for queries with two or more matches, and correlation score for single matches. Of the signal detections that passed our confirmation process, 52% were teleseismic first P, and 30% were regional phases.
Meshgi, Ali; Schmitter, Petra; Babovic, Vladan; Chui, Ting Fong May
2014-11-01
Developing reliable methods to estimate stream baseflow has been a subject of interest due to its importance in catchment response and sustainable watershed management. However, to date, in the absence of complex numerical models, baseflow is most commonly estimated using statistically derived empirical approaches that do not directly incorporate physically-meaningful information. On the other hand, Artificial Intelligence (AI) tools such as Genetic Programming (GP) offer unique capabilities to reduce the complexities of hydrological systems without losing relevant physical information. This study presents a simple-to-use empirical equation to estimate baseflow time series using GP so that minimal data is required and physical information is preserved. A groundwater numerical model was first adopted to simulate baseflow for a small semi-urban catchment (0.043 km2) located in Singapore. GP was then used to derive an empirical equation relating baseflow time series to time series of groundwater table fluctuations, which are relatively easily measured and are physically related to baseflow generation. The equation was then generalized for approximating baseflow in other catchments and validated for a larger vegetation-dominated basin located in the US (24 km2). Overall, this study used GP to propose a simple-to-use equation to predict baseflow time series based on only three parameters: minimum daily baseflow of the entire period, area of the catchment and groundwater table fluctuations. It serves as an alternative approach for baseflow estimation in un-gauged systems when only groundwater table and soil information is available, and is thus complementary to other methods that require discharge measurements.
International Nuclear Information System (INIS)
Brack, M.
1981-01-01
Strutinsky's shell-correction method is investigated in the framework of the microscopial Hartree-Fock-Bogoliubov method at finite temperature HFBT. Applying the Strutinsky energy averaging consistently to the normal and abnormal density matrices and to the entropy, we define a self-consistently average HFBT system as the solution of a variational problem. From the latter we derive the generalized Strutinsky energy theorem and the explicit expressions for the shell correction of a statistically excited system of BCS quasiparticles. Using numerical results of HF calculations, we demonstrate the convergence of the Strutinsky expansion and estimate the validity of the partical shell-correction approach. We also discuss the close connections of the Strutinsky energy averaging with semiclassical expansions and their usefulness for solving the average nuclear self-consistency problem. In particular we argue that the Hohenberg-Kohn theorem should hold for the averaged HFBT system and we thus provide a justification of the use of semiclassical density functionals. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.
1993-12-01
We obtain the analytic next-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N = 2, 4, 6, 8 of the non-singlet deep inelastic structure functions F{sub 2} and F{sub L}. We calculate the three-loop anomalous dimensions of the corresponding non-singlet operators and the three-loop coefficient functions of the structure function F{sub L}. (orig.).
International Nuclear Information System (INIS)
Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.
1993-12-01
We obtain the analytic next-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N = 2, 4, 6, 8 of the non-singlet deep inelastic structure functions F 2 and F L . We calculate the three-loop anomalous dimensions of the corresponding non-singlet operators and the three-loop coefficient functions of the structure function F L . (orig.)
MOSS-5: A Fast Method of Approximating Counts of 5-Node Graphlets in Large Graphs
Wang, Pinghui
2017-09-26
Counting 3-, 4-, and 5-node graphlets in graphs is important for graph mining applications such as discovering abnormal/evolution patterns in social and biology networks. In addition, it is recently widely used for computing similarities between graphs and graph classification applications such as protein function prediction and malware detection. However, it is challenging to compute these metrics for a large graph or a large set of graphs due to the combinatorial nature of the problem. Despite recent efforts in counting triangles (a 3-node graphlet) and 4-node graphlets, little attention has been paid to characterizing 5-node graphlets. In this paper, we develop a computationally efficient sampling method to estimate 5-node graphlet counts. We not only provide fast sampling methods and unbiased estimators of graphlet counts, but also derive simple yet exact formulas for the variances of the estimators which is of great value in practice-the variances can be used to bound the estimates\\' errors and determine the smallest necessary sampling budget for a desired accuracy. We conduct experiments on a variety of real-world datasets, and the results show that our method is several orders of magnitude faster than the state-of-the-art methods with the same accuracy.
Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation.
Madain, Alia; Abu Dalhoum, Abdel Latif; Sleit, Azzam
2018-06-01
The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.
Neese, Frank; Wennmohs, Frank; Hansen, Andreas
2009-03-21
Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Moller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol(-1). Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500
Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles
2011-06-01
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T
2008-01-01
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient
Gabor, A.F.; Ommeren, van J.C.W.
2006-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a (1+e,1)-reduction of the facility
Gabor, Adriana F.; van Ommeren, Jan C.W.
2006-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\varepsilon, 1)$-reduction of
Approximation algorithms for facility location problems with discrete subadditive cost functions
Gabor, A.F.; van Ommeren, Jan C.W.
2005-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present two facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\epsilon,1)$- reduction of the
Ogorodnikov, Yuri; Khachay, Michael; Pljonkin, Anton
2018-04-01
We describe the possibility of employing the special case of the 3-SAT problem stemming from the well known integer factorization problem for the quantum cryptography. It is known, that for every instance of our 3-SAT setting the given 3-CNF is satisfiable by a unique truth assignment, and the goal is to find this assignment. Since the complexity status of the factorization problem is still undefined, development of approximation algorithms and heuristics adopts interest of numerous researchers. One of promising approaches to construction of approximation techniques is based on real-valued relaxation of the given 3-CNF followed by minimizing of the appropriate differentiable loss function, and subsequent rounding of the fractional minimizer obtained. Actually, algorithms developed this way differ by the rounding scheme applied on their final stage. We propose a new rounding scheme based on Bayesian learning. The article shows that the proposed method can be used to determine the security in quantum key distribution systems. In the quantum distribution the Shannon rules is applied and the factorization problem is paramount when decrypting secret keys.
International Nuclear Information System (INIS)
Tang Xiangyang; Hsieh Jiang
2007-01-01
A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated
Directory of Open Access Journals (Sweden)
Yanqi Hao
2015-07-01
Full Text Available Alternative splicing acts on transcripts from almost all human multi-exon genes. Notwithstanding its ubiquity, fundamental ramifications of splicing on protein expression remain unresolved. The number and identity of spliced transcripts that form stably folded proteins remain the sources of considerable debate, due largely to low coverage of experimental methods and the resulting absence of negative data. We circumvent this issue by developing a semi-supervised learning algorithm, positive unlabeled learning for splicing elucidation (PULSE; http://www.kimlab.org/software/pulse, which uses 48 features spanning various categories. We validated its accuracy on sets of bona fide protein isoforms and directly on mass spectrometry (MS spectra for an overall AU-ROC of 0.85. We predict that around 32% of “exon skipping” alternative splicing events produce stable proteins, suggesting that the process engenders a significant number of previously uncharacterized proteins. We also provide insights into the distribution of positive isoforms in various functional classes and into the structural effects of alternative splicing.
Thacker, B. H.; Mcclung, R. C.; Millwater, H. R.
1990-01-01
An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.
Energy Technology Data Exchange (ETDEWEB)
Ribeiro, M., E-mail: ribeiro.jr@oorbit.com.br [Office of Operational Research for Business Intelligence and Technology, Principal Office, Buffalo, Wyoming 82834 (United States)
2015-06-21
Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost.
International Nuclear Information System (INIS)
Ribeiro, M.
2015-01-01
Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost
Directory of Open Access Journals (Sweden)
Ituen B. Okon
2017-01-01
Full Text Available We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP. We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT to compute expectation values r-2, r-1, T, and p2 for four different diatomic molecules: hydrogen molecule (H2, lithium hydride molecule (LiH, hydrogen chloride molecule (HCl, and carbon (II oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.
International Nuclear Information System (INIS)
Johnson, E.
1977-01-01
A theory for site-site pair distribution functions of molecular fluids is derived from the Ornstein-Zernike equation. Atom-atom pair distribution functions of this theory which were obtained by using different approximations for the Percus-Yevick site-site direct correlation functions are compared
DEFF Research Database (Denmark)
Maltais Lapointe, Genevieve; Lynnerup, Niels; Hoppa, Robert D
2016-01-01
The most common method to predict nasal projection for forensic facial approximation is Gerasimov's two-tangent method. Ullrich H, Stephan CN (J Forensic Sci, 2011; 56: 470) argued that the method has not being properly implemented and a revised interpretation was proposed. The aim of this study......, and Ullrich H, Stephan CN (J Forensic Sci, 2011; 56: 470) interpretation should be used instead....
Perlt, Eva; Ray, Promit; Hansen, Andreas; Malberg, Friedrich; Grimme, Stefan; Kirchner, Barbara
2018-05-01
Ionic liquids raise interesting but complicated questions for theoretical investigations due to the fact that a number of different inter-molecular interactions, e.g., hydrogen bonding, long-range Coulomb interactions, and dispersion interactions, need to be described properly. Here, we present a detailed study on the ionic liquids ethylammonium nitrate and 1-ethyl-3-methylimidazolium acetate, in which we compare different dispersion corrected density functional approximations to accurate local coupled cluster data in static calculations on ionic liquid clusters. The efficient new composite method B97-3c is tested and has been implemented in CP2K for future studies. Furthermore, tight-binding based approaches which may be used in large scale simulations are assessed. Subsequently, ab initio as well as classical molecular dynamics simulations are conducted and structural analyses are presented in order to shed light on the different short- and long-range structural patterns depending on the method and the system size considered in the simulation. Our results indicate the presence of strong hydrogen bonds in ionic liquids as well as the aggregation of alkyl side chains due to dispersion interactions.
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaofeng, E-mail: xfyang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Zhao, Jia, E-mail: zhao62@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States); Wang, Qi, E-mail: qwang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Beijing Computational Science Research Center, Beijing (China); School of Materials Science and Engineering, Nankai University, Tianjin (China)
2017-03-15
The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.
Frydel, Derek; Ma, Manman
2016-06-01
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
Study of internal rotation in molecules using molecular orbital method in the CNDO/BW approximation
International Nuclear Information System (INIS)
Pedrosa, M.S.
1987-10-01
It is presented a LCAO-MO-SCF study of Internal Rotation for the molecules C 2 H 6 , CH 3 NH 2 , H 2 O 2 , and N 2 H 4 by ysing the CNDO/BW approximation and an M-center energy partition. Our results are compared with those obtained with the CNDO/2 approximation. It is shown that there are differences in the analysis of the process involved in the internal rotation barriers mechanism. Thus the interpretation of the results is strongly dependent on the parametrization used. (author) [pt
International Nuclear Information System (INIS)
Lublinsky, M.
2004-01-01
A simple analytic expression for the non-singlet structure function fns is given. The expression is derived from the result of B. I. Ermolaev et al. (1996) obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD. (orig.)
Csordás, András; Graham, Robert; Szépfalusy, Péter
1997-01-01
The Bogoliubov equations of the quasi-particle excitations in a weakly interacting trapped Bose-condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasi-particle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasi-particle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function which can be observed by off-resonance inelastic light...
Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions
J.L. López; N.M. Temme (Nico)
1998-01-01
textabstractBernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for $B_n(nz+1/2)$ and $E_n(nz+1/2)$ in powers of $n^{-1$, with coefficients being rational functions of $z$ and hyperbolic functions of argument $1/2z$. These expansions are
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Groenwold, A.A.; Etman, L.F.P.
2008-01-01
We study the classical topology optimization problem, in which minimum compliance is sought, subject to linear constraints. Using a dual statement, we propose two separable and strictly convex subproblems for use in sequential approximate optimization (SAO) algorithms.Respectively, the subproblems
International Nuclear Information System (INIS)
Espinoza-Ojeda, O M; Santoyo, E; Andaverde, J
2011-01-01
Approximate and rigorous solutions of seven heat transfer models were statistically examined, for the first time, to estimate stabilized formation temperatures (SFT) of geothermal and petroleum boreholes. Constant linear and cylindrical heat source models were used to describe the heat flow (either conductive or conductive/convective) involved during a borehole drilling. A comprehensive statistical assessment of the major error sources associated with the use of these models was carried out. The mathematical methods (based on approximate and rigorous solutions of heat transfer models) were thoroughly examined by using four statistical analyses: (i) the use of linear and quadratic regression models to infer the SFT; (ii) the application of statistical tests of linearity to evaluate the actual relationship between bottom-hole temperatures and time function data for each selected method; (iii) the comparative analysis of SFT estimates between the approximate and rigorous predictions of each analytical method using a β ratio parameter to evaluate the similarity of both solutions, and (iv) the evaluation of accuracy in each method using statistical tests of significance, and deviation percentages between 'true' formation temperatures and SFT estimates (predicted from approximate and rigorous solutions). The present study also enabled us to determine the sensitivity parameters that should be considered for a reliable calculation of SFT, as well as to define the main physical and mathematical constraints where the approximate and rigorous methods could provide consistent SFT estimates
International Nuclear Information System (INIS)
Jung, J.; Alvarellos, J.E.; Garcia-Gonzalez, P.; Godby, R.W.
2004-01-01
The complex nature of electron-electron correlations is made manifest in the very simple but nontrivial problem of two electrons confined within a sphere. The description of highly nonlocal correlation and self-interaction effects by widely used local and semilocal exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles
International Nuclear Information System (INIS)
Polivanskij, V.P.
1989-01-01
The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs
Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E
2018-03-14
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.
2018-03-01
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
International Nuclear Information System (INIS)
Zhang, L.
1981-08-01
A method based on the tight-binding approximation is developed to calculate the electron-phonon matrix element for the disordered transition metals. With the method as a basis the experimental Tsub(c) data of the amorphous transition metal superconductors are re-analysed. Some comments on the superconductivity of the disordered materials are given
Creep analysis by the path function method
International Nuclear Information System (INIS)
Akin, J.E.; Pardue, R.M.
1977-01-01
The finite element method has become a common analysis procedure for the creep analysis of structures. The most recent programs are designed to handle a general class of material properties and are able to calculate elastic, plastic, and creep components of strain under general loading histories. The constant stress approach is too crude a model to accurately represent the actual behaviour of the stress for large time steps. The true path of a point in the effective stress-effective strain (sigmasup(e)-epsilonsup(c)) plane is often one in which the slope is rapidly changing. Thus the stress level quickly moves away from the initial stress level and then gradually approaches the final one. The result is that the assumed constant stress level quickly becomes inaccurate. What is required is a better method of approximation of the true path in the sigmasup(e)-epsilonsup(c) space. The method described here is called the path function approach because it employs an assumed function to estimate the motion of points in the sigmasup(e)-epsilonsup(c) space. (Auth.)
Approximation of Mixed-Type Functional Equations in Menger PN-Spaces
Directory of Open Access Journals (Sweden)
M. Eshaghi Gordji
2012-01-01
Full Text Available Let X and Y be vector spaces. We show that a function f:X→Y with f(0=0 satisfies Δf(x1,…,xn=0 for all x1,…,xn∈X, if and only if there exist functions C:X×X×X→Y, B:X×X→Y and A:X→Y such that f(x=C(x,x,x+B(x,x+A(x for all x∈X, where the function C is symmetric for each fixed one variable and is additive for fixed two variables, B is symmetric bi-additive, A is additive and Δf(x1,…,xn=∑k=2n(∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir+f(∑i=1nxi-2n-2∑i=2n(f(x1+xi+f(x1-xi+2n-1(n-2f(x1 (n∈N, n≥3 for all x1,…,xn∈X. Furthermore, we solve the stability problem for a given function f satisfying Δf(x1,…,xn=0, in the Menger probabilistic normed spaces.
Kryven, I.; Röblitz, S; Schütte, C.
2015-01-01
Background: The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents
International Nuclear Information System (INIS)
Montero-Alejo, Ana L.; Gonzalez-Santana, Susana; Montero-Cabrera, Luis A.; Hernandez-Rodriguez, Erix Wiliam; Fuentes-Montero, Maria Elena; Bunge-Molina, Carlos F.; Gonzalez, Augusto
2008-01-01
Theoretical prediction of vertical excitation energies and an estimation of charge distributions of polyatomic systems can be calculated, through the configuration interaction of single (CIS) excited determinants procedure, with the CNDOL (Complete Neglect of Differential Overlap considering the l azimuthal quantum number) Hamiltonians. This method does not use adjusted parameters to fit experimental data and only employ a priori data on atomic orbitals and simple formulas to substitute large computations of electronic integrals. In this sense, different functions for bi-electron integrals have been evaluated in order to improve the approximate Hamiltonian. The reliability of predictions and theoretical consistence has been tested with a benchmark set of organic molecules that covers important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic, hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. The calculations are done at identical geometries (MP2) with the same basis set (6-31G) for these medium-sized molecules and the obtained results were statistically compared with other analogous methods and experimental data. The accuracy of prediction of each CNDOL vertical transitions energy increases while the active space is more complete allowing the best variational optimization of CIS matrices i.e. molecular excited states. Moreover and due to the feasible computation procedure for large polyatomic systems, the studies have been extended, as a preliminary work, in the field of optoelectronic materials for photovoltaic applications. Hence, the excitation energies of different conjugated Phenyl-cored Thiophene Dendrimers optimized by DFT (Density Functional Theory) were calculated and show good agreement with the experiment data. The predicted charge distribution during the excitation contributes to understand the photophysics process on these kind materials. (Full text)
Accelerating the coupled-cluster singles and doubles method using the chain-of-sphere approximation
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2018-06-01
In this paper, we present a chain-of-sphere implementation of the external exchange term, the computational bottleneck of coupled-cluster calculations at the singles and doubles level. This implementation is compared to standard molecular orbital, atomic orbital and resolution of identity implementations of the same term within the ORCA package and turns out to be the most efficient one for larger molecules, with a better accuracy than the resolution-of-identity approximation. Furthermore, it becomes possible to perform a canonical CC calculation on a tetramer of nucleobases in 17 days, 20 hours.
Accuracy of approximations of solutions to Fredholm equations by kernel methods
Czech Academy of Sciences Publication Activity Database
Gnecco, G.; Kůrková, Věra; Sanguineti, M.
2012-01-01
Roč. 218, č. 14 (2012), s. 7481-7497 ISSN 0096-3003 R&D Projects: GA ČR GAP202/11/1368; GA MŠk OC10047 Grant - others:CNR-AV ČR(CZ-IT) Project 2010–2012 “Complexity of Neural -Network and Kernel Computational Models Institutional research plan: CEZ:AV0Z10300504 Keywords : approximate solutions to integral equations * radial and kernel-based networks * Gaussian kernels * model complexity * analysis of algorithms Subject RIV: IN - Informatics, Computer Science Impact factor: 1.349, year: 2012
Perturbation methods and the Melnikov functions for slowly varying oscillators
International Nuclear Information System (INIS)
Lakrad, Faouzi; Charafi, Moulay Mustapha
2005-01-01
A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the Lindstedt-Poincare method to determine an approximation of homoclinic solutions. It is shown that the resultant Melnikov condition is the same as that obtained in the usual way involving distance functions in three dimensions by Wiggins and Holmes [Homoclinic orbits in slowly varying oscillators. SIAM J Math Anal 1987;18(3):612
An approximate reasoning-based method for screening high-level-waste tanks for flammable gas
International Nuclear Information System (INIS)
Eisenhawer, S.W.; Bott, T.F.; Smith, R.E.
2000-01-01
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at the Hanford site have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop and improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. Approximate-reasoning models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. In a pilot study to investigate the utility of AR for flammable gas screening, the effort to implement such a model was found to be acceptable, and computational requirements were found to be reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts
An Approximate Reasoning-Based Method for Screening High-Level-Waste Tanks for Flammable Gas
International Nuclear Information System (INIS)
Eisenhawer, Stephen W.; Bott, Terry F.; Smith, Ronald E.
2000-01-01
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at the Hanford site have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop an improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. Approximate-reasoning models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. In a pilot study to investigate the utility of AR for flammable gas screening, the effort to implement such a model was found to be acceptable, and computational requirements were found to be reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts
An approximate reasoning-based method for screening high-level-waste tanks for flammable gas
Energy Technology Data Exchange (ETDEWEB)
Eisenhawer, S.W.; Bott, T.F.; Smith, R.E.
2000-06-01
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at the Hanford site have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop and improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. Approximate-reasoning models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. In a pilot study to investigate the utility of AR for flammable gas screening, the effort to implement such a model was found to be acceptable, and computational requirements were found to be reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts.
Directory of Open Access Journals (Sweden)
Hozejowski Leszek
2012-04-01
Full Text Available The paper is devoted to a computational problem of predicting a local heat transfer coefficient from experimental temperature data. The experimental part refers to boiling flow of a refrigerant in a minichannel. Heat is dissipated from heating alloy to the flowing liquid due to forced convection. The mathematical model of the problem consists of the governing Poisson equation and the proper boundary conditions. For accurate results it is required to smooth the measurements which was obtained by using Trefftz functions. The measurements were approximated with a linear combination of Trefftz functions. Due to the computational procedure in which the measurement errors are known, it was possible to smooth the data and also to reduce the residuals of approximation on the boundaries.
Functional approximations to posterior densities: a neural network approach to efficient sampling
L.F. Hoogerheide (Lennart); J.F. Kaashoek (Johan); H.K. van Dijk (Herman)
2002-01-01
textabstractThe performance of Monte Carlo integration methods like importance sampling or Markov Chain Monte Carlo procedures greatly depends on the choice of the importance or candidate density. Usually, such a density has to be "close" to the target density in order to yield numerically accurate
Frolov, Maxim; Chistiakova, Olga
2017-06-01
Paper is devoted to a numerical justification of the recent a posteriori error estimate for Reissner-Mindlin plates. This majorant provides a reliable control of accuracy of any conforming approximate solution of the problem including solutions obtained with commercial software for mechanical engineering. The estimate is developed on the basis of the functional approach and is applicable to several types of boundary conditions. To verify the approach, numerical examples with mesh refinements are provided.
Multidimensional method of spatially coupled approximation to the transverse escape in nodal codes
International Nuclear Information System (INIS)
Jatuff, F.E.
1990-01-01
A natural extension of the polynomic development programmed in RHENO code is presented, which adds to the variable order one-dimensional functions sum, a number of terms that represent functions of production. These new terms, which provide a direct determination of transverse escapes, are calculated from the new variables coupling among nodes: the 4 fluxes in rectangle vortices (bidimensional Cartesian geometry) or the 12 fluxes half-way through the parallelepiped edges (tridimensional Cartesian geometry). (Author) [es
Directory of Open Access Journals (Sweden)
Norhasimah Mahiddin
2014-01-01
Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.
Approximate method for treating dispersion in one-way quantum channels
International Nuclear Information System (INIS)
Stace, T. M.; Wiseman, H. M.
2006-01-01
Coupling the output of a source quantum system into a target quantum system is easily treated by cascaded systems theory if the intervening quantum channel is dispersionless. However, dispersion may be important in some transfer protocols, especially in solid-state systems. In this paper we show how to generalize cascaded systems theory to treat such dispersion, provided it is not too strong. We show that the technique also works for fermionic systems with a low flux, and can be extended to treat fermionic systems with large flux. To test our theory, we calculate the effect of dispersion on the fidelity of a simple protocol of quantum state transfer. We find good agreement with an approximate analytical theory that had been previously developed for this example
Approximation of a chaotic orbit as a cryptanalytical method on Baptista's cipher
International Nuclear Information System (INIS)
Skrobek, Adrian
2008-01-01
Many cryptographic schemes based on M.S. Baptista algorithm were created. The original algorithm and some of the versions that based upon it were put to test with various cryptanalytic techniques. This Letter shows the new approach to Baptista's cipher cryptanalysis. The presumption is that the attacker knows the mapping in between the characters of the plaintext and the numbers of the ε-interval. Then, depending on the amount of the knowledge about the key possessed, the estimation of all components of the key requires a different computational complexity, however it is possible. This Letter also takes into consideration, independently, all the components of the key from the M.S. Baptista's original algorithm. The main aim is the use of the approximation of the blurred chaotic orbit's real value in Baptista-type cipher cryptanalysis
Li, Zhendong; Liu, Wenjian
2010-08-14
The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Approximation Methods for Inference and Learning in Belief Networks: Progress and Future Directions
National Research Council Canada - National Science Library
Pazzan, Michael
1997-01-01
.... In this research project, we have investigated methods and implemented algorithms for efficiently making certain classes of inference in belief networks, and for automatically learning certain...
Li, Chen; Requist, Ryan; Gross, E. K. U.
2018-02-01
We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation—an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).
Energy Technology Data Exchange (ETDEWEB)
Rüger, Robert, E-mail: rueger@scm.com [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Lenthe, Erik van [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Heine, Thomas [Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Visscher, Lucas [Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands)
2016-05-14
We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.
A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree
Directory of Open Access Journals (Sweden)
Ali R. Soheili
2009-01-01
Full Text Available A gradient weighted moving finite element method (GWMFE based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
Energy Technology Data Exchange (ETDEWEB)
Smorodin, F.K.; Druzhinin, G.V.
1991-01-01
A mathematical model is proposed which describes the fracture behavior of amorphous materials during laser cutting. The model, which is based on boundary layer equations, is reduced to ordinary differential equations with the corresponding boundary conditions. The reduced model is used to develop an approximate method for calculating the fracture characteristics of nonmetallic materials.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Approximate methods for generation of covariance data for the structural materials of ENDF/B-VI
International Nuclear Information System (INIS)
Hetrick, D.M.; Larson, D.C.; Fu, C.Y.
1992-01-01
The considerations that governed the development of cross section uncertainty files for the isotopes of Cr, Fe, Ni, Cu, and Pb in ENDF/B-VI are summarized. Four different approaches were used in providing the uncertainty information. Illustrative examples are given which show the resulting standard deviations as a function of incident energy and the corresponding correlation matrices
Directory of Open Access Journals (Sweden)
Hee-Jong Choi
2011-12-01
Full Text Available In the present study, a new hull panel generation algorithm, namely panel cutting method, was developed to predict flow phenomena around a ship using the Rankine source potential based panel method, where the iterative method was used to satisfy the nonlinear free surface condition and the trim and sinkage of the ship was taken into account. Numerical computations were performed to investigate the validity of the proposed hull panel generation algorithm for Series 60 (CB=0.60 hull and KRISO container ship (KCS, a container ship designed by Maritime and Ocean Engineering Research Institute (MOERI. The computational results were validated by comparing with the existing experimental data.
Choi, Hee-Jong; Chun, Ho-Hwan; Park, Il-Ryong; Kim, Jin
2011-12-01
In the present study, a new hull panel generation algorithm, namely panel cutting method, was developed to predict flow phenomena around a ship using the Rankine source potential based panel method, where the iterative method was used to satisfy the nonlinear free surface condition and the trim and sinkage of the ship was taken into account. Numerical computations were performed to investigate the validity of the proposed hull panel generation algorithm for Series 60 (CB=0.60) hull and KRISO container ship (KCS), a container ship designed by Maritime and Ocean Engineering Research Institute (MOERI). The computational results were validated by comparing with the existing experimental data.
An approximate-reasoning-based method for screening high-level waste tanks for flammable gas
International Nuclear Information System (INIS)
Eisenhawer, S.W.; Bott, T.F.; Smith, R.E.
1998-01-01
The in situ retention of flammable gas produced by radiolysis and thermal decomposition in high-level waste can pose a safety problem if the gases are released episodically into the dome space of a storage tank. Screening efforts at Hanford have been directed at identifying tanks in which this situation could exist. Problems encountered in screening motivated an effort to develop an improved screening methodology. Approximate reasoning (AR) is a formalism designed to emulate the kinds of complex judgments made by subject matter experts. It uses inductive logic structures to build a sequence of forward-chaining inferences about a subject. AR models incorporate natural language expressions known as linguistic variables to represent evidence. The use of fuzzy sets to represent these variables mathematically makes it practical to evaluate quantitative and qualitative information consistently. The authors performed a pilot study to investigate the utility of AR for flammable gas screening. They found that the effort to implement such a model was acceptable and that computational requirements were reasonable. The preliminary results showed that important judgments about the validity of observational data and the predictive power of models could be made. These results give new insights into the problems observed in previous screening efforts
Bakker, Mark
2001-05-01
An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.
Quantum theory of anharmonic oscillators - a variational and systematic general approximation method
International Nuclear Information System (INIS)
Yamazaki, K.; Kyoto Univ.
1984-01-01
The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)
International Nuclear Information System (INIS)
Betcke, Marta M; Lionheart, William R B
2013-01-01
The mechanical motion of the gantry in conventional cone beam CT scanners restricts the speed of data acquisition in applications with near real time requirements. A possible resolution of this problem is to replace the moving source detector assembly with static parts that are electronically activated. An example of such a system is the Rapiscan Systems RTT80 real time tomography scanner, with a static ring of sources and axially offset static cylinder of detectors. A consequence of such a design is asymmetrical axial truncation of the cone beam projections resulting, in the sense of integral geometry, in severely incomplete data. In particular we collect data only in a fraction of the Tam–Danielsson window, hence the standard cone beam reconstruction techniques do not apply. In this work we propose a family of multi-sheet surface rebinning methods for reconstruction from such truncated projections. The proposed methods combine analytical and numerical ideas utilizing linearity of the ray transform to reconstruct data on multi-sheet surfaces, from which the volumetric image is obtained through deconvolution. In this first paper in the series, we discuss the rebinning to multi-sheet surfaces. In particular we concentrate on the underlying transforms on multi-sheet surfaces and their approximation with data collected by offset multi-source scanning geometries like the RTT. The optimal multi-sheet surface and the corresponding rebinning function are found as a solution of a variational problem. In the case of the quadratic objective, the variational problem for the optimal rebinning pair can be solved by a globally convergent iteration. Examples of optimal rebinning pairs are computed for different trajectories. We formulate the axial deconvolution problem for the recovery of the volumetric image from the reconstructions on multi-sheet surfaces. Efficient and stable solution of the deconvolution problem is the subject of the second paper in this series (Betcke and
International Nuclear Information System (INIS)
Frishman, A.; Hoffman, D.K.; Kouri, D.J.
1997-01-01
We report a distributed approximating functional (DAF) fit of the ab initio potential-energy data of Liu [J. Chem. Phys. 58, 1925 (1973)] and Siegbahn and Liu [ibid. 68, 2457 (1978)]. The DAF-fit procedure is based on a variational principle, and is systematic and general. Only two adjustable parameters occur in the DAF leading to a fit which is both accurate (to the level inherent in the input data; RMS error of 0.2765 kcal/mol) and smooth (open-quotes well-tempered,close quotes in DAF terminology). In addition, the LSTH surface of Truhlar and Horowitz based on this same data [J. Chem. Phys. 68, 2466 (1978)] is itself approximated using only the values of the LSTH surface on the same grid coordinate points as the ab initio data, and the same DAF parameters. The purpose of this exercise is to demonstrate that the DAF delivers a well-tempered approximation to a known function that closely mimics the true potential-energy surface. As is to be expected, since there is only roundoff error present in the LSTH input data, even more significant figures of fitting accuracy are obtained. The RMS error of the DAF fit, of the LSTH surface at the input points, is 0.0274 kcal/mol, and a smooth fit, accurate to better than 1cm -1 , can be obtained using more than 287 input data points. copyright 1997 American Institute of Physics
Zednikova Mala, Pavla; Veleminska, Jana
2018-01-01
This study measured the accuracy of traditional and validated newly proposed methods for globe positioning in lateral view. Eighty lateral head cephalograms of adult subjects from Central Europe were taken, and the actual and predicted dimensions were compared. The anteroposterior eyeball position was estimated as the most accurate method based on the proportion of the orbital height (SEE = 1.9 mm) and was followed by the "tangent to the iris method" showing SEE = 2.4 mm. The traditional "tangent to the cornea method" underestimated the eyeball projection by SEE = 5.8 mm. Concerning the superoinferior eyeball position, the results showed a deviation from a central to a more superior position by 0.3 mm, on average, and the traditional method of central positioning of the globe could not be rejected as inaccurate (SEE = 0.3 mm). Based on regression analyzes or proportionality of the orbital height, the SEE = 2.1 mm. © 2017 American Academy of Forensic Sciences.
Computational Methods and Function Theory
Saff, Edward; Salinas, Luis; Varga, Richard
1990-01-01
The volume is devoted to the interaction of modern scientific computation and classical function theory. Many problems in pure and more applied function theory can be tackled using modern computing facilities: numerically as well as in the sense of computer algebra. On the other hand, computer algorithms are often based on complex function theory, and dedicated research on their theoretical foundations can lead to great enhancements in performance. The contributions - original research articles, a survey and a collection of problems - cover a broad range of such problems.
An approximate-reasoning-based method for screening flammable gas tanks
International Nuclear Information System (INIS)
Eisenhawer, S.W.; Bott, T.F.; Smith, R.E.
1998-03-01
High-level waste (HLW) produces flammable gases as a result of radiolysis and thermal decomposition of organics. Under certain conditions, these gases can accumulate within the waste for extended periods and then be released quickly into the dome space of the storage tank. As part of the effort to reduce the safety concerns associated with flammable gas in HLW tanks at Hanford, a flammable gas watch list (FGWL) has been established. Inclusion on the FGWL is based on criteria intended to measure the risk associated with the presence of flammable gas. It is important that all high-risk tanks be identified with high confidence so that they may be controlled. Conversely, to minimize operational complexity, the number of tanks on the watchlist should be reduced as near to the true number of flammable risk tanks as the current state of knowledge will support. This report presents an alternative to existing approaches for FGWL screening based on the theory of approximate reasoning (AR) (Zadeh 1976). The AR-based model emulates the inference process used by an expert when asked to make an evaluation. The FGWL model described here was exercised by performing two evaluations. (1) A complete tank evaluation where the entire algorithm is used. This was done for two tanks, U-106 and AW-104. U-106 is a single shell tank with large sludge and saltcake layers. AW-104 is a double shell tank with over one million gallons of supernate. Both of these tanks had failed the screening performed by Hodgson et al. (2) Partial evaluations using a submodule for the predictor likelihood for all of the tanks on the FGWL that had been flagged previously by Whitney (1995)
Approximate calculation method for integral of mean square value of nonstationary response
International Nuclear Information System (INIS)
Aoki, Shigeru; Fukano, Azusa
2010-01-01
The response of the structure subjected to nonstationary random vibration such as earthquake excitation is nonstationary random vibration. Calculating method for statistical characteristics of such a response is complicated. Mean square value of the response is usually used to evaluate random response. Integral of mean square value of the response corresponds to total energy of the response. In this paper, a simplified calculation method to obtain integral of mean square value of the response is proposed. As input excitation, nonstationary white noise and nonstationary filtered white noise are used. Integrals of mean square value of the response are calculated for various values of parameters. It is found that the proposed method gives exact value of integral of mean square value of the response.
Approximation of the Monte Carlo Sampling Method for Reliability Analysis of Structures
Directory of Open Access Journals (Sweden)
Mahdi Shadab Far
2016-01-01
Full Text Available Structural load types, on the one hand, and structural capacity to withstand these loads, on the other hand, are of a probabilistic nature as they cannot be calculated and presented in a fully deterministic way. As such, the past few decades have witnessed the development of numerous probabilistic approaches towards the analysis and design of structures. Among the conventional methods used to assess structural reliability, the Monte Carlo sampling method has proved to be very convenient and efficient. However, it does suffer from certain disadvantages, the biggest one being the requirement of a very large number of samples to handle small probabilities, leading to a high computational cost. In this paper, a simple algorithm was proposed to estimate low failure probabilities using a small number of samples in conjunction with the Monte Carlo method. This revised approach was then presented in a step-by-step flowchart, for the purpose of easy programming and implementation.
On the application of the Williams-Weizsaecker-method to higher order S-matrix-approximations
International Nuclear Information System (INIS)
Ziegelbecker, R.C.
1983-05-01
In this paper the method of quasireal processes is investigated using a special example - pair production in the stationary field of a nucleus by an incident electron. As a result, the semi-classical version of the Williams-Weizsaecker-method is confirmed on the basis of all 3sup(rd)-order Feynman-diagrams. The spectra of quasireal processes, derived from quantum field theory, can also be applied simultaneously in several vertex points on one diagram and are valid for higher photon energies than the semiclassical spectrum; the restriction #betta# [de
International Nuclear Information System (INIS)
Sanchez, Richard.
1980-11-01
This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr
The derivation of the Doppler broadening function using Frobenius method
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C.
2006-01-01
An analytical approximation of the Doppler broadening function ψ(ξ,x) is proposed. This approximation is based on the solution of the differential equation for ψ(ξ,x) using the methods of Frobenius and parameters variation. The analytical form derived for ψ(ξ,x) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances, mainly for calculations of multigroup parameters and resonances self-protection factors, the latter being used to correct microscopic cross section measurements by the activation technique. (author)
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Gauss-Arnoldi quadrature for -1φ,φ> and rational Pade-type approximation for Markov-type functions
International Nuclear Information System (INIS)
Knizhnerman, L A
2008-01-01
The efficiency of Gauss-Arnoldi quadrature for the calculation of the quantity -1 φ,φ> is studied, where A is a bounded operator in a Hilbert space and φ is a non-trivial vector in this space. A necessary and a sufficient conditions are found for the efficiency of the quadrature in the case of a normal operator. An example of a non-normal operator for which this quadrature is inefficient is presented. It is shown that Gauss-Arnoldi quadrature is related in certain cases to rational Pade-type approximation (with the poles at Ritz numbers) for functions of Markov type and, in particular, can be used for the localization of the poles of a rational perturbation. Error estimates are found, which can also be used when classical Pade approximation does not work or it may not be efficient. Theoretical results and conjectures are illustrated by numerical experiments. Bibliography: 44 titles
Kwato-Njock, K
2002-01-01
A search is conducted for the determination of expectation values of r sup q between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models which have proven so far to yield accurate results are used. The recursive structure of formulae derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of q. Detailed numerical calculations concerning alkali-metal-like ions of the Li-, Na- and Cu-iso electronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.
Kwato-Njock, M G; Oumarou, B
2002-01-01
A search is conducted for the determination of expectation values of $r^q$ between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models which have proven so far to yield accurate results are used. The recursive structure of formulae derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of $q$. Detailed numerical calculations concerning alkali-metal-like ions of the Li-, Na- and Cu-iso electronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.
Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods
Directory of Open Access Journals (Sweden)
H. Vazquez-Leal
2013-01-01
Full Text Available The microelectronics area constantly demands better and improved circuit simulation tools. Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.
International Nuclear Information System (INIS)
Martín-Benito, Mercedes; Martín-de Blas, Daniel; Marugán, Guillermo A Mena
2014-01-01
We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann–Robertson–Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions. (paper)
A numeric-analytic method for approximating the chaotic Chen system
International Nuclear Information System (INIS)
Mossa Al-sawalha, M.; Noorani, M.S.M.
2009-01-01
The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge-Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic-numeric scheme is effective and accurate.
Method Ideology and State: Approximations based on Marx’s legacy
Directory of Open Access Journals (Sweden)
Davi Machado Perez
2018-02-01
Full Text Available This essay is the fruit of bibliographic research and offers reflections about the Marxist concepts of method, ideology and state, to question the idea that there is an economic determinism in the work of Karl Marx. It then dialogs with current Marxist authors who address the state in the era of monopoly capitalism, reaffirming Marx’s legacy as an essential starting point for the development of studies about the modern and contemporary state.
An attempt to use FMEA method for an approximate reliability assessment of machinery
Directory of Open Access Journals (Sweden)
Przystupa Krzysztof
2017-01-01
Full Text Available The paper presents a modified FMEA (Failure Mode and Effect Analysis method to assess reliability of the components that make up a wrench type 2145: MAX Impactol TM Driver Ingersoll Rand Company. This case concerns the analysis of reliability in conditions, when full service data is not known. The aim of the study is to determine the weakest element in the design of the tool.
S.V. Kryuchkov; E.I. Kukhar’; D.V. Zav’yalov
2015-01-01
The power of the elliptically polarized electromagnetic radiation absorbed by band-gap graphene in presence of constant magnetic field is calculated. The linewidth of cyclotron absorption is shown to be non-zero even if the scattering is absent. The calculations are performed analytically with the Boltzmann kinetic equation and confirmed numerically with the Monte Carlo method. The dependence of the linewidth of the cyclotron absorption on temperature applicable for a band-gap graphene in the...
Vega Corona, Antonio; Zárate Banda, Magdalena; Barron Adame, Jose Miguel; Martínez Celorio, René Alfredo; Andina de la Fuente, Diego
2008-01-01
The present study describes the design of an Artificial Neural Network to synthesize the Approximation Function of a Pedometer for the Healthy Life Style Promotion. Experimentally, the approximation function is synthesized using three basic digital pedometers of low cost, these pedometers were calibrated with an advanced pedometer that calculates calories consumed and computes distance travelled with personal stride input. The synthesized approximation function by means of the designed neural...
A Perceptually Reweighted Mixed-Norm Method for Sparse Approximation of Audio Signals
DEFF Research Database (Denmark)
Christensen, Mads Græsbøll; Sturm, Bob L.
2011-01-01
using standard software. A prominent feature of the new method is that it solves a problem that is closely related to the objective of coding, namely rate-distortion optimization. In computer simulations, we demonstrate the properties of the algorithm and its application to real audio signals.......In this paper, we consider the problem of finding sparse representations of audio signals for coding purposes. In doing so, it is of utmost importance that when only a subset of the present components of an audio signal are extracted, it is the perceptually most important ones. To this end, we...... propose a new iterative algorithm based on two principles: 1) a reweighted l1-norm based measure of sparsity; and 2) a reweighted l2-norm based measure of perceptual distortion. Using these measures, the considered problem is posed as a constrained convex optimization problem that can be solved optimally...
Energy Technology Data Exchange (ETDEWEB)
Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Methods for Functional Connectivity Analyses
2012-12-13
motor , or hand motor function (green, red, or blue shading, respectively). Thus, this work produced the first comprehensive analysis of ECoG...Computer Engineering, University of Texas at El Paso , TX, USA 3Department of Neurology, Albany Medical College, Albany, NY, USA 4Department of Computer...Department of Health, Albany, NY, USA bDepartment of Electrical and Computer Engineering, University of Texas at El Paso , TX, USA cDepartment of Neurology
Application of the first approximation of the K-harmonics method to the O+ states of 16O
International Nuclear Information System (INIS)
Alcaras, J.A.C.; Silveira, H.V. da.
1977-01-01
The energy levels of the O + states, the charge form factor and the root mean square charge radius of the 16 O were calculated in the first approximation of the K-harmonics method. The calculation were done for six different potentials. The results obtained for the ground state energy, charge form factor and rms charge radius are in agreement with the experimental results, but this is not the case for the energies of the O + excited states