WorldWideScience

Sample records for series expansion methods

  1. Series expansions without diagrams

    International Nuclear Information System (INIS)

    Bhanot, G.; Creutz, M.; Horvath, I.; Lacki, J.; Weckel, J.

    1994-01-01

    We discuss the use of recursive enumeration schemes to obtain low- and high-temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagrammatic approaches and is easily generalizable. We illustrate the approach using Ising and Potts models. We present low-temperature series results in up to five dimensions and high-temperature series in three dimensions. The method is general and can be applied to any discrete model

  2. Sumudu transform series expansion method for solving the local fractional Laplace equation in fractal thermal problems

    Directory of Open Access Journals (Sweden)

    Guo Zheng-Hong

    2016-01-01

    Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.

  3. Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

    OpenAIRE

    Li, Xiaowang; Deng, Zhongmin

    2016-01-01

    A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white no...

  4. Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2013-01-01

    Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

  5. Numerical simulation of stratified shear flow using a higher order Taylor series expansion method

    Energy Technology Data Exchange (ETDEWEB)

    Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)

    1995-09-01

    A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.

  6. Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

  7. Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

    Directory of Open Access Journals (Sweden)

    SURE KÖME

    2014-12-01

    Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

  8. Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

    Directory of Open Access Journals (Sweden)

    Xiaowang Li

    2016-01-01

    Full Text Available A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.

  9. Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

    Directory of Open Access Journals (Sweden)

    Sun Huan

    2016-01-01

    Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

  10. expansion method

    Indian Academy of Sciences (India)

    of a system under investigation is to model the system in terms of some ... The organization of the paper is as follows: In §2, a brief account of the (G /G)- expansion ...... It is interesting to note that from the general results, one can easily recover.

  11. A Power Series Expansion and Its Applications

    Science.gov (United States)

    Chen, Hongwei

    2006-01-01

    Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

  12. Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options

    NARCIS (Netherlands)

    Ruijter, M.J.; Oosterlee, C.W.

    2012-01-01

    The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher

  13. Design method for low order two-degree-of-freedom controller based on Pade approximation of the denominator series expansion

    International Nuclear Information System (INIS)

    Ishikawa, Nobuyuki; Suzuki, Katsuo

    1999-01-01

    Having advantages of setting independently feedback characteristics such as disturbance rejection specification and reference response characteristics, two-degree-of-freedom (2DOF) control is widely utilized to improve the control performance. The ordinary design method such as model matching usually derives high-ordered feedforward element of 2DOF controller. In this paper, we propose a new design method for low order feedforward element which is based on Pade approximation of the denominator series expansion. The features of the proposed method are as follows: (1) it is suited to realize reference response characteristics in low frequency region, (2) the order of the feedforward element can be selected apart from the feedback element. These are essential to the 2DOF controller design. With this method, 2DOF reactor power controller is designed and its control performance is evaluated by numerical simulation with reactor dynamics model. For this evaluation, it is confirmed that the controller designed by the proposed method possesses equivalent control characteristics to the controller by the ordinary model matching method. (author)

  14. Application of the perturbation series expansion quantum Monte Carlo method to multiorbital systems having Hund's coupling

    International Nuclear Information System (INIS)

    Sakai, Shiro; Arita, Ryotaro; Aoki, Hideo

    2006-01-01

    We propose a new quantum Monte Carlo method especially intended to couple with the dynamical mean-field theory. The algorithm is not only much more efficient than the conventional Hirsch-Fye algorithm, but is applicable to multiorbital systems having an SU(2)-symmetric Hund's coupling as well

  15. Series expansion of the modified Einstein Procedure

    Science.gov (United States)

    Seema Chandrakant Shah-Fairbank

    2009-01-01

    This study examines calculating total sediment discharge based on the Modified Einstein Procedure (MEP). A new procedure based on the Series Expansion of the Modified Einstein Procedure (SEMEP) has been developed. This procedure contains four main modifications to MEP. First, SEMEP solves the Einstein integrals quickly and accurately based on a series expansion. Next,...

  16. Optimal separable bases and series expansions

    International Nuclear Information System (INIS)

    Poirier, B.

    1997-01-01

    A method is proposed for the efficient calculation of the Green close-quote s functions and eigenstates for quantum systems of two or more dimensions. For a given Hamiltonian, the best possible separable approximation is obtained from the set of all Hilbert-space operators. It is shown that this determination itself, as well as the solution of the resultant approximation, is a problem of reduced dimensionality. Moreover, the approximate eigenstates constitute the optimal separable basis, in the sense of self-consistent field theory. The full solution is obtained from the approximation via iterative expansion. In the time-independent perturbation expansion for instance, all of the first-order energy corrections are zero. In the Green close-quote s function case, we have a distorted-wave Born series with optimized convergence properties. This series may converge even when the usual Born series diverges. Analytical results are presented for an application of the method to the two-dimensional shifted harmonic-oscillator system, in the course of which the quantum tanh 2 potential problem is solved exactly. The universal presence of bound states in the latter is shown to imply long-lived resonances in the former. In a comparison with other theoretical methods, we find that the reaction path Hamiltonian fails to predict such resonances. copyright 1997 The American Physical Society

  17. A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

    Science.gov (United States)

    Grimm, C. A.

    This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

  18. Comment on ‘Series expansions from the corner transfer matrix renormalization group method: the hard-squares model’

    International Nuclear Information System (INIS)

    Jensen, Iwan

    2012-01-01

    Earlier this year Chan extended the low-density series for the hard-squares partition function κ(z) to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity z d which lies on the negative fugacity axis. We find that the series has a confluent singularity of order at least 2 at z d with exponents θ = 0.833 33(2) and θ′ = 1.6676(3). We thus confirm that the exponent θ has the exact value 5/6 as observed by Dhar. (comment)

  19. Series expansion in fractional calculus and fractional differential equations

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2009-01-01

    Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

  20. An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

    Science.gov (United States)

    Yang, Lei; Yan, Hongyong; Liu, Hong

    2017-03-01

    Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

  1. Recurrence formulas for evaluating expansion series of depletion functions

    International Nuclear Information System (INIS)

    Vukadin, Z.

    1991-01-01

    A high-accuracy analytical method for solving the depletion equations for chains of radioactive nuclides is based on the formulation of depletion functions. When all the arguments of the depletion function are too close to each other, series expansions of the depletion function have to be used. However, the high-accuracy series expressions for the depletion functions of high index become too complicated. Recursion relations are derived which enable an efficient high-accuracy evaluation of the depletion functions with high indices. (orig.) [de

  2. The loop expansion as a divergent-power-series expansion

    International Nuclear Information System (INIS)

    Murai, N.

    1981-01-01

    The loop expansion should be divergent, possibly an asymptotic one, in the Euclidean path integral formulation. This consideration is important in applications of the symmetric and mass-independent renormalization. The [1,1] Pade approximant is calculated in a PHI 4 model. Its classical vacua may be not truely stable for nonzero coupling constant. (author)

  3. Correlation expansion: a powerful alternative multiple scattering calculation method

    International Nuclear Information System (INIS)

    Zhao Haifeng; Wu Ziyu; Sebilleau, Didier

    2008-01-01

    We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion

  4. Stochastic series expansion simulation of the t -V model

    Science.gov (United States)

    Wang, Lei; Liu, Ye-Hua; Troyer, Matthias

    2016-04-01

    We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.

  5. Growth And Export Expansion In Mauritius - A Time Series Analysis ...

    African Journals Online (AJOL)

    Growth And Export Expansion In Mauritius - A Time Series Analysis. ... RV Sannassee, R Pearce ... Using Granger Causality tests, the short-run analysis results revealed that there is significant reciprocal causality between real export earnings ...

  6. On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

    International Nuclear Information System (INIS)

    Sai Venkata Ramana, A.

    2014-01-01

    The coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids

  7. Off-diagonal series expansion for quantum partition functions

    Science.gov (United States)

    Hen, Itay

    2018-05-01

    We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.

  8. Modulated Hermite series expansions and the time-bandwidth product

    NARCIS (Netherlands)

    Brinker, den A.C.; Sarroukh, B.E.

    2000-01-01

    The harmonically modulated Hermite series constitute an orthonormal basis in the Hilbert space of square-integrable functions. This basis comprises three free parameters, namely a translation, a modulation, and a scale factor. In practical situations, we are interested in series expansions that are

  9. Student understanding of Taylor series expansions in statistical mechanics

    Directory of Open Access Journals (Sweden)

    Trevor I. Smith

    2013-08-01

    Full Text Available One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.

  10. Student understanding of Taylor series expansions in statistical mechanics

    Science.gov (United States)

    Smith, Trevor I.; Thompson, John R.; Mountcastle, Donald B.

    2013-12-01

    One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.

  11. LPV system identification using series expansion models

    NARCIS (Netherlands)

    Toth, R.; Heuberger, P.S.C.; Hof, Van den P.M.J.; Santos, dos P.L.; Perdicoúlis, T.P.A.; Novara, C.; Ramos, J.A.; Rivera, D.E.

    2011-01-01

    This review volume reports the state-of-the-art in Linear Parameter Varying (LPV) system identification. Written by world renowned researchers, the book contains twelve chapters, focusing on the most recent LPV identification methods for both discrete-time and continuous-time models, using different

  12. High-temperature series expansions for random Potts models

    Directory of Open Access Journals (Sweden)

    M.Hellmund

    2005-01-01

    Full Text Available We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique, quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2 and 4-state Potts model in three dimensions up to the order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.

  13. Ground state energies from converging and diverging power series expansions

    International Nuclear Information System (INIS)

    Lisowski, C.; Norris, S.; Pelphrey, R.; Stefanovich, E.; Su, Q.; Grobe, R.

    2016-01-01

    It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh–Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state’s spatial extension is comparable to L. Once the binding strength is so strong that the ground state’s extension is less than L, the power expansion becomes divergent, consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.

  14. Ground state energies from converging and diverging power series expansions

    Energy Technology Data Exchange (ETDEWEB)

    Lisowski, C.; Norris, S.; Pelphrey, R.; Stefanovich, E., E-mail: eugene-stefanovich@usa.net; Su, Q.; Grobe, R.

    2016-10-15

    It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh–Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state’s spatial extension is comparable to L. Once the binding strength is so strong that the ground state’s extension is less than L, the power expansion becomes divergent, consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.

  15. Synchronization of complex chaotic systems in series expansion form

    International Nuclear Information System (INIS)

    Ge Zhengming; Yang Chenghsiung

    2007-01-01

    This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy

  16. Asymptotic Expansions - Methods and Applications

    International Nuclear Information System (INIS)

    Harlander, R.

    1999-01-01

    Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed. (author)

  17. Disjoint sum expansion method in FTA

    International Nuclear Information System (INIS)

    Ruan Keqiang

    1987-01-01

    An expansion formula for transforming boolean algebraic expressions into disjoint form was proved. Based on this expansion formula, a method for transforming system failure function into disjoint form was devised. The fact that the expansion can be done for several elements simulatneously makes the method flexible and fast. Some examples from fault tree analysis (FTA) and network analysis were examined by the new method to show its algorithm and its merit. Besides, by means of the proved expansion formula some boolean algebraic relations can proved very easily

  18. Expansion of infinite series containing modified Bessel functions of the second kind

    International Nuclear Information System (INIS)

    Fucci, Guglielmo; Kirsten, Klaus

    2015-01-01

    The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory. (paper)

  19. Application of Rational Expansion Method for Differential-Difference Equation

    International Nuclear Information System (INIS)

    Wang Qi

    2011-01-01

    In this paper, we applied the rational formal expansion method to construct a series of soliton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions. The efficiency of the method can be demonstrated on Toda Lattice and Ablowitz-Ladik Lattice. (general)

  20. Power Series Expansion of Propagator for Path Integral and Its Applications

    International Nuclear Information System (INIS)

    Ou Yuanjin; Liang Xianting

    2007-01-01

    In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.

  1. Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions

    International Nuclear Information System (INIS)

    Boyd, John P.; Rangan, C.; Bucksbaum, P.H.

    2003-01-01

    The Fourier-sine-with-mapping pseudospectral algorithm of Fattal et al. [Phys. Rev. E 53 (1996) 1217] has been applied in several quantum physics problems. Here, we compare it with pseudospectral methods using Laguerre functions and rational Chebyshev functions. We show that Laguerre and Chebyshev expansions are better suited for solving problems in the interval r in R set of [0,∞] (for example, the Coulomb-Schroedinger equation), than the Fourier-sine-mapping scheme. All three methods give similar accuracy for the hydrogen atom when the scaling parameter L is optimum, but the Laguerre and Chebyshev methods are less sensitive to variations in L. We introduce a new variant of rational Chebyshev functions which has a more uniform spacing of grid points for large r, and gives somewhat better results than the rational Chebyshev functions of Boyd [J. Comp. Phys. 70 (1987) 63

  2. Temporal quadratic expansion nodal Green's function method

    International Nuclear Information System (INIS)

    Liu Cong; Jing Xingqing; Xu Xiaolin

    2000-01-01

    A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

  3. Approximate expressions for the period of a simple pendulum using a Taylor series expansion

    International Nuclear Information System (INIS)

    Belendez, Augusto; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi; Arribas, Enrique

    2011-01-01

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be performed which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the Kidd-Fogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.

  4. Approximate expressions for the period of a simple pendulum using a Taylor series expansion

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, Augusto; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Arribas, Enrique, E-mail: a.belendez@ua.es [Departamento de Fisica Aplicada, Escuela Superior de IngenierIa Informatica, Universidad de Castilla-La Mancha, Avda de Espana, s/n, E-02071 Albacete (Spain)

    2011-09-15

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be performed which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the Kidd-Fogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.

  5. Energy of the amplitude mode in the bicubic antiferromagnet: Series expansion results

    Science.gov (United States)

    Oitmaa, J.

    2018-05-01

    Series expansion methods are used to study the quantum critical behavior of the bicubic spin-1/2 antiferromagnet. Excitation energies are computed throughout the Brillouin zone, for both the Néel and dimer phases. We compute the energy of the amplitude/Higgs mode and show that it becomes degenerate with the magnon modes at the quantum critical point, as expected on general symmetry grounds.

  6. The asymptotic expansion method via symbolic computation

    OpenAIRE

    Navarro, Juan F.

    2012-01-01

    This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

  7. The Asymptotic Expansion Method via Symbolic Computation

    Directory of Open Access Journals (Sweden)

    Juan F. Navarro

    2012-01-01

    Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

  8. The optimizied expansion method for wavefield extrapolation

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2013-01-01

    , for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number

  9. Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions

    International Nuclear Information System (INIS)

    Ohtani, Nobuo

    1976-01-01

    A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)

  10. Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions

    International Nuclear Information System (INIS)

    Altac, Zekeriya

    2007-01-01

    Generalized exponential integral functions (GEIF) are encountered in multi-dimensional thermal radiative transfer problems in the integral equation kernels. Several series expansions for the first-order generalized exponential integral function, along with a series expansion for the general nth order GEIF, are derived. The convergence issues of these series expansions are investigated numerically as well as theoretically, and a recurrence relation which does not require derivatives of the GEIF is developed. The exact series expansions of the two dimensional cylindrical and/or two-dimensional planar integral kernels as well as their spatial moments have been explicitly derived and compared with numerical values

  11. Optimized t-expansion method for the Rabi Hamiltonian

    International Nuclear Information System (INIS)

    Travenec, Igor; Samaj, Ladislav

    2011-01-01

    A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E 0 of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E 0 is assumed to be stationary with respect to the free parameters. A high accuracy of E 0 estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10 -4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E 1 , with the relative error smaller than 10 -2 (1%). -- Highlights: → We study the ground state energy of the Rabi Hamiltonian. → We use the t-expansion method with an optimized trial function. → High accuracy of estimates is achieved, the relative error being smaller than 0.01%. → The calculation of the first excited state energy is made. The method has a general applicability.

  12. Expansion of Sobolev functions in series in Laguerre polynomials

    International Nuclear Information System (INIS)

    Selyakov, K.I.

    1985-01-01

    The solution of the integral equation for the Sobolev functions is represented in the form of series in Laguerre polynomials. The coefficients of these series are simultaneously the coefficients of the power series for the Ambartsumyan-Chandrasekhar H functions. Infinite systems of linear algebraic equations with Toeplitz matrices are given for the coefficients of the series. Numerical results and approximate expressions are given for the case of isotropic scattering

  13. Analytic structure and power series expansion of the Jost function for the two-dimensional problem

    International Nuclear Information System (INIS)

    Rakityansky, S A; Elander, N

    2012-01-01

    For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. (paper)

  14. Series expansion of two-dimensional fields produced by iron-core magnets

    International Nuclear Information System (INIS)

    Satoh, Kotaro.

    1997-02-01

    This paper discusses the validity of a series expansion of two-dimensional magnetic fields with harmonic functions, and suggests that the series may not converge outside of the pole gap. It also points out that this difficulty may appear due to a slow convergence of the series near to the pole edge, even within the convergent area. (author)

  15. Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

    Directory of Open Access Journals (Sweden)

    Okan Ozer

    2013-01-01

    Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

  16. Novel approach to the Helmholtz integral equation solution by Fourier series expansion for acoustic radiation and scattering problems

    CSIR Research Space (South Africa)

    Shatalov, MY

    2006-01-01

    Full Text Available -scale structure to guarantee the numerical accuracy of solution. In the present paper the authors propose to use a novel method of solution of the Helmholtz integral equation, which is based on expansion of the integrands in double Fourier series. The main...

  17. Density-functional expansion methods: Grand challenges.

    Science.gov (United States)

    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.

  18. Mahler Measure Variations, Eisenstein Series and Instanton Expansions

    NARCIS (Netherlands)

    Stienstra, J.

    2007-01-01

    This paper points at an intriguing inverse function relation with on the one hand the coefficients of the Eisenstein series in Rodriguez Villegas’ paper on “Modular Mahler Measures” and on the other hand the instanton numbers in papers on “Non-Critical Strings” by Klemm- Mayr-Vafa and

  19. The optimizied expansion method for wavefield extrapolation

    KAUST Repository

    Wu, Zedong

    2013-01-01

    Spectral methods are fast becoming an indispensable tool for wave-field extrapolation, especially in anisotropic media, because of its dispersion and artifact free, as well as highly accurate, solutions of the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number of inverse FFT required per time extrapolation step, and thus, a lower rank admits faster extrapolations. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its low rank representation.Thus,we obtain more accurate wave-fields using lower rank representation, and thus cheaper extrapolations. The optimization operation to define the low rank representation depends only on the velocity model, and this is done only once, and valid for a full reverse time migration (many shots) or one iteration of full waveform inversion. Applications on the BP model yielded superior results than those obtained using the decomposition approach. For transversely isotopic media, the solutions were free of the shear wave artifacts, and does not require that eta>0.

  20. A nonlinear analytic function expansion nodal method for transient calculations

    Energy Technology Data Exchange (ETDEWEB)

    Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1998-12-31

    The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

  1. A nonlinear analytic function expansion nodal method for transient calculations

    Energy Technology Data Exchange (ETDEWEB)

    Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1999-12-31

    The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)

  2. Teaching Graphical Simulations of Fourier Series Expansion of Some Periodic Waves Using Spreadsheets

    Science.gov (United States)

    Singh, Iqbal; Kaur, Bikramjeet

    2018-01-01

    The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

  3. A Time Series Forecasting Method

    Directory of Open Access Journals (Sweden)

    Wang Zhao-Yu

    2017-01-01

    Full Text Available This paper proposes a novel time series forecasting method based on a weighted self-constructing clustering technique. The weighted self-constructing clustering processes all the data patterns incrementally. If a data pattern is not similar enough to an existing cluster, it forms a new cluster of its own. However, if a data pattern is similar enough to an existing cluster, it is removed from the cluster it currently belongs to and added to the most similar cluster. During the clustering process, weights are learned for each cluster. Given a series of time-stamped data up to time t, we divide it into a set of training patterns. By using the weighted self-constructing clustering, the training patterns are grouped into a set of clusters. To estimate the value at time t + 1, we find the k nearest neighbors of the input pattern and use these k neighbors to decide the estimation. Experimental results are shown to demonstrate the effectiveness of the proposed approach.

  4. Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

    Science.gov (United States)

    Fukushima, Toshio

    2018-02-01

    In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

  5. A double expansion method for the frequency response of finite-length beams with periodic parameters

    Science.gov (United States)

    Ying, Z. G.; Ni, Y. Q.

    2017-03-01

    A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response

  6. Regularization and asymptotic expansion of certain distributions defined by divergent series

    Directory of Open Access Journals (Sweden)

    Ricardo Estrada

    1995-01-01

    Full Text Available The regularization of the distribution ∑n=−∞∞δ(x−pn. which gives a regularized value to the divergent series ∑n=−∞∞φ(pn is obtained in several spaces of test functions. The asymptotic expansion as ϵ→0+of series of the type ∑n=0∞φ(ϵ pn is also obtained.

  7. Teaching graphical simulations of Fourier series expansion of some periodic waves using spreadsheets

    Science.gov (United States)

    Singh, Iqbal; Kaur, Bikramjeet

    2018-05-01

    The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave, half wave rectifier and full wave rectifier signals.

  8. Series expansion solution of the Wegner-Houghton renormalisation group equation

    International Nuclear Information System (INIS)

    Margaritis, A.; Odor, G.; Patkos, A.

    1987-11-01

    The momentum independent projection of the Wegner-Houghton renormalisation group equation is solved with power series expansion. Convergence rate is analyzed for the n-vector model. Further evidence is presented for the first order nature of the chiral symmetry restoration at finite temperature in QCD with 3 light flavors. (author) 16 refs

  9. A Series Expansion Approach to Risk Analysis of an Inventory System with Sourcing

    NARCIS (Netherlands)

    Berkhout, J.; Heidergott, B.F.

    2014-01-01

    In this paper we extend the series expansion approach for uni-chain Markov processes to a special case of finite multi-chains with possible transient states. We will show that multi-chain Markov models arise naturally in simple models such as a single item inventory system with sourcing, i.e., with

  10. Stochastic Simulation and Forecast of Hydrologic Time Series Based on Probabilistic Chaos Expansion

    Science.gov (United States)

    Li, Z.; Ghaith, M.

    2017-12-01

    Hydrological processes are characterized by many complex features, such as nonlinearity, dynamics and uncertainty. How to quantify and address such complexities and uncertainties has been a challenging task for water engineers and managers for decades. To support robust uncertainty analysis, an innovative approach for the stochastic simulation and forecast of hydrologic time series is developed is this study. Probabilistic Chaos Expansions (PCEs) are established through probabilistic collocation to tackle uncertainties associated with the parameters of traditional hydrological models. The uncertainties are quantified in model outputs as Hermite polynomials with regard to standard normal random variables. Sequentially, multivariate analysis techniques are used to analyze the complex nonlinear relationships between meteorological inputs (e.g., temperature, precipitation, evapotranspiration, etc.) and the coefficients of the Hermite polynomials. With the established relationships between model inputs and PCE coefficients, forecasts of hydrologic time series can be generated and the uncertainties in the future time series can be further tackled. The proposed approach is demonstrated using a case study in China and is compared to a traditional stochastic simulation technique, the Markov-Chain Monte-Carlo (MCMC) method. Results show that the proposed approach can serve as a reliable proxy to complicated hydrological models. It can provide probabilistic forecasting in a more computationally efficient manner, compared to the traditional MCMC method. This work provides technical support for addressing uncertainties associated with hydrological modeling and for enhancing the reliability of hydrological modeling results. Applications of the developed approach can be extended to many other complicated geophysical and environmental modeling systems to support the associated uncertainty quantification and risk analysis.

  11. Application of potential harmonic expansion method to BEC ...

    Indian Academy of Sciences (India)

    We adopt the potential harmonics expansion method for an ab initio solu- ... commonly adopted mean-field theories, our method is capable of handling ..... potentials in self-consistent mean-field calculation [7] gives wrong results as the.

  12. Using Fourier and Taylor series expansion in semi-analytical deformation analysis of thick-walled isotropic and wound composite structures

    Directory of Open Access Journals (Sweden)

    Jiran L.

    2016-06-01

    Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.

  13. expansion method for the Burgers, Burgers–Huxley and modified

    Indian Academy of Sciences (India)

    expansion method; Burgers equation; Burgers–Huxley equation; modified. Burgers–KdV equation .... Substituting the solution set (12) and the corresponding solutions of (4) into (8), we have ..... During the past several years, many have done.

  14. IRP methods for Environmental Impact Statements of utility expansion plans

    International Nuclear Information System (INIS)

    Cavallo, J.D.; Hemphill, R.C.; Veselka, T.D.

    1992-01-01

    Most large electric utilities and a growing number of gas utilities in the United States are using a planning method -- Integrated Resource Planning (IRP) - which incorporates demand-side management (DSM) programs whenever the marginal cost of the DSM programs are lower than the marginal cost of supply-side expansion options. Argonne National Laboratory has applied the IRP method in its socio-economic analysis of an Environmental Impact Statement (EIS) of power marketing for a system of electric utilities in the mountain and western regions of the United States. Applying the IRP methods provides valuable information to the participants in an EIS process involving capacity expansion of an electric or gas utility. The major challenges of applying the IRP method within an EIS are the time consuming and costly task of developing a least cost expansion path for each altemative, the detailed quantification of environmental damages associated with capacity expansion, and the explicit inclusion of societal-impacts to the region

  15. Deconvolution of X-ray diffraction profiles using series expansion: a line-broadening study of polycrystalline 9-YSZ

    Energy Technology Data Exchange (ETDEWEB)

    Sanchez-Bajo, F. [Universidad de Extremadura, Badajoz (Spain). Dept. de Electronica e Ingenieria Electromecanica; Ortiz, A.L.; Cumbrera, F.L. [Universidad de Extremadura, Badajoz (Spain). Dept. de Fisica

    2001-07-01

    Deconvolution of X-ray diffraction profiles is a fundamental step in obtaining reliable results in the microstructural characterization (crystallite size, lattice microstrain, etc) of polycrystalline materials. In this work we have analyzed a powder sample of 9-YSZ using a technique based on the Fourier series expansion of the pure profile. This procedure, which can be combined with regularization methods, is specially powerful to minimize the effects of the ill-posed nature of the linear integral equation involved in the kinematical theory of X-ray diffraction. Finally, the deconvoluted profiles have been used to obtain microstructural parameters by means of the integral-breadth method. (orig.)

  16. Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach

    Directory of Open Access Journals (Sweden)

    Weiping Li

    2016-03-01

    Full Text Available In this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each term in our pricing formula. The hedging formulas (greek letters for the arithmetic Asian options are obtained as well. Our formulas for the long lasting question on pricing and hedging arithmetic Asian options are easy to implement with enough accuracy. Our numerical illustration shows that the arithmetic Asian options worths less than the European options under the standard Black-Scholes assumptions, verifies theoretically that the volatility of the arithmetic average is less than the one of the underlying assets, and also discovers an interesting phenomena that the arithmetic Asian option for large fixed strikes such as stocks has higher volatility (elasticity than the plain European option. However, the elasticity of the arithmetic Asian options for small fixed strikes as trading in currencies and commodity products is much less than the elasticity of the plain European option. These findings are consistent with the ones from the hedgings with respect to the time to expiration, the strike, the present underlying asset price, the interest rate and the volatility.

  17. Taylor-series method for four-nucleon wave functions

    International Nuclear Information System (INIS)

    Sandulescu, A.; Tarnoveanu, I.; Rizea, M.

    1977-09-01

    Taylor-series method for transforming the infinite or finite well two-nucleon wave functions from individual coordinates to relative and c.m. coordinates, by expanding the single particle shell model wave functions around c.m. of the system, is generalized to four-nucleon wave functions. Also the connections with the Talmi-Moshinsky method for two and four harmonic oscillator wave functions are deduced. For both methods Fortran IV programs for the expansion coefficients have been written and the equivalence of corresponding expressions numerically proved. (author)

  18. Genealogical series method. Hyperpolar points screen effect

    International Nuclear Information System (INIS)

    Gorbatov, A.M.

    1991-01-01

    The fundamental values of the genealogical series method -the genealogical integrals (sandwiches) have been investigated. The hyperpolar points screen effect has been found. It allows one to calculate the sandwiches for the Fermion systems with large number of particles and to ascertain the validity of the iterated-potential method as well. For the first time the genealogical-series method has been realized numerically for the central spin-independent potential

  19. Methods in Clinical Pharmacology Series

    Science.gov (United States)

    Beaumont, Claire; Young, Graeme C; Cavalier, Tom; Young, Malcolm A

    2014-01-01

    Human radiolabel studies are traditionally conducted to provide a definitive understanding of the human absorption, distribution, metabolism and excretion (ADME) properties of a drug. However, advances in technology over the past decade have allowed alternative methods to be employed to obtain both clinical ADME and pharmacokinetic (PK) information. These include microdose and microtracer approaches using accelerator mass spectrometry, and the identification and quantification of metabolites in samples from classical human PK studies using technologies suitable for non-radiolabelled drug molecules, namely liquid chromatography-mass spectrometry and nuclear magnetic resonance spectroscopy. These recently developed approaches are described here together with relevant examples primarily from experiences gained in support of drug development projects at GlaxoSmithKline. The advantages of these study designs together with their limitations are described. We also discuss special considerations which should be made for a successful outcome to these new approaches and also to the more traditional human radiolabel study in order to maximize knowledge around the human ADME properties of drug molecules. PMID:25041729

  20. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

    Science.gov (United States)

    Murase, Kenya

    2016-01-01

    Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

  1. Nonperturbative Series Expansion of Green's Functions: The Anatomy of Resonant Inelastic X-Ray Scattering in the Doped Hubbard Model

    Science.gov (United States)

    Lu, Yi; Haverkort, Maurits W.

    2017-12-01

    We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.

  2. expansion method and travelling wave solutions for the perturbed ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...

  3. The extended (G/G)-expansion method and travelling wave ...

    Indian Academy of Sciences (India)

    In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters.

  4. Application of potential harmonic expansion method to BEC

    Indian Academy of Sciences (India)

    We adopt the potential harmonics expansion method for an ab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations.

  5. Electronic and magnetic structures of GdS layers investigated by first principle and series expansions calculations

    Energy Technology Data Exchange (ETDEWEB)

    Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco)

    2014-04-01

    Self-consistent ab initio calculations, based on Density Functional Theory (DFT) approach and using Full Potential Linear Augmented Plane Wave (FLAPW) method within GGA+U approximation, are performed to investigate both electronic and magnetic properties of the GdS layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Gd layers. Magnetic moment considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the High Temperature Series Expansions (HTSEs) calculations to compute other magnetic parameters. Using the Heisenberg model, the exchange interactions between the magnetic atoms Gd–Gd in the same layer and between the magnetic atoms in the adjacent bilayers are estimated. This estimate is obtained using the antiferromagnetic and ferromagnetic energies computed by abinitio calculations for GdS layers. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility of GdS with antiferromagnetic moment (m{sub Gd}) is given up to sixth order series versus of (J{sub 11}(Gd–Gd)/k{sub B}T). The Néel temperature T{sub N} is obtained by mean field theory and by HTSEs of the magnetic susceptibility series using the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is calculated for GdS layers. - Highlights: • Electronic and magnetic properties of GdS are investigated using the ab initio calculations. • Obtained data from abinitio calculations are used as input for HTSEs to compute other magnetic parameters. • Néel temperature and critical exponent are deduced using HTSE method.

  6. Electronic and magnetic structures of GdS layers investigated by first principle and series expansions calculations

    International Nuclear Information System (INIS)

    Masrour, R.; Hlil, E.K.; Hamedoun, M.; Benyoussef, A.

    2014-01-01

    Self-consistent ab initio calculations, based on Density Functional Theory (DFT) approach and using Full Potential Linear Augmented Plane Wave (FLAPW) method within GGA+U approximation, are performed to investigate both electronic and magnetic properties of the GdS layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Gd layers. Magnetic moment considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the High Temperature Series Expansions (HTSEs) calculations to compute other magnetic parameters. Using the Heisenberg model, the exchange interactions between the magnetic atoms Gd–Gd in the same layer and between the magnetic atoms in the adjacent bilayers are estimated. This estimate is obtained using the antiferromagnetic and ferromagnetic energies computed by abinitio calculations for GdS layers. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility of GdS with antiferromagnetic moment (m Gd ) is given up to sixth order series versus of (J 11 (Gd–Gd)/k B T). The Néel temperature T N is obtained by mean field theory and by HTSEs of the magnetic susceptibility series using the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is calculated for GdS layers. - Highlights: • Electronic and magnetic properties of GdS are investigated using the ab initio calculations. • Obtained data from abinitio calculations are used as input for HTSEs to compute other magnetic parameters. • Néel temperature and critical exponent are deduced using HTSE method

  7. Efficient generation of series expansions for ±J Ising spin glasses in a classical or a quantum field

    Science.gov (United States)

    Singh, R. R. P.; Young, A. P.

    2017-12-01

    We discuss generation of series expansions for Ising spin glasses with a symmetric ±J (i.e., bimodal) distribution on d -dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us to go to higher order than for a general distribution. We discuss two types of problems, one classical and one quantum. The classical problem is that of the Ising spin glass in a longitudinal magnetic field h , for which we obtain high temperature series expansions in variables tanh(J /T ) and tanh(h /T ) . The quantum problem is a T =0 study of the Ising spin glass in a transverse magnetic field hT for which we obtain a perturbation theory in powers of J /hT . These methods require (i) enumeration and counting of all connected clusters that can be embedded in the lattice up to some order n , and (ii) an evaluation of the contribution of each cluster for the quantity being calculated, known as the weight. We discuss a general method that takes the much smaller list (and count) of all no free-end (NFE) clusters on a lattice up to some order n and automatically generates all other clusters and their counts up to the same order. The weights for finite clusters in both cases have a simple graphical interpretation that allows us to proceed efficiently for a general configuration of the ±J bonds and at the end perform suitable disorder averaging. The order of our computations is limited by the weight calculations for the high-temperature expansions of the classical model, while they are limited by graph counting for the T =0 quantum system. Details of the calculational methods are presented.

  8. Laurent series expansion of sunrise-type diagrams using configuration space techniques

    International Nuclear Information System (INIS)

    Groote, S.; Koerner, J.G.; Pivovarov, A.A.

    2004-01-01

    We show that configuration space techniques can be used to efficiently calculate the complete Laurent series ε-expansion of sunrise-type diagrams to any loop order in D-dimensional space-time for any external momentum and for arbitrary mass configurations. For negative powers of ε the results are obtained in analytical form. For positive powers of ε including the finite ε 0 contribution the result is obtained numerically in terms of low-dimensional integrals. We present general features of the calculation and provide exemplary results up to five-loop order which are compared to available results in the literature. (orig.)

  9. Parameterization using Fourier series expansion of the diffuse reflectance of human skin to vary the concentration of the melanocytes

    Science.gov (United States)

    Narea, J. Freddy; Muñoz, Aarón A.; Castro, Jorge; Muñoz, Rafael A.; Villalba, Caroleny E.; Martinez, María. F.; Bravo, Kelly D.

    2013-11-01

    Human skin has been studied in numerous investigations, given the interest in knowing information about physiology, morphology and chemical composition. These parameters can be determined using non invasively optical techniques in vivo, such as the diffuse reflectance spectroscopy. The human skin color is determined by many factors, but primarily by the amount and distribution of the pigment melanin. The melanin is produced by the melanocytes in the basal layer of the epidermis. This research characterize the spectral response of the human skin using the coefficients of Fourier series expansion. Simulating the radiative transfer equation for the Monte Carlo method to vary the concentration of the melanocytes (fme) in a simplified model of human skin. It fits relating the Fourier series coefficient a0 with fme. Therefore it is possible to recover the skin biophysical parameter.

  10. Coupling parameter series expansion for fluid with square-well plus repulsive-square-barrier potential

    Directory of Open Access Journals (Sweden)

    Shiqi Zhou

    2013-10-01

    Full Text Available Monte Carlo simulations in the canonical ensemble are performed for fluid with potential consisting of a square-well plus a square-barrier to obtain thermodynamic properties such as pressure, excess energy, constant volume excess heat capacity, and excess chemical potential, and structural property such as radial distribution function. The simulations cover a wide density range for the fluid phase, several temperatures, and different combinations of the parameters defining the potential. These simulation data have been used to test performances of a coupling parameter series expansion (CPSE recently proposed by one of the authors [S. Zhou, Phys. Rev. E 74, 031119 (2006], and a traditional 2nd-order high temperature series expansion (HTSE based on a macroscopic compressibility approximation (MAC used with confidence since its introduction in 1967. It is found that (i the MCA-based 2nd-order HTSE unexpectedly and depressingly fails for most situations investigated, and the present simulation results can serve well as strict criteria for testing liquid state theories. (ii The CPSE perturbation scheme is shown to be capable of predicting very accurately most of the thermodynamic properties simulated, but the most appropriate level of truncating the CPSE differs and depends on the range of the potential to be calculated; in particular, the shorter the potential range is, the higher the most appropriate truncating level can be, and along with rising of the potential range the performance of the CPSE perturbation scheme will decrease at higher truncating level. (iii The CPSE perturbation scheme can calculate satisfactorily bulk fluid rdf, and such calculations can be done for all fluid states of the whole phase diagram. (iv The CPSE is a convergent series at higher temperatures, but show attribute of asymptotic series at lower temperatures, and as a result, the surest asymptotic value occurs at lower-order truncation.

  11. The extended (G/G)-expansion method and travelling wave ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 82; Issue 6. The extended (′/)-expansion method and travelling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. Zaiyun Zhang Jianhua Huang Juan Zhong Sha-Sha Dou Jiao Liu Dan Peng Ting Gao. Research Articles ...

  12. Quality of potential harmonics expansion method for dilute Bose ...

    Indian Academy of Sciences (India)

    Abstract. We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correla- tions for dilute Bose–Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the ...

  13. A method for summing nonalternating asymptotic series

    International Nuclear Information System (INIS)

    Kazakov, D.I.

    1980-01-01

    A method for reconstructing a function from its nonalternating asymptotic series is proposed. It can also be applied when only a limited number of coefficients and their high order asymptotic behaviour are known. The method is illustrated by examples of the ordinary simple integral simulating a functional integral in a theory with degenerate minimum and of the double-well unharmonic oscillator

  14. The method of boson expansions in quantum theory

    International Nuclear Information System (INIS)

    Garbaczewski, P.

    1977-06-01

    A review is presented of boson expansion methods applied in quantum theory, e.g. expansions of spin, bifermion and fermion operators in cases of finite and infinite number of degrees of freedom. The basic purpose of the paper is to formulate the most general criterion allowing one to obtain the so-called finite spin approximation of any given Bose field theory and the class of fermion theories associated with it. On the other hand, we also need to be able to reconstruct the primary Bose field theory, when any finite spin or Fermi systems are given

  15. On power series expansions of the S-resolvent operator and the Taylor formula

    Science.gov (United States)

    Colombo, Fabrizio; Gantner, Jonathan

    2016-12-01

    The S-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of n-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of S-spectrum and of S-resolvent operator. Since most of the properties that hold for the Riesz-Dunford functional calculus extend to the S-functional calculus, it can be considered its non commutative version. In this paper we show that the Taylor formula of the Riesz-Dunford functional calculus can be generalized to the S-functional calculus. The proof is not a trivial extension of the classical case because there are several obstructions due to the non commutativity of the setting in which we work that have to be overcome. To prove the Taylor formula we need to introduce a new series expansion of the S-resolvent operators associated to the sum of two n-tuples of operators. This result is a crucial step in the proof of our main results, but it is also of independent interest because it gives a new series expansion for the S-resolvent operators. This paper is addressed to researchers working in operator theory and in hypercomplex analysis.

  16. Experiences using DAKOTA stochastic expansion methods in computational simulations.

    Energy Technology Data Exchange (ETDEWEB)

    Templeton, Jeremy Alan; Ruthruff, Joseph R.

    2012-01-01

    Uncertainty quantification (UQ) methods bring rigorous statistical connections to the analysis of computational and experiment data, and provide a basis for probabilistically assessing margins associated with safety and reliability. The DAKOTA toolkit developed at Sandia National Laboratories implements a number of UQ methods, which are being increasingly adopted by modeling and simulation teams to facilitate these analyses. This report disseminates results as to the performance of DAKOTA's stochastic expansion methods for UQ on a representative application. Our results provide a number of insights that may be of interest to future users of these methods, including the behavior of the methods in estimating responses at varying probability levels, and the expansion levels for the methodologies that may be needed to achieve convergence.

  17. Monitoring rubber plantation expansion using Landsat data time series and a Shapelet-based approach

    Science.gov (United States)

    Ye, Su; Rogan, John; Sangermano, Florencia

    2018-02-01

    The expansion of tree plantations in tropical forests for commercial rubber cultivation threatens biodiversity which may affect ecosystem services, and hinders ecosystem productivity, causing net carbon emission. Numerous studies refer to the challenge of reliably distinguishing rubber plantations from natural forest, using satellite data, due to their similar spectral signatures, even when phenology is incorporated into an analysis. This study presents a novel approach for monitoring the establishment and expansion of rubber plantations in Seima Protection Forest (SPF), Cambodia (1995-2015), by detecting and analyzing the 'shapelet' structure in a Landsat-NDVI time series. This paper introduces a new classification procedure consisting of two steps: (1) an exhaustive-searching algorithm to detect shapelets that represent a period for relatively low NDVI values within an image time series; and (2) a t-test used to determine if NDVI values of detected shapelets are significantly different than their non-shapelet trend, thereby indicating the presence of rubber plantations. Using this approach, historical rubber plantation events were mapped over the twenty-year timespan. The shapelet algorithm produced two types of information: (1) year of rubber plantation establishment; and (2) pre-conversion land-cover type (i.e., agriculture, or natural forest). The overall accuracy of the rubber plantation map for the year of 2015 was 89%. The multi-temporal map products reveal that more than half of the rubber planting activity (57%) took place in 2010 and 2011, following the granting of numerous rubber concessions two years prior. Seventy-three percent of the rubber plantations were converted from natural forest and twenty-three percent were established on non-forest land-cover. The shapelet approach developed here can be used reliably to improve our understanding of the expansion of rubber production beyond Seima Protection Forest of Cambodia, and likely elsewhere in the

  18. Antiferromagnetic spintronics of Mn{sub 2}Au: An experiment, first principle, mean field and series expansions calculations study

    Energy Technology Data Exchange (ETDEWEB)

    Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000, Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Boutahar, A.; Lassri, H. [LPMMAT, Université Hassan II-Casablanca, Faculté des Sciences, BP 5366 Maârif (Morocco)

    2015-11-01

    The self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the Mn{sub 2}Au. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn plans. Magnetic moment considered to lie along (110) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Mn–Mn in Mn{sub 2}Au are given by using the experiment results and the mean field theory. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility with the magnetic moments in Mn{sub 2}Au (m{sub Mn}) is given up to tenth order series in, 1/k{sub B}T. The Néel temperature T{sub N} is obtained by HTSEs combined with the Padé approximant method. The critical exponent associated with the magnetic susceptibility is deduced as well. - Highlights: • The both electronic and magnetic properties of the Mn{sub 2}Au are studied. • The exchange interactions between the magnetic atoms Mn–Mn in Mn{sub 2}Au are given. • The Néel temperature T{sub N} of Mn{sub 2}Au is obtained by HTSEs method. • The critical exponent associated with the magnetic susceptibility is deduced.

  19. A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong; Zhang Hongqing

    2005-01-01

    In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation

  20. Elliptic equation rational expansion method and new exact travelling solutions for Whitham-Broer-Kaup equations

    International Nuclear Information System (INIS)

    Chen Yong; Wang Qi; Li Biao

    2005-01-01

    Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally

  1. A new extended elliptic equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

    International Nuclear Information System (INIS)

    Wang Baodong; Song Lina; Zhang Hongqing

    2007-01-01

    In this paper, we present a new elliptic equation rational expansion method to uniformly construct a series of exact solutions for nonlinear partial differential equations. As an application of the method, we choose the (2 + 1)-dimensional Burgers equation to illustrate the method and successfully obtain some new and more general solutions

  2. High temperature series expansions with a multiple-exchange Hamiltonian for the bcc and hcp phases of solid 3He

    International Nuclear Information System (INIS)

    Roger, M.; Suaudeau, E.; Bernier, M.E.R.

    1987-08-01

    High temperature series expansions with a multiple-exchange Hamiltonian are performed to fourth order in arbitrary magnetic field for both phases of solid 3 He. The susceptibility series are analysed with Pade approximants and compared with recent experimental results. For the hcp phase we estimate the ferromagnetic ordering temperature from susceptibility series and discuss the influence of four-particle exchange in lowering the transition

  3. Design of materials with extreme thermal expansion using a three-phase topology optimization method

    DEFF Research Database (Denmark)

    Sigmund, Ole; Torquato, S.

    1997-01-01

    Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases...... materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion...

  4. International Franchising as a Method for Business Expansion

    OpenAIRE

    Karpushina, Darya Evgenjevna

    2009-01-01

    The present Master Thesis investigates the concept of international franchising from both business and legal standpoints. The actuality of the topic is obvious: Franchising becomes one of the most perspective and fast-developing method for business expansion, and this Diploma was written as a reflection of such tendency. In the meantime, Franchising is an extremely complex and arguable business issue and still causes a kind of confusion in people's mind. For this reason, my effort in this Wor...

  5. Monte Carlo methods for flux expansion solutions of transport problems

    International Nuclear Information System (INIS)

    Spanier, J.

    1999-01-01

    Adaptive Monte Carlo methods, based on the use of either correlated sampling or importance sampling, to obtain global solutions to certain transport problems have recently been described. The resulting learning algorithms are capable of achieving geometric convergence when applied to the estimation of a finite number of coefficients in a flux expansion representation of the global solution. However, because of the nonphysical nature of the random walk simulations needed to perform importance sampling, conventional transport estimators and source sampling techniques require modification to be used successfully in conjunction with such flux expansion methods. It is shown how these problems can be overcome. First, the traditional path length estimators in wide use in particle transport simulations are generalized to include rather general detector functions (which, in this application, are the individual basis functions chosen for the flus expansion). Second, it is shown how to sample from the signed probabilities that arise as source density functions in these applications, without destroying the zero variance property needed to ensure geometric convergence to zero error

  6. Retrieving the optical parameters of biological tissues using diffuse reflectance spectroscopy and Fourier series expansions. I. theory and application.

    Science.gov (United States)

    Muñoz Morales, Aarón A; Vázquez Y Montiel, Sergio

    2012-10-01

    The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.

  7. Time series analysis time series analysis methods and applications

    CERN Document Server

    Rao, Tata Subba; Rao, C R

    2012-01-01

    The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. Comprehensively presents the various aspects of statistical methodology Discusses a wide variety of diverse applications and recent developments Contributors are internationally renowened experts in their respect...

  8. Precision die design by the die expansion method

    CERN Document Server

    Ibhadode, A O Akii

    2009-01-01

    This book presents a new method for the design of the precision dies used in cold-forging, extrusion and drawing processes. The method is based upon die expansion, and attempts to provide a clear-cut theoretical basis for the selection of critical die dimensions for this group of precision dies when the tolerance on product diameter (or thickness) is specified. It also presents a procedure for selecting the minimum-production-cost die from among a set of design alternatives. The mathematical content of the book is relatively simple and will present no difficulty to those who have taken basic c

  9. Detecting settlement expansion using hyper-temporal SAR time-series

    CSIR Research Space (South Africa)

    Kleynhans, W

    2014-07-01

    Full Text Available The detection of new informal settlements in South Africa using time-series data derived from coarse resolution satellite imagery has recently been an active area of research. Most of the previous methods presented using hyper-temporal satellite...

  10. Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions

    International Nuclear Information System (INIS)

    Rudaz, S.

    1990-01-01

    Asymptotic series for the Hurwitz zeta function, its derivative, and related functions (including the Riemann zeta function of odd integer argument) are derived as an illustration of a simple, direct method of broad applicability, inspired by the calculus of finite differences

  11. A multi-stage stochastic transmission expansion planning method

    International Nuclear Information System (INIS)

    Akbari, Tohid; Rahimikian, Ashkan; Kazemi, Ahad

    2011-01-01

    Highlights: → We model a multi-stage stochastic transmission expansion planning problem. → We include available transfer capability (ATC) in our model. → Involving this criterion will increase the ATC between source and sink points. → Power system reliability will be increased and more money can be saved. - Abstract: This paper presents a multi-stage stochastic model for short-term transmission expansion planning considering the available transfer capability (ATC). The ATC can have a huge impact on the power market outcomes and the power system reliability. The transmission expansion planning (TEP) studies deal with many uncertainties, such as system load uncertainties that are considered in this paper. The Monte Carlo simulation method has been applied for generating different scenarios. A scenario reduction technique is used for reducing the number of scenarios. The objective is to minimize the sum of investment costs (IC) and the expected operation costs (OC). The solution technique is based on the benders decomposition algorithm. The N-1 contingency analysis is also done for the TEP problem. The proposed model is applied to the IEEE 24 bus reliability test system and the results are efficient and promising.

  12. Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions

    Science.gov (United States)

    Kerimov, M. K.

    2018-01-01

    This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.

  13. Analytic function expansion nodal method for nuclear reactor core design

    International Nuclear Information System (INIS)

    Noh, Hae Man

    1995-02-01

    In most advanced nodal methods the transverse integration is commonly used to reduce the multi-dimensional diffusion equation into equivalent one- dimensional diffusion equations when derving the nodal coupling equations. But the use of the transverse integration results in some limitations. The first limitation is that the transverse leakage term which appears in the transverse integration procedure must be appropriately approximated. The second limitation is that the one-dimensional flux shapes in each spatial direction resulted from the nodal calculation are not accurate enough to be directly used in reconstructing the pinwise flux distributions. Finally the transverse leakage defined for a non-rectangular node such as a hexagonal node or a triangular node is too complicated to be easily handled and may contain non-physical singular terms of step-function and delta-function types. In this thesis, the Analytic Function Expansion Nodal (AFEN) method and its two variations : the Polynomial Expansion Nodal (PEN) method and the hybrid of the AFEN and PEN methods, have been developed to overcome the limitations of the transverse integration procedure. All of the methods solve the multidimensional diffusion equation without the transverse integration. The AFEN method which we believe is the major contribution of this study to the reactor core analysis expands the homogeneous flux distributions within a node in non-separable analytic basis functions satisfying the neutron diffusion equations at any point of the node and expresses the coefficients of the flux expansion in terms of the nodal unknowns which comprise a node-average flux, node-interface fluxes, and corner-point fluxes. Then, the nodal coupling equations composed of the neutron balance equations, the interface current continuity equations, and the corner-point leakage balance equations are solved iteratively to determine all the nodal unknowns. Since the AFEN method does not use the transverse integration in

  14. Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

    KAUST Repository

    Chu, Chunlei

    2012-07-01

    Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.

  15. About peculiarities of application of the method of fast expansions in the solution of the Navier-Stokes equations

    Directory of Open Access Journals (Sweden)

    A. D. Chernyshov

    2017-01-01

    Full Text Available The brief presentation of the method of fast expansions is given to solve nonlinear differential equations. Application  rules of the operator of fast expansions are specified for solving differential equations. According to the method of fast expansions, an unknown function can be represented as the sum of the boundary function and Fourier series sines and cosines for one variable. The special construction of the boundary functions leads to reasonably fast convergence of the Fourier series, so that for engineering calculations, it is sufficient to consider only the first three members. The method is applicable both to linear and nonlinear integro-differential systems. By means of applying the method of fast expansions to nonlinear Navier-Stokes equations the problem is reduced to a closed system of ordinary differential equations, which solution doesn't represent special difficulties. We can reapply the method of fast expansions to the resulting system of differential equations and reduce the original problem to a system of algebraic equations. If the problem is n-dimensional, then after n-fold application of the method of fast expansions the problem will be reduced to a closed algebraic system. Finally, we obtain an analytic-form solution of complicated boundary value problem in partial derivatives. The flow of an incompressible viscous fluid of Navier–Stokes is considered in a curvilinear pipe. The problem is reduced to solving a closed system of ordinary differential equations with boundary conditions by the method of fast expansions. The article considers peculiarities of finding the coefficients of boundary functions and Fourier coefficients for the zero-order and first-order operators of fast expansions. Obtaining the analytic-form solution is of great interest, because it allows to analyze and to investigate the influence of various factors on the properties of the viscous fluid in specific cases.

  16. Palmprint Verification Using Time Series Method

    Directory of Open Access Journals (Sweden)

    A. A. Ketut Agung Cahyawan Wiranatha

    2013-11-01

    Full Text Available The use of biometrics as an automatic recognition system is growing rapidly in solving security problems, palmprint is one of biometric system which often used. This paper used two steps in center of mass moment method for region of interest (ROI segmentation and apply the time series method combined with block window method as feature representation. Normalized Euclidean Distance is used to measure the similarity degrees of two feature vectors of palmprint. System testing is done using 500 samples palms, with 4 samples as the reference image and the 6 samples as test images. Experiment results show that this system can achieve a high performance with success rate about 97.33% (FNMR=1.67%, FMR=1.00 %, T=0.036.

  17. The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics

    NARCIS (Netherlands)

    de Munck, J.C.; de Munck, J.C.; Hämäläinen, M.S.; Peters, M.J.

    1991-01-01

    When a function is expressed as an infinite series of spherical harmonics the convergence can be accelerated by subtracting its asymptotic expansion and adding it in analytically closed form. In the present article this technique is applied to two biophysical cases: to the potential distribution in

  18. Character expansion methods for matrix models of dually weighted graphs

    International Nuclear Information System (INIS)

    Kazakov, V.A.; Staudacher, M.; Wynter, T.

    1996-01-01

    We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large N limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices. (orig.). With 4 figs

  19. Feasibility of wavelet expansion methods to treat the energy variable

    International Nuclear Information System (INIS)

    Van Rooijen, W. F. G.

    2012-01-01

    This paper discusses the use of the Discrete Wavelet Transform (DWT) to implement a functional expansion of the energy variable in neutron transport. The motivation of the work is to investigate the possibility of adapting the expansion level of the neutron flux in a material region to the complexity of the cross section in that region. If such an adaptive treatment is possible, 'simple' material regions (e.g., moderator regions) require little effort, while a detailed treatment is used for 'complex' regions (e.g., fuel regions). Our investigations show that in fact adaptivity cannot be achieved. The most fundamental reason is that in a multi-region system, the energy dependence of the cross section in a material region does not imply that the neutron flux in that region has a similar energy dependence. If it is chosen to sacrifice adaptivity, then the DWT method can be very accurate, but the complexity of such a method is higher than that of an equivalent hyper-fine group calculation. The conclusion is thus that, unfortunately, the DWT approach is not very practical. (authors)

  20. An alternative solver for the nodal expansion method equations - 106

    International Nuclear Information System (INIS)

    Carvalho da Silva, F.; Carlos Marques Alvim, A.; Senra Martinez, A.

    2010-01-01

    An automated procedure for nuclear reactor core design is accomplished by using a quick and accurate 3D nodal code, aiming at solving the diffusion equation, which describes the spatial neutron distribution in the reactor. This paper deals with an alternative solver for nodal expansion method (NEM), with only two inner iterations (mesh sweeps) per outer iteration, thus having the potential to reduce the time required to calculate the power distribution in nuclear reactors, but with accuracy similar to the ones found in conventional NEM. The proposed solver was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of the method for practical purposes. (authors)

  1. Monitoring agricultural expansion in Burkina Faso over 14 years with 30 m resolution time series

    DEFF Research Database (Denmark)

    Knauer, Kim; Gessner, Ursula; Fensholt, Rasmus

    2017-01-01

    Burkina Faso ranges amongst the fastest growing countries in the world with an annual population growth rate of more than three percent. This trend has consequences for food security since agricultural productivity is still on a comparatively low level in Burkina Faso. In order to compensate...... for the low productivity, the agricultural areas are expanding quickly. The mapping and monitoring of this expansion is difficult, even on the basis of remote sensing imagery, since the extensive farming practices and frequent cloud coverage in the area make the delineation of cultivated land from other land...... cover and land use types a challenging task. However, as the rapidly increasing population could have considerable effects on the natural resources and on the regional development of the country, methods for improved mapping of LULCC (land use and land cover change) are needed. For this study, we...

  2. Methods of solving sequence and series problems

    CERN Document Server

    Grigorieva, Ellina

    2016-01-01

    This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions,Met...

  3. Improved vertical displacements induced by a refined thermal expansion model and its quantitative analysis in GPS height time series

    Science.gov (United States)

    Wang, Kaihua; Chen, Hua; Jiang, Weiping; Li, Zhao; Ma, Yifang; Deng, Liansheng

    2018-04-01

    There are apparent seasonal variations in GPS height time series, and thermal expansion is considered to be one of the potential geophysical contributors. The displacements introduced by thermal expansion are usually derived without considering the annex height and underground part of the monument (e.g. located on roof or top of the buildings), which may bias the geophysical explanation of the seasonal oscillation. In this paper, the improved vertical displacements are derived by a refined thermal expansion model where the annex height and underground depth of the monument are taken into account, and then 560 IGS stations are adopted to validate the modeled thermal expansion (MTE) displacements. In order to evaluate the impact of thermal expansion on GPS heights, the MTE displacements of 80 IGS stations with less data discontinuities are selected to compare with their observed GPS vertical (OGV) displacements with the modeled surface loading (MSL) displacements removed in advance. Quantitative analysis results show the maximum annual and semiannual amplitudes of the MTE are 6.65 mm (NOVJ) and 0.51 mm (IISC), respectively, and the maximum peak-to-peak oscillation of the MTE displacements can be 19.4 mm. The average annual amplitude reductions are 0.75 mm and 1.05 mm respectively after removing the MTE and MSL displacements from the OGV, indicating the seasonal oscillation induced by thermal expansion is equivalent to >75% of the impact of surface loadings. However, there are rarely significant reductions for the semiannual amplitude. Given the result in this study that thermal expansion can explain 17.3% of the annual amplitude in GPS heights on average, it must be precisely modeled both in GPS precise data processing and GPS time series analysis, especially for those stations located in the middle and high latitudes with larger annual temperature oscillation, or stations with higher monument.

  4. Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to (2+1)-Dimensional Stochastic Dispersive Long Wave System

    International Nuclear Information System (INIS)

    Song Lina; Zhang Hongqing

    2007-01-01

    In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

  5. An Expansion Method to Unfold Proton Recoil Spectra

    Energy Technology Data Exchange (ETDEWEB)

    Kockum, J

    1970-07-01

    A method is given to obtain a good estimate of the input neutron spectrum from a pulse-height distribution measured with proportional counters filled with a hydrogenous gas. The method consists of expanding the sought estimate as a product of two functions where one is obtained by differentiating the pulse-height distribution and the other is a power series of the neutron energy. The coefficients of this series are determined by a least-squares fit of the calculated pulse-height distribution to the measured one. The method has been tested on pulse-height distributions obtained by calculations from a realistic neutron spectrum and response functions for a spherical counter 3. 94 cm in diameter and filled with 7 atm. of methane and 1 atm. of hydrogen, respectively. In the former case it is possible with the method described, to unfold pulse-height distributions up to a neutron energy of about 3 MeV to within 10 % of the input spectrum. The differentiating procedure included in the method ensures that all spectral details not smoothed out by the finite resolution of the counter, are kept in the spectrum estimate. A realistic estimate of the statistical uncertainty of each neutron spectrum value is given. Some of the possible systematical errors caused by uncertainties in input data have been investigated.

  6. Methods for summing general Kapteyn series

    Energy Technology Data Exchange (ETDEWEB)

    Tautz, R C [Zentrum fuer Astronomie und Astrophysik, Technische Universitaet Berlin, Hardenbergstrasse 36, D-10623 Berlin (Germany); Lerche, I [Institut fuer Geowissenschaften, Naturwissenschaftliche Fakultaet III, Martin-Luther-Universitaet Halle, D-06099 Halle (Germany); Dominici, D, E-mail: rct@gmx.eu, E-mail: lercheian@yahoo.com, E-mail: dominicd@newpaltz.edu [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr, New Paltz, NY 12561-2443 (United States)

    2011-09-23

    The general features and characteristics of Kapteyn series, which are a special type of series involving the Bessel function, are investigated. For many applications in physics, astrophysics and mathematics, it is crucial to have closed-form expressions in order to determine their functional structure and parametric behavior. The closed-form expressions of Kapteyn series have mostly been limited to special cases, even though there are often similarities in the approaches used to reduce the series to analytically tractable forms. The goal of this paper is to review the previous work in the area and to show that Kapteyn series can be expressed as trigonometric or gamma function series, which can be evaluated in a closed form for specific parameters. Two examples with a similar structure are given, showing the complexity of Kapteyn series. (paper)

  7. Modified Chapman–Enskog expansion: A new way to treat divergent series

    International Nuclear Information System (INIS)

    She Zhen-Su

    2017-01-01

    The resolution by Chen and Sun of divergent Chapman–Enskog expansion problem will not only build a unified foundation for non-equilibrium dynamics modeling at all Mach number and Knudsen number, but also shed light to a large class of difficult theoretical problems involving divergent expansion on strong nonlinearity. (paper)

  8. Breaking the Link between Environmental Degradation and Oil Palm Expansion: A Method for Enabling Sustainable Oil Palm Expansion

    Science.gov (United States)

    Smit, Hans Harmen; Meijaard, Erik; van der Laan, Carina; Mantel, Stephan; Budiman, Arif; Verweij, Pita

    2013-01-01

    Land degradation is a global concern. In tropical areas it primarily concerns the conversion of forest into non-forest lands and the associated losses of environmental services. Defining such degradation is not straightforward hampering effective reduction in degradation and use of already degraded lands for more productive purposes. To facilitate the processes of avoided degradation and land rehabilitation, we have developed a methodology in which we have used international environmental and social sustainability standards to determine the suitability of lands for sustainable agricultural expansion. The method was developed and tested in one of the frontiers of agricultural expansion, West Kalimantan province in Indonesia. The focus was on oil palm expansion, which is considered as a major driver for deforestation in tropical regions globally. The results suggest that substantial changes in current land-use planning are necessary for most new plantations to comply with international sustainability standards. Through visualizing options for sustainable expansion with our methodology, we demonstrate that the link between oil palm expansion and degradation can be broken. Application of the methodology with criteria and thresholds similar to ours could help the Indonesian government and the industry to achieve its pro-growth, pro-job, pro-poor and pro-environment development goals. For sustainable agricultural production, context specific guidance has to be developed in areas suitable for expansion. Our methodology can serve as a template for designing such commodity and country specific tools and deliver such guidance. PMID:24039700

  9. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

    Science.gov (United States)

    Murase, Kenya

    2014-01-01

    Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

  10. Series expansions of the density of states in SU(2) lattice gauge theory

    International Nuclear Information System (INIS)

    Denbleyker, A.; Du, Daping; Liu, Yuzhi; Meurice, Y.; Velytsky, A.

    2008-01-01

    We calculate numerically the density of states n(S) for SU(2) lattice gauge theory on L 4 lattices [S is the Wilson's action and n(S) measures the relative number of ways S can be obtained]. Small volume dependences are resolved for small values of S. We compare ln(n(S)) with weak and strong coupling expansions. Intermediate order expansions show a good overlap for values of S corresponding to the crossover. We relate the convergence of these expansions to those of the average plaquette. We show that, when known logarithmic singularities are subtracted from ln(n(S)), expansions in Legendre polynomials appear to converge and could be suitable to determine the Fisher's zeros of the partition function.

  11. Solution of the agglomerate Brownian coagulation using Taylor-expansion moment method.

    Science.gov (United States)

    Yu, Mingzhou; Lin, Jianzhong

    2009-08-01

    The newly proposed Taylor-expansion moment method (TEMOM) is extended to solve agglomerate coagulation in the free-molecule regime and in the continuum regime, respectively. The moment equations with respect to fractal dimension are derived based on 3rd Taylor-series expansion technique. The validation of this method is done by comparing its result with the published data at each limited size regime. By comparing with analytical method, sectional method (SM) and quadrature method of moments (QMOMs), this new approach is shown to produce the most efficiency without losing much accuracy. At each limited size regime, the effect of fractal dimension on the decay of particle number and particle size growth is mainly investigated, and especially in the continuum regime the relation of mean diameters of size distributions with different fractal dimensions is first proposed. The agglomerate size distribution is found to be sensitive to the fractal dimension and the initial geometric mean deviation before the self-preserving size distribution is achieved in the continuum regime.

  12. Estimating the Impact of Urban Expansion on Land Subsidence Using Time Series of DMSP Night-Time Light Satellite Imagery

    Science.gov (United States)

    Jiao, S.; Yu, J.; Wang, Y.; Zhu, L.; Zhou, Q.

    2018-04-01

    In recent decades, urbanization has resulted a massive increase in the amount of infrastructure especially large buildings in large cities worldwide. There has been a noticeable expansion of entire cities both horizontally and vertically. One of the common consequences of urban expansion is the increase of ground loads, which may trigger land subsidence and can be a potential threat of public safety. Monitoring trends of urban expansion and land subsidence using remote sensing technology is needed to ensure safety along with urban planning and development. The Defense Meteorological Satellite Program Operational Line scan System (DMSP/OLS) Night-Time Light (NTL) images have been used to study urbanization at a regional scale, proving the capability of recognizing urban expansion patterns. In the current study, a normalized illuminated urban area dome volume (IUADV) based on inter-calibrated DMSP/OLS NTL images is shown as a practical approach for estimating urban expansion of Beijing at a single period in time and over subsequent years. To estimate the impact of urban expansion on land subsidence, IUADV was correlated with land subsidence rates obtained using the Stanford Method for Persistent Scatterers (StaMPS) approach within the Persistent Scatterers InSAR (PSInSAR) methodology. Moderate correlations are observed between the urban expansion based on the DMSP/OLS NTL images and land subsidence. The correlation coefficients between the urban expansion of each year and land subsidence tends to gradually decrease over time (Coefficient of determination R = 0.80 - 0.64 from year 2005 to year 2010), while the urban expansion of two sequential years exhibit an opposite trend (R = 0.29 - 0.57 from year 2005 to year 2010) except for the two sequential years between 2007 and 2008 (R = 0.14).

  13. A multiple-scale power series method for solving nonlinear ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2016-02-01

    Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

  14. The investigation of trapped thickness shear modes in a contoured AT-cut quartz plate using the power series expansion technique

    Science.gov (United States)

    Li, Peng; Jin, Feng

    2018-01-01

    The dynamic model about the anti-plane vibration of a contoured quartz plate with thickness changing continuously is established by ignoring the effect of small elastic constant c 56. The governing equation is solved using the power series expansion technique, and the trapped thickness shear modes caused by bulge thickness are revealed. Theoretically, the proposed method is more general, which can be capable of handling various thickness profiles defined mathematically. After the convergence of the series is demonstrated and the correctness is numerically validated with the aid of finite element method results, systematic parametric studies are subsequently carried out to quantify the effects of the geometry parameter upon the trapped modes, including resonant frequency and mode shape. After that, the band structures of thickness shear waves propagation in a periodically contoured quartz plate, as well as the power transmission spectra, are obtained based on the power series expansion technique. It is revealed that broad stop bands below cut-off frequency exist owing to the trapped modes excited by the geometry inhomogeneity, which has little relationship with the structural periodicity, and its physical mechanism is different from the Bragg scattering effect. The outcome is widely applicable, and can be utilized to provide theoretical and practical guidance for the design and manufacturing of quartz resonators and wave filters.

  15. Electromotive force analysis of current transformer during lightning surge inflow using Fourier series expansion

    Directory of Open Access Journals (Sweden)

    Youngsun Kim

    2017-05-01

    Full Text Available The most common structure used for current transformers (CTs consists of secondary windings around a ferromagnetic core past the primary current being measured. A CT used as a surge protection device (SPD may experience large inrushes of current, like surges. However, when a large current flows into the primary winding, measuring the magnitude of the current is difficult because the ferromagnetic core becomes magnetically saturated. Several approaches to reduce the saturation effect are described in the literature. A Rogowski coil is representative of several devices that measure large currents. It is an electrical device that measures alternating current (AC or high-frequency current. However, such devices are very expensive in application. In addition, the volume of a CT must be increased to measure sufficiently large currents, but for installation spaces that are too small, other methods must be used. To solve this problem, it is necessary to analyze the magnetic field and electromotive force (EMF characteristics when designing a CT. Thus, we proposed an analysis method for the CT under an inrush current using the time-domain finite element method (TDFEM. The input source current of a surge waveform is expanded by a Fourier series to obtain an instantaneous value. An FEM model of the device is derived in a two-dimensional system and coupled with EMF circuits. The time-derivative term in the differential equation is solved in each time step by the finite difference method. It is concluded that the proposed algorithm is useful for analyzing CT characteristics, including the field distribution. Consequently, the proposed algorithm yields a reference for obtaining the effects of design parameters and magnetic materials for special shapes and sizes before the CT is designed and manufactured.

  16. Electromotive force analysis of current transformer during lightning surge inflow using Fourier series expansion

    Science.gov (United States)

    Kim, Youngsun

    2017-05-01

    The most common structure used for current transformers (CTs) consists of secondary windings around a ferromagnetic core past the primary current being measured. A CT used as a surge protection device (SPD) may experience large inrushes of current, like surges. However, when a large current flows into the primary winding, measuring the magnitude of the current is difficult because the ferromagnetic core becomes magnetically saturated. Several approaches to reduce the saturation effect are described in the literature. A Rogowski coil is representative of several devices that measure large currents. It is an electrical device that measures alternating current (AC) or high-frequency current. However, such devices are very expensive in application. In addition, the volume of a CT must be increased to measure sufficiently large currents, but for installation spaces that are too small, other methods must be used. To solve this problem, it is necessary to analyze the magnetic field and electromotive force (EMF) characteristics when designing a CT. Thus, we proposed an analysis method for the CT under an inrush current using the time-domain finite element method (TDFEM). The input source current of a surge waveform is expanded by a Fourier series to obtain an instantaneous value. An FEM model of the device is derived in a two-dimensional system and coupled with EMF circuits. The time-derivative term in the differential equation is solved in each time step by the finite difference method. It is concluded that the proposed algorithm is useful for analyzing CT characteristics, including the field distribution. Consequently, the proposed algorithm yields a reference for obtaining the effects of design parameters and magnetic materials for special shapes and sizes before the CT is designed and manufactured.

  17. Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

    KAUST Repository

    Pestana, Reynam C.

    2009-01-01

    We show that the wave equation solution using a conventional finite‐difference scheme, derived commonly by the Taylor series approach, can be derived directly from the rapid expansion method (REM). After some mathematical manipulation we consider an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second order time finite‐difference scheme that is frequently used in more conventional finite‐difference implementations. We then show that if we use more terms from the REM we can obtain a more accurate time integration of the wave field. Consequently, we have demonstrated that the REM is more accurate than the usual finite‐difference schemes and it provides a wave equation solution which allows us to march in large time steps without numerical dispersion and is numerically stable. We illustrate the method with post and pre stack migration results.

  18. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

    Science.gov (United States)

    Murase, Kenya

    2015-01-01

    In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

  19. Modeling urban expansion in Yangon, Myanmar using Landsat time-series and stereo GeoEye Images

    Science.gov (United States)

    Sritarapipat, Tanakorn; Takeuchi, Wataru

    2016-06-01

    This research proposed a methodology to model the urban expansion based dynamic statistical model using Landsat and GeoEye Images. Landsat Time-Series from 1978 to 2010 have been applied to extract land covers from the past to the present. Stereo GeoEye Images have been employed to obtain the height of the building. The class translation was obtained by observing land cover from the past to the present. The height of the building can be used to detect the center of the urban area (mainly commercial area). It was assumed that the class translation and the distance of multi-centers of the urban area also the distance of the roads affect the urban growth. The urban expansion model based on the dynamic statistical model was defined to refer to three factors; (1) the class translation, (2) the distance of the multicenters of the urban areas, and (3) the distance from the roads. Estimation and prediction of urban expansion by using our model were formulated and expressed in this research. The experimental area was set up in Yangon, Myanmar. Since it is the major of country's economic with more than five million population and the urban areas have rapidly increased. The experimental results indicated that our model of urban expansion estimated urban growth in both estimation and prediction steps in efficiency.

  20. Highly comparative time-series analysis: the empirical structure of time series and their methods.

    Science.gov (United States)

    Fulcher, Ben D; Little, Max A; Jones, Nick S

    2013-06-06

    The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording and analysing the dynamics of different processes, an extensive organization of scientific time-series data and analysis methods has never been performed. Addressing this, annotated collections of over 35 000 real-world and model-generated time series, and over 9000 time-series analysis algorithms are analysed in this work. We introduce reduced representations of both time series, in terms of their properties measured by diverse scientific methods, and of time-series analysis methods, in terms of their behaviour on empirical time series, and use them to organize these interdisciplinary resources. This new approach to comparing across diverse scientific data and methods allows us to organize time-series datasets automatically according to their properties, retrieve alternatives to particular analysis methods developed in other scientific disciplines and automate the selection of useful methods for time-series classification and regression tasks. The broad scientific utility of these tools is demonstrated on datasets of electroencephalograms, self-affine time series, heartbeat intervals, speech signals and others, in each case contributing novel analysis techniques to the existing literature. Highly comparative techniques that compare across an interdisciplinary literature can thus be used to guide more focused research in time-series analysis for applications across the scientific disciplines.

  1. Nonlinear time series theory, methods and applications with R examples

    CERN Document Server

    Douc, Randal; Stoffer, David

    2014-01-01

    FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre

  2. Thermophysical Properties of Matter - the TPRC Data Series. Volume 13. Thermal Expansion - Nonmetallic Solids

    Science.gov (United States)

    1977-01-01

    topography of the state of knowledge on the thermal expansion of nonmetallic solids. We believe there is also much food for reflec- West Lafayette...34 Lithium Silicates ......... 713 209 Magnesium Metasilicate MgSiO. .. ......... 715 210 Magnesium Orthosilicate Mg2 SiO . . . . . . . . . . . . 718 211...Antiferromagnetism of Praseodymium," Phys. Rev. Letters, 12(20), 553-5, 1964. 66. Goode, J.M., "Phase Transition Temperature of Polonium ,"J. Chem. Phys., 26(5), 1269

  3. Thermophysical Properties of Matter - the TPRC Data Series. Volume 12. Thermal Expansion Metallic Elements and Alloys

    Science.gov (United States)

    1975-01-01

    the thermal expansion of metallic elements, alloys, and intermetallic compounds. We believe there is also much food for reflection by the specialist...24 39 Plutonium Pu ........ ............... 260 40’ t Polonium Po ..... ............... 270 41* Potassium K ..... ............... 271 42...923 209 NIckel-Palladium NI-Pd..................926 210 * Nickel-Pitaum Ni-Pt.................90 211 Nickel-Silicon NI-SI.................932 212

  4. Quantifying urban growth patterns in Hanoi using landscape expansion modes and time series spatial metrics.

    Science.gov (United States)

    Nong, Duong H; Lepczyk, Christopher A; Miura, Tomoaki; Fox, Jefferson M

    2018-01-01

    Urbanization has been driven by various social, economic, and political factors around the world for centuries. Because urbanization continues unabated in many places, it is crucial to understand patterns of urbanization and their potential ecological and environmental impacts. Given this need, the objectives of our study were to quantify urban growth rates, growth modes, and resultant changes in the landscape pattern of urbanization in Hanoi, Vietnam from 1993 to 2010 and to evaluate the extent to which the process of urban growth in Hanoi conformed to the diffusion-coalescence theory. We analyzed the spatiotemporal patterns and dynamics of the built-up land in Hanoi using landscape expansion modes, spatial metrics, and a gradient approach. Urbanization was most pronounced in the periods of 2001-2006 and 2006-2010 at a distance of 10 to 35 km around the urban center. Over the 17 year period urban expansion in Hanoi was dominated by infilling and edge expansion growth modes. Our findings support the diffusion-coalescence theory of urbanization. The shift of the urban growth areas over time and the dynamic nature of the spatial metrics revealed important information about our understanding of the urban growth process and cycle. Furthermore, our findings can be used to evaluate urban planning policies and aid in urbanization issues in rapidly urbanizing countries.

  5. Quantifying urban growth patterns in Hanoi using landscape expansion modes and time series spatial metrics

    Science.gov (United States)

    Lepczyk, Christopher A.; Miura, Tomoaki; Fox, Jefferson M.

    2018-01-01

    Urbanization has been driven by various social, economic, and political factors around the world for centuries. Because urbanization continues unabated in many places, it is crucial to understand patterns of urbanization and their potential ecological and environmental impacts. Given this need, the objectives of our study were to quantify urban growth rates, growth modes, and resultant changes in the landscape pattern of urbanization in Hanoi, Vietnam from 1993 to 2010 and to evaluate the extent to which the process of urban growth in Hanoi conformed to the diffusion-coalescence theory. We analyzed the spatiotemporal patterns and dynamics of the built-up land in Hanoi using landscape expansion modes, spatial metrics, and a gradient approach. Urbanization was most pronounced in the periods of 2001–2006 and 2006–2010 at a distance of 10 to 35 km around the urban center. Over the 17 year period urban expansion in Hanoi was dominated by infilling and edge expansion growth modes. Our findings support the diffusion-coalescence theory of urbanization. The shift of the urban growth areas over time and the dynamic nature of the spatial metrics revealed important information about our understanding of the urban growth process and cycle. Furthermore, our findings can be used to evaluate urban planning policies and aid in urbanization issues in rapidly urbanizing countries. PMID:29734346

  6. Electronic and magnetic structures of Fe{sub 3}O{sub 4} ferrimagnetic investigated by first principle, mean field and series expansions calculations

    Energy Technology Data Exchange (ETDEWEB)

    Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000, Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O.; El Moussaoui, H. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)

    2015-03-15

    Self-consistent ab initio calculations, based on density functional theory (DFT) approach and using a full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the Fe{sub 3}O{sub 4}. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Fe plans. Magnetic moment considered to lie along (010) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Fe–Fe in Fe{sub 3}O{sub 4} are given using the mean field theory. The high temperature series expansions (HTSEs) of the magnetic susceptibility of with the magnetic moments, m{sub Fe} in Fe{sub 3}O{sub 4} is given up to seventh order series in (1/k{sub B}T). The Néel temperature T{sub N} is obtained by HTSEs of the magnetic susceptibility series combined with the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is deduced as well. - Highlights: • Ab initio calculations, based on DFT approach and FLAPW are used to study the electronic properties of Fe{sub 3}O{sub 4}. • Magnetic moments of Fe{sub 1} and Fe{sub 2} are estimated to −/+3.44 µ{sub B}. • HTSE method is used to calculate the Néel temperature of Fe{sub 3}O{sub 4}.

  7. Three-dimensional static and dynamic reactor calculations by the nodal expansion method

    International Nuclear Information System (INIS)

    Christensen, B.

    1985-05-01

    This report reviews various method for the calculation of the neutron-flux- and power distribution in an nuclear reactor. The nodal expansion method (NEM) is especially described in much detail. The nodal expansion method solves the diffusion equation. In this method the reactor core is divided into nodes, typically 10 to 20 cm in each direction, and the average flux in each node is calculated. To obtain the coupling between the nodes the local flux inside each node is expressed by use of a polynomial expansion. The expansion is one-dimensional, so inside each node such three expansions occur. To calculate the expansion coefficients it is necessary that the polynomial expansion is a solution to the one-dimensional diffusion equation. When the one-dimensional diffusion equation is established a term with the transversal leakage occur, and this term is expanded after the same polynomials. The resulting equation system with the expansion coefficients as the unknowns is solved with weigthed residual technique. The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The program and input to it are described. The program is tested on a number of examples extending from small theoretical one up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested. (author)

  8. Transportation Energy Futures Series: Alternative Fuel Infrastructure Expansion: Costs, Resources, Production Capacity, and Retail Availability for Low-Carbon Scenarios

    Energy Technology Data Exchange (ETDEWEB)

    Melaina, M. W.; Heath, G.; Sandor, D.; Steward, D.; Vimmerstedt, L.; Warner, E.; Webster, K. W.

    2013-04-01

    Achieving the Department of Energy target of an 80% reduction in greenhouse gas emissions by 2050 depends on transportation-related strategies combining technology innovation, market adoption, and changes in consumer behavior. This study examines expanding low-carbon transportation fuel infrastructure to achieve deep GHG emissions reductions, with an emphasis on fuel production facilities and retail components serving light-duty vehicles. Three distinct low-carbon fuel supply scenarios are examined: Portfolio: Successful deployment of a range of advanced vehicle and fuel technologies; Combustion: Market dominance by hybridized internal combustion engine vehicles fueled by advanced biofuels and natural gas; Electrification: Market dominance by electric drive vehicles in the LDV sector, including battery electric, plug-in hybrid, and fuel cell vehicles, that are fueled by low-carbon electricity and hydrogen. A range of possible low-carbon fuel demand outcomes are explored in terms of the scale and scope of infrastructure expansion requirements and evaluated based on fuel costs, energy resource utilization, fuel production infrastructure expansion, and retail infrastructure expansion for LDVs. This is one of a series of reports produced as a result of the Transportation Energy Futures (TEF) project, a Department of Energy-sponsored multi-agency project initiated to pinpoint underexplored transportation-related strategies for abating GHGs and reducing petroleum dependence.

  9. Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

    International Nuclear Information System (INIS)

    Doha, E H; Ahmed, H M

    2004-01-01

    A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed

  10. Kinetics of oriented crystallization of polymers in the linear stress-orientation range in the series expansion approach

    Directory of Open Access Journals (Sweden)

    L. Jarecki

    2018-04-01

    Full Text Available An analytical formula is derived for the oriented crystallization coefficient governing kinetics of oriented crystallization under uniaxial amorphous orientation in the entire temperature range. A series expansion approach is applied to the free energy of crystallization in the Hoffman-Lauritzen kinetic model of crystallization at accounting for the entropy of orientation of the amorphous chains. The series expansion coefficients are calculated for systems of Gaussian chains in linear stress-orientation range. Oriented crystallization rate functions are determined basing on the ‘proportional expansion’ approach proposed by Ziabicki in the steady-state limit. Crystallization kinetics controlled by separate predetermined and sporadic primary nucleation is considered, as well as the kinetics involving both nucleation mechanisms potentially present in oriented systems. The involvement of sporadic nucleation in the transformation kinetics is predicted to increase with increasing amorphous orientation. Example computations illustrate the dependence of the calculated functions on temperature and amorphous orientation, as well as qualitative agreement of the calculations with experimental results.

  11. Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion

    Science.gov (United States)

    Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi

    2011-01-01

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…

  12. Taylor's series method for solving the nonlinear point kinetics equations

    International Nuclear Information System (INIS)

    Nahla, Abdallah A.

    2011-01-01

    Highlights: → Taylor's series method for nonlinear point kinetics equations is applied. → The general order of derivatives are derived for this system. → Stability of Taylor's series method is studied. → Taylor's series method is A-stable for negative reactivity. → Taylor's series method is an accurate computational technique. - Abstract: Taylor's series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor's series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor's series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

  13. The use of many-body expansions and geometry optimizations in fragment-based methods.

    Science.gov (United States)

    Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo

    2014-09-16

    many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures.

  14. A novel weight determination method for time series data aggregation

    Science.gov (United States)

    Xu, Paiheng; Zhang, Rong; Deng, Yong

    2017-09-01

    Aggregation in time series is of great importance in time series smoothing, predicting and other time series analysis process, which makes it crucial to address the weights in times series correctly and reasonably. In this paper, a novel method to obtain the weights in time series is proposed, in which we adopt induced ordered weighted aggregation (IOWA) operator and visibility graph averaging (VGA) operator and linearly combine the weights separately generated by the two operator. The IOWA operator is introduced to the weight determination of time series, through which the time decay factor is taken into consideration. The VGA operator is able to generate weights with respect to the degree distribution in the visibility graph constructed from the corresponding time series, which reflects the relative importance of vertices in time series. The proposed method is applied to two practical datasets to illustrate its merits. The aggregation of Construction Cost Index (CCI) demonstrates the ability of proposed method to smooth time series, while the aggregation of The Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) illustrate how proposed method maintain the variation tendency of original data.

  15. Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit: Divergences and resolution

    International Nuclear Information System (INIS)

    Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng

    2014-01-01

    We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process

  16. The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

    Directory of Open Access Journals (Sweden)

    Hasibun Naher

    2011-01-01

    Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.

  17. Ab initio, mean field theory and series expansions calculations study of electronic and magnetic properties of antiferromagnetic MnSe alloys

    Energy Technology Data Exchange (ETDEWEB)

    Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, BP. 63, 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O.; El Moussaoui, H. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)

    2014-06-01

    Self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the MnSe lattice. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn lattices. Magnetic moments considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The zero-field high temperature static susceptibility series of the spin −4.28 nearest-neighbor Ising model on face centered cubic (fcc) and lattices is thoroughly analyzed by means of a power series coherent anomaly method (CAM). The exchange interaction between the magnetic atoms and the Néel temperature are deduced using the mean filed and HTSEs theories. - Highlights: • Ab initio calculations are used to investigate both electronic and magnetic properties of the MnSe alloys. • Obtained data from ab initio calculations are used as input for the HTSEs. • The Néel temperature is obtained for MnSe alloys.

  18. On the comparsion of the Spherical Wave Expansion-to-Plane Wave Expansion and the Sources Reconstruction Method for Antenna Diagnostics

    DEFF Research Database (Denmark)

    Alvarez, Yuri; Cappellin, Cecilia; Las-Heras, Fernando

    2008-01-01

    A comparison between two recently developed methods for antenna diagnostics is presented. On one hand, the Spherical Wave Expansion-to-Plane Wave Expansion (SWE-PWE), based on the relationship between spherical and planar wave modes. On the other hand, the Sources Reconstruction Method (SRM), based...

  19. Modeling laser beam diffraction and propagation by the mode-expansion method.

    Science.gov (United States)

    Snyder, James J

    2007-08-01

    In the mode-expansion method for modeling propagation of a diffracted beam, the beam at the aperture can be expanded as a weighted set of orthogonal modes. The parameters of the expansion modes are chosen to maximize the weighting coefficient of the lowest-order mode. As the beam propagates, its field distribution can be reconstructed from the set of weighting coefficients and the Gouy phase of the lowest-order mode. We have developed a simple procedure to implement the mode-expansion method for propagation through an arbitrary ABCD matrix, and we have demonstrated that it is accurate in comparison with direct calculations of diffraction integrals and much faster.

  20. Summation of Divergent Series and Zeldovich's Regularization Method

    International Nuclear Information System (INIS)

    Mur, V.D.; Pozdnyakov, S.G.; Popruzhenko, S.V.; Popov, V.S.

    2005-01-01

    A method for summing divergent series, including perturbation-theory series, is considered. This method is an analog of Zeldovich's regularization method in the theory of quasistationary states. It is shown that the method in question is more powerful than the well-known Abel and Borel methods, but that it is compatible with them (that is, it leads to the same value for the sum of a series). The constraints on the parameter domain that arise upon the removal of the regularization of divergent integrals by this method are discussed. The dynamical Stark shifts and widths of loosely bound s states in the field of a circularly polarized electromagnetic wave are calculated at various values of the Keldysh adiabaticity parameter and the multiquantum parameter

  1. A nodal expansion method using conformal mapping for hexagonal geometry

    International Nuclear Information System (INIS)

    Chao, Y.A.; Shatilla, Y.A.

    1993-01-01

    Hexagonal nodal methods adopting the same transverse integration process used for square nodal methods face the subtle theoretical problem that this process leads to highly singular nonphysical terms in the diffusion equation. Lawrence, in developing the DIF3D-N code, tried to approximate the singular terms with relatively simple polynomials. In the HEX-NOD code, Wagner ignored the singularities to simplify the diffusion equation and introduced compensating terms in the nodal equations to restore the nodal balance relation. More recently developed hexagonal nodal codes, such as HEXPE-DITE and the hexagonal version of PANTHER, used methods similar to Wagner's. It will be shown that for light water reactor applications, these two different approximations significantly degraded the accuracy of the respective method as compared to the established square nodal methods. Alternatively, the method of conformal mapping was suggested to map a hexagon to a rectangle, with the unique feature of leaving the diffusion operator invariant, thereby fundamentally resolving the problems associated with transverse integration. This method is now implemented in the Westinghouse hexagonal nodal code ANC-H. In this paper we report on the results of comparing the three methods for a variety of problems via benchmarking against the fine-mesh finite difference code

  2. Magnetic properties of spinels GeNi2-xCoxO4 systems: Green's function and high-temperature series expansions

    Science.gov (United States)

    El Grini, A.; Salmi, S.; Masrour, R.; Hamedoun, M.; Bouslykhane, K.; Marzouk, A.; Hourmatallah, A.; Benzakour, N.

    2018-06-01

    The Green's function theory and high-temperature series expansions technical have been developed for magnetic systems GeNi2-xCoxO4. We have applied the Green's function theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, considering all components of the magnetization when an external magnetic field is applied in (x,z)-plane. The second theory combined with the Padé approximants method for a randomly diluted Heisenberg magnet is used to deduce the magnetic phase diagram of GeNi2 - xCoxO4 systems. The critical exponents ? and ? and associated with the magnetic susceptibility ? and the correlation length ξ, respectively, have been deduced. The theoretical results are compared with those given by magnetic measurements.

  3. Monitoring Agricultural Expansion in Burkina Faso over 14 Years with 30 m Resolution Time Series: The Role of Population Growth and Implications for the Environment

    Directory of Open Access Journals (Sweden)

    Kim Knauer

    2017-02-01

    Full Text Available Burkina Faso ranges amongst the fastest growing countries in the world with an annual population growth rate of more than three percent. This trend has consequences for food security since agricultural productivity is still on a comparatively low level in Burkina Faso. In order to compensate for the low productivity, the agricultural areas are expanding quickly. The mapping and monitoring of this expansion is difficult, even on the basis of remote sensing imagery, since the extensive farming practices and frequent cloud coverage in the area make the delineation of cultivated land from other land cover and land use types a challenging task. However, as the rapidly increasing population could have considerable effects on the natural resources and on the regional development of the country, methods for improved mapping of LULCC (land use and land cover change are needed. For this study, we applied the newly developed ESTARFM (Enhanced Spatial and Temporal Adaptive Reflectance Fusion Model framework to generate high temporal (8-day and high spatial (30 m resolution NDVI time series for all of Burkina Faso for the years 2001, 2007, and 2014. For this purpose, more than 500 Landsat scenes and 3000 MODIS scenes were processed with this automated framework. The generated ESTARFM NDVI time series enabled extraction of per-pixel phenological features that all together served as input for the delineation of agricultural areas via random forest classification at 30 m spatial resolution for entire Burkina Faso and the three years. For training and validation, a randomly sampled reference dataset was generated from Google Earth images and based on expert knowledge. The overall accuracies of 92% (2001, 91% (2007, and 91% (2014 indicate the well-functioning of the applied methodology. The results show an expansion of agricultural area of 91% between 2001 and 2014 to a total of 116,900 km². While rainfed agricultural areas account for the major part of this

  4. Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.

    Science.gov (United States)

    Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel

    2009-11-01

    A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.

  5. Summation of divergent series and Zel'dovich's regularization method

    International Nuclear Information System (INIS)

    Mur, V.D.; Pozdnyakov, S.G.; Popruzhenko, S.V.; Popov, V.S.

    2005-01-01

    The method of summation of divergent series, including series of a perturbation theory, which is an analog of the Zel'dovich regularization procedure in the theory of quasistationary states is considered. It is shown that this method is more powerful than the well-known Abel and Borel methods, but compatible with them (i. e., gives the same value for the sum of the series). The restrictions to the range of parameters which appear after removal of the regularization of integrals by this method are discussed. The dynamical Stark shifts and widths of weakly bound s states in a field of circularly polarized electromagnetic wave are calculated at different values of the Keldysh adiabaticity parameter and multiquantum parameter [ru

  6. Time evolution of the wave equation using rapid expansion method

    KAUST Repository

    Pestana, Reynam C.; Stoffa, Paul L.

    2010-01-01

    Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.

  7. Time evolution of the wave equation using rapid expansion method

    KAUST Repository

    Pestana, Reynam C.

    2010-07-01

    Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.

  8. An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong; Zhang Hongqing

    2005-01-01

    With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

  9. The Sturmian expansion: A well-depth-method for orbitals in a deformed potential

    International Nuclear Information System (INIS)

    Bang, J.M.; Vaagen, J.S.

    1980-01-01

    The Sturmian expansion method has over the years successfully been used to generate orbitals in a deformed potential. In this paper we review the method in detail including more recent extentions. The convergence properties are discussed in terms of examples of current interest for nucleon-transfer reactions. Comparisons with other methods are also made. (orig.)

  10. Liquid theory with high accuracy and broad applicability: Coupling parameter series expansion and non hard sphere perturbation strategy

    Directory of Open Access Journals (Sweden)

    Shiqi Zhou

    2011-12-01

    Full Text Available Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426 1st-order high temperature series expansion (HTSE TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861, have some serious shortcomings: (i the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE and a non hard sphere (HS perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii We give a quantitative analysis on why

  11. Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation

    International Nuclear Information System (INIS)

    Wang Dengshan; Zhang Hongqing

    2005-01-01

    In this paper, with the aid of the symbolic computation we improve the extended F-expansion method in [Chaos, Solitons and Fractals 2004; 22:111] and propose the further improved F-expansion method. Using this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. In addition,the solutions we get are more general than the solutions that the extended F-expansion method gets.The solutions we get include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on. Our method can also apply to other partial differential equations and can also get many new exact solutions

  12. Higher order polynomial expansion nodal method for hexagonal core neutronics analysis

    International Nuclear Information System (INIS)

    Jin, Young Cho; Chang, Hyo Kim

    1998-01-01

    A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy

  13. A second-order shock-expansion method applicable to bodies of revolution near zero lift

    Science.gov (United States)

    1957-01-01

    A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.

  14. Using nodal expansion method in calculation of reactor core with square fuel assemblies

    International Nuclear Information System (INIS)

    Abdollahzadeh, M. Y.; Boroushaki, M.

    2009-01-01

    A polynomial nodal method is developed to solve few-group neutron diffusion equations in cartesian geometry. In this article, the effective multiplication factor, group flux and power distribution based on the nodal polynomial expansion procedure is presented. In addition, by comparison of the results the superiority of nodal expansion method on finite-difference and finite-element are fully demonstrated. The comparison of the results obtained by these method with those of the well known benchmark problems have shown that they are in very good agreement.

  15. Brillouin Corrosion Expansion Sensors for Steel Reinforced Concrete Structures Using a Fiber Optic Coil Winding Method

    Directory of Open Access Journals (Sweden)

    Xingjun Lv

    2011-11-01

    Full Text Available In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.

  16. Brillouin corrosion expansion sensors for steel reinforced concrete structures using a fiber optic coil winding method.

    Science.gov (United States)

    Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping

    2011-01-01

    In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.

  17. Design of materials with extreme thermal expansion using a three-phase topology optimization method

    DEFF Research Database (Denmark)

    Sigmund, Ole; Torquato, S.

    1997-01-01

    We show how composites with extremal or unusual thermal expansion coefficients can be designed using a numerical topology optimization method. The composites are composed of two different material phases and void. The optimization method is illustrated by designing materials having maximum therma...

  18. New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method

    International Nuclear Information System (INIS)

    Pandir, Yusuf; Duzgun, Hasan Huseyin

    2017-01-01

    In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)

  19. Engineered high expansion glass-ceramics having near linear thermal strain and methods thereof

    Energy Technology Data Exchange (ETDEWEB)

    Dai, Steve Xunhu; Rodriguez, Mark A.; Lyon, Nathanael L.

    2018-01-30

    The present invention relates to glass-ceramic compositions, as well as methods for forming such composition. In particular, the compositions include various polymorphs of silica that provide beneficial thermal expansion characteristics (e.g., a near linear thermal strain). Also described are methods of forming such compositions, as well as connectors including hermetic seals containing such compositions.

  20. A polynomial expansion method and its application in the coupled Zakharov-Kuznetsov equations

    International Nuclear Information System (INIS)

    Huang Wenhua

    2006-01-01

    A polynomial expansion method is presented to solve nonlinear evolution equations. Applying this method, the coupled Zakharov-Kuznetsov equations in fluid system are studied and many exact travelling wave solutions are obtained. These solutions include solitary wave solutions, periodic solutions and rational type solutions

  1. Mathematical methods in time series analysis and digital image processing

    CERN Document Server

    Kurths, J; Maass, P; Timmer, J

    2008-01-01

    The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences. In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/enviromental sciences, is also addressed. This volume coherently summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing.

  2. Financial time series analysis based on information categorization method

    Science.gov (United States)

    Tian, Qiang; Shang, Pengjian; Feng, Guochen

    2014-12-01

    The paper mainly applies the information categorization method to analyze the financial time series. The method is used to examine the similarity of different sequences by calculating the distances between them. We apply this method to quantify the similarity of different stock markets. And we report the results of similarity in US and Chinese stock markets in periods 1991-1998 (before the Asian currency crisis), 1999-2006 (after the Asian currency crisis and before the global financial crisis), and 2007-2013 (during and after global financial crisis) by using this method. The results show the difference of similarity between different stock markets in different time periods and the similarity of the two stock markets become larger after these two crises. Also we acquire the results of similarity of 10 stock indices in three areas; it means the method can distinguish different areas' markets from the phylogenetic trees. The results show that we can get satisfactory information from financial markets by this method. The information categorization method can not only be used in physiologic time series, but also in financial time series.

  3. Investigation and experimental data de-noising of Damavand tokamak by using fourier series expansion and wavelet code

    International Nuclear Information System (INIS)

    Sadeghi, Y.

    2006-01-01

    Computer Programs are important tools in physics. Analysis of the experimental data and the control of complex handle physical phenomenon and the solution of numerical problem in physics help scientist to the behavior and simulate the process. In this paper, calculation of several Fourier series gives us a visual and analytic impression of data analyses from Fourier series. One of important aspect in data analyses is to find optimum method for de-noising. Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution corresponding to its scale. They have advantages over usual traditional methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Transformed data by wavelets in frequency space has time information and can clearly show the exact location in time of the discontinuity. This aspect makes wavelets an excellent tool in the field of data analysis. In this paper, we show how Fourier series and wavelets can analyses data in Damavand tokamak. ?

  4. Non-intrusive uncertainty quantification in structural-acoustic systems using polynomial chaos expansion method

    Directory of Open Access Journals (Sweden)

    Wang Mingjie

    2017-01-01

    Full Text Available A framework of non-intrusive polynomial chaos expansion method (PC was proposed to investigate the statistic characteristics of the response of structural-acoustic system containing random uncertainty. The PC method does not need to reformulate model equations, and the statistics of the response can be evaluated directly. The results show that compared to the direct Monte Carlo method (MCM based on the original numerical model, the PC method is effective and more efficient.

  5. Minimum entropy density method for the time series analysis

    Science.gov (United States)

    Lee, Jeong Won; Park, Joongwoo Brian; Jo, Hang-Hyun; Yang, Jae-Suk; Moon, Hie-Tae

    2009-01-01

    The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the pattern is revealed most. The MEDM is applied to the financial time series of Standard and Poor’s 500 index from February 1983 to April 2006. Then the temporal behavior of structure scale is obtained and analyzed in relation to the information delivery time and efficient market hypothesis.

  6. Generalized series method in the theory of atomic nucleus

    International Nuclear Information System (INIS)

    Gorbatov, A.M.

    1991-01-01

    On a hypersphere of a prescribed radius the so-called genealogical basis has been constructed. By making use of this basis, the many-body Schroedinger equation has been obtained for bound states of various physical systems. The genealogical series method, being in general outline the extension of the angular potential functions method, deals with the potential harmonics of any generation needed. The new approach provides an exact numerical description of the hadron systems with two-body higher interaction

  7. A Study on the Profile Change Measurement of Steam Generator Tubes with Tube Expansion Methods

    International Nuclear Information System (INIS)

    Kim, Young Kyu; Song Myung Ho; Choi, Myung Sik

    2011-01-01

    Steam generator tubes for nuclear power plants contain the local shape transitions on their inner or outer surface such as dent, bulge, over-expansion, eccentricity, deflection, and so on by the application of physical force during the tube manufacturing and steam generator assembling and by the sludge (that is, corrosion products) produced during the plant operation. The structural integrity of tubes will be degraded by generating the corrosive crack at that location. The profilometry using the traditional bobbin probes which are currently applied for measuring the profile change of tubes gives us basic information such as axial locations and average magnitudes of deformations. However, the three-dimensional quantitative evaluation on circumferential locations, distributional angle, and size of deformations will have to be conducted to understand the effects of residual stresses increased by local deformations on corrosive cracking of tubes. Steam generator tubes of Korean standard nuclear power plants expanded within their tube-sheets by the explosive expansion method and suffered from corrosive cracks in the early stage of power operation. Thus, local deformations of steam generator tubes at the top of tube-sheet were measured with an advanced rotating probe and a laser profiling system for the two cases where the tubes expanded by the explosive expansion method and hydraulic expansion. Also, the trends of eccentricity, deflection, and over-expansion of tubes were evaluated. The advanced eddy current profilometry was confirmed to provide accurate information of local deformations compared with laser profilometry

  8. Methods for obtaining sorption data from uranium-series disequilibria

    International Nuclear Information System (INIS)

    Finnegan, D.L.; Bryant, E.A.

    1987-12-01

    Two possible methods have been identified for obtaining in situ retardation factors from measurements of uranium-series disequilibria at Yucca Mountain. The first method would make use of the enhanced 234 U/ 238 U ratio in groundwater to derive a signature for exchangeable uranium sorbed on the rock; the exchangeable uranium would be leached and assayed. The second method would use the ratio of 222 Rn to 234 U in solution, corrected for weathering, to infer the retardation factor for uranium. Similar methods could be applied to thorium and radium

  9. Ultra-wideband pose detection system for boom-type roadheader based on Caffery transform and Taylor series expansion

    Science.gov (United States)

    Fu, Shichen; Li, Yiming; Zhang, Minjun; Zong, Kai; Cheng, Long; Wu, Miao

    2018-01-01

    To realize unmanned pose detection of a coalmine boom-type roadheader, an ultra-wideband (UWB) pose detection system (UPDS) for a roadheader is designed, which consists of four UWB positioning base stations and three roadheader positioning nodes. The positioning base stations are used in turn to locate the positioning nodes of the roadheader fuselage. Using 12 sets of distance measurement information, a time-of-arrival (TOA) positioning model is established to calculate the 3D coordinates of three positioning nodes of the roadheader fuselage, and the three attitude angles (heading, pitch, and roll angles) of the roadheader fuselage are solved. A range accuracy experiment of a UWB P440 module was carried out in a narrow and closed tunnel, and the experiment data show that the mean error and standard deviation of the module can reach below 2 cm. Based on the TOA positioning model of the UPDS, we propose a fusion-positioning algorithm based on a Caffery transform and Taylor series expansion (CTFPA). We derived the complete calculation process, designed a flowchart, and carried out a simulation of CTFPA in MATLAB, comparing 1000 simulated positioning nodes of CTFPA and the Caffery positioning algorithm (CPA) for a 95 m long tunnel. The positioning error field of the tunnel was established, and the influence of the spatial variation on the positioning accuracy of CPA and CTFPA was analysed. The simulation results show that, compared with CPA, the positioning accuracy of CTFPA is clearly improved, and the accuracy of each axis can reach more than 5 mm. The accuracy of the X-axis is higher than that of the Y- and Z-axes. In section X-Y of the tunnel, the root mean square error (RMSE) contours of CTFPA are clear and orderly, and with an increase in the measuring distance, RMSE increases linearly. In section X-Z, the RMSE contours are concentric circles, and the variation ratio is nonlinear.

  10. The Fourier decomposition method for nonlinear and non-stationary time series analysis.

    Science.gov (United States)

    Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

    2017-03-01

    for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

  11. Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

    KAUST Repository

    Pestana, Reynam C.; Stoffa, Paul L.

    2009-01-01

    an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second

  12. The Taylor-expansion method of moments for the particle system with bimodal distribution

    Directory of Open Access Journals (Sweden)

    Liu Yan-Hua

    2013-01-01

    Full Text Available This paper derives the multipoint Taylor expansion method of moments for the bimodal particle system. The collision effects are modeled by the internal and external coagulation terms. Simple theory and numerical tests are performed to prove the effect of the current model.

  13. Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events

    DEFF Research Database (Denmark)

    Madsen, Henrik; Rasmussen, Peter F.; Rosbjerg, Dan

    1997-01-01

    Two different models for analyzing extreme hydrologic events, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a generalized Pareto distribution for modeling threshold exceedances corresponding to a generalized extreme value......). In the case of ML estimation, the PDS model provides the most efficient T-year event estimator. In the cases of MOM and PWM estimation, the PDS model is generally preferable for negative shape parameters, whereas the AMS model yields the most efficient estimator for positive shape parameters. A comparison...... of the considered methods reveals that in general, one should use the PDS model with MOM estimation for negative shape parameters, the PDS model with exponentially distributed exceedances if the shape parameter is close to zero, the AMS model with MOM estimation for moderately positive shape parameters, and the PDS...

  14. A two-dimensional, semi-analytic expansion method for nodal calculations

    International Nuclear Information System (INIS)

    Palmtag, S.P.

    1995-08-01

    Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure

  15. Thermal Expansion and Magnetostriction Measurements at Cryogenic Temperature Using the Strain Gauge Method.

    Science.gov (United States)

    Wang, Wei; Liu, Huiming; Huang, Rongjin; Zhao, Yuqiang; Huang, Chuangjun; Guo, Shibin; Shan, Yi; Li, Laifeng

    2018-01-01

    Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra-low temperature (thermal expansion and magnetostriction at cryogenic temperature using the strain gauge method based on a Physical Properties Measurements System (PPMS). The interfacing software and automation were developed using LabVIEW. The sample temperature range can be tuned continuously between 1.8 and 400 K. With this PPMS-aided measuring system, we can observe temperature and magnetic field dependence of the linear thermal expansion of different solid materials easily and accurately.

  16. Thermal Expansion and Magnetostriction Measurements at Cryogenic Temperature Using the Strain Gauge Method

    Directory of Open Access Journals (Sweden)

    Wei Wang

    2018-03-01

    Full Text Available Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra-low temperature (<77 K environment easily. This paper describes the design and test results of thermal expansion and magnetostriction at cryogenic temperature using the strain gauge method based on a Physical Properties Measurements System (PPMS. The interfacing software and automation were developed using LabVIEW. The sample temperature range can be tuned continuously between 1.8 and 400 K. With this PPMS-aided measuring system, we can observe temperature and magnetic field dependence of the linear thermal expansion of different solid materials easily and accurately.

  17. Thermal expansion and magnetostriction measurements at cryogenic temperature using the strain gage method

    Science.gov (United States)

    Wang, Wei; Liu, Huiming; Huang, Rongjin; Zhao, Yuqiang; Huang, Chuangjun; Guo, Shibin; Shan, Yi; Li, Laifeng

    2018-03-01

    Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra low temperature (<77 K) environment easily. This paper describes the design and test results of thermal expansion and magnetostriction at cryogenic temperature using the strain gage method based on a Physical Properties Measurements System (PPMS). The interfacing software and automation were developed using LabVIEW. The sample temperature range can be tuned continuously between 1.8 K and 400 K. With this PPMS-aided measuring system, we can observe temperature and magnetic field dependence of the linear thermal expansion of different solid materials easily and accurately.

  18. Time series analysis methods and applications for flight data

    CERN Document Server

    Zhang, Jianye

    2017-01-01

    This book focuses on different facets of flight data analysis, including the basic goals, methods, and implementation techniques. As mass flight data possesses the typical characteristics of time series, the time series analysis methods and their application for flight data have been illustrated from several aspects, such as data filtering, data extension, feature optimization, similarity search, trend monitoring, fault diagnosis, and parameter prediction, etc. An intelligent information-processing platform for flight data has been established to assist in aircraft condition monitoring, training evaluation and scientific maintenance. The book will serve as a reference resource for people working in aviation management and maintenance, as well as researchers and engineers in the fields of data analysis and data mining.

  19. Which DTW Method Applied to Marine Univariate Time Series Imputation

    OpenAIRE

    Phan , Thi-Thu-Hong; Caillault , Émilie; Lefebvre , Alain; Bigand , André

    2017-01-01

    International audience; Missing data are ubiquitous in any domains of applied sciences. Processing datasets containing missing values can lead to a loss of efficiency and unreliable results, especially for large missing sub-sequence(s). Therefore, the aim of this paper is to build a framework for filling missing values in univariate time series and to perform a comparison of different similarity metrics used for the imputation task. This allows to suggest the most suitable methods for the imp...

  20. The power series method in the effectiveness factor calculations

    OpenAIRE

    Filipich, C. P.; Villa, L. T.; Grossi, Ricardo Oscar

    2017-01-01

    In the present paper, exact analytical solutions are obtained for nonlinear ordinary differential equations which appear in complex diffusionreaction processes. A technique based on the power series method is used. Numerical results were computed for a number of cases which correspond to boundary value problems available in the literature. Additionally, new numerical results were generated for several important cases. Fil: Filipich, C. P.. Universidad Tecnológica Nacional. Facultad Regiona...

  1. A window-based time series feature extraction method.

    Science.gov (United States)

    Katircioglu-Öztürk, Deniz; Güvenir, H Altay; Ravens, Ursula; Baykal, Nazife

    2017-10-01

    This study proposes a robust similarity score-based time series feature extraction method that is termed as Window-based Time series Feature ExtraCtion (WTC). Specifically, WTC generates domain-interpretable results and involves significantly low computational complexity thereby rendering itself useful for densely sampled and populated time series datasets. In this study, WTC is applied to a proprietary action potential (AP) time series dataset on human cardiomyocytes and three precordial leads from a publicly available electrocardiogram (ECG) dataset. This is followed by comparing WTC in terms of predictive accuracy and computational complexity with shapelet transform and fast shapelet transform (which constitutes an accelerated variant of the shapelet transform). The results indicate that WTC achieves a slightly higher classification performance with significantly lower execution time when compared to its shapelet-based alternatives. With respect to its interpretable features, WTC has a potential to enable medical experts to explore definitive common trends in novel datasets. Copyright © 2017 Elsevier Ltd. All rights reserved.

  2. Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

    International Nuclear Information System (INIS)

    Bekir Ahmet; Güner Özkan

    2013-01-01

    In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

  3. Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

    Directory of Open Access Journals (Sweden)

    Wei Li

    2014-01-01

    Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

  4. A method for generating high resolution satellite image time series

    Science.gov (United States)

    Guo, Tao

    2014-10-01

    There is an increasing demand for satellite remote sensing data with both high spatial and temporal resolution in many applications. But it still is a challenge to simultaneously improve spatial resolution and temporal frequency due to the technical limits of current satellite observation systems. To this end, much R&D efforts have been ongoing for years and lead to some successes roughly in two aspects, one includes super resolution, pan-sharpen etc. methods which can effectively enhance the spatial resolution and generate good visual effects, but hardly preserve spectral signatures and result in inadequate analytical value, on the other hand, time interpolation is a straight forward method to increase temporal frequency, however it increase little informative contents in fact. In this paper we presented a novel method to simulate high resolution time series data by combing low resolution time series data and a very small number of high resolution data only. Our method starts with a pair of high and low resolution data set, and then a spatial registration is done by introducing LDA model to map high and low resolution pixels correspondingly. Afterwards, temporal change information is captured through a comparison of low resolution time series data, and then projected onto the high resolution data plane and assigned to each high resolution pixel according to the predefined temporal change patterns of each type of ground objects. Finally the simulated high resolution data is generated. A preliminary experiment shows that our method can simulate a high resolution data with a reasonable accuracy. The contribution of our method is to enable timely monitoring of temporal changes through analysis of time sequence of low resolution images only, and usage of costly high resolution data can be reduces as much as possible, and it presents a highly effective way to build up an economically operational monitoring solution for agriculture, forest, land use investigation

  5. Methods for deconvolving sparse positive delta function series

    International Nuclear Information System (INIS)

    Trussell, H.J.; Schwalbe, L.A.

    1981-01-01

    Sparse delta function series occur as data in many chemical analyses and seismic methods. These original data are often sufficiently degraded by the recording instrument response that the individual delta function peaks are difficult to distinguish and measure. A method, which has been used to measure these peaks, is to fit a parameterized model by a nonlinear least-squares fitting algorithm. The deconvolution approaches described have the advantage of not requiring a parameterized point spread function, nor do they expect a fixed number of peaks. Two new methods are presented. The maximum power technique is reviewed. A maximum a posteriori technique is introduced. Results on both simulated and real data by the two methods are presented. The characteristics of the data can determine which method gives superior results. 5 figures

  6. Statistical methods of parameter estimation for deterministically chaotic time series

    Science.gov (United States)

    Pisarenko, V. F.; Sornette, D.

    2004-03-01

    We discuss the possibility of applying some standard statistical methods (the least-square method, the maximum likelihood method, and the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional dynamic system (the logistic map) containing an observational noise. A “segmentation fitting” maximum likelihood (ML) method is suggested to estimate the structural parameter of the logistic map along with the initial value x1 considered as an additional unknown parameter. The segmentation fitting method, called “piece-wise” ML, is similar in spirit but simpler and has smaller bias than the “multiple shooting” previously proposed. Comparisons with different previously proposed techniques on simulated numerical examples give favorable results (at least, for the investigated combinations of sample size N and noise level). Besides, unlike some suggested techniques, our method does not require the a priori knowledge of the noise variance. We also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed Bayesian approaches. We note the trade off between the need of using a large number of data points in the ML analysis to decrease the bias (to guarantee consistency of the estimation) and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition. The method of statistical moments for the estimation of the parameter of the logistic map is discussed. This method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically (not only numerically).

  7. Transportation Energy Futures Series: Alternative Fuel Infrastructure Expansion: Costs, Resources, Production Capacity, and Retail Availability for Low-Carbon Scenarios

    Energy Technology Data Exchange (ETDEWEB)

    Melaina, W. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Heath, Garvin [National Renewable Energy Lab. (NREL), Golden, CO (United States); Sandor, Debra [National Renewable Energy Lab. (NREL), Golden, CO (United States); Steward, Darlene [National Renewable Energy Lab. (NREL), Golden, CO (United States); Vimmerstedt, Laura [National Renewable Energy Lab. (NREL), Golden, CO (United States); Warner, Ethan [National Renewable Energy Lab. (NREL), Golden, CO (United States); Webster, Karen W. [National Renewable Energy Lab. (NREL), Golden, CO (United States)

    2013-04-01

    The petroleum-based transportation fuel system is complex and highly developed, in contrast to the nascent low-petroleum, low-carbon alternative fuel system. This report examines how expansion of the low-carbon transportation fuel infrastructure could contribute to deep reductions in petroleum use and greenhouse gas (GHG) emissions across the U.S. transportation sector. Three low-carbon scenarios, each using a different combination of low-carbon fuels, were developed to explore infrastructure expansion trends consistent with a study goal of reducing transportation sector GHG emissions to 80% less than 2005 levels by 2050.These scenarios were compared to a business-as-usual (BAU) scenario and were evaluated with respect to four criteria: fuel cost estimates, resource availability, fuel production capacity expansion, and retail infrastructure expansion.

  8. Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations

    Directory of Open Access Journals (Sweden)

    Azizallah Alvandi

    2017-06-01

    Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.

  9. Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ-Expansion Method Implementation

    Directory of Open Access Journals (Sweden)

    Nur Alam

    2016-02-01

    Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.

  10. A robust and efficient stepwise regression method for building sparse polynomial chaos expansions

    Energy Technology Data Exchange (ETDEWEB)

    Abraham, Simon, E-mail: Simon.Abraham@ulb.ac.be [Vrije Universiteit Brussel (VUB), Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, 1050 Brussels (Belgium); Raisee, Mehrdad [School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box: 11155-4563, Tehran (Iran, Islamic Republic of); Ghorbaniasl, Ghader; Contino, Francesco; Lacor, Chris [Vrije Universiteit Brussel (VUB), Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, 1050 Brussels (Belgium)

    2017-03-01

    Polynomial Chaos (PC) expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters. The computational cost of classical PC solution schemes is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension. This considerably restricts the practical use of PC at the industrial level. A common approach to address such problems is to make use of sparse PC expansions. This paper presents a non-intrusive regression-based method for building sparse PC expansions. The most important PC contributions are detected sequentially through an automatic search procedure. The variable selection criterion is based on efficient tools relevant to probabilistic method. Two benchmark analytical functions are used to validate the proposed algorithm. The computational efficiency of the method is then illustrated by a more realistic CFD application, consisting of the non-deterministic flow around a transonic airfoil subject to geometrical uncertainties. To assess the performance of the developed methodology, a detailed comparison is made with the well established LAR-based selection technique. The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem. Moreover, the most important stochastic features are captured at a reduced computational cost compared to the LAR method. The results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs.

  11. A Multivariate Time Series Method for Monte Carlo Reactor Analysis

    International Nuclear Information System (INIS)

    Taro Ueki

    2008-01-01

    A robust multivariate time series method has been established for the Monte Carlo calculation of neutron multiplication problems. The method is termed Coarse Mesh Projection Method (CMPM) and can be implemented using the coarse statistical bins for acquisition of nuclear fission source data. A novel aspect of CMPM is the combination of the general technical principle of projection pursuit in the signal processing discipline and the neutron multiplication eigenvalue problem in the nuclear engineering discipline. CMPM enables reactor physicists to accurately evaluate major eigenvalue separations of nuclear reactors with continuous energy Monte Carlo calculation. CMPM was incorporated in the MCNP Monte Carlo particle transport code of Los Alamos National Laboratory. The great advantage of CMPM over the traditional Fission Matrix method is demonstrated for the three space-dimensional modeling of the initial core of a pressurized water reactor

  12. Method for calculating anisotropic neutron transport using scattering kernel without polynomial expansion

    International Nuclear Information System (INIS)

    Takahashi, Akito; Yamamoto, Junji; Ebisuya, Mituo; Sumita, Kenji

    1979-01-01

    A new method for calculating the anisotropic neutron transport is proposed for the angular spectral analysis of D-T fusion reactor neutronics. The method is based on the transport equation with new type of anisotropic scattering kernels formulated by a single function I sub(i) (μ', μ) instead of polynomial expansion, for instance, Legendre polynomials. In the calculation of angular flux spectra by using scattering kernels with the Legendre polynomial expansion, we often observe the oscillation with negative flux. But in principle this oscillation disappears by this new method. In this work, we discussed anisotropic scattering kernels of the elastic scattering and the inelastic scatterings which excite discrete energy levels. The other scatterings were included in isotropic scattering kernels. An approximation method, with use of the first collision source written by the I sub(i) (μ', μ) function, was introduced to attenuate the ''oscillations'' when we are obliged to use the scattering kernels with the Legendre polynomial expansion. Calculated results with this approximation showed remarkable improvement for the analysis of the angular flux spectra in a slab system of lithium metal with the D-T neutron source. (author)

  13. Application of wavelet scaling function expansion continuous-energy resonance calculation method to MOX fuel problem

    International Nuclear Information System (INIS)

    Yang, W.; Wu, H.; Cao, L.

    2012-01-01

    More and more MOX fuels are used in all over the world in the past several decades. Compared with UO 2 fuel, it contains some new features. For example, the neutron spectrum is harder and more resonance interference effects within the resonance energy range are introduced because of more resonant nuclides contained in the MOX fuel. In this paper, the wavelets scaling function expansion method is applied to study the resonance behavior of plutonium isotopes within MOX fuel. Wavelets scaling function expansion continuous-energy self-shielding method is developed recently. It has been validated and verified by comparison to Monte Carlo calculations. In this method, the continuous-energy cross-sections are utilized within resonance energy, which means that it's capable to solve problems with serious resonance interference effects without iteration calculations. Therefore, this method adapts to treat the MOX fuel resonance calculation problem natively. Furthermore, plutonium isotopes have fierce oscillations of total cross-section within thermal energy range, especially for 240 Pu and 242 Pu. To take thermal resonance effect of plutonium isotopes into consideration the wavelet scaling function expansion continuous-energy resonance calculation code WAVERESON is enhanced by applying the free gas scattering kernel to obtain the continuous-energy scattering source within thermal energy range (2.1 eV to 4.0 eV) contrasting against the resonance energy range in which the elastic scattering kernel is utilized. Finally, all of the calculation results of WAVERESON are compared with MCNP calculation. (authors)

  14. Normalization methods in time series of platelet function assays

    Science.gov (United States)

    Van Poucke, Sven; Zhang, Zhongheng; Roest, Mark; Vukicevic, Milan; Beran, Maud; Lauwereins, Bart; Zheng, Ming-Hua; Henskens, Yvonne; Lancé, Marcus; Marcus, Abraham

    2016-01-01

    Abstract Platelet function can be quantitatively assessed by specific assays such as light-transmission aggregometry, multiple-electrode aggregometry measuring the response to adenosine diphosphate (ADP), arachidonic acid, collagen, and thrombin-receptor activating peptide and viscoelastic tests such as rotational thromboelastometry (ROTEM). The task of extracting meaningful statistical and clinical information from high-dimensional data spaces in temporal multivariate clinical data represented in multivariate time series is complex. Building insightful visualizations for multivariate time series demands adequate usage of normalization techniques. In this article, various methods for data normalization (z-transformation, range transformation, proportion transformation, and interquartile range) are presented and visualized discussing the most suited approach for platelet function data series. Normalization was calculated per assay (test) for all time points and per time point for all tests. Interquartile range, range transformation, and z-transformation demonstrated the correlation as calculated by the Spearman correlation test, when normalized per assay (test) for all time points. When normalizing per time point for all tests, no correlation could be abstracted from the charts as was the case when using all data as 1 dataset for normalization. PMID:27428217

  15. Stability analysis of CMFD acceleration for the wavelet expansion method of neutron transport equation

    International Nuclear Information System (INIS)

    Zheng Youqi; Wu Hongchun; Cao Liangzhi

    2013-01-01

    This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is defined as the stability criterion, which is the least upper bound (LUB) of the largest eigenvalue of Fourier analysis matrix. The stability analysis considers the effect of mesh size (spectral length), coarse mesh division and scattering ratio. The results show that for the wavelet expansion method, the CMFD acceleration is conditionally stable. The small size of fine mesh brings stability and fast convergent. With the increase of the mesh size, the stability becomes worse. The scattering ratio does not impact the stability obviously. It makes the CMFD acceleration highly efficient in the strong scattering case. The results of Fourier analysis are verified by the numerical tests based on a homogeneous slab problem.

  16. The verification of the Taylor-expansion moment method in solving aerosol breakage

    Directory of Open Access Journals (Sweden)

    Yu Ming-Zhou

    2012-01-01

    Full Text Available The combination of the method of moment, characterizing the particle population balance, and the computational fluid dynamics has been an emerging research issue in the studies on the aerosol science and on the multiphase flow science. The difficulty of solving the moment equation arises mainly from the closure of some fractal moment variables which appears in the transform from the non-linear integral-differential population balance equation to the moment equations. Within the Taylor-expansion moment method, the breakage-dominated Taylor-expansion moment equation is first derived here when the symmetric fragmentation mechanism is involved. Due to the high efficiency and the high precision, this proposed moment model is expected to become an important tool for solving population balance equations.

  17. Hybrid perturbation methods based on statistical time series models

    Science.gov (United States)

    San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

    2016-04-01

    In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

  18. Series interconnected photovoltaic cells and method for making same

    Science.gov (United States)

    Albright, Scot P.; Chamberlin, Rhodes R.; Thompson, Roger A.

    1995-01-01

    A novel photovoltaic module (10) and method for constructing the same are disclosed. The module (10) includes a plurality of photovoltaic cells (12) formed on a substrate (14) and laterally separated by interconnection regions (15). Each cell (12) includes a bottom electrode (16), a photoactive layer (18) and a top electrode layer (20). Adjacent cells (12) are connected in electrical series by way of a conductive-buffer line (22). The buffer line (22) is also useful in protecting the bottom electrode (16) against severing during downstream layer cutting processes.

  19. Two-energy group solution of the diffusion equation by the multidimensional nodal polynomial expansion method

    International Nuclear Information System (INIS)

    Ribeiro, R.D.M.; Vellozo, S.O.; Botelho, D.A.

    1983-01-01

    The EPON computer code based in a Nodal Polynomial Expansion Method, wrote in Fortran IV, for steady-state, square geometry, one-dimensional or two-dimensional geometry and for one or two-energy group is presented. The neutron and power flux distributions for nuclear power plants were calculated, comparing with codes that use similar or different methodologies. The availability, economy and speed of the methodology is demonstrated. (E.G.) [pt

  20. Thermodynamics of non-ideal QGP using Mayers cluster expansion method

    International Nuclear Information System (INIS)

    Prasanth, J.P; Simji, P.; Bannur, Vishnu M.

    2013-01-01

    The Quark gluon plasma (QGP) is the state in which the individual hadrons dissolve into a system of free (or almost free) quarks and gluons in strongly compressed system at high temperature. The present paper aims to calculate the critical temperature at which a non-ideal three quark plasma condenses into droplet of three quarks (i.e., into a liquid of baryons) using Mayers cluster expansion method

  1. Expansion and compression shock wave calculation in pipes with the C.V.M. numerical method

    International Nuclear Information System (INIS)

    Raymond, P.; Caumette, P.; Le Coq, G.; Libmann, M.

    1983-03-01

    The Control Variables Method for fluid transients computations has been used to compute expansion and compression shock waves propagations. In this paper, first analytical solutions for shock wave and rarefaction wave propagation are detailed. Then after a rapid description of the C.V.M. technique and its stability and monotonicity properties, we will present some results about standard shock tube problem, reflection of shock wave, finally a comparison between experimental results obtained on the ELF facility and calculations is given

  2. Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method

    International Nuclear Information System (INIS)

    Saddique, I.; Nazar, K.

    2009-01-01

    In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)

  3. New generalized and improved (G′/G-expansion method for nonlinear evolution equations in mathematical physics

    Directory of Open Access Journals (Sweden)

    Hasibun Naher

    2014-10-01

    Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.

  4. An incident flux expansion transport theory method suitable for coupling to diffusion theory methods in hexagonal geometry

    International Nuclear Information System (INIS)

    Hayward, Robert M.; Rahnema, Farzad; Zhang, Dingkang

    2013-01-01

    Highlights: ► A new hybrid stochastic–deterministic transport theory method to couple with diffusion theory. ► The method is implemented in 2D hexagonal geometry. ► The new method produces excellent results when compared with Monte Carlo reference solutions. ► The method is fast, solving all test cases in less than 12 s. - Abstract: A new hybrid stochastic–deterministic transport theory method, which is designed to couple with diffusion theory, is presented. The new method is an extension of the incident flux response expansion method, and it combines the speed of diffusion theory with the accuracy of transport theory. With ease of use in mind, the new method is derived in such a way that it can be implemented with only minimal modifications to an existing diffusion theory method. A new angular expansion, which is necessary for the diffusion theory coupling, is developed in 2D and 3D. The method is implemented in 2D hexagonal geometry, and an HTTR benchmark problem is used to test its accuracy in a standalone configuration. It is found that the new method produces excellent results (with average relative error in partial current less than 0.033%) when compared with Monte Carlo reference solutions. Furthermore, the method is fast, solving all test cases in less than 12 s

  5. Evaluation of tube to collector connection by hydraulic expansion method in PGV-1000 steam generators

    International Nuclear Information System (INIS)

    Dashti, H.G.; Hashemi, B.; Jahromi, S.A.

    2011-01-01

    Research highlights: → The produced residual stresses in the collector body due to hydraulic expansion method have been compared with explosive method. → The residual stresses were obtained using two methods of FEM and strain gauging tests. → The effect of clearance between tube and collector on the residual stresses was investigated. → The contact stresses between the tube and collector interface were modeled and the required connection strength between tube and collector is estimated based on ASME rules and compared with FE results. - Abstract: Investigations on steam generators failure due to cracking in collector ligaments at perforated parts determined that connection process of the tubes to collector could be one of the main breakdown causes. The stability and strength of tube to collector joint is dependent to the geometry of tube and collector, the joining process and the operational conditions. In this research hydraulic expansion method has been considered as connection method of tube to collector. The Finite Element Method (FEM) was used to simulate the hydraulic expansion process and determine stress condition of the joints. The contact stresses between the tube and collector interface were modeled using contact elements of ANSYS program. Furthermore, the effect of clearance between tube and collector on the residual stresses around of joints was investigated. Some specimens from collector and tube materials were tested at various temperatures and their results were used at rate-independent multi-linear Mises plasticity model for FE analysis. Required connection strength between tube and collector is estimated based on ASME rules and compared with FE results. The results show that the residual tensile stresses could be greatly increased by decreasing of initial clearance. The highest value of residual stresses was observed around of collector holes nevertheless it was considerably lesser than obtained residual stresses in explosive method. The

  6. Linear Discontinuous Expansion Method using the Subcell Balances for Unstructured Geometry SN Transport

    International Nuclear Information System (INIS)

    Hong, Ser Gi; Kim, Jong Woon; Lee, Young Ouk; Kim, Kyo Youn

    2010-01-01

    The subcell balance methods have been developed for one- and two-dimensional SN transport calculations. In this paper, a linear discontinuous expansion method using sub-cell balances (LDEM-SCB) is developed for neutral particle S N transport calculations in 3D unstructured geometrical problems. At present, this method is applied to the tetrahedral meshes. As the name means, this method assumes the linear distribution of the particle flux in each tetrahedral mesh and uses the balance equations for four sub-cells of each tetrahedral mesh to obtain the equations for the four sub-cell average fluxes which are unknowns. This method was implemented in the computer code MUST (Multi-group Unstructured geometry S N Transport). The numerical tests show that this method gives more robust solution than DFEM (Discontinuous Finite Element Method)

  7. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

    Directory of Open Access Journals (Sweden)

    WANG Minhao

    2017-08-01

    Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

  8. Plume expansion of a laser-induced plasma studied with the particle-in-cell method

    DEFF Research Database (Denmark)

    Ellegaard, O.; Nedelea, T.; Schou, Jørgen

    2002-01-01

    energy as well as electron energy. We have estimated the time constant for energy transfer between the electrons and the ions. The scaling of these processes is given by a single parameter determined by the Debye length obtained from the electron density in the plasma outside the surface. (C) 2002......The initial stage of laser-induced plasma plume expansion from a solid in vacuum and the effect of the Coulomb field have been studied. We have performed a one-dimensional numerical calculation by mapping the charge on a computational grid according to the particle-in-cell (PIC) method of Birdsall...... et al. It is assumed that the particle ablation from a surface with a fixed temperature takes place as a pulse, i.e. within a finite period of time. A number of characteristic quantities for the plasma plume are compared with similar data for expansion of neutrals as well as fluid models: Density...

  9. Non-linear triangle-based polynomial expansion nodal method for hexagonal core analysis

    International Nuclear Information System (INIS)

    Cho, Jin Young; Cho, Byung Oh; Joo, Han Gyu; Zee, Sung Qunn; Park, Sang Yong

    2000-09-01

    This report is for the implementation of triangle-based polynomial expansion nodal (TPEN) method to MASTER code in conjunction with the coarse mesh finite difference(CMFD) framework for hexagonal core design and analysis. The TPEN method is a variation of the higher order polynomial expansion nodal (HOPEN) method that solves the multi-group neutron diffusion equation in the hexagonal-z geometry. In contrast with the HOPEN method, only two-dimensional intranodal expansion is considered in the TPEN method for a triangular domain. The axial dependence of the intranodal flux is incorporated separately here and it is determined by the nodal expansion method (NEM) for a hexagonal node. For the consistency of node geometry of the MASTER code which is based on hexagon, TPEN solver is coded to solve one hexagonal node which is composed of 6 triangular nodes directly with Gauss elimination scheme. To solve the CMFD linear system efficiently, stabilized bi-conjugate gradient(BiCG) algorithm and Wielandt eigenvalue shift method are adopted. And for the construction of the efficient preconditioner of BiCG algorithm, the incomplete LU(ILU) factorization scheme which has been widely used in two-dimensional problems is used. To apply the ILU factorization scheme to three-dimensional problem, a symmetric Gauss-Seidel Factorization scheme is used. In order to examine the accuracy of the TPEN solution, several eigenvalue benchmark problems and two transient problems, i.e., a realistic VVER1000 and VVER440 rod ejection benchmark problems, were solved and compared with respective references. The results of eigenvalue benchmark problems indicate that non-linear TPEN method is very accurate showing less than 15 pcm of eigenvalue errors and 1% of maximum power errors, and fast enough to solve the three-dimensional VVER-440 problem within 5 seconds on 733MHz PENTIUM-III. In the case of the transient problems, the non-linear TPEN method also shows good results within a few minute of

  10. On-line reconstruction of in-core power distribution by harmonics expansion method

    International Nuclear Information System (INIS)

    Wang Changhui; Wu Hongchun; Cao Liangzhi; Yang Ping

    2011-01-01

    Highlights: → A harmonics expansion method for the on-line in-core power reconstruction is proposed. → A harmonics data library is pre-generated off-line and a code named COMS is developed. → Numerical results show that the maximum relative error of the reconstruction is less than 5.5%. → This method has a high computational speed compared to traditional methods. - Abstract: Fixed in-core detectors are most suitable in real-time response to in-core power distributions in pressurized water reactors (PWRs). In this paper, a harmonics expansion method is used to reconstruct the in-core power distribution of a PWR on-line. In this method, the in-core power distribution is expanded by the harmonics of one reference case. The expansion coefficients are calculated using signals provided by fixed in-core detectors. To conserve computing time and improve reconstruction precision, a harmonics data library containing the harmonics of different reference cases is constructed. Upon reconstruction of the in-core power distribution on-line, the two closest reference cases are searched from the harmonics data library to produce expanded harmonics by interpolation. The Unit 1 reactor of DayaBay Nuclear Power Plant (DayaBay NPP) in China is considered for verification. The maximum relative error between the measurement and reconstruction results is less than 5.5%, and the computing time is about 0.53 s for a single reconstruction, indicating that this method is suitable for the on-line monitoring of PWRs.

  11. Mapping Impervious Surface Expansion using Medium-resolution Satellite Image Time Series: A Case Study in the Yangtze River Delta, China

    Science.gov (United States)

    Gao, Feng; DeColstoun, Eric Brown; Ma, Ronghua; Weng, Qihao; Masek, Jeffrey G.; Chen, Jin; Pan, Yaozhong; Song, Conghe

    2012-01-01

    Cities have been expanding rapidly worldwide, especially over the past few decades. Mapping the dynamic expansion of impervious surface in both space and time is essential for an improved understanding of the urbanization process, land-cover and land-use change, and their impacts on the environment. Landsat and other medium-resolution satellites provide the necessary spatial details and temporal frequency for mapping impervious surface expansion over the past four decades. Since the US Geological Survey opened the historical record of the Landsat image archive for free access in 2008, the decades-old bottleneck of data limitation has gone. Remote-sensing scientists are now rich with data, and the challenge is how to make best use of this precious resource. In this article, we develop an efficient algorithm to map the continuous expansion of impervious surface using a time series of four decades of medium-resolution satellite images. The algorithm is based on a supervised classification of the time-series image stack using a decision tree. Each imerpervious class represents urbanization starting in a different image. The algorithm also allows us to remove inconsistent training samples because impervious expansion is not reversible during the study period. The objective is to extract a time series of complete and consistent impervious surface maps from a corresponding times series of images collected from multiple sensors, and with a minimal amount of image preprocessing effort. The approach was tested in the lower Yangtze River Delta region, one of the fastest urban growth areas in China. Results from nearly four decades of medium-resolution satellite data from the Landsat Multispectral Scanner (MSS), Thematic Mapper (TM), Enhanced Thematic Mapper plus (ETM+) and China-Brazil Earth Resources Satellite (CBERS) show a consistent urbanization process that is consistent with economic development plans and policies. The time-series impervious spatial extent maps derived

  12. Seismic assessment of a site using the time series method

    International Nuclear Information System (INIS)

    Krutzik, N.J.; Rotaru, I.; Bobei, M.; Mingiuc, C.; Serban, V.; Androne, M.

    1997-01-01

    To increase the safety of a NPP located on a seismic site, the seismic acceleration level to which the NPP should be qualified must be as representative as possible for that site, with a conservative degree of safety but not too exaggerated. The consideration of the seismic events affecting the site as independent events and the use of statistic methods to define some safety levels with very low annual occurrence probability (10 -4 ) may lead to some exaggerations of the seismic safety level. The use of some very high value for the seismic acceleration imposed by the seismic safety levels required by the hazard analysis may lead to very costly technical solutions that can make the plant operation more difficult and increase maintenance costs. The considerations of seismic events as a time series with dependence among the events produced, may lead to a more representative assessment of a NPP site seismic activity and consequently to a prognosis on the seismic level values to which the NPP would be ensured throughout its life-span. That prognosis should consider the actual seismic activity (including small earthquakes in real time) of the focuses that affect the plant site. The paper proposes the applications of Autoregressive Time Series to issue a prognosis on the seismic activity of a focus and presents the analysis on Vrancea focus that affects NPP Cernavoda site, by this method. The paper also presents the manner to analyse the focus activity as per the new approach and it assesses the maximum seismic acceleration that may affect NPP Cernavoda throughout its life-span (∼ 30 years). Development and applications of new mathematical analysis method, both for long - and short - time intervals, may lead to important contributions in the process of foretelling the seismic events in the future. (authors)

  13. Standard test method for linear thermal expansion of glaze frits and ceramic whiteware materials by the interferometric method

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    1995-01-01

    1.1 This test method covers the interferometric determination of linear thermal expansion of premelted glaze frits and fired ceramic whiteware materials at temperatures lower than 1000°C (1830°F). 1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

  14. A Parsimonious Bootstrap Method to Model Natural Inflow Energy Series

    Directory of Open Access Journals (Sweden)

    Fernando Luiz Cyrino Oliveira

    2014-01-01

    Full Text Available The Brazilian energy generation and transmission system is quite peculiar in its dimension and characteristics. As such, it can be considered unique in the world. It is a high dimension hydrothermal system with huge participation of hydro plants. Such strong dependency on hydrological regimes implies uncertainties related to the energetic planning, requiring adequate modeling of the hydrological time series. This is carried out via stochastic simulations of monthly inflow series using the family of Periodic Autoregressive models, PAR(p, one for each period (month of the year. In this paper it is shown the problems in fitting these models by the current system, particularly the identification of the autoregressive order “p” and the corresponding parameter estimation. It is followed by a proposal of a new approach to set both the model order and the parameters estimation of the PAR(p models, using a nonparametric computational technique, known as Bootstrap. This technique allows the estimation of reliable confidence intervals for the model parameters. The obtained results using the Parsimonious Bootstrap Method of Moments (PBMOM produced not only more parsimonious model orders but also adherent stochastic scenarios and, in the long range, lead to a better use of water resources in the energy operation planning.

  15. Series solutions to partial differential equations. A study of the singularities, expansions, and solutions of Schroedinger's equation for the helium atom

    International Nuclear Information System (INIS)

    Mahlab, M.S.

    1975-01-01

    All the presently available techniques for solving Schroedinger's differential equation for helium-like atoms display poor convergence of the wave function in the neighborhood of the singularities of the Hamiltonian operator. In general most of the methods of solving this equation will converge in the appropriate limit to the exact wave function; however, convergence is slow, especially near the singularities of this differential equation. These difficulties become readily apparent from local energy studies. A technique is presented that avoids these difficulties. The wave function it produces is specifically most accurate at the singularities of the Hamiltonian. The novel aspect of this treatment is the subdivision of the space spanned by the wave function. Different expansions are picked such that they converge rapidly in each of the different subdivisions. These expansions may be constructed in such a way that they obey the boundary conditions in their respective subdivision. Most importantly, all the information available from the recursion relations associated with the differential equation may be incorporated into these expansions. A systematic procedure is presented such that these expansions may be brought together to form a wave function that satisfies all the continuity requirements. An S-state helium wave function was constructed to demonstrate that this method of treatment is feasible, and capable of indefinite systematic improvement. A discussion of several new asymptotic expansions that were constructed for the helium wave function, as well as an improved functional form for the small electron-nucleus wave function, is included in this presentation

  16. Separable expansions of the NN t-matrix via exact half off the energy shell methods

    International Nuclear Information System (INIS)

    Pisent, G.; Amos, K.; Dortmans, P.J.

    1992-01-01

    Recently a method was proposed by which one can obtain rank 1 (for uncoupled channels) and rank 2 (for coupled channels), energy dependent t-matrix representations which are exact on- and half off of the energy shell. Fully off shell, this representation, though accurate at low energies, is flawed. For uncoupled channels, if the phase shift passes through zero, the representation has a pathology. Two methods which overcome this are investigated one due to Haberzettl which was extended to coupled channels, and the second which is based upon selective combination of the elements of Sturmian expansions. All methods of separation over a range of energies up to 250 MeV for the 1 S 0 and 3 S 1 channels are compared with the Paris interaction. Special attention is paid to the convergence of the higher order Haberzettl expansion and to the comparison of the extended methods for energies around the zero phase shift pathology for the 1 S 0 channel. The method describes well the fully off-shell properties of the t-matrices up to quite high energies, while keeping the rank of the separation as low as possible in order to be used in three or more body calculations. 39 refs., 10 figs

  17. A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation.

    Science.gov (United States)

    Rupp, K; Jungemann, C; Hong, S-M; Bina, M; Grasser, T; Jüngel, A

    The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.

  18. Accelerating the loop expansion

    International Nuclear Information System (INIS)

    Ingermanson, R.

    1986-01-01

    This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi 4 theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs

  19. Conformal expansions and renormalons

    Energy Technology Data Exchange (ETDEWEB)

    Rathsman, J.

    2000-02-07

    The coefficients in perturbative expansions in gauge theories are factorially increasing, predominantly due to renormalons. This type of factorial increase is not expected in conformal theories. In QCD conformal relations between observables can be defined in the presence of a perturbative infrared fixed-point. Using the Banks-Zaks expansion the authors study the effect of the large-order behavior of the perturbative series on the conformal coefficients. The authors find that in general these coefficients become factorially increasing. However, when the factorial behavior genuinely originates in a renormalon integral, as implied by a postulated skeleton expansion, it does not affect the conformal coefficients. As a consequence, the conformal coefficients will indeed be free of renormalon divergence, in accordance with previous observations concerning the smallness of these coefficients for specific observables. The authors further show that the correspondence of the BLM method with the skeleton expansion implies a unique scale-setting procedure. The BLM coefficients can be interpreted as the conformal coefficients in the series relating the fixed-point value of the observable with that of the skeleton effective charge. Through the skeleton expansion the relevance of renormalon-free conformal coefficients extends to real-world QCD.

  20. A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

    International Nuclear Information System (INIS)

    Sabry, R.; Zahran, M.A.; Fan Engui

    2004-01-01

    A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found

  1. Methods of abdominal wall expansion for repair of incisional herniae: a systematic review.

    Science.gov (United States)

    Alam, N N; Narang, S K; Pathak, S; Daniels, I R; Smart, N J

    2016-04-01

    To systematically review the available literature regarding methods for abdominal wall expansion and compare the outcome of primary fascial closure rates. A systematic search of Pubmed and Embase databases was conducted using the search terms "Abdominal wall hernia", "ventral hernia", "midline hernia", "Botulinum toxin", "botox", "dysport", "progressive preoperative pneumoperitoneum", and "tissue expanders". Study quality was assessed using the Methodological Index for Non-Randomised Studies. 21 of the 105 studies identified met the inclusion criteria. Progressive preoperative pneumoperitoneum (PPP) was performed in 269 patients across 15 studies with primary fascial closure being achieved in 226 (84%). 16 patients had a recurrence (7.2%) and the complication rate was 12% with 2 reported mortalities. There were 4 studies with 14 patients in total undergoing abdominal wall expansion using tissue expanders with a fascial closure rate of 92.9% (n = 13). A recurrence rate of 10.0% (n = 1) was reported with 1 complication and no mortalities. Follow up ranged from 3 to 36 months across the studies. There were 2 studies reporting the use of botulinum toxin with 29 patients in total. A primary fascial closure rate of 100% (n = 29) was demonstrated although a combination of techniques including component separation and Rives-Stoppa repair were used. There were no reported complications related to the use of Botulinum Toxin. However, the short-term follow up in many cases and the lack of routine radiological assessment for recurrence suggests that the recurrence rate has been underestimated. PPP, tissue expanders and Botulinum toxin are safe and feasible methods for abdominal wall expansion prior to incisional hernia repair. In combination with existing techniques for repair, these methods may help provide the crucial extra tissue mobility required to achieve primary closure.

  2. An adaptive mesh refinement approach for average current nodal expansion method in 2-D rectangular geometry

    International Nuclear Information System (INIS)

    Poursalehi, N.; Zolfaghari, A.; Minuchehr, A.

    2013-01-01

    Highlights: ► A new adaptive h-refinement approach has been developed for a class of nodal method. ► The resulting system of nodal equations is more amenable to efficient numerical solution. ► The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. ► Spatially adaptive approach greatly enhances the accuracy of the solution. - Abstract: The aim of this work is to develop a spatially adaptive coarse mesh strategy that progressively refines the nodes in appropriate regions of domain to solve the neutron balance equation by zeroth order nodal expansion method. A flux gradient based a posteriori estimation scheme has been utilized for checking the approximate solutions for various nodes. The relative surface net leakage of nodes has been considered as an assessment criterion. In this approach, the core module is called in by adaptive mesh generator to determine gradients of node surfaces flux to explore the possibility of node refinements in appropriate regions and directions of the problem. The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. For this purpose, a computer program ANRNE-2D, Adaptive Node Refinement Nodal Expansion, has been developed to solve neutron diffusion equation using average current nodal expansion method for 2D rectangular geometries. Implementing the adaptive algorithm confirms its superiority in enhancing the accuracy of the solution without using fine nodes throughout the domain and increasing the number of unknown solution. Some well-known benchmarks have been investigated and improvements are reported

  3. Seismic assessment of a site using the time series method

    International Nuclear Information System (INIS)

    Krutzik, N.J.; Rotaru, I.; Bobei, M.; Mingiuc, C.; Serban, V.; Androne, M.

    2001-01-01

    1. To increase the safety of a NPP located on a seismic site, the seismic acceleration level to which the NPP should be qualified must be as representative as possible for that site, with a conservative degree of safety but not too exaggerated. 2. The consideration of the seismic events affecting the site as independent events and the use of statistic methods to define some safety levels with very low annual occurrence probabilities (10 -4 ) may lead to some exaggerations of the seismic safety level. 3. The use of some very high values for the seismic accelerations imposed by the seismic safety levels required by the hazard analysis may lead to very expensive technical solutions that can make the plant operation more difficult and increase the maintenance costs. 4. The consideration of seismic events as a time series with dependence among the events produced may lead to a more representative assessment of a NPP site seismic activity and consequently to a prognosis on the seismic level values to which the NPP would be ensured throughout its life-span. That prognosis should consider the actual seismic activity (including small earthquakes in real time) of the focuses that affect the plant site. The method is useful for two purposes: a) research, i.e. homogenizing the history data basis by the generation of earthquakes during periods lacking information and correlation of the information with the existing information. The aim is to perform the hazard analysis using a homogeneous data set in order to determine the seismic design data for a site; b) operation, i.e. the performance of a prognosis on the seismic activity on a certain site and consideration of preventive measures to minimize the possible effects of an earthquake. 5. The paper proposes the application of Autoregressive Time Series to issue a prognosis on the seismic activity of a focus and presents the analysis on Vrancea focus that affects Cernavoda NPP site by this method. 6. The paper also presents the

  4. The investigation of the non-orthogonal basis expansion method for a three-fermion system

    International Nuclear Information System (INIS)

    Baoqiu Chen; Kentucky Univ., Lexington, KY

    1992-01-01

    In this paper, the non-orthogonal basis expansion method has been extended to solve a three-fermion system. The radial wavefunction of such a system is expanded in terms of a non-orthogonal Gaussian basis. All matrix elements of the Hamiltonian, including the central, tensor and spin-orbit potentials are derived in analytical forms. The new method simplifies the three-body system calculations, which are usually rather tedious by other methods. The method can be used to calculate energies for both the ground state and low excited states and has been used further to investigate the other nuclear properties of a three-body system such as Λ 3 H. (Author)

  5. The local quantum-mechanical stress tensor in Thomas-Fermi approximation and gradient expansion method

    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

  6. Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

    International Nuclear Information System (INIS)

    Zhou, Xiafeng; Guo, Jiong; Li, Fu

    2015-01-01

    Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

  7. Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

    Directory of Open Access Journals (Sweden)

    Ying Wang

    2014-06-01

    Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.

  8. Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn

    2015-12-15

    Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

  9. Self-Consistency Method to Evaluate a Linear Expansion Thermal Coefficient of Composite with Dispersed Inclusions

    Directory of Open Access Journals (Sweden)

    V. S. Zarubin

    2015-01-01

    Full Text Available The rational use of composites as structural materials, while perceiving the thermal and mechanical loads, to a large extent determined by their thermoelastic properties. From the presented review of works devoted to the analysis of thermoelastic characteristics of composites, it follows that the problem of estimating these characteristics is important. Among the thermoelastic properties of composites occupies an important place its temperature coefficient of linear expansion.Along with fiber composites are widely used in the technique of dispersion hardening composites, in which the role of inclusions carry particles of high-strength and high-modulus materials, including nanostructured elements. Typically, the dispersed particles have similar dimensions in all directions, which allows the shape of the particles in the first approximation the ball.In an article for the composite with isotropic spherical inclusions of a plurality of different materials by the self-produced design formulas relating the temperature coefficient of linear expansion with volume concentration of inclusions and their thermoelastic characteristics, as well as the thermoelastic properties of the matrix of the composite. Feature of the method is the self-accountability thermomechanical interaction of a single inclusion or matrix particles with a homogeneous isotropic medium having the desired temperature coefficient of linear expansion. Averaging over the volume of the composite arising from such interaction perturbation strain and stress in the inclusions and the matrix particles and makes it possible to obtain such calculation formulas.For the validation of the results of calculations of the temperature coefficient of linear expansion of the composite of this type used two-sided estimates that are based on the dual variational formulation of linear thermoelasticity problem in an inhomogeneous solid containing two alternative functional (such as Lagrange and Castigliano

  10. Rapid maxillary expansion effects: An alternative assessment method by means of cone-beam tomography

    Directory of Open Access Journals (Sweden)

    Camilo Aquino Melgaço

    2014-10-01

    Full Text Available INTRODUCTION: This study aims to develop a method to assess the changes in palatal and lingual cross-sectional areas in patients submitted to rapid maxillary expansion (RME. METHODS: The sample comprised 31 Class I malocclusion individuals submitted to RME and divided into two groups treated with Haas (17 patients and Hyrax (14 patients expanders. Cone-beam computed tomography scans were acquired at T0 (before expansion and T1 (six months after screw stabilization. Maxillary and mandibular cross-sectional areas were assessed at first permanent molars and first premolars regions and compared at T0 and T1. Mandibular occlusal area was also analyzed. RESULTS: Maxillary cross-sectional areas increased in 56.18 mm2 and 44.32 mm2 for the posterior and anterior regions. These values were smaller for the mandible, representing augmentation of 40.32 mm2 and 39.91 mm2 for posterior and anterior sections. No differences were found when comparing both expanders. Mandibular occlusal area increased 43.99mm2 and mandibular incisors proclined. Increments of 1.74 mm and 1.7 mm occurred in mandibular intermolar and interpremolar distances. These same distances presented increments of 5.5 mm and 5.57 mm for the maxillary arch. CONCLUSION: Occlusal and cross-sectional areas increased significantly after RME. The method described seems to be reliable and precise to assess intraoral area changes.

  11. X-linked hypophosphatemic rickets and sagittal craniosynostosis: three patients requiring operative cranial expansion: case series and literature review.

    Science.gov (United States)

    Jaszczuk, Phillip; Rogers, Gary F; Guzman, Raphael; Proctor, Mark R

    2016-05-01

    A defect in a phosphate-regulating gene leads to the most common form of rickets: X-linked hypophosphatemic rickets (XLH) or vitamin D-resistant rickets (VDDR). XLH has been associated with craniosynostosis, the sagittal suture being the most commonly involved. We present three patients with rickets and symptomatic sagittal suture craniosynostosis all of whom presented late (>2 years of age). Two had a severe phenotype and papilledema, while the third presented with an osseous bulging near the anterior fontanel and experienced chronic headaches. All underwent successful cranial vault expansion. Rachitic patients with scaphocephaly should be screened for craniosynostosis.

  12. A new evolutionary solution method for dynamic expansion planning of DG-integrated primary distribution networks

    International Nuclear Information System (INIS)

    Ahmadigorji, Masoud; Amjady, Nima

    2014-01-01

    Highlights: • A new dynamic distribution network expansion planning model is presented. • A Binary Enhanced Particle Swarm Optimization (BEPSO) algorithm is proposed. • A Modified Differential Evolution (MDE) algorithm is proposed. • A new bi-level optimization approach composed of BEPSO and MDE is presented. • The effectiveness of the proposed optimization approach is extensively illustrated. - Abstract: Reconstruction in the power system and appearing of new technologies for generation capacity of electrical energy has led to significant innovation in Distribution Network Expansion Planning (DNEP). Distributed Generation (DG) includes the application of small/medium generation units located in power distribution networks and/or near the load centers. Appropriate utilization of DG can affect the various technical and operational indices of the distribution network such as the feeder loading, energy losses and voltage profile. In addition, application of DG in proper size is an essential tool to achieve the DG maximum potential benefits. In this paper, a time-based (dynamic) model for DNEP is proposed to determine the optimal size, location and installation year of DG in distribution system. Also, in this model, the Optimal Power Flow (OPF) is exerted to determine the optimal generation of DGs for every potential solution in order to minimize the investment and operation costs following the load growth in a specified planning period. Besides, the reinforcement requirements of existing distribution feeders are considered, simultaneously. The proposed optimization problem is solved by the combination of evolutionary methods of a new Binary Enhanced Particle Swarm Optimization (BEPSO) and Modified Differential Evolution (MDE) to find the optimal expansion strategy and solve OPF, respectively. The proposed planning approach is applied to two typical primary distribution networks and compared with several other methods. These comparisons illustrate the

  13. The Nodal Polynomial Expansion method to solve the multigroup diffusion equations

    International Nuclear Information System (INIS)

    Ribeiro, R.D.M.

    1983-03-01

    The methodology of the solutions of the multigroup diffusion equations and uses the Nodal Polynomial Expansion Method is covered. The EPON code was developed based upon the above mentioned method for stationary state, rectangular geometry, one-dimensional or two-dimensional and for one or two energy groups. Then, one can study some effects such as the influence of the baffle on the thermal flux by calculating the flux and power distribution in nuclear reactors. Furthermore, a comparative study with other programs which use Finite Difference (CITATION and PDQ5) and Finite Element (CHD and FEMB) Methods was undertaken. As a result, the coherence, feasibility, speed and accuracy of the methodology used were demonstrated. (Author) [pt

  14. Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

    Science.gov (United States)

    Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

    2018-01-01

    Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

  15. Use of orthonormal polynomial expansion method to the description of the energy spectra of biological liquids

    International Nuclear Information System (INIS)

    Bogdanova, N.B.; Todorov, S.T.; Ososkov, G.A.

    2015-01-01

    Orthonormal polynomial expansion method (OPEM) is applied to the data obtained by the method of energy spectra to the liquid of the biomass of wheat in the case when herbicides are used. Since the biomass of a biological object contains liquid composed mainly of water, the method of water spectra is applicable to this case as well. For comparison, the similar data obtained from control sample consisting of wheat liquid without the application of herbicides are shown. The total variance OPEM is involved including errors in both dependent and independent variables. Special criteria are used for evaluating the optimal polynomial degree and the number of iterations. The presented numerical results show good agreement with the experimental data. The developed analysis frame is of interest for future analysis in theoretical ecology.

  16. Towards automatic global error control: Computable weak error expansion for the tau-leap method

    KAUST Repository

    Karlsson, Peer Jesper; Tempone, Raul

    2011-01-01

    This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms, a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie Algorithm or the Stochastic Simulation Slgorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term. © de Gruyter 2011.

  17. Pellet by pellet neutron flux calculations coupled with nodal expansion method

    International Nuclear Information System (INIS)

    Aldo, Dall'Osso

    2003-01-01

    We present a technique whose aim is to replace 2-dimensional pin by pin de-homogenization, currently done in core reactor calculations with the nodal expansion method (NEM), by a 3-dimensional finite difference diffusion calculation. This fine calculation is performed as a zoom in each node taking as boundary conditions the results of the NEM calculations. The size of fine mesh is of the order of a fuel pellet. The coupling between fine and NEM calculations is realised by an albedo like boundary condition. Some examples are presented showing fine neutron flux shape near control rods or assembly grids. Other fine flux behaviour as the thermal flux rise in the fuel near the reflector is emphasised. In general the results show the interest of the method in conditions where the separability of radial and axial directions is not granted. (author)

  18. Validation of the activity expansion method with ultrahigh pressure shock equations of state

    International Nuclear Information System (INIS)

    Rogers, F.J.; Young, D.A.

    1997-01-01

    Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. copyright 1997 The American Physical Society

  19. Validation of the activity expansion method with ultrahigh pressure shock equations of state

    Science.gov (United States)

    Rogers, Forrest J.; Young, David A.

    1997-11-01

    Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter.

  20. Validation of the activity expansion method with ultrahigh pressure shock equations of state

    Energy Technology Data Exchange (ETDEWEB)

    Rogers, F.J.; Young, D.A. [Physics Department, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (United States)

    1997-11-01

    Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. {copyright} {ital 1997} {ital The American Physical Society}

  1. Series-parallel method of direct solar array regulation

    Science.gov (United States)

    Gooder, S. T.

    1976-01-01

    A 40 watt experimental solar array was directly regulated by shorting out appropriate combinations of series and parallel segments of a solar array. Regulation switches were employed to control the array at various set-point voltages between 25 and 40 volts. Regulation to within + or - 0.5 volt was obtained over a range of solar array temperatures and illumination levels as an active load was varied from open circuit to maximum available power. A fourfold reduction in regulation switch power dissipation was achieved with series-parallel regulation as compared to the usual series-only switching for direct solar array regulation.

  2. Methods of ex vivo expansion of human cord blood cells: challenges, successes and clinical implications.

    Science.gov (United States)

    Baron, Frédéric; Ruggeri, Annalisa; Nagler, Arnon

    2016-03-01

    More than 40,000 unrelated cord blood transplantations (UCBT) have been performed worldwide as treatment for patients with malignant or non-malignant life threatening hematologic disorders. However, low absolute numbers of hematopoietic stem and progenitor cells (HSPCs) within a single cord blood unit has remained a limiting factor for this transplantation modality, particularly in adult recipients. Further, because UCB contains low numbers of mostly naïve T cells, immune recovery after UCBT is slow, predisposing patients to severe infections. Other causes of UCBT failure has included graft-versus-host disease (GVHD) and relapse of the underlying disease. In this article, we first review the current landscape of cord blood engineering aimed at improving engraftment. This includes approaches of UCB-HSPCs expansion and methods aimed at improving UCB-HSCPs homing. We then discuss recent approaches of cord blood engineering developed to prevent infection [generation of multivirus-specific cytotoxic T cells (VSTs) from UCB], relapse [transduction of UCB-T cells with tumor-specific chimeric receptor antigens (CARs)] and GVHD (expansion of regulatory T cells from UCB). Although many of these techniques of UCB engineering remain currently technically challenging and expensive, they are likely to revolutionize the field of UCBT in the next decades.

  3. An operator expansion technique for path integral analysis

    International Nuclear Information System (INIS)

    Tsvetkov, I.V.

    1995-01-01

    A new method of path integral analysis in the framework of a power series technique is presented. The method is based on the operator expansion of an exponential. A regular procedure to calculate the correction terms is found. (orig.)

  4. An Enhanced Plane Wave Expansion Method to Solve Piezoelectric Phononic Crystal with Resonant Shunting Circuits

    Directory of Open Access Journals (Sweden)

    Ziyang Lian

    2016-01-01

    Full Text Available An enhanced plane wave expansion (PWE method is proposed to solve piezoelectric phononic crystal (PPC connected with resonant shunting circuits (PPC-C, which is named as PWE-PPC-C. The resonant shunting circuits can not only bring about the locally resonant (LR band gap for the PPC-C but also conveniently tune frequency and bandwidth of band gaps through adjusting circuit parameters. However, thus far, more than one-dimensional PPC-C has been studied just by Finite Element method. Compared with other methods, the PWE has great advantages in solving more than one-dimensional PC as well as various lattice types. Nevertheless, the conventional PWE cannot accurately solve coupling between the structure and resonant shunting circuits of the PPC-C since only taking one-way coupling from displacements to electrical parameters into consideration. A two-dimensional PPC-C model of orthorhombic lattice is established to demonstrate the whole solving process of PWE-PPC-C. The PWE-PPC-C method is validated by Transfer Matrix method as well as Finite Element method. The dependence of band gaps on circuit parameters has been investigated in detail by PWE-PPC-C. Its advantage in solving various lattice types is further illustrated by calculating the PPC-C of triangular and hexagonal lattices, respectively.

  5. Time Series Analysis of Insar Data: Methods and Trends

    Science.gov (United States)

    Osmanoglu, Batuhan; Sunar, Filiz; Wdowinski, Shimon; Cano-Cabral, Enrique

    2015-01-01

    Time series analysis of InSAR data has emerged as an important tool for monitoring and measuring the displacement of the Earth's surface. Changes in the Earth's surface can result from a wide range of phenomena such as earthquakes, volcanoes, landslides, variations in ground water levels, and changes in wetland water levels. Time series analysis is applied to interferometric phase measurements, which wrap around when the observed motion is larger than one-half of the radar wavelength. Thus, the spatio-temporal ''unwrapping" of phase observations is necessary to obtain physically meaningful results. Several different algorithms have been developed for time series analysis of InSAR data to solve for this ambiguity. These algorithms may employ different models for time series analysis, but they all generate a first-order deformation rate, which can be compared to each other. However, there is no single algorithm that can provide optimal results in all cases. Since time series analyses of InSAR data are used in a variety of applications with different characteristics, each algorithm possesses inherently unique strengths and weaknesses. In this review article, following a brief overview of InSAR technology, we discuss several algorithms developed for time series analysis of InSAR data using an example set of results for measuring subsidence rates in Mexico City.

  6. Applying the expansion method in hierarchical functions to the solution of Navier-Stokes equations for incompressible fluids

    International Nuclear Information System (INIS)

    Sabundjian, Gaiane

    1999-01-01

    This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)

  7. Nolinear stability analysis of nuclear reactors : expansion methods for stability domains

    International Nuclear Information System (INIS)

    Yang, Chae Yong

    1992-02-01

    Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are developed in this study: an improved Chang and Thorp's method based on expansion of a Lyapunov function and a new method based on expansion of any positive definite function. The methods are established on the concept of stability definitions of Lyapunov itself. The first method provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions in order to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most dynamic systems are stiff. The second method (new method) requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for stiff systems. The methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared. A reactor feedback model for a pressurized water reactor (PWR) considering fuel and moderator temperature effects is developed and the nonlinear stability regions are estimated for the various values of design parameters by using the new method. The steady-state properties of the nonlinear reactor system are analyzed via bifurcation theory. The analysis of nonlinear phenomena is carried out for the various forms of reactivity feedback coefficients that are both temperature- (or power-) independent and dependent. If one of two temperature coefficients is positive, unstable limit cycles or multiplicity of the steady-state solutions appear when the other temperature coefficient exceeds a certain critical value. As an example, even though the fuel temperature coefficient is negative, if the moderator temperature

  8. A new diffusion nodal method based on analytic basis function expansion

    International Nuclear Information System (INIS)

    Noh, J.M.; Cho, N.Z.

    1993-01-01

    The transverse integration procedure commonly used in most advanced nodal methods results in some limitations. The first is that the transverse leakage term that appears in the transverse integration procedure must be appropriately approximated. In most advanced nodal methods, this term is expanded in a quadratic polynomial. The second arises when reconstructing the pinwise flux distribution within a node. The available one-dimensional flux shapes from nodal calculation in each spatial direction cannot be used directly in the flux reconstruction. Finally, the transverse leakage defined for a hexagonal node becomes so complicated as not to be easily handled and contains nonphysical singular terms. In this paper, a new nodal method called the analytic function expansion nodal (AFEN) method is described for both the rectangular geometry and the hexagonal geometry in order to overcome these limitations. This method does not solve the transverse-integrated one-dimensional diffusion equations but instead solves directly the original multidimensional diffusion equation within a node. This is a accomplished by expanding the solution (or the intranodal homogeneous flux distribution) in terms of nonseparable analytic basis functions satisfying the diffusion equation at any point in the node

  9. High order spatial expansion for the method of characteristics applied to 3-D geometries

    International Nuclear Information System (INIS)

    Naymeh, L.; Masiello, E.; Sanchez, R.

    2013-01-01

    The method of characteristics is an efficient and flexible technique to solve the neutron transport equation and has been extensively used in two-dimensional calculations because it permits to deal with complex geometries. However, because of a very fast increase in storage requirements and number of floating operations, its direct application to three-dimensional routine transport calculations it is not still possible. In this work we introduce and analyze several modifications aimed to reduce memory requirements and to diminish the computing burden. We explore high-order spatial approximation, the use of intermediary trajectory-dependent flux expansions and the possibility of dynamic trajectory reconstruction from local tracking for typed subdomains. (authors)

  10. A direct method to transform between expansions in the configuration state function and Slater determinant bases

    International Nuclear Information System (INIS)

    Olsen, Jeppe

    2014-01-01

    A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10 6 coefficients in the CSF basis is obtained from the 150 × 10 6 coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require

  11. Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.

    Science.gov (United States)

    Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko

    2014-04-01

    The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.

  12. Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method.

    Science.gov (United States)

    Akbar, M Ali; Hj Mohd Ali, Norhashidah

    2014-01-01

    The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.

  13. Investigation on the reliability of expansion joint for piping with probabilistic method

    International Nuclear Information System (INIS)

    Ishii, Y.; Kambe, M.

    1980-01-01

    The reduction of the plant size is necessitated as one of the major targets in LMFBR design. Usually, piping work system is extensively used to absorb thermal expansion between two components anywhere. Besides above, expansion joint for piping seems to be attractive lately for the same object. This paper describes the significance of expansion joint with multiple boundaries, breakdown probability of expansion joint assembly and partly the bellows by introducing several hypothetical conditions in connection with piping. Also, an importance of in-service inspection (ISI) for expansion joint was discussed using a comparative table and probabilities on reliability from partly broken to full penetration. In conclusion, the expansion joint with ISI should be manufactured with excellent reliability in order to cope with piping work system; several conditions of the practical application for piping systems are suggested. (author)

  14. Investigation on the reliability of expansion joint for piping with probabilistic method

    Energy Technology Data Exchange (ETDEWEB)

    Ishii, Y; Kambe, M

    1980-02-01

    The reduction of the plant size is necessitated as one of the major targets in LMFBR design. Usually, piping work system is extensively used to absorb thermal expansion between two components anywhere. Besides above, expansion joint for piping seems to be attractive lately for the same object. This paper describes the significance of expansion joint with multiple boundaries, breakdown probability of expansion joint assembly and partly the bellows by introducing several hypothetical conditions in connection with piping. Also, an importance of in-service inspection (ISI) for expansion joint was discussed using a comparative table and probabilities on reliability from partly broken to full penetration. In conclusion, the expansion joint with ISI should be manufactured with excellent reliability in order to cope with piping work system; several conditions of the practical application for piping systems are suggested. (author)

  15. Investigation on the reliability of expansion joint for piping with probabilistic method

    International Nuclear Information System (INIS)

    Ishii, Yoichiro; Kambe, Mitsuru.

    1979-11-01

    The reduction of the plant size if necessitated as one of the major target in LMFBR design. Usually, piping work system is extensively used to absorb thermal expansion between two components anywhere. Besides above, expansion joint for piping seems to be attractive lately for the same object. This paper describes about the significance of expansion joint with multiple boundaries, breakdown probability of expansion joint assembly and partly the bellows by introducing several hypothetical conditions in connection with piping. Also, an importance of inservice inspection (ISI) for expansion joint was discussed using by comparative table and probabilities on reliability from partly broken to full penetration. In the conclusion, the expansion joint with ISI should be manufactured with excellent reliability in order to cope with piping work system, and several conditions of the practical application for piping systems are suggested. (author)

  16. 8760-Based Method for Representing Variable Generation Capacity Value in Capacity Expansion Models

    Energy Technology Data Exchange (ETDEWEB)

    Frew, Bethany A [National Renewable Energy Laboratory (NREL), Golden, CO (United States)

    2017-08-03

    Capacity expansion models (CEMs) are widely used to evaluate the least-cost portfolio of electricity generators, transmission, and storage needed to reliably serve load over many years or decades. CEMs can be computationally complex and are often forced to estimate key parameters using simplified methods to achieve acceptable solve times or for other reasons. In this paper, we discuss one of these parameters -- capacity value (CV). We first provide a high-level motivation for and overview of CV. We next describe existing modeling simplifications and an alternate approach for estimating CV that utilizes hourly '8760' data of load and VG resources. We then apply this 8760 method to an established CEM, the National Renewable Energy Laboratory's (NREL's) Regional Energy Deployment System (ReEDS) model (Eurek et al. 2016). While this alternative approach for CV is not itself novel, it contributes to the broader CEM community by (1) demonstrating how a simplified 8760 hourly method, which can be easily implemented in other power sector models when data is available, more accurately captures CV trends than a statistical method within the ReEDS CEM, and (2) providing a flexible modeling framework from which other 8760-based system elements (e.g., demand response, storage, and transmission) can be added to further capture important dynamic interactions, such as curtailment.

  17. Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

    Science.gov (United States)

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-01-01

    In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

  18. Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

    Science.gov (United States)

    Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

    2013-09-01

    Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

  19. Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

    International Nuclear Information System (INIS)

    Gao, Z.; Xu, Y.; Downar, T.

    2013-01-01

    Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

  20. Analytical method for estimating the thermal expansion coefficient of metals at high temperature

    International Nuclear Information System (INIS)

    Takamoto, S; Izumi, S; Nakata, T; Sakai, S; Oinuma, S; Nakatani, Y

    2015-01-01

    In this paper, we propose an analytical method for estimating the thermal expansion coefficient (TEC) of metals at high-temperature ranges. Although the conventional method based on quasiharmonic approximation (QHA) shows good results at low temperatures, anharmonic effects caused by large-amplitude thermal vibrations reduces its accuracy at high temperatures. Molecular dynamics (MD) naturally includes the anharmonic effect. However, since the computational cost of MD is relatively high, in order to make an interatomic potential capable of reproducing TEC, an analytical method is essential. In our method, analytical formulation of the radial distribution function (RDF) at finite temperature realizes the estimation of the TEC. Each peak of the RDF is approximated by the Gaussian distribution. The average and variance of the Gaussian distribution are formulated by decomposing the fluctuation of interatomic distance into independent elastic waves. We incorporated two significant anharmonic effects into the method. One is the increase in the averaged interatomic distance caused by large amplitude vibration. The second is the variation in the frequency of elastic waves. As a result, the TECs of fcc and bcc crystals estimated by our method show good agreement with those of MD. Our method enables us to make an interatomic potential that reproduces the TEC at high temperature. We developed the GEAM potential for nickel. The TEC of the fitted potential showed good agreement with experimental data from room temperature to 1000 K. As compared with the original potential, it was found that the third derivative of the wide-range curve was modified, while the zeroth, first and second derivatives were unchanged. This result supports the conventional theory of solid state physics. We believe our analytical method and developed interatomic potential will contribute to future high-temperature material development. (paper)

  1. Critical node treatment in the analytic function expansion method for Pin Power Reconstruction

    Energy Technology Data Exchange (ETDEWEB)

    Gao, Z. [Rice University, MS 318, 6100 Main Street, Houston, TX 77005 (United States); Xu, Y. [Argonne National Laboratory, 9700 South Case Ave., Argonne, IL 60439 (United States); Downar, T. [Department of Nuclear Engineering, University of Michigan, 2355 Bonisteel blvd., Ann Arbor, MI 48109 (United States)

    2013-07-01

    Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)

  2. Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

    Directory of Open Access Journals (Sweden)

    Mahmoud Paripour

    2014-08-01

    Full Text Available In this paper, the Bernstein polynomials are used to approximatethe solutions of linear integral equations with multiple time lags (IEMTL through expansion methods (collocation method, partition method, Galerkin method. The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is carried out

  3. A novel time series link prediction method: Learning automata approach

    Science.gov (United States)

    Moradabadi, Behnaz; Meybodi, Mohammad Reza

    2017-09-01

    Link prediction is a main social network challenge that uses the network structure to predict future links. The common link prediction approaches to predict hidden links use a static graph representation where a snapshot of the network is analyzed to find hidden or future links. For example, similarity metric based link predictions are a common traditional approach that calculates the similarity metric for each non-connected link and sort the links based on their similarity metrics and label the links with higher similarity scores as the future links. Because people activities in social networks are dynamic and uncertainty, and the structure of the networks changes over time, using deterministic graphs for modeling and analysis of the social network may not be appropriate. In the time-series link prediction problem, the time series link occurrences are used to predict the future links In this paper, we propose a new time series link prediction based on learning automata. In the proposed algorithm for each link that must be predicted there is one learning automaton and each learning automaton tries to predict the existence or non-existence of the corresponding link. To predict the link occurrence in time T, there is a chain consists of stages 1 through T - 1 and the learning automaton passes from these stages to learn the existence or non-existence of the corresponding link. Our preliminary link prediction experiments with co-authorship and email networks have provided satisfactory results when time series link occurrences are considered.

  4. Long-memory time series theory and methods

    CERN Document Server

    Palma, Wilfredo

    2007-01-01

    Wilfredo Palma, PhD, is Chairman and Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. Dr. Palma has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics.

  5. Comparison of FDTD numerical computations and analytical multipole expansion method for plasmonics-active nanosphere dimers.

    Science.gov (United States)

    Dhawan, Anuj; Norton, Stephen J; Gerhold, Michael D; Vo-Dinh, Tuan

    2009-06-08

    This paper describes a comparative study of finite-difference time-domain (FDTD) and analytical evaluations of electromagnetic fields in the vicinity of dimers of metallic nanospheres of plasmonics-active metals. The results of these two computational methods, to determine electromagnetic field enhancement in the region often referred to as "hot spots" between the two nanospheres forming the dimer, were compared and a strong correlation observed for gold dimers. The analytical evaluation involved the use of the spherical-harmonic addition theorem to relate the multipole expansion coefficients between the two nanospheres. In these evaluations, the spacing between two nanospheres forming the dimer was varied to obtain the effect of nanoparticle spacing on the electromagnetic fields in the regions between the nanostructures. Gold and silver were the metals investigated in our work as they exhibit substantial plasmon resonance properties in the ultraviolet, visible, and near-infrared spectral regimes. The results indicate excellent correlation between the two computational methods, especially for gold nanosphere dimers with only a 5-10% difference between the two methods. The effect of varying the diameters of the nanospheres forming the dimer, on the electromagnetic field enhancement, was also studied.

  6. The renormalized Hamiltonian truncation method in the large E{sub T} expansion

    Energy Technology Data Exchange (ETDEWEB)

    Elias-Miró, J. [SISSA and INFN, I-34136 Trieste (Italy); Montull, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); Riembau, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); DESY, Notkestrasse 85, 22607 Hamburg (Germany)

    2016-04-22

    Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in refs. http://dx.doi.org/10.1103/PhysRevD.91.085011; http://dx.doi.org/10.1103/PhysRevD.93.065014; http://dx.doi.org/10.1103/PhysRevD.91.025005. The method is general but as an example we calculate the exact g{sup 2} and some of the g{sup 3} contributions for the ϕ{sup 4} theory in two dimensions. The coefficients of the local expansion calculated in ref. http://dx.doi.org/10.1103/PhysRevD.91.085011 are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.

  7. The verification of the Taylor-expansion moment method for the nanoparticle coagulation in the entire size regime due to Brownian motion

    International Nuclear Information System (INIS)

    Yu Mingzhou; Lin Jianzhong; Jin Hanhui; Jiang Ying

    2011-01-01

    The closure of moment equations for nanoparticle coagulation due to Brownian motion in the entire size regime is performed using a newly proposed method of moments. The equations in the free molecular size regime and the continuum plus near-continuum regime are derived separately in which the fractal moments are approximated by three-order Taylor-expansion series. The moment equations for coagulation in the entire size regime are achieved by the harmonic mean solution and the Dahneke’s solution. The results produced by the quadrature method of moments (QMOM), the Pratsinis’s log-normal moment method (PMM), the sectional method (SM), and the newly derived Taylor-expansion moment method (TEMOM) are presented and compared in accuracy and efficiency. The TEMOM method with Dahneke’s solution produces the most accurate results with a high efficiency than other existing moment models in the entire size regime, and thus it is recommended to be used in the following studies on nanoparticle dynamics due to Brownian motion.

  8. Winter Holts Oscillatory Method: A New Method of Resampling in Time Series.

    Directory of Open Access Journals (Sweden)

    Muhammad Imtiaz Subhani

    2016-12-01

    Full Text Available The core proposition behind this research is to create innovative methods of bootstrapping that can be applied in time series data. In order to find new methods of bootstrapping, various methods were reviewed; The data of automotive Sales, Market Shares and Net Exports of the top 10 countries, which includes China, Europe, United States of America (USA, Japan, Germany, South Korea, India, Mexico, Brazil, Spain and, Canada from 2002 to 2014 were collected through various sources which includes UN Comtrade, Index Mundi and World Bank. The findings of this paper confirmed that Bootstrapping for resampling through winter forecasting by Oscillation and Average methods give more robust results than the winter forecasting by any general methods.

  9. Traveling wave solutions of a biological reaction-convection-diffusion equation model by using $(G'/G$ expansion method

    Directory of Open Access Journals (Sweden)

    Shahnam Javadi

    2013-07-01

    Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.

  10. Numerical divergence effects of equivalence theory in the nodal expansion method

    International Nuclear Information System (INIS)

    Zika, M.R.; Downar, T.J.

    1993-01-01

    Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible

  11. The optimized expansion based low-rank method for wavefield extrapolation

    KAUST Repository

    Wu, Zedong

    2014-03-01

    Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that n > 0. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.

  12. An analytic method for S-expansion involving resonance and reduction

    Energy Technology Data Exchange (ETDEWEB)

    Ipinza, M.C.; Penafiel, D.M. [Departamento de Fisica, Universidad de Concepcion (Chile); DISAT, Politecnico di Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino (Italy); Lingua, F. [DISAT, Politecnico di Torino (Italy); Ravera, L. [DISAT, Politecnico di Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino (Italy)

    2016-11-15

    In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0{sub S}-resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras. This analytic method gives us a simple set of expressions to find the subset decomposition of the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras. We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  13. The cross-section dividing method and a stochastic interpretation of the moliere expansion

    International Nuclear Information System (INIS)

    Nakatsuka, T.; Okei, K.

    2004-01-01

    Properties of Moliere scattering process are investigated through the cross-section dividing method. We divide the single-scattering at an adequate angle into the moderate scattering and the large-angle scattering. We have found the expansion parameter or the shape parameter B of Moliere, which corresponds to the splitting angle of the single scattering at e B/2 times the screening angle, acts as the probability parameter to receive the large-angle scattering. A mathematical formulation to derive the angular distribution through the cross-section dividing method is proposed. Small distortions from the gaussian distribution were found in the central distribution produced by the moderate scattering of Moliere, due to the higher Fourier components. Smaller splitting angles than Moliere, e.g. the one-scattering angle χ C , will be effective for rapid sampling sequences of Moliere angular distribution, giving almost gaussian central distributions as the product of moderate scattering and low-frequent single-scatterings as the product of large-angle scatterings. (author)

  14. Frequency domain analysis and design of nonlinear systems based on Volterra series expansion a parametric characteristic approach

    CERN Document Server

    Jing, Xingjian

    2015-01-01

    This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain.  The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis a...

  15. The evidence of the rugoscopy effectiveness as a human identification method in patients submitted to rapid palatal expansion.

    Science.gov (United States)

    Barbieri, Ana A; Scoralick, Raquel A; Naressi, Suely C M; Moraes, Mari E L; Daruge, Eduardo; Daruge, Eduardo

    2013-01-01

    The objective of this study was to demonstrate the effectiveness of rugoscopy as a human identification method, even when the patient is submitted to rapid palatal expansion, which in theory would introduce doubt. With this intent, the Rugoscopic Identity was obtained for each subject using the classification formula proposed by Santos based on the intra-oral casts made before and after treatment from patients who were subjected to palatal expansion. The casts were labeled with the patients' initials and randomly arranged for studying. The palatine rugae kept the same patterns in every case studied. The technical error of the intra-evaluator measurement provided a confidence interval of 95%, making rugoscopy a reliable identification method for patients who were submitted to rapid palatal expansion, because even in the presence of intra-oral changes owing to the use of palatal expanders, the palatine rugae retained the biological and technical requirements for the human identification process. © 2012 American Academy of Forensic Sciences.

  16. Trend analysis using non-stationary time series clustering based on the finite element method

    OpenAIRE

    Gorji Sefidmazgi, M.; Sayemuzzaman, M.; Homaifar, A.; Jha, M. K.; Liess, S.

    2014-01-01

    In order to analyze low-frequency variability of climate, it is useful to model the climatic time series with multiple linear trends and locate the times of significant changes. In this paper, we have used non-stationary time series clustering to find change points in the trends. Clustering in a multi-dimensional non-stationary time series is challenging, since the problem is mathematically ill-posed. Clustering based on the finite element method (FEM) is one of the methods ...

  17. Multimodal method for scattering of sound at a sudden area expansion in a duct with subsonic flow

    NARCIS (Netherlands)

    Kooijman, G.; Testud, P.; Aurégan, Y.; Hirschberg, A.

    2008-01-01

    The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both two-dimensional (2D) rectangular

  18. Mechanical and thermal expansion properties of β-eucryptite prepared by sol-gel methods and hot pressing

    International Nuclear Information System (INIS)

    Xia, L.; Wen, G.W.; Qin, C.L.; Wang, X.Y.; Song, L.

    2011-01-01

    Research highlights: → Dense LAS glass-ceramics were fabricated by sol-gel and hot pressing technique. → The LAS glass-ceramics have relative good mechanical properties. → The negative thermal expansion behavior of LAS glass-ceramics was investigated. -- Abstract: The microstructures, mechanical properties and thermal expansion behavior of monolithic lithium aluminosilicate glass-ceramics, prepared by sol-gel method and hot pressing, were investigated by using X-ray diffraction, scanning and transmission electron microscopies, three-point bend tests and dilatometry. β-eucryptite appeared as main phase in the monolithic lithium aluminosilicate glass-ceramics. The glass ceramics exhibited high relative densities and the average flexural strength and fracture toughness values were 154 MPa and 2.46 MPa m 1/2 , respectively. The lithium aluminosilicate glass-ceramics hot pressed 1300 and 1350 o C demonstrated negative coefficient of thermal expansion, which was affected by amount and type of crystalline phases.

  19. 8760-Based Method for Representing Variable Generation Capacity Value in Capacity Expansion Models: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Frew, Bethany A [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Cole, Wesley J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Sun, Yinong [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Mai, Trieu T [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Richards, James [National Renewable Energy Laboratory (NREL), Golden, CO (United States)

    2017-08-01

    Capacity expansion models (CEMs) are widely used to evaluate the least-cost portfolio of electricity generators, transmission, and storage needed to reliably serve demand over the evolution of many years or decades. Various CEM formulations are used to evaluate systems ranging in scale from states or utility service territories to national or multi-national systems. CEMs can be computationally complex, and to achieve acceptable solve times, key parameters are often estimated using simplified methods. In this paper, we focus on two of these key parameters associated with the integration of variable generation (VG) resources: capacity value and curtailment. We first discuss common modeling simplifications used in CEMs to estimate capacity value and curtailment, many of which are based on a representative subset of hours that can miss important tail events or which require assumptions about the load and resource distributions that may not match actual distributions. We then present an alternate approach that captures key elements of chronological operation over all hours of the year without the computationally intensive economic dispatch optimization typically employed within more detailed operational models. The updated methodology characterizes the (1) contribution of VG to system capacity during high load and net load hours, (2) the curtailment level of VG, and (3) the potential reductions in curtailments enabled through deployment of storage and more flexible operation of select thermal generators. We apply this alternate methodology to an existing CEM, the Regional Energy Deployment System (ReEDS). Results demonstrate that this alternate approach provides more accurate estimates of capacity value and curtailments by explicitly capturing system interactions across all hours of the year. This approach could be applied more broadly to CEMs at many different scales where hourly resource and load data is available, greatly improving the representation of challenges

  20. Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

    Science.gov (United States)

    Singh, R. R. P.; Young, A. P.

    2017-08-01

    We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

  1. Method for measurement of relative differences in thermal expansion coefficients (LWBR development program)

    International Nuclear Information System (INIS)

    Alexander, J.E.

    1978-06-01

    The report describes a test which was conducted to determine the variation in thermal expansion coefficients of specimens from several material heats of Type 304 stainless steel. The purpose of this document is to identify the procedures, equipment, and analysis used in performing this test. From a review of the data which were used in establishing the values given for mean coefficient of thermal expansion in the 1968 ASME Boiler and Pressure Vessel Code, Section III, a +-3.3-percent maximum variation was determined for Type 304 CRES in the temperature range of interest. The results of the test reduced this variation to +-0.53 percent based on a 95/99-percent tolerance interval for the material tested. The testing equipment, procedure, and analysis are not complicated and this type of test is recommended for applications in which the variation in thermal expansion coefficients is desired for a limited number of material heats

  2. Empirical method to measure stochasticity and multifractality in nonlinear time series

    Science.gov (United States)

    Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping

    2013-12-01

    An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

  3. A Comparison of Various Forecasting Methods for Autocorrelated Time Series

    Directory of Open Access Journals (Sweden)

    Karin Kandananond

    2012-07-01

    Full Text Available The accuracy of forecasts significantly affects the overall performance of a whole supply chain system. Sometimes, the nature of consumer products might cause difficulties in forecasting for the future demands because of its complicated structure. In this study, two machine learning methods, artificial neural network (ANN and support vector machine (SVM, and a traditional approach, the autoregressive integrated moving average (ARIMA model, were utilized to predict the demand for consumer products. The training data used were the actual demand of six different products from a consumer product company in Thailand. Initially, each set of data was analysed using Ljung‐Box‐Q statistics to test for autocorrelation. Afterwards, each method was applied to different sets of data. The results indicated that the SVM method had a better forecast quality (in terms of MAPE than ANN and ARIMA in every category of products.

  4. Transformation-cost time-series method for analyzing irregularly sampled data.

    Science.gov (United States)

    Ozken, Ibrahim; Eroglu, Deniz; Stemler, Thomas; Marwan, Norbert; Bagci, G Baris; Kurths, Jürgen

    2015-06-01

    Irregular sampling of data sets is one of the challenges often encountered in time-series analysis, since traditional methods cannot be applied and the frequently used interpolation approach can corrupt the data and bias the subsequence analysis. Here we present the TrAnsformation-Cost Time-Series (TACTS) method, which allows us to analyze irregularly sampled data sets without degenerating the quality of the data set. Instead of using interpolation we consider time-series segments and determine how close they are to each other by determining the cost needed to transform one segment into the following one. Using a limited set of operations-with associated costs-to transform the time series segments, we determine a new time series, that is our transformation-cost time series. This cost time series is regularly sampled and can be analyzed using standard methods. While our main interest is the analysis of paleoclimate data, we develop our method using numerical examples like the logistic map and the Rössler oscillator. The numerical data allows us to test the stability of our method against noise and for different irregular samplings. In addition we provide guidance on how to choose the associated costs based on the time series at hand. The usefulness of the TACTS method is demonstrated using speleothem data from the Secret Cave in Borneo that is a good proxy for paleoclimatic variability in the monsoon activity around the maritime continent.

  5. Transformation-cost time-series method for analyzing irregularly sampled data

    Science.gov (United States)

    Ozken, Ibrahim; Eroglu, Deniz; Stemler, Thomas; Marwan, Norbert; Bagci, G. Baris; Kurths, Jürgen

    2015-06-01

    Irregular sampling of data sets is one of the challenges often encountered in time-series analysis, since traditional methods cannot be applied and the frequently used interpolation approach can corrupt the data and bias the subsequence analysis. Here we present the TrAnsformation-Cost Time-Series (TACTS) method, which allows us to analyze irregularly sampled data sets without degenerating the quality of the data set. Instead of using interpolation we consider time-series segments and determine how close they are to each other by determining the cost needed to transform one segment into the following one. Using a limited set of operations—with associated costs—to transform the time series segments, we determine a new time series, that is our transformation-cost time series. This cost time series is regularly sampled and can be analyzed using standard methods. While our main interest is the analysis of paleoclimate data, we develop our method using numerical examples like the logistic map and the Rössler oscillator. The numerical data allows us to test the stability of our method against noise and for different irregular samplings. In addition we provide guidance on how to choose the associated costs based on the time series at hand. The usefulness of the TACTS method is demonstrated using speleothem data from the Secret Cave in Borneo that is a good proxy for paleoclimatic variability in the monsoon activity around the maritime continent.

  6. Trend analysis using non-stationary time series clustering based on the finite element method

    Science.gov (United States)

    Gorji Sefidmazgi, M.; Sayemuzzaman, M.; Homaifar, A.; Jha, M. K.; Liess, S.

    2014-05-01

    In order to analyze low-frequency variability of climate, it is useful to model the climatic time series with multiple linear trends and locate the times of significant changes. In this paper, we have used non-stationary time series clustering to find change points in the trends. Clustering in a multi-dimensional non-stationary time series is challenging, since the problem is mathematically ill-posed. Clustering based on the finite element method (FEM) is one of the methods that can analyze multidimensional time series. One important attribute of this method is that it is not dependent on any statistical assumption and does not need local stationarity in the time series. In this paper, it is shown how the FEM-clustering method can be used to locate change points in the trend of temperature time series from in situ observations. This method is applied to the temperature time series of North Carolina (NC) and the results represent region-specific climate variability despite higher frequency harmonics in climatic time series. Next, we investigated the relationship between the climatic indices with the clusters/trends detected based on this clustering method. It appears that the natural variability of climate change in NC during 1950-2009 can be explained mostly by AMO and solar activity.

  7. The (G′/G-Expansion Method and Its Application for Higher-Order Equations of KdV (III

    Directory of Open Access Journals (Sweden)

    Huizhang Yang

    2014-01-01

    Full Text Available New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G′/G-expansion method, where G=G(ξ satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. The property of this method is that it is quite simple and understandable.

  8. New exact solutions of (2 + 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method

    International Nuclear Information System (INIS)

    Chen Yong; Yan Zhenya

    2005-01-01

    In this paper (2 + 1)-dimensional Gardner equation is investigated using a sine-Gordon equation expansion method, which was presented via a generalized sine-Gordon reduction equation and a new transformation. As a consequence, it is shown that the method is more powerful to obtain many types of new doubly periodic solutions of (2 + 1)-dimensional Gardner equation. In particular, solitary wave solutions are also given as simple limits of doubly periodic solutions

  9. Interpretation of Piezocones in Silt, Using Cavity Expansion and Critical State Methods

    DEFF Research Database (Denmark)

    Bakmar, Christian LeBlanc; Randolph, M. F.

    2008-01-01

    was simulated using cylindrical cavity expansion in conjunction with a plasticity model formulated within the framework of critical state soil mechanics. The results readily explain the low cone tip resistance measured in silt sediments; this is a derived effect of the silt having a large slope of the critical...... state line, resulting in rather weak and compressible behaviour at high mean effective stresses....

  10. Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

    Science.gov (United States)

    Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

    2014-01-01

    Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

  11. Comparison of transfer entropy methods for financial time series

    Science.gov (United States)

    He, Jiayi; Shang, Pengjian

    2017-09-01

    There is a certain relationship between the global financial markets, which creates an interactive network of global finance. Transfer entropy, a measurement for information transfer, offered a good way to analyse the relationship. In this paper, we analysed the relationship between 9 stock indices from the U.S., Europe and China (from 1995 to 2015) by using transfer entropy (TE), effective transfer entropy (ETE), Rényi transfer entropy (RTE) and effective Rényi transfer entropy (ERTE). We compared the four methods in the sense of the effectiveness for identification of the relationship between stock markets. In this paper, two kinds of information flows are given. One reveals that the U.S. took the leading position when in terms of lagged-current cases, but when it comes to the same date, China is the most influential. And ERTE could provide superior results.

  12. The relationship between the Johnson-Baranger time-dependent folded diagram expansion and the time-independent methods of perturbation theory

    International Nuclear Information System (INIS)

    Passos, E.M.J. de

    1976-01-01

    The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt

  13. Determination of power distribution in reactor with nodal expansion method; Izrachun porazdelitve mochi v reaktorju z metodo nodalne ekspanzije

    Energy Technology Data Exchange (ETDEWEB)

    Kromar, M; Trkov, A [Institut Jozef Stefan, Ljubljana (Yugoslavia); Pregl, G [Tehnishka Fakulteta Maribor Univ. (Yugoslavia)

    1988-07-01

    Nodal expansion method (NEM) is one of the advanced coarse-mesh methods based on integral form of few-group diffusion equation. NEM can be characterized by high accuracy and computational efficiency. Method was tested by development of computer code NEXT. Validation of the code was performed by calculation of 2-D and 3-D IAEA benchmark problem. NEXT was compared with codes based on other methods (finite differences, finite elements) and has been found to be accurate as well as fast. (author)

  14. Method of γ expansions in the electronic theory of disordered alloys

    International Nuclear Information System (INIS)

    Masanskii, I.V.; Tokar', V.I.

    1989-01-01

    In the electronic theory of disordered alloys an expansion with respect to the parameter γ = exp( -1/ξ ), where ξ is the dimensionless correlation length of the single-electron Green's function, is proposed. This expansion makes it possible to take into account the presence in the alloy of short-range order and the effects of multiple scattering of the electrons by different sites. It is shown that in the case of sufficiently strong disorder γ is a small parameter of the coherent potential approximation, and the corrections to this approximation are found. It is also shown that in the framework of this approximation the equilibrium values of the parameters of the short-range order can be calculated

  15. Aerodynamic optimization of wind turbine rotors using a blade element momentum method with corrections for wake rotation and expansion

    DEFF Research Database (Denmark)

    Døssing, Mads; Aagaard Madsen, Helge; Bak, Christian

    2012-01-01

    The blade element momentum (BEM) method is widely used for calculating the quasi-steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now...... by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM....... In short, allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd....

  16. Thermal Expansion and Magnetostriction Measurements at Cryogenic Temperature Using the Strain Gauge Method

    OpenAIRE

    Wei Wang; Wei Wang; Huiming Liu; Rongjin Huang; Rongjin Huang; Yuqiang Zhao; Chuangjun Huang; Shibin Guo; Yi Shan; Laifeng Li; Laifeng Li; Laifeng Li

    2018-01-01

    Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra-low temperature (<77 K) environment easily. This paper describes the design and ...

  17. Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations

    International Nuclear Information System (INIS)

    Zhou Yubin; Li Chao

    2009-01-01

    A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. (general)

  18. New exact solutions of the(2+1-dimensional Broer-Kaup equation by the consistent Riccati expansion method

    Directory of Open Access Journals (Sweden)

    Jiang Ying

    2017-01-01

    Full Text Available In this work, we study the (2+1-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

  19. Hadron formation in a non-ideal quark gluon plasma using Mayer's method of cluster expansion

    International Nuclear Information System (INIS)

    Prasanth, J.P.; Bannur, Vishnu M.

    2015-01-01

    This work investigates the applicability of using the Mayer's cluster expansion method to derive the equation of state (EoS) of the quark-antiquark plasma. Dissociation of heavier hadrons in QGP is studied. The possibility of the existence of quarkonium after deconfinement at higher temperature than the critical temperature T > T c is investigated. The EoS has been studied by calculating second and third cluster integrals. The results are compared and discussed with available works. (author)

  20. A prediction method based on wavelet transform and multiple models fusion for chaotic time series

    International Nuclear Information System (INIS)

    Zhongda, Tian; Shujiang, Li; Yanhong, Wang; Yi, Sha

    2017-01-01

    In order to improve the prediction accuracy of chaotic time series, a prediction method based on wavelet transform and multiple models fusion is proposed. The chaotic time series is decomposed and reconstructed by wavelet transform, and approximate components and detail components are obtained. According to different characteristics of each component, least squares support vector machine (LSSVM) is used as predictive model for approximation components. At the same time, an improved free search algorithm is utilized for predictive model parameters optimization. Auto regressive integrated moving average model (ARIMA) is used as predictive model for detail components. The multiple prediction model predictive values are fusion by Gauss–Markov algorithm, the error variance of predicted results after fusion is less than the single model, the prediction accuracy is improved. The simulation results are compared through two typical chaotic time series include Lorenz time series and Mackey–Glass time series. The simulation results show that the prediction method in this paper has a better prediction.

  1. The principal component analysis method used with polynomial Chaos expansion to propagate uncertainties through critical transport problems

    Energy Technology Data Exchange (ETDEWEB)

    Rising, M. E.; Prinja, A. K. [Univ. of New Mexico, Dept. of Chemical and Nuclear Engineering, Albuquerque, NM 87131 (United States)

    2012-07-01

    A critical neutron transport problem with random material properties is introduced. The total cross section and the average neutron multiplicity are assumed to be uncertain, characterized by the mean and variance with a log-normal distribution. The average neutron multiplicity and the total cross section are assumed to be uncorrected and the material properties for differing materials are also assumed to be uncorrected. The principal component analysis method is used to decompose the covariance matrix into eigenvalues and eigenvectors and then 'realizations' of the material properties can be computed. A simple Monte Carlo brute force sampling of the decomposed covariance matrix is employed to obtain a benchmark result for each test problem. In order to save computational time and to characterize the moments and probability density function of the multiplication factor the polynomial chaos expansion method is employed along with the stochastic collocation method. A Gauss-Hermite quadrature set is convolved into a multidimensional tensor product quadrature set and is successfully used to compute the polynomial chaos expansion coefficients of the multiplication factor. Finally, for a particular critical fuel pin assembly the appropriate number of random variables and polynomial expansion order are investigated. (authors)

  2. Interpolation in Time Series : An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment

    NARCIS (Netherlands)

    Lepot, M.J.; Aubin, Jean Baptiste; Clemens, F.H.L.R.

    2017-01-01

    A thorough review has been performed on interpolation methods to fill gaps in time-series, efficiency criteria, and uncertainty quantifications. On one hand, there are numerous available methods: interpolation, regression, autoregressive, machine learning methods, etc. On the other hand, there are

  3. Formulating and testing a method for perturbing precipitation time series to reflect anticipated climatic changes

    DEFF Research Database (Denmark)

    Sørup, Hjalte Jomo Danielsen; Georgiadis, Stylianos; Gregersen, Ida Bülow

    2017-01-01

    Urban water infrastructure has very long planning horizons, and planning is thus very dependent on reliable estimates of the impacts of climate change. Many urban water systems are designed using time series with a high temporal resolution. To assess the impact of climate change on these systems......, similarly high-resolution precipitation time series for future climate are necessary. Climate models cannot at their current resolutions provide these time series at the relevant scales. Known methods for stochastic downscaling of climate change to urban hydrological scales have known shortcomings...... in constructing realistic climate-changed precipitation time series at the sub-hourly scale. In the present study we present a deterministic methodology to perturb historical precipitation time series at the minute scale to reflect non-linear expectations to climate change. The methodology shows good skill...

  4. Long-Term Reserve Expansion of Power Systems With High Wind Power Penetration Using Universal Generating Function Methods

    DEFF Research Database (Denmark)

    DING, YI; Wang, Peng; Goel, Lalit

    2010-01-01

    from long term planning point of view utilizing universal generating function (UGF) methods. The reliability models of wind farms and conventional generators are represented as the correspondin UGFs and the special operators for these UGFs are defined to evaluate the customer and the system...... reliabilities. The effect of transmission network on customer reliabilities is also considered in the system UGF. The power output models of wind turbine generators in a wind farm considering wind speed correlation and un-correlation are developed, respectively. A reliability-based reserve expansion method...

  5. A modified precise integration method based on Magnus expansion for transient response analysis of time varying dynamical structure

    International Nuclear Information System (INIS)

    Yue, Cong; Ren, Xingmin; Yang, Yongfeng; Deng, Wangqun

    2016-01-01

    This paper provides a precise and efficacious methodology for manifesting forced vibration response with respect to the time-variant linear rotational structure subjected to unbalanced excitation. A modified algorithm based on time step precise integration method and Magnus expansion is developed for instantaneous dynamic problems. The iterative solution is achieved by the ideology of transition and dimensional increment matrix. Numerical examples on a typical accelerating rotation system considering gyroscopic moment and mass unbalance force comparatively demonstrate the validity, effectiveness and accuracy with Newmark-β method. It is shown that the proposed algorithm has high accuracy without loss efficiency.

  6. Short-term prediction method of wind speed series based on fractal interpolation

    International Nuclear Information System (INIS)

    Xiu, Chunbo; Wang, Tiantian; Tian, Meng; Li, Yanqing; Cheng, Yi

    2014-01-01

    Highlights: • An improved fractal interpolation prediction method is proposed. • The chaos optimization algorithm is used to obtain the iterated function system. • The fractal extrapolate interpolation prediction of wind speed series is performed. - Abstract: In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series

  7. Research on the Statistical Characteristics of Crosstalk in Naval Ships Wiring Harness Based on Polynomial Chaos Expansion Method

    Directory of Open Access Journals (Sweden)

    Chi Yaodan

    2017-08-01

    Full Text Available Crosstalk in wiring harness has been studied extensively for its importance in the naval ships electromagnetic compatibility field. An effective and high-efficiency method is proposed in this paper for analyzing Statistical Characteristics of crosstalk in wiring harness with random variation of position based on Polynomial Chaos Expansion (PCE. A typical 14-cable wiring harness was simulated as the object of research. Distance among interfering cable, affected cable and GND is synthesized and analyzed in both frequency domain and time domain. The model of naval ships wiring harness distribution parameter was established by utilizing Legendre orthogonal polynomials as basis functions along with prediction model of statistical characters. Detailed mean value, mean square error, probability density function and reasonable varying range of crosstalk in naval ships wiring harness are described in both time domain and frequency domain. Numerical experiment proves that the method proposed in this paper, not only has good consistency with the MC method can be applied in the naval ships EMC research field to provide theoretical support for guaranteeing safety, but also has better time-efficiency than the MC method. Therefore, the Polynomial Chaos Expansion method.

  8. Radial expansion for spinning conformal blocks

    CERN Document Server

    Costa, Miguel S.; Penedones, João; Trevisani, Emilio

    2016-07-12

    This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we explain how to write closed form recursion relations for the coefficients of the expansions. We study three examples of four point functions in detail: one vector and three scalars; two vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the case of two external vectors, we also provide a more efficient way to generate the series expansion using the analytic structure of the blocks as a function of the scaling dimension of the exchanged operator.

  9. Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

    Science.gov (United States)

    Faria, Luiz; Rosales, Rodolfo

    2017-11-01

    We introduce an alternative to the method of matched asymptotic expansions. In the ``traditional'' implementation, approximate solutions, valid in different (but overlapping) regions are matched by using ``intermediate'' variables. Here we propose to match at the level of the equations involved, via a ``uniform expansion'' whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the ``simplest'' set of equations that capture the behavior. Ruben Rosales work was partially supported by NSF Grants DMS-1614043 and DMS-1719637.

  10. Multimodal method for scattering of sound at a sudden area expansion in a duct with subsonic flow

    Science.gov (United States)

    Kooijman, G.; Testud, P.; Aurégan, Y.; Hirschberg, A.

    2008-03-01

    The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both two-dimensional (2D) rectangular and 2D cylindrical geometry and uniform mean flow as well as non-uniform mean flow profiles are considered. Model results for the scattering of plane waves in case of uniform flow, in which case an infinitely thin shear layer is formed downstream of the area expansion, are compared to results obtained by other models in literature. Generally good agreement is found. Furthermore, model results for the scattering are compared to experimental data found in literature. Also here fairly good correspondence is observed. When employing a turbulent pipe flow profile in the model, instead of a uniform flow profile, the prediction for the downstream transmission- and upstream reflection coefficient is improved. However, worse agreement is observed for the upstream transmission and downstream reflection coefficient. On the contrary, employing a non-uniform jet flow profile, which represents a typical shear layer flow downstream of the expansion, gives worse agreement for the downstream transmission- and the upstream reflection coefficient, whereas prediction for the upstream transmission and downstream reflection coefficient improves.

  11. A formal power series expansion-regularization approach for Lévy stable distributions: the symmetric case with \\alpha =2/M (M positive integer)

    Science.gov (United States)

    Crisanto-Neto, J. C.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.

    2016-09-01

    In practice, the Lévy α-stable distribution is usually expressed in terms of the Fourier integral of its characteristic function. Indeed, known closed form expressions are relatively scarce given the huge parameters space: 0\\lt α ≤slant 2 ({{L\\'{e}vy}} {{index}}), -1≤slant β ≤slant 1 ({{skewness}}),σ \\gt 0 ({{scale}}), and -∞ \\lt μ \\lt ∞ ({{shift}}). Hence, systematic efforts have been made towards the development of proper methods for analytically solving the mentioned integral. As a further contribution in this direction, here we propose a new way to tackle the problem. We consider an approach in which one first solves the Fourier integral through a formal (thus not necessarily convergent) series representation. Then, one uses (if necessary) a pertinent sum-regularization procedure to the resulting divergent series, so as to obtain an exact formula for the distribution, which is amenable to direct numerical calculations. As a concrete study, we address the centered, symmetric, unshifted and unscaled distribution (β =0, μ =0, σ =1), with α ={α }M=2/M, M=1,2,3\\ldots . Conceivably, the present protocol could be applied to other sets of parameter values.

  12. Tribal Science 2017 Webinar Series: Arctic Research, One Health and the Local Environmental Observer (LEO) Network: Ongoing Activities and Expansion to Lower 48

    Science.gov (United States)

    The U.S. EPA Sustainable and Healthy Communities Seminar Series presents the Tribal Science Webinar Series that will look to develop a forum for discussion of the complex environmental issues facing many tribal and indigenous communities.

  13. Treatment of divergent expansions in scattering theory

    International Nuclear Information System (INIS)

    Gersten, A.; Malin, S.

    1978-01-01

    One of the biggest obstacles in applying quantum field theory to realistic scattering problems are the divergencies of pertubation expansions for large coupling constants and the divergencies of partial wave expansions for massless particles exchanges. There exist, however, methods of summation of the divergent expansions which can lead to significant application in physics. In this paper we treat the problem of summing such expansions using three methods: (i) a generalization of the Pade approximation to the multivariable case. The suggested definition is unique and preserves unitarity. (ii) The summation of divergent partial waves for arbitrary spins. (iii) A successful application of a series inversion to the 3 P 1 nucleon-nucleon phase shift up to 200 MeV. (orig./WL) [de

  14. Improved time series prediction with a new method for selection of model parameters

    International Nuclear Information System (INIS)

    Jade, A M; Jayaraman, V K; Kulkarni, B D

    2006-01-01

    A new method for model selection in prediction of time series is proposed. Apart from the conventional criterion of minimizing RMS error, the method also minimizes the error on the distribution of singularities, evaluated through the local Hoelder estimates and its probability density spectrum. Predictions of two simulated and one real time series have been done using kernel principal component regression (KPCR) and model parameters of KPCR have been selected employing the proposed as well as the conventional method. Results obtained demonstrate that the proposed method takes into account the sharp changes in a time series and improves the generalization capability of the KPCR model for better prediction of the unseen test data. (letter to the editor)

  15. Cumulants in perturbation expansions for non-equilibrium field theory

    International Nuclear Information System (INIS)

    Fauser, R.

    1995-11-01

    The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)

  16. The CACAO Method for Smoothing, Gap Filling, and Characterizing Seasonal Anomalies in Satellite Time Series

    Science.gov (United States)

    Verger, Aleixandre; Baret, F.; Weiss, M.; Kandasamy, S.; Vermote, E.

    2013-01-01

    Consistent, continuous, and long time series of global biophysical variables derived from satellite data are required for global change research. A novel climatology fitting approach called CACAO (Consistent Adjustment of the Climatology to Actual Observations) is proposed to reduce noise and fill gaps in time series by scaling and shifting the seasonal climatological patterns to the actual observations. The shift and scale CACAO parameters adjusted for each season allow quantifying shifts in the timing of seasonal phenology and inter-annual variations in magnitude as compared to the average climatology. CACAO was assessed first over simulated daily Leaf Area Index (LAI) time series with varying fractions of missing data and noise. Then, performances were analyzed over actual satellite LAI products derived from AVHRR Long-Term Data Record for the 1981-2000 period over the BELMANIP2 globally representative sample of sites. Comparison with two widely used temporal filtering methods-the asymmetric Gaussian (AG) model and the Savitzky-Golay (SG) filter as implemented in TIMESAT-revealed that CACAO achieved better performances for smoothing AVHRR time series characterized by high level of noise and frequent missing observations. The resulting smoothed time series captures well the vegetation dynamics and shows no gaps as compared to the 50-60% of still missing data after AG or SG reconstructions. Results of simulation experiments as well as confrontation with actual AVHRR time series indicate that the proposed CACAO method is more robust to noise and missing data than AG and SG methods for phenology extraction.

  17. Determining the significance of associations between two series of discrete events : bootstrap methods /

    Energy Technology Data Exchange (ETDEWEB)

    Niehof, Jonathan T.; Morley, Steven K.

    2012-01-01

    We review and develop techniques to determine associations between series of discrete events. The bootstrap, a nonparametric statistical method, allows the determination of the significance of associations with minimal assumptions about the underlying processes. We find the key requirement for this method: one of the series must be widely spaced in time to guarantee the theoretical applicability of the bootstrap. If this condition is met, the calculated significance passes a reasonableness test. We conclude with some potential future extensions and caveats on the applicability of these methods. The techniques presented have been implemented in a Python-based software toolkit.

  18. Residual power series method for fractional Sharma-Tasso-Olever equation

    Directory of Open Access Journals (Sweden)

    Amit Kumar

    2016-02-01

    Full Text Available In this paper, we introduce a modified analytical approximate technique to obtain solution of time fractional Sharma-Tasso-Olever equation. First, we present an alternative framework of the Residual power series method (RPSM which can be used simply and effectively to handle nonlinear fractional differential equations arising in several physical phenomena. This method is basically based on the generalized Taylor series formula and residual error function. A good result is found between our solution and the given solution. It is shown that the proposed method is reliable, efficient and easy to implement on all kinds of fractional nonlinear problems arising in science and technology.

  19. Planning method for integration and expansion of renewable energy sources with special attention to security supply in distribution system

    Energy Technology Data Exchange (ETDEWEB)

    Cerda-Arias, Jose Luis

    2012-07-01

    Today's structure of power systems with competitive wholesale markets for electricity encourages the introduction of new agents and products, customers with self-generating capacity and the specialization of generators, network operators and power suppliers. Furthermore one has to take into account the variation of the fossil fuel prices in the world market, which even anticipates the closeness of its scarcity, the instability of the fulfilment of contracts, and the existence of import restrictions. In addition the implementation of policies aiming to control CO{sub 2} emissions, and efficient use of energy plus the advent of more efficient technologies have to be incorporated in new network expansion projects. These are forcing utilities and society to seek new forms of electric system expansion without affecting their economic growth. This expresses a challenge to sustain such a growth changing the vision for the power system and the required security of electricity supply, usually based on internal factors of the electric sector, without considering the connection between the current transmission and distribution networks, the uncertainties related to the competition in the electricity market and the effect of distributed generation units. The high penetration of distributed generation resources, based on renewable energy sources, is increasingly observed worldwide and it depends on the cost of the technologies, market design, and subsidies. On that account, it is necessary to find alternatives and offers to develop a sustainable strategic plan for power system expansion. Currently, efforts are oriented to develop planning models which consider the income of power generation based on renewable energy sources founded on these new requirements, bearing in mind the relationship between the competitive markets and the power system planning. In this Thesis a general planning method for the expansion of the power grids is proposed. This planning method should

  20. Development of a method for calculating steady-state equipment sensible heat ratio of direct expansion air conditioning units

    International Nuclear Information System (INIS)

    Xia Liang; Chan, M.Y.; Deng Shiming

    2008-01-01

    A complete set of calculation method for steady-state equipment sensible heat ratio (SHR) for a direct expansion (DX) cooling coil has been developed and reported. The method was based on the fundamentals of energy conservation and heat and mass transfer taking place in the DX cooling coil, and was experimentally validated using an experimental DX A/C rig. With the method developed, the effect of refrigerant evaporating temperature at fixed inlet air conditions on equipment SHR has been theoretically analyzed. The validated method can be useful in further studying the inherent operating characteristics of a DX air conditioning (A/C) unit and in developing suitable control strategies for achieving higher energy efficiency and better indoor thermal environment

  1. Comparison of missing value imputation methods in time series: the case of Turkish meteorological data

    Science.gov (United States)

    Yozgatligil, Ceylan; Aslan, Sipan; Iyigun, Cem; Batmaz, Inci

    2013-04-01

    This study aims to compare several imputation methods to complete the missing values of spatio-temporal meteorological time series. To this end, six imputation methods are assessed with respect to various criteria including accuracy, robustness, precision, and efficiency for artificially created missing data in monthly total precipitation and mean temperature series obtained from the Turkish State Meteorological Service. Of these methods, simple arithmetic average, normal ratio (NR), and NR weighted with correlations comprise the simple ones, whereas multilayer perceptron type neural network and multiple imputation strategy adopted by Monte Carlo Markov Chain based on expectation-maximization (EM-MCMC) are computationally intensive ones. In addition, we propose a modification on the EM-MCMC method. Besides using a conventional accuracy measure based on squared errors, we also suggest the correlation dimension (CD) technique of nonlinear dynamic time series analysis which takes spatio-temporal dependencies into account for evaluating imputation performances. Depending on the detailed graphical and quantitative analysis, it can be said that although computational methods, particularly EM-MCMC method, are computationally inefficient, they seem favorable for imputation of meteorological time series with respect to different missingness periods considering both measures and both series studied. To conclude, using the EM-MCMC algorithm for imputing missing values before conducting any statistical analyses of meteorological data will definitely decrease the amount of uncertainty and give more robust results. Moreover, the CD measure can be suggested for the performance evaluation of missing data imputation particularly with computational methods since it gives more precise results in meteorological time series.

  2. Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

    Science.gov (United States)

    Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

    2018-06-01

    In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

  3. Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment

    Directory of Open Access Journals (Sweden)

    Mathieu Lepot

    2017-10-01

    Full Text Available A thorough review has been performed on interpolation methods to fill gaps in time-series, efficiency criteria, and uncertainty quantifications. On one hand, there are numerous available methods: interpolation, regression, autoregressive, machine learning methods, etc. On the other hand, there are many methods and criteria to estimate efficiencies of these methods, but uncertainties on the interpolated values are rarely calculated. Furthermore, while they are estimated according to standard methods, the prediction uncertainty is not taken into account: a discussion is thus presented on the uncertainty estimation of interpolated/extrapolated data. Finally, some suggestions for further research and a new method are proposed.

  4. Development of fabrication method for thermal expansion difference irradiation temperature monitor

    International Nuclear Information System (INIS)

    Noguchi, Kouichi; Takatsudo, Hiroshi; Miyakawa, Shun-ichi; Kobori, Takahisa; Miyo, Toshimasa

    1998-03-01

    This report describes the development activities for the fabrication of the Thermal Expansion Difference irradiation temperature monitor (TED) at the Oarai Engineering Center (OEC)/PNC. TED is used for various irradiation tests in the experimental fast reactor JOYO. TED is the most accurate off-line temperature monitor used for irradiation examination. The TED is composed of a metallic sphere lid and either a stainless steel or nickel alloy container. Once the container is filled with sodium, the metallic sphere lid is sealed by using a resistance weld. This capsule is then loaded into a reactor. Once a TED is loaded into the JOYO reactor, the sodium inside the metallic container increases as a result of thermal expansion. The TED identifies the peak irradiation temperature of the reactor based on a formula correlating temperature to increment values. This formula is established specifically for the particular TED being used during a calibration process performed when the TED is fabricated. Initially the TED was developed by Argonne National Laboratory (ANL) in the United States, and was imported by PNC for use in the JOYO reactor. In 1992 PNC decided to fabricate TED domestically in order to ensure the stability of future supplies. Based on technical information provided by ANL, PNC began fabrication of a TED on an experimental basis. In addition, PNC endeavored to make the domestically produced TED more efficient. This involved improving the techniques used in the sodium filling and the metallic sphere welding processes. These quality control efforts led to PNC's development of processes enabling the capsules to be filled with sodium to nearly 100%. As a result, the accuracy of the temperature dispersion in the out-pile calibration test was improved from +/-10degC to +/-5degC. In 1996 the new domestically fabricated TED was attached to a JOYO irradiation rig. In March of 1997, irradiation of the rig was started on the 30th duty cycle operation, and should be

  5. A robust anomaly based change detection method for time-series remote sensing images

    Science.gov (United States)

    Shoujing, Yin; Qiao, Wang; Chuanqing, Wu; Xiaoling, Chen; Wandong, Ma; Huiqin, Mao

    2014-03-01

    Time-series remote sensing images record changes happening on the earth surface, which include not only abnormal changes like human activities and emergencies (e.g. fire, drought, insect pest etc.), but also changes caused by vegetation phenology and climate changes. Yet, challenges occur in analyzing global environment changes and even the internal forces. This paper proposes a robust Anomaly Based Change Detection method (ABCD) for time-series images analysis by detecting abnormal points in data sets, which do not need to follow a normal distribution. With ABCD we can detect when and where changes occur, which is the prerequisite condition of global change studies. ABCD was tested initially with 10-day SPOT VGT NDVI (Normalized Difference Vegetation Index) times series tracking land cover type changes, seasonality and noise, then validated to real data in a large area in Jiangxi, south of China. Initial results show that ABCD can precisely detect spatial and temporal changes from long time series images rapidly.

  6. Practical method for generation expansion planning based on the dynamic programming. Dynamic programming ni motozuku dengen keikaku shuho

    Energy Technology Data Exchange (ETDEWEB)

    Tanabe, R.; Yasuda, K.; Yokoyama, R. (Tokyo Metropolitan Univ., Tokyo (Japan))

    1992-05-20

    To supply cheap, high-reliable and a planty of the electricity is an important task of the electric supply system because the requirement for the electricity is rapidly increased in Japan. In order to solve this problem, the authors of the paper are developing a most suitable practical method based on algorithm, according to which the generation expansion planning is divided into two problems: the optimal generation mix and the optimal generation construction process and the two problems are solved respectively. But there are some bad points in the method, for example, there are only approximative practical restriction of the capacity of single machine and the existing electric supply etc., because the optimal generation mix is determined on the basis of non-linear planning. So, in the present paper, the electric supply support system is practically constructed while proposing an unified generation expansion planning based on the dynamic programming that is possible to consider these restrictions strictly and the usefullness of the method is inspected. 12 refs., 7 figs., 5 tabs.

  7. Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    Tarikul Islam

    2018-03-01

    Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

  8. A cluster merging method for time series microarray with production values.

    Science.gov (United States)

    Chira, Camelia; Sedano, Javier; Camara, Monica; Prieto, Carlos; Villar, Jose R; Corchado, Emilio

    2014-09-01

    A challenging task in time-course microarray data analysis is to cluster genes meaningfully combining the information provided by multiple replicates covering the same key time points. This paper proposes a novel cluster merging method to accomplish this goal obtaining groups with highly correlated genes. The main idea behind the proposed method is to generate a clustering starting from groups created based on individual temporal series (representing different biological replicates measured in the same time points) and merging them by taking into account the frequency by which two genes are assembled together in each clustering. The gene groups at the level of individual time series are generated using several shape-based clustering methods. This study is focused on a real-world time series microarray task with the aim to find co-expressed genes related to the production and growth of a certain bacteria. The shape-based clustering methods used at the level of individual time series rely on identifying similar gene expression patterns over time which, in some models, are further matched to the pattern of production/growth. The proposed cluster merging method is able to produce meaningful gene groups which can be naturally ranked by the level of agreement on the clustering among individual time series. The list of clusters and genes is further sorted based on the information correlation coefficient and new problem-specific relevant measures. Computational experiments and results of the cluster merging method are analyzed from a biological perspective and further compared with the clustering generated based on the mean value of time series and the same shape-based algorithm.

  9. Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam-Carlitz I polynomials

    International Nuclear Information System (INIS)

    Doha, E H; Ahmed, H M

    2005-01-01

    Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives D p q f(x), and for the moments x l D p q f(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described

  10. R/S method for evaluation of pollutant time series in environmental quality assessment

    Directory of Open Access Journals (Sweden)

    Bu Quanmin

    2008-12-01

    Full Text Available The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods: the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.

  11. An evaluation of dynamic mutuality measurements and methods in cyclic time series

    Science.gov (United States)

    Xia, Xiaohua; Huang, Guitian; Duan, Na

    2010-12-01

    Several measurements and techniques have been developed to detect dynamic mutuality and synchronicity of time series in econometrics. This study aims to compare the performances of five methods, i.e., linear regression, dynamic correlation, Markov switching models, concordance index and recurrence quantification analysis, through numerical simulations. We evaluate the abilities of these methods to capture structure changing and cyclicity in time series and the findings of this paper would offer guidance to both academic and empirical researchers. Illustration examples are also provided to demonstrate the subtle differences of these techniques.

  12. Higher-Order Scheme-Independent Series Expansions of $γ_{\\barψψ,IR}$ and $β'_{IR}$ in Conformal Field Theories

    DEFF Research Database (Denmark)

    Ryttov, Thomas A.; Shrock, Robert

    2017-01-01

    We study a vectorial asymptotically free gauge theory, with gauge group $G$ and $N_f$ massless fermions in a representation $R$ of this group, that exhibits an infrared (IR) zero in its beta function, $\\beta$, at the coupling $\\alpha=\\alpha_{IR}$ in the non-Abelian Coulomb phase. For general $G......_f$-dependent expansion variable. These are the highest orders to which these expansions have been calculated. We apply these general results to theories with $G={\\rm SU}(N_c)$ and $R$ equal to the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. It is shown that for all...

  13. R package imputeTestbench to compare imputations methods for univariate time series

    OpenAIRE

    Bokde, Neeraj; Kulat, Kishore; Beck, Marcus W; Asencio-Cortés, Gualberto

    2016-01-01

    This paper describes the R package imputeTestbench that provides a testbench for comparing imputation methods for missing data in univariate time series. The imputeTestbench package can be used to simulate the amount and type of missing data in a complete dataset and compare filled data using different imputation methods. The user has the option to simulate missing data by removing observations completely at random or in blocks of different sizes. Several default imputation methods are includ...

  14. Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method

    Directory of Open Access Journals (Sweden)

    Seçil YALAZ

    2016-10-01

    Full Text Available Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT and to estimate future an equation has created by applying fuzzy least square regression (FLSR method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.

  15. Large J expansion in ABJM theory revisited.

    Science.gov (United States)

    Dimov, H; Mladenov, S; Rashkov, R C

    Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of the AdS/CFT correspondence. On the string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of a large-charge expansion of the dispersion relations for simple semiclassical strings in an [Formula: see text] background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three methods look different, power series expansions show their consistency.

  16. Extended Krenciglowa-Kuo method and perturbation expansion of Q-box

    International Nuclear Information System (INIS)

    Shimizu, Genki; Otsuka, Takaharu; Takayanagi, Kazuo

    2015-01-01

    The Extended Krenciglowa-Kuo (EKK) method is a microscopic method to construct the energy-independent effective Hamiltonian H eff ; provided with an exact Q-box of the system, we can show which eigenstates are described by H eff given by the EKK method. In actual calculations, however, we can calculate the Q-box only up to a finite order in the perturbation theory. In this work, we examine the EKK method with the approximate Q-box, and show that the perturbative calculation of the Q-box does not harm the convergence properties of the EKK iterative method. (author)

  17. Chemical graph-theoretic cluster expansions

    International Nuclear Information System (INIS)

    Klein, D.J.

    1986-01-01

    A general computationally amenable chemico-graph-theoretic cluster expansion method is suggested as a paradigm for incorporation of chemical structure concepts in a systematic manner. The cluster expansion approach is presented in a formalism general enough to cover a variety of empirical, semiempirical, and even ab initio applications. Formally such approaches for the utilization of chemical structure-related concepts may be viewed as discrete analogues of Taylor series expansions. The efficacy of the chemical structure concepts then is simply bound up in the rate of convergence of the cluster expansions. In many empirical applications, e.g., boiling points, chromatographic separation coefficients, and biological activities, this rate of convergence has been observed to be quite rapid. More note will be made here of quantum chemical applications. Relations to questions concerning size extensivity of energies and size consistency of wave functions are addressed

  18. Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

    Science.gov (United States)

    Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

    2013-01-01

    The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

  19. Accuracy and Sensitivity of a Method of Jump Detection, Evaluated by Simulated Time Series

    Czech Academy of Sciences Publication Activity Database

    Chapanov, Y.; Ron, Cyril; Vondrák, Jan

    2017-01-01

    Roč. 14, č. 1 (2017), s. 73-82 ISSN 1214-9705 R&D Projects: GA ČR GA13-15943S Institutional support: RVO:67985815 Keywords : time series * data jump detection * high-sensitive method Subject RIV: DE - Earth Magnetism, Geodesy, Geography OBOR OECD: Physical geography Impact factor: 0.699, year: 2016

  20. Series elasticity of the human triceps surae muscle : Measurement by controlled-release vs. resonance methods.

    NARCIS (Netherlands)

    Hof, AL; Boom, H; Robinson, C; Rutten, W; Neuman, M; Wijkstra, H

    1997-01-01

    With a newly developed Controlled-Release Ergometer the complete characteristic of the series elastic component can be measured in human muscles. Previous estimates were based on the resonance method: muscle elasticity was assessed from the resonance frequency of the muscle elasticity connected to a

  1. (G /G) -expansion method and its application to Sharma–Tasso ...

    Indian Academy of Sciences (India)

    Liaoning 110034, People's Republic of China. ∗. Corresponding ... The validity and advantage of the proposed method are illustrated by its ... competitive point of this method is that there is no need to set a restriction to the function fitted for G.

  2. The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2014-09-01

    Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.

  3. Turbulence time series data hole filling using Karhunen-Loeve and ARIMA methods

    International Nuclear Information System (INIS)

    Chang, M P J L; Nazari, H; Font, C O; Gilbreath, G C; Oh, E

    2007-01-01

    Measurements of optical turbulence time series data using unattended instruments over long time intervals inevitably lead to data drop-outs or degraded signals. We present a comparison of methods using both Principal Component Analysis, which is also known as the Karhunen-Loeve decomposition, and ARIMA that seek to correct for these event-induced and mechanically-induced signal drop-outs and degradations. We report on the quality of the correction by examining the Intrinsic Mode Functions generated by Empirical Mode Decomposition. The data studied are optical turbulence parameter time series from a commercial long path length optical anemometer/scintillometer, measured over several hundred metres in outdoor environments

  4. Image reconstruction method for electrical capacitance tomography based on the combined series and parallel normalization model

    International Nuclear Information System (INIS)

    Dong, Xiangyuan; Guo, Shuqing

    2008-01-01

    In this paper, a novel image reconstruction method for electrical capacitance tomography (ECT) based on the combined series and parallel model is presented. A regularization technique is used to obtain a stabilized solution of the inverse problem. Also, the adaptive coefficient of the combined model is deduced by numerical optimization. Simulation results indicate that it can produce higher quality images when compared to the algorithm based on the parallel or series models for the cases tested in this paper. It provides a new algorithm for ECT application

  5. Relativistic rise measurement by cluster counting method in time expansion chamber

    International Nuclear Information System (INIS)

    Rehak, P.; Walenta, A.H.

    1979-10-01

    A new approach to the measurement of the ionization energy loss for the charged particle identification in the region of the relativistic rise was tested experimentally. The method consists of determining in a special drift chamber (TEC) the number of clusters of the primary ionization. The method gives almost the full relativistic rise and narrower landau distribution. The consequences for a practical detector are discussed

  6. New significance test methods for Fourier analysis of geophysical time series

    Directory of Open Access Journals (Sweden)

    Z. Zhang

    2011-09-01

    Full Text Available When one applies the discrete Fourier transform to analyze finite-length time series, discontinuities at the data boundaries will distort its Fourier power spectrum. In this paper, based on a rigid statistics framework, we present a new significance test method which can extract the intrinsic feature of a geophysical time series very well. We show the difference in significance level compared with traditional Fourier tests by analyzing the Arctic Oscillation (AO and the Nino3.4 time series. In the AO, we find significant peaks at about 2.8, 4.3, and 5.7 yr periods and in Nino3.4 at about 12 yr period in tests against red noise. These peaks are not significant in traditional tests.

  7. Divergent series, summability and resurgence III resurgent methods and the first Painlevé equation

    CERN Document Server

    Delabaere, Eric

    2016-01-01

    The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1. .

  8. Simulation of transients with space-dependent feedback by coarse mesh flux expansion method

    International Nuclear Information System (INIS)

    Langenbuch, S.; Maurer, W.; Werner, W.

    1975-01-01

    For the simulation of the time-dependent behaviour of large LWR-cores, even the most efficient Finite-Difference (FD) methods require a prohibitive amount of computing time in order to achieve results of acceptable accuracy. Static CM-solutions computed with a mesh-size corresponding to the fuel element structure (about 20 cm) are at least as accurate as FD-solutions computed with about 5 cm mesh-size. For 3d-calculations this results in a reduction of storage requirements by a factor 60 and of computing costs by a factor 40, relative to FD-methods. These results have been obtained for pure neutronic calculations, where feedback is not taken into account. In this paper it is demonstrated that the method retains its accuracy also in kinetic calculations, even in the presence of strong space dependent feedback. (orig./RW) [de

  9. Predictability of monthly temperature and precipitation using automatic time series forecasting methods

    Science.gov (United States)

    Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris

    2018-02-01

    We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naïve one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naïve and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.

  10. Action First--Understanding Follows: An Expansion of Skills-Based Training Using Action Method.

    Science.gov (United States)

    Martin, Colin

    1988-01-01

    This paper discusses the concept of training trainers in the skills they need to perform competently as trainers and how they follow their skills mastery with discussion on their new theoretical insight. Moreno's action method (psychodrama, sociodrama, sociometry, and role training) is the model used. (JOW)

  11. Electromagnetic modelling of large complex 3-D structures with LEGO and the eigencurrent expansion method

    NARCIS (Netherlands)

    Lancellotti, V.; Hon, de B.P.; Tijhuis, A.G.

    2009-01-01

    Linear embedding via Green's operators (LEGO) is a computational method in which the multiple scattering between adjacent objects - forming a large composite structure - is determined through the interaction of simple-shaped building domains, whose electromagnetic (EM) behavior is accounted for by

  12. A Multipixel Time Series Analysis Method Accounting for Ground Motion, Atmospheric Noise, and Orbital Errors

    Science.gov (United States)

    Jolivet, R.; Simons, M.

    2018-02-01

    Interferometric synthetic aperture radar time series methods aim to reconstruct time-dependent ground displacements over large areas from sets of interferograms in order to detect transient, periodic, or small-amplitude deformation. Because of computational limitations, most existing methods consider each pixel independently, ignoring important spatial covariances between observations. We describe a framework to reconstruct time series of ground deformation while considering all pixels simultaneously, allowing us to account for spatial covariances, imprecise orbits, and residual atmospheric perturbations. We describe spatial covariances by an exponential decay function dependent of pixel-to-pixel distance. We approximate the impact of imprecise orbit information and residual long-wavelength atmosphere as a low-order polynomial function. Tests on synthetic data illustrate the importance of incorporating full covariances between pixels in order to avoid biased parameter reconstruction. An example of application to the northern Chilean subduction zone highlights the potential of this method.

  13. Adsorption of ionic surfactants at microscopic air-water interfaces using the micropipette interfacial area-expansion method

    DEFF Research Database (Denmark)

    Kinoshita, Koji; Parra, Elisa; Needham, David

    2017-01-01

    The dynamic adsorption of ionic surfactants at air-water interfaces have been less-well studied than that of the simpler non-ionics since experimental limitations on dynamic surface tension (DST) measurements create inconsistencies in their kinetic analysis. Using our newly designed "Micropipette...... interfacial area-expansion method", we have measured and evaluated both equilibrium and dynamic adsorption of a well-known anionic surfactant, sodium dodecyl sulphate (SDS), in the absence or presence of 100mM NaCl. Our focus was to determine if and to what extent the inclusion of a new correction parameter...... for the "ideal ionic activity", A±i, can renormalize both equilibrium and dynamic surface tension measurements and provide better estimates of the diffusion coefficient of ionic surfactants in aqueous media obtained from electroneutral models, namely extended Frumkin isotherm and Ward-Tordai adsorption models...

  14. Year Ahead Demand Forecast of City Natural Gas Using Seasonal Time Series Methods

    Directory of Open Access Journals (Sweden)

    Mustafa Akpinar

    2016-09-01

    Full Text Available Consumption of natural gas, a major clean energy source, increases as energy demand increases. We studied specifically the Turkish natural gas market. Turkey’s natural gas consumption increased as well in parallel with the world‘s over the last decade. This consumption growth in Turkey has led to the formation of a market structure for the natural gas industry. This significant increase requires additional investments since a rise in consumption capacity is expected. One of the reasons for the consumption increase is the user-based natural gas consumption influence. This effect yields imbalances in demand forecasts and if the error rates are out of bounds, penalties may occur. In this paper, three univariate statistical methods, which have not been previously investigated for mid-term year-ahead monthly natural gas forecasting, are used to forecast natural gas demand in Turkey’s Sakarya province. Residential and low-consumption commercial data is used, which may contain seasonality. The goal of this paper is minimizing more or less gas tractions on mid-term consumption while improving the accuracy of demand forecasting. In forecasting models, seasonality and single variable impacts reinforce forecasts. This paper studies time series decomposition, Holt-Winters exponential smoothing and autoregressive integrated moving average (ARIMA methods. Here, 2011–2014 monthly data were prepared and divided into two series. The first series is 2011–2013 monthly data used for finding seasonal effects and model requirements. The second series is 2014 monthly data used for forecasting. For the ARIMA method, a stationary series was prepared and transformation process prior to forecasting was done. Forecasting results confirmed that as the computation complexity of the model increases, forecasting accuracy increases with lower error rates. Also, forecasting errors and the coefficients of determination values give more consistent results. Consequently

  15. Development of a code in three-dimensional cylindrical geometry based on analytic function expansion nodal (AFEN) method

    International Nuclear Information System (INIS)

    Lee, Joo Hee

    2006-02-01

    There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)

  16. Off-diagonal expansion quantum Monte Carlo.

    Science.gov (United States)

    Albash, Tameem; Wagenbreth, Gene; Hen, Itay

    2017-12-01

    We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

  17. Generalized separable expansion method of the two-body and the three-body scattering amplitudes

    International Nuclear Information System (INIS)

    Oryu, S.; Ishihara, T.

    1976-01-01

    A systematic method is proposed for obtaining new N-rank separable amplitudes of the two-body and the three-body equations. First of all, the authors start from the Amado equation which is modified from the three-body Faddeev equation by using the two-body Yamaguchi potential for the nucleon-nucleon interaction. It is well known that the Amado equation can be integrated on the real axis because the kernel has a logarithmic cut on the real axis. However, a separable three-body form factor which is regular on the real axis except for the cut has been found. (Auth.)

  18. Univariate Time Series Prediction of Solar Power Using a Hybrid Wavelet-ARMA-NARX Prediction Method

    Energy Technology Data Exchange (ETDEWEB)

    Nazaripouya, Hamidreza; Wang, Yubo; Chu, Chi-Cheng; Pota, Hemanshu; Gadh, Rajit

    2016-05-02

    This paper proposes a new hybrid method for super short-term solar power prediction. Solar output power usually has a complex, nonstationary, and nonlinear characteristic due to intermittent and time varying behavior of solar radiance. In addition, solar power dynamics is fast and is inertia less. An accurate super short-time prediction is required to compensate for the fluctuations and reduce the impact of solar power penetration on the power system. The objective is to predict one step-ahead solar power generation based only on historical solar power time series data. The proposed method incorporates discrete wavelet transform (DWT), Auto-Regressive Moving Average (ARMA) models, and Recurrent Neural Networks (RNN), while the RNN architecture is based on Nonlinear Auto-Regressive models with eXogenous inputs (NARX). The wavelet transform is utilized to decompose the solar power time series into a set of richer-behaved forming series for prediction. ARMA model is employed as a linear predictor while NARX is used as a nonlinear pattern recognition tool to estimate and compensate the error of wavelet-ARMA prediction. The proposed method is applied to the data captured from UCLA solar PV panels and the results are compared with some of the common and most recent solar power prediction methods. The results validate the effectiveness of the proposed approach and show a considerable improvement in the prediction precision.

  19. Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

    Science.gov (United States)

    Dakos, Vasilis; Carpenter, Stephen R.; Brock, William A.; Ellison, Aaron M.; Guttal, Vishwesha; Ives, Anthony R.; Kéfi, Sonia; Livina, Valerie; Seekell, David A.; van Nes, Egbert H.; Scheffer, Marten

    2012-01-01

    Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data. PMID:22815897

  20. An energy recondensation method using the discrete generalized multigroup energy expansion theory

    International Nuclear Information System (INIS)

    Zhu Lei; Forget, Benoit

    2011-01-01

    Highlights: → Discrete-generalized multigroup method was implemented as a recondensation scheme. → Coarse group cross-sections were recondensed from core-level solution. → Neighboring effect of reflector and MOX bundle was improved. → Methodology was shown to be fully consistent when a flat angular flux approximation is used. - Abstract: In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially.

  1. A maximal chromatic expansion method of mapping multichannel imagery into color space. [North Dakota

    Science.gov (United States)

    Juday, R. D.; Abotteen, R. A. (Principal Investigator)

    1978-01-01

    The author has identified the following significant results. A color film generation method that maximally expands the chromaticity and aligns Kauth brightness with the gray axis was presented. In comparison with the current LACIE film product, the new color film product has more contrast and more colors and appears to be brighter. The field boundaries in the new product were more pronounced than in the current LACIE product. The speckle effect was one problem in the new product. The yellowness speckle can be treated using an equation. This equation can be used to eliminate any speckle introduced by the greenness. This product leads logically toward another that will employ quantitative colorimetry which will account for some of the eye's perception of color stimuli.

  2. The effects of micro-implant assisted rapid palatal expansion (MARPE) on the nasomaxillary complex--a finite element method (FEM) analysis.

    Science.gov (United States)

    MacGinnis, Matt; Chu, Howard; Youssef, George; Wu, Kimberley W; Machado, Andre Wilson; Moon, Won

    2014-08-29

    Orthodontic palatal expansion appliances have been widely used with satisfactory and, most often, predictable clinical results. Recently, clinicians have successfully utilized micro-implants with palatal expander designs to work as anchors to the palate to achieve more efficient skeletal expansion and to decrease undesired dental effects. The purpose of the study was to use finite element method (FEM) to determine the stress distribution and displacement within the craniofacial complex when simulated conventional and micro-implant-assisted rapid palatal expansion (MARPE) expansion forces are applied to the maxilla. The simulated stress distribution produced within the palate and maxillary buttresses in addition to the displacement and rotation of the maxilla could then be analyzed to determine if micro-implants aid in skeletal expansion. A three-dimensional (3D) mesh model of the cranium with associated maxillary sutures was developed using computed tomography (CT) images and Mimics modeling software. To compare transverse expansion stresses in rapid palatal expansion (RPE) and MARPE, expansion forces were distributed to differing points on the maxilla and evaluated with ANSYS simulation software. The stresses distributed from forces applied to the maxillary teeth are distributed mainly along the trajectories of the three maxillary buttresses. In comparison, the MARPE showed tension and compression directed to the palate, while showing less rotation, and tipping of the maxillary complex. In addition, the conventional hyrax displayed a rotation of the maxilla around the teeth as opposed to the midpalatal suture of the MARPE. This data suggests that the MARPE causes the maxilla to bend laterally, while preventing unwanted rotation of the complex. In conclusion, the MARPE may be beneficial for hyperdivergent patients, or those that have already experienced closure of the midpalatal suture, who require palatal expansion and would worsen from buccal tipping of the teeth

  3. Approximate k-NN delta test minimization method using genetic algorithms: Application to time series

    CERN Document Server

    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 ...

  4. Analytical Method of Malculation of the Current and Torque a Reluctance Stepper Motor via Fourier Series

    Directory of Open Access Journals (Sweden)

    Pavel Zaskalicky

    2008-01-01

    Full Text Available Reluctance stepper motors are becoming to be very attractive transducer to conversion of electric signal to the mechanical position. Due to its simple construction is reluctance machine considered a very reliable machine which not requiring any maintenance. Present paper proposes a mathematical method of an analytical calculus of a phase current and electromagnetic torque of the motor via Fourier series. Saturation effect and winding reluctance are neglected.

  5. Forecasting with quantitative methods the impact of special events in time series

    OpenAIRE

    Nikolopoulos, Konstantinos

    2010-01-01

    Abstract Quantitative methods are very successful for producing baseline forecasts of time series; however these models fail to forecast neither the timing nor the impact of special events such as promotions or strikes. In most of the cases the timing of such events is not known so they are usually referred as shocks (economics) or special events (forecasting). Sometimes the timing of such events is known a priori (i.e. a future promotion); but even then the impact of the forthcom...

  6. Detecting method for crude oil price fluctuation mechanism under different periodic time series

    International Nuclear Information System (INIS)

    Gao, Xiangyun; Fang, Wei; An, Feng; Wang, Yue

    2017-01-01

    Highlights: • We proposed the concept of autoregressive modes to indicate the fluctuation patterns. • We constructed transmission networks for studying the fluctuation mechanism. • There are different fluctuation mechanism under different periodic time series. • Only a few types of autoregressive modes control the fluctuations in crude oil price. • There are cluster effects during the fluctuation mechanism of autoregressive modes. - Abstract: Current existing literatures can characterize the long-term fluctuation of crude oil price time series, however, it is difficult to detect the fluctuation mechanism specifically under short term. Because each fluctuation pattern for one short period contained in a long-term crude oil price time series have dynamic characteristics of diversity; in other words, there exhibit various fluctuation patterns in different short periods and transmit to each other, which reflects the reputedly complicate and chaotic oil market. Thus, we proposed an incorporated method to detect the fluctuation mechanism, which is the evolution of the different fluctuation patterns over time from the complex network perspective. We divided crude oil price time series into segments using sliding time windows, and defined autoregressive modes based on regression models to indicate the fluctuation patterns of each segment. Hence, the transmissions between different types of autoregressive modes over time form a transmission network that contains rich dynamic information. We then capture transmission characteristics of autoregressive modes under different periodic time series through the structure features of the transmission networks. The results indicate that there are various autoregressive modes with significantly different statistical characteristics under different periodic time series. However, only a few types of autoregressive modes and transmission patterns play a major role in the fluctuation mechanism of the crude oil price, and these

  7. Comparison of time-series registration methods in breast dynamic infrared imaging

    Science.gov (United States)

    Riyahi-Alam, S.; Agostini, V.; Molinari, F.; Knaflitz, M.

    2015-03-01

    Automated motion reduction in dynamic infrared imaging is on demand in clinical applications, since movement disarranges time-temperature series of each pixel, thus originating thermal artifacts that might bias the clinical decision. All previously proposed registration methods are feature based algorithms requiring manual intervention. The aim of this work is to optimize the registration strategy specifically for Breast Dynamic Infrared Imaging and to make it user-independent. We implemented and evaluated 3 different 3D time-series registration methods: 1. Linear affine, 2. Non-linear Bspline, 3. Demons applied to 12 datasets of healthy breast thermal images. The results are evaluated through normalized mutual information with average values of 0.70 ±0.03, 0.74 ±0.03 and 0.81 ±0.09 (out of 1) for Affine, Bspline and Demons registration, respectively, as well as breast boundary overlap and Jacobian determinant of the deformation field. The statistical analysis of the results showed that symmetric diffeomorphic Demons' registration method outperforms also with the best breast alignment and non-negative Jacobian values which guarantee image similarity and anatomical consistency of the transformation, due to homologous forces enforcing the pixel geometric disparities to be shortened on all the frames. We propose Demons' registration as an effective technique for time-series dynamic infrared registration, to stabilize the local temperature oscillation.

  8. Neural networks and traditional time series methods: a synergistic combination in state economic forecasts.

    Science.gov (United States)

    Hansen, J V; Nelson, R D

    1997-01-01

    Ever since the initial planning for the 1997 Utah legislative session, neural-network forecasting techniques have provided valuable insights for analysts forecasting tax revenues. These revenue estimates are critically important since agency budgets, support for education, and improvements to infrastructure all depend on their accuracy. Underforecasting generates windfalls that concern taxpayers, whereas overforecasting produces budget shortfalls that cause inadequately funded commitments. The pattern finding ability of neural networks gives insightful and alternative views of the seasonal and cyclical components commonly found in economic time series data. Two applications of neural networks to revenue forecasting clearly demonstrate how these models complement traditional time series techniques. In the first, preoccupation with a potential downturn in the economy distracts analysis based on traditional time series methods so that it overlooks an emerging new phenomenon in the data. In this case, neural networks identify the new pattern that then allows modification of the time series models and finally gives more accurate forecasts. In the second application, data structure found by traditional statistical tools allows analysts to provide neural networks with important information that the networks then use to create more accurate models. In summary, for the Utah revenue outlook, the insights that result from a portfolio of forecasts that includes neural networks exceeds the understanding generated from strictly statistical forecasting techniques. In this case, the synergy clearly results in the whole of the portfolio of forecasts being more accurate than the sum of the individual parts.

  9. Travelling Wave Solutions of Coupled Burger’s Equations of Time-Space Fractional Order by Novel (Gʹ/G-Expansion Method

    Directory of Open Access Journals (Sweden)

    Rashida Hussain

    2017-04-01

    Full Text Available In this paper, Novel (Gʹ/G-expansion method is used to find new generalized exact travelling wave solutions of fractional order coupled Burger’s equations in terms of trigonometric functions, rational functions and hyperbolic functions with arbitrary parameters. For the conversion of the partial differential equation to the ordinary differential equation, complex transformation method is used. Novel (Gʹ/G-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear equations. Moreover, for the representation of these exact solutions we have plotted graphs for different values of parameters which were in travelling waveform.

  10. The Forecasting of Labour Force Participation and the Unemployment Rate in Poland and Turkey Using Fuzzy Time Series Methods

    Directory of Open Access Journals (Sweden)

    Yolcu Ufuk

    2016-06-01

    Full Text Available Fuzzy time series methods based on the fuzzy set theory proposed by Zadeh (1965 was first introduced by Song and Chissom (1993. Since fuzzy time series methods do not have the assumptions that traditional time series do and have effective forecasting performance, the interest on fuzzy time series approaches is increasing rapidly. Fuzzy time series methods have been used in almost all areas, such as environmental science, economy and finance. The concepts of labour force participation and unemployment have great importance in terms of both the economy and sociology of countries. For this reason there are many studies on their forecasting. In this study, we aim to forecast the labour force participation and unemployment rate in Poland and Turkey using different fuzzy time series methods.

  11. Multidimensional scaling analysis of financial time series based on modified cross-sample entropy methods

    Science.gov (United States)

    He, Jiayi; Shang, Pengjian; Xiong, Hui

    2018-06-01

    Stocks, as the concrete manifestation of financial time series with plenty of potential information, are often used in the study of financial time series. In this paper, we utilize the stock data to recognize their patterns through out the dissimilarity matrix based on modified cross-sample entropy, then three-dimensional perceptual maps of the results are provided through multidimensional scaling method. Two modified multidimensional scaling methods are proposed in this paper, that is, multidimensional scaling based on Kronecker-delta cross-sample entropy (MDS-KCSE) and multidimensional scaling based on permutation cross-sample entropy (MDS-PCSE). These two methods use Kronecker-delta based cross-sample entropy and permutation based cross-sample entropy to replace the distance or dissimilarity measurement in classical multidimensional scaling (MDS). Multidimensional scaling based on Chebyshev distance (MDSC) is employed to provide a reference for comparisons. Our analysis reveals a clear clustering both in synthetic data and 18 indices from diverse stock markets. It implies that time series generated by the same model are easier to have similar irregularity than others, and the difference in the stock index, which is caused by the country or region and the different financial policies, can reflect the irregularity in the data. In the synthetic data experiments, not only the time series generated by different models can be distinguished, the one generated under different parameters of the same model can also be detected. In the financial data experiment, the stock indices are clearly divided into five groups. Through analysis, we find that they correspond to five regions, respectively, that is, Europe, North America, South America, Asian-Pacific (with the exception of mainland China), mainland China and Russia. The results also demonstrate that MDS-KCSE and MDS-PCSE provide more effective divisions in experiments than MDSC.

  12. Thermal expansion

    International Nuclear Information System (INIS)

    Yun, Y.

    2015-01-01

    Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)

  13. A Two-Dimensional Solar Tracking Stationary Guidance Method Based on Feature-Based Time Series

    Directory of Open Access Journals (Sweden)

    Keke Zhang

    2018-01-01

    Full Text Available The amount of satellite energy acquired has a direct impact on operational capacities of the satellite. As for practical high functional density microsatellites, solar tracking guidance design of solar panels plays an extremely important role. Targeted at stationary tracking problems incurred in a new system that utilizes panels mounted in the two-dimensional turntable to acquire energies to the greatest extent, a two-dimensional solar tracking stationary guidance method based on feature-based time series was proposed under the constraint of limited satellite attitude coupling control capability. By analyzing solar vector variation characteristics within an orbit period and solar vector changes within the whole life cycle, such a method could be adopted to establish a two-dimensional solar tracking guidance model based on the feature-based time series to realize automatic switching of feature-based time series and stationary guidance under the circumstance of different β angles and the maximum angular velocity control, which was applicable to near-earth orbits of all orbital inclination. It was employed to design a two-dimensional solar tracking stationary guidance system, and a mathematical simulation for guidance performance was carried out in diverse conditions under the background of in-orbit application. The simulation results show that the solar tracking accuracy of two-dimensional stationary guidance reaches 10∘ and below under the integrated constraints, which meet engineering application requirements.

  14. The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

    Science.gov (United States)

    Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef

    2013-01-01

    Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

  15. Multi-Scale Entropy Analysis as a Method for Time-Series Analysis of Climate Data

    Directory of Open Access Journals (Sweden)

    Heiko Balzter

    2015-03-01

    Full Text Available Evidence is mounting that the temporal dynamics of the climate system are changing at the same time as the average global temperature is increasing due to multiple climate forcings. A large number of extreme weather events such as prolonged cold spells, heatwaves, droughts and floods have been recorded around the world in the past 10 years. Such changes in the temporal scaling behaviour of climate time-series data can be difficult to detect. While there are easy and direct ways of analysing climate data by calculating the means and variances for different levels of temporal aggregation, these methods can miss more subtle changes in their dynamics. This paper describes multi-scale entropy (MSE analysis as a tool to study climate time-series data and to identify temporal scales of variability and their change over time in climate time-series. MSE estimates the sample entropy of the time-series after coarse-graining at different temporal scales. An application of MSE to Central European, variance-adjusted, mean monthly air temperature anomalies (CRUTEM4v is provided. The results show that the temporal scales of the current climate (1960–2014 are different from the long-term average (1850–1960. For temporal scale factors longer than 12 months, the sample entropy increased markedly compared to the long-term record. Such an increase can be explained by systems theory with greater complexity in the regional temperature data. From 1961 the patterns of monthly air temperatures are less regular at time-scales greater than 12 months than in the earlier time period. This finding suggests that, at these inter-annual time scales, the temperature variability has become less predictable than in the past. It is possible that climate system feedbacks are expressed in altered temporal scales of the European temperature time-series data. A comparison with the variance and Shannon entropy shows that MSE analysis can provide additional information on the

  16. An empirical method for approximating stream baseflow time series using groundwater table fluctuations

    Science.gov (United States)

    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.

  17. Summation of series

    CERN Document Server

    Jolley, LB W

    2004-01-01

    Over 1,100 common series, all grouped for easy reference. Arranged by category, these series include arithmetical and geometrical progressions, powers and products of natural numbers, figurate and polygonal numbers, inverse natural numbers, exponential and logarithmic series, binomials, simple inverse products, factorials, trigonometrical and hyperbolic expansions, and additional series. 1961 edition.

  18. Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

    Science.gov (United States)

    Alam, Md Nur; Akbar, M Ali

    2013-01-01

    The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

  19. A Fast Multi-layer Subnetwork Connection Method for Time Series InSAR Technique

    Directory of Open Access Journals (Sweden)

    WU Hong'an

    2016-10-01

    Full Text Available Nowadays, times series interferometric synthetic aperture radar (InSAR technique has been widely used in ground deformation monitoring, especially in urban areas where lots of stable point targets can be detected. However, in standard time series InSAR technique, affected by atmospheric correlation distance and the threshold of linear model coherence, the Delaunay triangulation for connecting point targets can be easily separated into many discontinuous subnetworks. Thus it is difficult to retrieve ground deformation in non-urban areas. In order to monitor ground deformation in large areas efficiently, a novel multi-layer subnetwork connection (MLSC method is proposed for connecting all subnetworks. The advantage of the method is that it can quickly reduce the number of subnetworks with valid edges layer-by-layer. This method is compared with the existing complex network connecting mehod. The experimental results demonstrate that the data processing time of the proposed method is only 32.56% of the latter one.

  20. A Time-Series Water Level Forecasting Model Based on Imputation and Variable Selection Method.

    Science.gov (United States)

    Yang, Jun-He; Cheng, Ching-Hsue; Chan, Chia-Pan

    2017-01-01

    Reservoirs are important for households and impact the national economy. This paper proposed a time-series forecasting model based on estimating a missing value followed by variable selection to forecast the reservoir's water level. This study collected data from the Taiwan Shimen Reservoir as well as daily atmospheric data from 2008 to 2015. The two datasets are concatenated into an integrated dataset based on ordering of the data as a research dataset. The proposed time-series forecasting model summarily has three foci. First, this study uses five imputation methods to directly delete the missing value. Second, we identified the key variable via factor analysis and then deleted the unimportant variables sequentially via the variable selection method. Finally, the proposed model uses a Random Forest to build the forecasting model of the reservoir's water level. This was done to compare with the listing method under the forecasting error. These experimental results indicate that the Random Forest forecasting model when applied to variable selection with full variables has better forecasting performance than the listing model. In addition, this experiment shows that the proposed variable selection can help determine five forecast methods used here to improve the forecasting capability.

  1. A Time-Series Water Level Forecasting Model Based on Imputation and Variable Selection Method

    Directory of Open Access Journals (Sweden)

    Jun-He Yang

    2017-01-01

    Full Text Available Reservoirs are important for households and impact the national economy. This paper proposed a time-series forecasting model based on estimating a missing value followed by variable selection to forecast the reservoir’s water level. This study collected data from the Taiwan Shimen Reservoir as well as daily atmospheric data from 2008 to 2015. The two datasets are concatenated into an integrated dataset based on ordering of the data as a research dataset. The proposed time-series forecasting model summarily has three foci. First, this study uses five imputation methods to directly delete the missing value. Second, we identified the key variable via factor analysis and then deleted the unimportant variables sequentially via the variable selection method. Finally, the proposed model uses a Random Forest to build the forecasting model of the reservoir’s water level. This was done to compare with the listing method under the forecasting error. These experimental results indicate that the Random Forest forecasting model when applied to variable selection with full variables has better forecasting performance than the listing model. In addition, this experiment shows that the proposed variable selection can help determine five forecast methods used here to improve the forecasting capability.

  2. A matched expansion approach to practical self-force calculations

    International Nuclear Information System (INIS)

    Anderson, Warren G; Wiseman, Alan G

    2005-01-01

    We discuss a practical method of computing the self-force on a particle moving through a curved spacetime. This method involves two expansions to calculate the self-force, one arising from the particle's immediate past and the other from the more distant past. The expansion in the immediate past is a covariant Taylor series and can be carried out for all geometries. The more distant expansion is a mode sum, and may be carried out in those cases where the wave equation for the field mediating the self-force admits a mode expansion of the solution. In particular, this method can be used to calculate the gravitational self-force for a particle of mass μ orbiting a black hole of mass M to order μ 2 , provided μ/M << 1. We discuss how to use these two expansions to construct a full self-force, and in particular investigate criteria for matching the two expansions. As with all methods of computing self-forces for particles moving in black hole spacetimes, one encounters considerable technical difficulty in applying this method; nevertheless, it appears that the convergence of each series is good enough that a practical implementation may be plausible

  3. Electric Grid Expansion Planning with High Levels of Variable Generation

    Energy Technology Data Exchange (ETDEWEB)

    Hadley, Stanton W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); You, Shutang [Univ. of Tennessee, Knoxville, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Liu, Yilu [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2016-02-01

    Renewables are taking a large proportion of generation capacity in U.S. power grids. As their randomness has increasing influence on power system operation, it is necessary to consider their impact on system expansion planning. To this end, this project studies the generation and transmission expansion co-optimization problem of the US Eastern Interconnection (EI) power grid with a high wind power penetration rate. In this project, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. This study analyzed a time series creation method to capture the diversity of load and wind power across balancing regions in the EI system. The obtained time series can be easily introduced into the MIP co-optimization problem and then solved robustly through available MIP solvers. Simulation results show that the proposed time series generation method and the expansion co-optimization model and can improve the expansion result significantly after considering the diversity of wind and load across EI regions. The improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare. This study shows that modelling load and wind variations and diversities across balancing regions will produce significantly different expansion result compared with former studies. For example, if wind is modeled in more details (by increasing the number of wind output levels) so that more wind blocks are considered in expansion planning, transmission expansion will be larger and the expansion timing will be earlier. Regarding generation expansion, more wind scenarios will slightly reduce wind generation expansion in the EI system and increase the expansion of other generation such as gas. Also, adopting detailed wind scenarios will reveal that it may be uneconomic to expand transmission networks for transmitting a large amount of wind power through a long distance

  4. Age of Saurashtra miliolites by U-Th decay series methods: possible implications to their origin

    International Nuclear Information System (INIS)

    Hussain, N.; Bhandari, N.; Ramanathan, K.R.; Somayajulu, B.L.K.

    1980-01-01

    The miliolite deposits of Saurashtra have been dated by 234 U, 230 Th, 231 Pa and 14 C methods. Concordant ages of approximately 10 5 years using the U decay series isotopes are obtained which agree with the ages of the coral reefs of Okha-Dwaraka coast suggesting a contemporaneous origin for both. The lower 14 C ages (<= 40,000 years) may be due to a recent influx of seawater or ground water. Quartz and clay minerals together constitute only <= 10% by weight, as such the aeolin characteristics of quartz grains may not be relevant to the origin of the miliolites. (auth.)

  5. The partial duration series method in regional index-flood modeling

    DEFF Research Database (Denmark)

    Madsen, Henrik; Rosbjerg, Dan

    1997-01-01

    A regional index-flood method based on the partial duration series model is introduced. The model comprises the assumptions of a Poisson-distributed number of threshold exceedances and generalized Pareto (GP) distributed peak magnitudes. The regional T-year event estimator is based on a regional...... estimator is superior to the at-site estimator even in extremely heterogenous regions, the performance of the regional estimator being relatively better in regions with a negative shape parameter. When the record length increases, the relative performance of the regional estimator decreases, but it is still...

  6. A SPIRAL-BASED DOWNSCALING METHOD FOR GENERATING 30 M TIME SERIES IMAGE DATA

    Directory of Open Access Journals (Sweden)

    B. Liu

    2017-09-01

    Full Text Available The spatial detail and updating frequency of land cover data are important factors influencing land surface dynamic monitoring applications in high spatial resolution scale. However, the fragmentized patches and seasonal variable of some land cover types (e. g. small crop field, wetland make it labor-intensive and difficult in the generation of land cover data. Utilizing the high spatial resolution multi-temporal image data is a possible solution. Unfortunately, the spatial and temporal resolution of available remote sensing data like Landsat or MODIS datasets can hardly satisfy the minimum mapping unit and frequency of current land cover mapping / updating at the same time. The generation of high resolution time series may be a compromise to cover the shortage in land cover updating process. One of popular way is to downscale multi-temporal MODIS data with other high spatial resolution auxiliary data like Landsat. But the usual manner of downscaling pixel based on a window may lead to the underdetermined problem in heterogeneous area, result in the uncertainty of some high spatial resolution pixels. Therefore, the downscaled multi-temporal data can hardly reach high spatial resolution as Landsat data. A spiral based method was introduced to downscale low spatial and high temporal resolution image data to high spatial and high temporal resolution image data. By the way of searching the similar pixels around the adjacent region based on the spiral, the pixel set was made up in the adjacent region pixel by pixel. The underdetermined problem is prevented to a large extent from solving the linear system when adopting the pixel set constructed. With the help of ordinary least squares, the method inverted the endmember values of linear system. The high spatial resolution image was reconstructed on the basis of high spatial resolution class map and the endmember values band by band. Then, the high spatial resolution time series was formed with these

  7. Regularization of the Fourier series of discontinuous functions by various summation methods

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad, S.S.; Beghi, L. (Padua Univ. (Italy). Seminario Matematico)

    1983-07-01

    In this paper the regularization by various summation methods of the Fourier series of functions containing discontinuities of the first and second kind are studied and the results of the numerical analyses referring to some typical periodic functions are presented. In addition to the Cesaro and Lanczos weightings, a new (i.e. cosine) weighting for accelerating the convergence rate is proposed. A comparison with the results obtained by Garibotti and Massaro with the punctual Pade approximants (PPA) technique in case of a periodic step function is also carried out.

  8. Age of Saurashtra miliolites by U-Th decay series methods: possible implications to their origin

    Energy Technology Data Exchange (ETDEWEB)

    Hussain, N; Bhandari, N; Ramanathan, K R; Somayajulu, B L.K. [Physical Research Lab., Ahmedabad (India)

    1980-03-01

    The miliolite deposits of Saurashtra have been dated by /sup 234/U, /sup 230/Th, /sup 231/Pa and /sup 14/C methods. Concordant ages of approximately 10/sup 5/ years using the U decay series isotopes are obtained which agree with the ages of the coral reefs of Okha-Dwaraka coast suggesting a contemporaneous origin for both. The lower /sup 14/C ages (<= 40,000 years) may be due to a recent influx of seawater or ground water. Quartz and clay minerals together constitute only <= 10% by weight, as such the aeolin characteristics of quartz grains may not be relevant to the origin of the miliolites.

  9. Application of the finite-element method and the eigenmode expansion method to investigate the periodic and spectral characteristic of discrete phase-shift fiber Bragg grating

    Science.gov (United States)

    He, Yue-Jing; Hung, Wei-Chih; Syu, Cheng-Jyun

    2017-12-01

    The finite-element method (FEM) and eigenmode expansion method (EEM) were adopted to analyze the guided modes and spectrum of phase-shift fiber Bragg grating at five phase-shift degrees (including zero, 1/4π, 1/2π, 3/4π, and π). In previous studies on optical fiber grating, conventional coupled-mode theory was crucial. This theory contains abstruse knowledge about physics and complex computational processes, and thus is challenging for users. Therefore, a numerical simulation method was coupled with a simple and rigorous design procedure to help beginners and users to overcome difficulty in entering the field; in addition, graphical simulation results were presented. To reduce the difference between the simulated context and the actual context, a perfectly matched layer and perfectly reflecting boundary were added to the FEM and the EEM. When the FEM was used for grid cutting, the object meshing method and the boundary meshing method proposed in this study were used to effectively enhance computational accuracy and substantially reduce the time required for simulation. In summary, users can use the simulation results in this study to easily and rapidly design an optical fiber communication system and optical sensors with spectral characteristics.

  10. A Simple Method for Determining Thermal Expansion Coefficient of Solid Materials with a Computer-aided Electromagnetic Dilatometer Measuring System

    Directory of Open Access Journals (Sweden)

    Z. EZZOUINE

    2015-07-01

    Full Text Available In this study, we present a newly designed electromagnetic dilatometer with micrometer accuracy for the measurement of the coefficient of thermal expansion of a solid in the 30 °C – 96 °C temperature range .The device has a graphical user interface to view real time data measurement. Iron and copper were subjected to temperature change in the thermal expansion experiment causing them to expand linearly. The voltage delivered in the electromagnetic dilatometer system, which includes the information about linear expansion and temperature change were transferred to a computer via a data acquisition card, presented by a program created in the LabVIEW environment, and the amount of linear expansion was detected in real time. The minimal change in length of the sample that can be resolved is 5µm, which yields the sensitivity comprised between 10-4 µm and 10-5 µm. In order to calibrate the electromagnetic dilatometer, thermal expansion coefficients of copper and Iron have been measured. By this technique, the thermal expansion coefficient can be determined with an acceptable accuracy. The present results appear also to agree well with those reported previously in the literature.

  11. Multipole expansion of acoustical Bessel beams with arbitrary order and location.

    Science.gov (United States)

    Gong, Zhixiong; Marston, Philip L; Li, Wei; Chai, Yingbin

    2017-06-01

    An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

  12. A Statistical Method to Predict Flow Permanence in Dryland Streams from Time Series of Stream Temperature

    Directory of Open Access Journals (Sweden)

    Ivan Arismendi

    2017-12-01

    Full Text Available Intermittent and ephemeral streams represent more than half of the length of the global river network. Dryland freshwater ecosystems are especially vulnerable to changes in human-related water uses as well as shifts in terrestrial climates. Yet, the description and quantification of patterns of flow permanence in these systems is challenging mostly due to difficulties in instrumentation. Here, we took advantage of existing stream temperature datasets in dryland streams in the northwest Great Basin desert, USA, to extract critical information on climate-sensitive patterns of flow permanence. We used a signal detection technique, Hidden Markov Models (HMMs, to extract information from daily time series of stream temperature to diagnose patterns of stream drying. Specifically, we applied HMMs to time series of daily standard deviation (SD of stream temperature (i.e., dry stream channels typically display highly variable daily temperature records compared to wet stream channels between April and August (2015–2016. We used information from paired stream and air temperature data loggers as well as co-located stream temperature data loggers with electrical resistors as confirmatory sources of the timing of stream drying. We expanded our approach to an entire stream network to illustrate the utility of the method to detect patterns of flow permanence over a broader spatial extent. We successfully identified and separated signals characteristic of wet and dry stream conditions and their shifts over time. Most of our study sites within the entire stream network exhibited a single state over the entire season (80%, but a portion of them showed one or more shifts among states (17%. We provide recommendations to use this approach based on a series of simple steps. Our findings illustrate a successful method that can be used to rigorously quantify flow permanence regimes in streams using existing records of stream temperature.

  13. A statistical method to predict flow permanence in dryland streams from time series of stream temperature

    Science.gov (United States)

    Arismendi, Ivan; Dunham, Jason B.; Heck, Michael; Schultz, Luke; Hockman-Wert, David

    2017-01-01

    Intermittent and ephemeral streams represent more than half of the length of the global river network. Dryland freshwater ecosystems are especially vulnerable to changes in human-related water uses as well as shifts in terrestrial climates. Yet, the description and quantification of patterns of flow permanence in these systems is challenging mostly due to difficulties in instrumentation. Here, we took advantage of existing stream temperature datasets in dryland streams in the northwest Great Basin desert, USA, to extract critical information on climate-sensitive patterns of flow permanence. We used a signal detection technique, Hidden Markov Models (HMMs), to extract information from daily time series of stream temperature to diagnose patterns of stream drying. Specifically, we applied HMMs to time series of daily standard deviation (SD) of stream temperature (i.e., dry stream channels typically display highly variable daily temperature records compared to wet stream channels) between April and August (2015–2016). We used information from paired stream and air temperature data loggers as well as co-located stream temperature data loggers with electrical resistors as confirmatory sources of the timing of stream drying. We expanded our approach to an entire stream network to illustrate the utility of the method to detect patterns of flow permanence over a broader spatial extent. We successfully identified and separated signals characteristic of wet and dry stream conditions and their shifts over time. Most of our study sites within the entire stream network exhibited a single state over the entire season (80%), but a portion of them showed one or more shifts among states (17%). We provide recommendations to use this approach based on a series of simple steps. Our findings illustrate a successful method that can be used to rigorously quantify flow permanence regimes in streams using existing records of stream temperature.

  14. Non-invasive breast biopsy method using GD-DTPA contrast enhanced MRI series and F-18-FDG PET/CT dynamic image series

    Science.gov (United States)

    Magri, Alphonso William

    This study was undertaken to develop a nonsurgical breast biopsy from Gd-DTPA Contrast Enhanced Magnetic Resonance (CE-MR) images and F-18-FDG PET/CT dynamic image series. A five-step process was developed to accomplish this. (1) Dynamic PET series were nonrigidly registered to the initial frame using a finite element method (FEM) based registration that requires fiducial skin markers to sample the displacement field between image frames. A commercial FEM package (ANSYS) was used for meshing and FEM calculations. Dynamic PET image series registrations were evaluated using similarity measurements SAVD and NCC. (2) Dynamic CE-MR series were nonrigidly registered to the initial frame using two registration methods: a multi-resolution free-form deformation (FFD) registration driven by normalized mutual information, and a FEM-based registration method. Dynamic CE-MR image series registrations were evaluated using similarity measurements, localization measurements, and qualitative comparison of motion artifacts. FFD registration was found to be superior to FEM-based registration. (3) Nonlinear curve fitting was performed for each voxel of the PET/CT volume of activity versus time, based on a realistic two-compartmental Patlak model. Three parameters for this model were fitted; two of them describe the activity levels in the blood and in the cellular compartment, while the third characterizes the washout rate of F-18-FDG from the cellular compartment. (4) Nonlinear curve fitting was performed for each voxel of the MR volume of signal intensity versus time, based on a realistic two-compartment Brix model. Three parameters for this model were fitted: rate of Gd exiting the compartment, representing the extracellular space of a lesion; rate of Gd exiting a blood compartment; and a parameter that characterizes the strength of signal intensities. Curve fitting used for PET/CT and MR series was accomplished by application of the Levenburg-Marquardt nonlinear regression

  15. New solitary wave solutions of the time-fractional Cahn-Allen equation via the improved (G'/G)-expansion method

    Science.gov (United States)

    Batool, Fiza; Akram, Ghazala

    2018-05-01

    An improved (G'/G)-expansion method is proposed for extracting more general solitary wave solutions of the nonlinear fractional Cahn-Allen equation. The temporal fractional derivative is taken in the sense of Jumarie's fractional derivative. The results of this article are generalized and extended version of previously reported solutions.

  16. Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

    International Nuclear Information System (INIS)

    Hong, Ser Gi; Lee, Deokjung

    2015-01-01

    A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)

  17. An Active Power Sharing Method among Distributed Energy Sources in an Islanded Series Micro-Grid

    Directory of Open Access Journals (Sweden)

    Wei-Man Yang

    2014-11-01

    Full Text Available Active power-sharing among distributed energy sources (DESs is not only an important way to realize optimal operation of micro-grids, but also the key to maintaining stability for islanded operation. Due to the unique configuration of series micro-grids (SMGs, the power-sharing method adopted in an ordinary AC, DC, and hybrid AC/DC system cannot be directly applied into SMGs. Power-sharing in one SMG with multiple DESs involves two aspects. On the one hand, capacitor voltage stability based on an energy storage system (ESS in the DC link must be complemented. Actually, this is a problem of power allocation between the generating unit and the ESS in the DES; an extensively researched, similar problem has been grid-off distributed power generation, for which there are good solutions. On the other hand, power-sharing among DESs should be considered to optimize the operation of a series micro-grid. In this paper, a novel method combining master control with auxiliary control is proposed. Master action of a quasi-proportional resonant controller is responsible for stability of the islanded SMG; auxiliary action based on state of charge (SOC realizes coordinated allocation of load power among the source. At the same time, it is important to ensure that the auxiliary control does not influence the master action.

  18. Cooling load calculation by the radiant time series method - effect of solar radiation models

    Energy Technology Data Exchange (ETDEWEB)

    Costa, Alexandre M.S. [Universidade Estadual de Maringa (UEM), PR (Brazil)], E-mail: amscosta@uem.br

    2010-07-01

    In this work was analyzed numerically the effect of three different models for solar radiation on the cooling load calculated by the radiant time series' method. The solar radiation models implemented were clear sky, isotropic sky and anisotropic sky. The radiant time series' method (RTS) was proposed by ASHRAE (2001) for replacing the classical methods of cooling load calculation, such as TETD/TA. The method is based on computing the effect of space thermal energy storage on the instantaneous cooling load. The computing is carried out by splitting the heat gain components in convective and radiant parts. Following the radiant part is transformed using time series, which coefficients are a function of the construction type and heat gain (solar or non-solar). The transformed result is added to the convective part, giving the instantaneous cooling load. The method was applied for investigate the influence for an example room. The location used was - 23 degree S and 51 degree W and the day was 21 of January, a typical summer day in the southern hemisphere. The room was composed of two vertical walls with windows exposed to outdoors with azimuth angles equals to west and east directions. The output of the different models of solar radiation for the two walls in terms of direct and diffuse components as well heat gains were investigated. It was verified that the clear sky exhibited the less conservative (higher values) for the direct component of solar radiation, with the opposite trend for the diffuse component. For the heat gain, the clear sky gives the higher values, three times higher for the peek hours than the other models. Both isotropic and anisotropic models predicted similar magnitude for the heat gain. The same behavior was also verified for the cooling load. The effect of room thermal inertia was decreasing the cooling load during the peak hours. On the other hand the higher thermal inertia values are the greater for the non peak hours. The effect

  19. Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

    Science.gov (United States)

    Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

    2015-01-01

    The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

  20. Thermal expansion data

    International Nuclear Information System (INIS)

    Taylor, D.

    1984-01-01

    This paper gives regression data for a modified second order polynomial fitted to the expansion data of, and percentage expansions for dioxides with (a) the fluorite and antifluorite structure: AmO 2 , BkO 2 , CeO 2 , CmO 2 , HfO 2 , Li 2 O, NpO 2 , PrO 2 , PuO 2 , ThO 2 , UO 2 , ZrO 2 , and (b) the rutile structure: CrO 2 , GeO 2 , IrO 2 , MnO 2 , NbO 2 , PbO 2 , SiO 2 , SnO 2 , TeO 2 , TiO 2 and VO 2 . Reduced expansion curves for the dioxides showed only partial grouping into iso-electronic series for the fluorite structures and showed that the 'law of corresponding states' did not apply to the rutile structures. (author)

  1. Adjustment method for embedded metrology engine in an EM773 series microcontroller.

    Science.gov (United States)

    Blazinšek, Iztok; Kotnik, Bojan; Chowdhury, Amor; Kačič, Zdravko

    2015-09-01

    This paper presents the problems of implementation and adjustment (calibration) of a metrology engine embedded in NXP's EM773 series microcontroller. The metrology engine is used in a smart metering application to collect data about energy utilization and is controlled with the use of metrology engine adjustment (calibration) parameters. The aim of this research is to develop a method which would enable the operators to find and verify the optimum parameters which would ensure the best possible accuracy. Properly adjusted (calibrated) metrology engines can then be used as a base for variety of products used in smart and intelligent environments. This paper focuses on the problems encountered in the development, partial automatisation, implementation and verification of this method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  2. A REDUCE program for symbolic computation of Puiseux expansions

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Tiller, P.

    1991-01-01

    The program is described for computation of Puiseux expansions of algebraic functions. The Newton diagram method is used for construction of initial coefficients of all the Puiseux series at the given point. The program is written in computer algebra language Reduce. Some illustrative examples are given. 20 refs

  3. Discrete Data Qualification System and Method Comprising Noise Series Fault Detection

    Science.gov (United States)

    Fulton, Christopher; Wong, Edmond; Melcher, Kevin; Bickford, Randall

    2013-01-01

    A Sensor Data Qualification (SDQ) function has been developed that allows the onboard flight computers on NASA s launch vehicles to determine the validity of sensor data to ensure that critical safety and operational decisions are not based on faulty sensor data. This SDQ function includes a novel noise series fault detection algorithm for qualification of the output data from LO2 and LH2 low-level liquid sensors. These sensors are positioned in a launch vehicle s propellant tanks in order to detect propellant depletion during a rocket engine s boost operating phase. This detection capability can prevent the catastrophic situation where the engine operates without propellant. The output from each LO2 and LH2 low-level liquid sensor is a discrete valued signal that is expected to be in either of two states, depending on whether the sensor is immersed (wet) or exposed (dry). Conventional methods for sensor data qualification, such as threshold limit checking, are not effective for this type of signal due to its discrete binary-state nature. To address this data qualification challenge, a noise computation and evaluation method, also known as a noise fault detector, was developed to detect unreasonable statistical characteristics in the discrete data stream. The method operates on a time series of discrete data observations over a moving window of data points and performs a continuous examination of the resulting observation stream to identify the presence of anomalous characteristics. If the method determines the existence of anomalous results, the data from the sensor is disqualified for use by other monitoring or control functions.

  4. On Fourier re-expansions

    OpenAIRE

    Liflyand, E.

    2012-01-01

    We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.

  5. A Method for Exploring the Link between Urban Area Expansion over Time and the Opportunity for Crime in Saudi Arabia

    Directory of Open Access Journals (Sweden)

    Mofza Algahtany

    2016-10-01

    Full Text Available Urban area expansion is one of the most critical types of worldwide change, and most urban areas are experiencing increased growth in population and infrastructure development. Urban change leads to many changes in the daily activities of people living within an affected area. Many studies have suggested that urbanization and crime are related. However, they focused particularly on land uses, types of land use, and urban forms, such as the physical features of neighbourhoods, roads, shopping centres, and bus stations. Understanding the correlation between urban area expansion and crime is very important for criminologists and urban planning decision-makers. In this study, we have used satellite images to measure urban expansion over a 10-year period and tested the correlations between these expansions and the number of criminal activities within these specific areas. The results show that there is a measurable relationship between urban expansion and criminal activities. Our findings support the crime opportunity theory as one possibility, which suggests that population density and crime are conceptually related. We found the correlations are stronger where there has been greater urban growth. Many other factors that may affect crime rate are not included in this paper, such as information on the spatial details of the population, city planning, economic considerations, the distance from the city centre, neighbourhood quality, and police numbers. However, this study will be of particular interest to those who aim to use remote sensing to study patterns of crime.

  6. Improved vertical streambed flux estimation using multiple diurnal temperature methods in series

    Science.gov (United States)

    Irvine, Dylan J.; Briggs, Martin A.; Cartwright, Ian; Scruggs, Courtney; Lautz, Laura K.

    2017-01-01

    Analytical solutions that use diurnal temperature signals to estimate vertical fluxes between groundwater and surface water based on either amplitude ratios (Ar) or phase shifts (Δϕ) produce results that rarely agree. Analytical solutions that simultaneously utilize Ar and Δϕ within a single solution have more recently been derived, decreasing uncertainty in flux estimates in some applications. Benefits of combined (ArΔϕ) methods also include that thermal diffusivity and sensor spacing can be calculated. However, poor identification of either Ar or Δϕ from raw temperature signals can lead to erratic parameter estimates from ArΔϕ methods. An add-on program for VFLUX 2 is presented to address this issue. Using thermal diffusivity selected from an ArΔϕ method during a reliable time period, fluxes are recalculated using an Ar method. This approach maximizes the benefits of the Ar and ArΔϕ methods. Additionally, sensor spacing calculations can be used to identify periods with unreliable flux estimates, or to assess streambed scour. Using synthetic and field examples, the use of these solutions in series was particularly useful for gaining conditions where fluxes exceeded 1 m/d.

  7. Investigation of thermal expansion and compressibility of rare-earth orthovanadates using a dielectric chemical bond method.

    Science.gov (United States)

    Zhang, Siyuan; Zhou, Shihong; Li, Huaiyong; Li, Ling

    2008-09-01

    The chemical bond properties, lattice energies, linear expansion coefficients, and mechanical properties of ReVO 4 (Re = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Sc, Y) are investigated systematically by the dielectric chemical bond theory. The calculated results show that the covalencies of Re-O bonds are increasing slightly from La to Lu and that the covalencies of V-O bonds in crystals are decreasing slightly from La to Lu. The linear expansion coefficients decrease progressively from LaVO 4 to LuVO 4; on the contrary, the bulk moduli increase progressively. Our calculated results are in good agreement with some experimental values for linear expansion coefficients and bulk moduli.

  8. Advanced Methods for Incorporating Solar Energy Technologies into Electric Sector Capacity-Expansion Models: Literature Review and Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Sullivan, P.; Eurek, K.; Margolis, R.

    2014-07-01

    Because solar power is a rapidly growing component of the electricity system, robust representations of solar technologies should be included in capacity-expansion models. This is a challenge because modeling the electricity system--and, in particular, modeling solar integration within that system--is a complex endeavor. This report highlights the major challenges of incorporating solar technologies into capacity-expansion models and shows examples of how specific models address those challenges. These challenges include modeling non-dispatchable technologies, determining which solar technologies to model, choosing a spatial resolution, incorporating a solar resource assessment, and accounting for solar generation variability and uncertainty.

  9. A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series

    Science.gov (United States)

    Wang, Wen-Chuan; Chau, Kwok-Wing; Cheng, Chun-Tian; Qiu, Lin

    2009-08-01

    SummaryDeveloping a hydrological forecasting model based on past records is crucial to effective hydropower reservoir management and scheduling. Traditionally, time series analysis and modeling is used for building mathematical models to generate hydrologic records in hydrology and water resources. Artificial intelligence (AI), as a branch of computer science, is capable of analyzing long-series and large-scale hydrological data. In recent years, it is one of front issues to apply AI technology to the hydrological forecasting modeling. In this paper, autoregressive moving-average (ARMA) models, artificial neural networks (ANNs) approaches, adaptive neural-based fuzzy inference system (ANFIS) techniques, genetic programming (GP) models and support vector machine (SVM) method are examined using the long-term observations of monthly river flow discharges. The four quantitative standard statistical performance evaluation measures, the coefficient of correlation ( R), Nash-Sutcliffe efficiency coefficient ( E), root mean squared error (RMSE), mean absolute percentage error (MAPE), are employed to evaluate the performances of various models developed. Two case study river sites are also provided to illustrate their respective performances. The results indicate that the best performance can be obtained by ANFIS, GP and SVM, in terms of different evaluation criteria during the training and validation phases.

  10. River catchment rainfall series analysis using additive Holt-Winters method

    Science.gov (United States)

    Puah, Yan Jun; Huang, Yuk Feng; Chua, Kuan Chin; Lee, Teang Shui

    2016-03-01

    Climate change is receiving more attention from researchers as the frequency of occurrence of severe natural disasters is getting higher. Tropical countries like Malaysia have no distinct four seasons; rainfall has become the popular parameter to assess climate change. Conventional ways that determine rainfall trends can only provide a general result in single direction for the whole study period. In this study, rainfall series were modelled using additive Holt-Winters method to examine the rainfall pattern in Langat River Basin, Malaysia. Nine homogeneous series of more than 25 years data and less than 10% missing data were selected. Goodness of fit of the forecasted models was measured. It was found that seasonal rainfall model forecasts are generally better than the monthly rainfall model forecasts. Three stations in the western region exhibited increasing trend. Rainfall in southern region showed fluctuation. Increasing trends were discovered at stations in the south-eastern region except the seasonal analysis at station 45253. Decreasing trend was found at station 2818110 in the east, while increasing trend was shown at station 44320 that represents the north-eastern region. The accuracies of both rainfall model forecasts were tested using the recorded data of years 2010-2012. Most of the forecasts are acceptable.

  11. Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

    Science.gov (United States)

    Nishimoto, Yoshio

    2015-09-07

    We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.

  12. Derivation of Mayer Series from Canonical Ensemble

    International Nuclear Information System (INIS)

    Wang Xian-Zhi

    2016-01-01

    Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula. (paper)

  13. Derivation of Mayer Series from Canonical Ensemble

    Science.gov (United States)

    Wang, Xian-Zhi

    2016-02-01

    Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.

  14. Learning from environmental data: Methods for analysis of forest nutrition time series

    Energy Technology Data Exchange (ETDEWEB)

    Sulkava, M. (Helsinki Univ. of Technology, Espoo (Finland). Computer and Information Science)

    2008-07-01

    Data analysis methods play an important role in increasing our knowledge of the environment as the amount of data measured from the environment increases. This thesis fits under the scope of environmental informatics and environmental statistics. They are fields, in which data analysis methods are developed and applied for the analysis of environmental data. The environmental data studied in this thesis are time series of nutrient concentration measurements of pine and spruce needles. In addition, there are data of laboratory quality and related environmental factors, such as the weather and atmospheric depositions. The most important methods used for the analysis of the data are based on the self-organizing map and linear regression models. First, a new clustering algorithm of the self-organizing map is proposed. It is found to provide better results than two other methods for clustering of the self-organizing map. The algorithm is used to divide the nutrient concentration data into clusters, and the result is evaluated by environmental scientists. Based on the clustering, the temporal development of the forest nutrition is modeled and the effect of nitrogen and sulfur deposition on the foliar mineral composition is assessed. Second, regression models are used for studying how much environmental factors and properties of the needles affect the changes in the nutrient concentrations of the needles between their first and second year of existence. The aim is to build understandable models with good prediction capabilities. Sparse regression models are found to outperform more traditional regression models in this task. Third, fusion of laboratory quality data from different sources is performed to estimate the precisions of the analytical methods. Weighted regression models are used to quantify how much the precision of observations can affect the time needed to detect a trend in environmental time series. The results of power analysis show that improving the

  15. Expansion dynamics

    International Nuclear Information System (INIS)

    Knoll, J.

    1985-10-01

    A quantum dynamical model is suggested which describes the expansion and disassembly phase of highly excited compounds formed in energetic heavy-ion collisions. First applications in two space and one time dimensional model world are discussed and qualitatively compared to standard freeze-out concepts. (orig.)

  16. Separation of Stochastic and Deterministic Information from Seismological Time Series with Nonlinear Dynamics and Maximum Entropy Methods

    International Nuclear Information System (INIS)

    Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias

    2007-01-01

    We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information

  17. Analysis of rhythmic variance - ANORVA. A new simple method for detecting rhythms in biological time series

    Directory of Open Access Journals (Sweden)

    Peter Celec

    2004-01-01

    Full Text Available Cyclic variations of variables are ubiquitous in biomedical science. A number of methods for detecting rhythms have been developed, but they are often difficult to interpret. A simple procedure for detecting cyclic variations in biological time series and quantification of their probability is presented here. Analysis of rhythmic variance (ANORVA is based on the premise that the variance in groups of data from rhythmic variables is low when a time distance of one period exists between the data entries. A detailed stepwise calculation is presented including data entry and preparation, variance calculating, and difference testing. An example for the application of the procedure is provided, and a real dataset of the number of papers published per day in January 2003 using selected keywords is compared to randomized datasets. Randomized datasets show no cyclic variations. The number of papers published daily, however, shows a clear and significant (p<0.03 circaseptan (period of 7 days rhythm, probably of social origin

  18. A time series approach to inferring groundwater recharge using the water table fluctuation method

    Science.gov (United States)

    Crosbie, Russell S.; Binning, Philip; Kalma, Jetse D.

    2005-01-01

    The water table fluctuation method for determining recharge from precipitation and water table measurements was originally developed on an event basis. Here a new multievent time series approach is presented for inferring groundwater recharge from long-term water table and precipitation records. Additional new features are the incorporation of a variable specific yield based upon the soil moisture retention curve, proper accounting for the Lisse effect on the water table, and the incorporation of aquifer drainage so that recharge can be detected even if the water table does not rise. A methodology for filtering noise and non-rainfall-related water table fluctuations is also presented. The model has been applied to 2 years of field data collected in the Tomago sand beds near Newcastle, Australia. It is shown that gross recharge estimates are very sensitive to time step size and specific yield. Properly accounting for the Lisse effect is also important to determining recharge.

  19. "Rehabilitation schools for scoliosis" thematic series: describing the methods and results

    Directory of Open Access Journals (Sweden)

    Grivas Theodoros B

    2010-12-01

    Full Text Available Abstract The Scoliosis Rehabilitation model begins with the correct diagnosis and evaluation of the patient, to make treatment decisions oriented to the patient. The treatment is based on observation, education, scoliosis specific exercises, and bracing. The state of research in the field of conservative treatment is insufficient. There is some evidence supporting scoliosis specific exercises as a part of the rehabilitation treatment, however, the evidence is poor and the different methods are not known by most of the scientific community. The only way to improve the knowledge and understanding of the different physiotherapy methodologies (specific exercises, integrated into the whole rehabilitation program, is to establish a single and comprehensive source of information about it. This is what the SCOLIOSIS Journal is going to do through the "Rehabilitation Schools for Scoliosis" Thematic Series, where technical papers coming from the different schools will be published.

  20. Over-deterministic method: The influence of rounding numbers on the accuracy of the values of williams’ expansion terms

    Czech Academy of Sciences Publication Activity Database

    Růžička, V.; Malíková, Lucie; Seitl, Stanislav

    2017-01-01

    Roč. 11, č. 42 (2017), s. 128-135 ISSN 1971-8993 R&D Projects: GA ČR GA17-01589S Institutional support: RVO:68081723 Keywords : Over-deterministic * Fracture mechanics * Rounding numbers * Stress field * Williams’ expansion Subject RIV: JL - Materials Fatigue, Friction Mechanics OBOR OECD: Audio engineering, reliability analysis

  1. Extrusion-formed uranium-2.4 wt. % article with decreased linear thermal expansion and method for making the same

    International Nuclear Information System (INIS)

    Anderson, R.C.; Jones, J.M.; Kollie, T.G.

    1982-01-01

    The present invention is directed to the fabrication of an article of uranium-2.4 wt. % niobium alloy in which the linear thermal expansion in the direction transverse to the extrusion direction is less than about 0.98% between 22 0 C and 600 0 C which corresponds to a value greater than the 1.04% provided by previous extrusion operations over the same temperature range. The article with the improved thermal expansion possesses a yield strength at 0.2% offset of at least 400 mpa, an ultimate tensile strength of 1050 mpa, a compressive yield strength of at least 2% offset of at least 675 mpa, and an elongation of at lea 25% over 25.4 mm/sec. To provide this article with the improv thermal expansion, the uranium alloy billet is heated to 630 0 C and extruded in the alpha phase through a die with a reduction ratio of at least 8.4:1 at a ram speed no greater than 6.8 mm/sec. These critical extrusion parameters provide the article with the desired decrease in the linear thermal expansion while maintaining the selected mechanical properties without encountering crystal disruption in the article

  2. The ab initio model potential method. Second series transition metal elements

    International Nuclear Information System (INIS)

    Barandiaran, Z.; Seijo, L.; Huzinaga, S.

    1990-01-01

    The ab initio core method potential model (AIMP) has already been presented in its nonrelativistic version and applied to the main group and first series transition metal elements [J. Chem. Phys. 86, 2132 (1987); 91, 7011 (1989)]. In this paper we extend the AIMP method to include relativistic effects within the Cowan--Griffin approximation and we present relativistic Zn-like core model potentials and valence basis sets, as well as their nonrelativistic Zn-like core and Kr-like core counterparts. The pilot molecular calculations on YO, TcO, AgO, and AgH reveal that the 4p orbital is indeed a core orbital only at the end part of the series, whereas the 4s orbital can be safely frozen from Y to Cd. The all-electron and model potential results agree in 0.01--0.02 A in R e and 25--50 cm -1 in bar ν e if the same type of valence part of the basis set is used. The comparison of the relativistic results on AgH with those of the all-electron Dirac--Fock calculations by Lee and McLean is satisfactory: the absolute value of R e is reproduced within the 0.01 A margin and the relativistic contraction of 0.077 A is also very well reproduced (0.075 A). Finally, the relative magnitude of the effects of the core orbital change, mass--velocity potential, and Darwin potential on the net relativistic effects are analyzed in the four molecules studied

  3. Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

    Science.gov (United States)

    Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

    2018-05-01

    The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

  4. A statistical method linking geological and historical eruption time series for volcanic hazard estimations: Applications to active polygenetic volcanoes

    Science.gov (United States)

    Mendoza-Rosas, Ana Teresa; De la Cruz-Reyna, Servando

    2008-09-01

    The probabilistic analysis of volcanic eruption time series is an essential step for the assessment of volcanic hazard and risk. Such series describe complex processes involving different types of eruptions over different time scales. A statistical method linking geological and historical eruption time series is proposed for calculating the probabilities of future eruptions. The first step of the analysis is to characterize the eruptions by their magnitudes. As is the case in most natural phenomena, lower magnitude events are more frequent, and the behavior of the eruption series may be biased by such events. On the other hand, eruptive series are commonly studied using conventional statistics and treated as homogeneous Poisson processes. However, time-dependent series, or sequences including rare or extreme events, represented by very few data of large eruptions require special methods of analysis, such as the extreme-value theory applied to non-homogeneous Poisson processes. Here we propose a general methodology for analyzing such processes attempting to obtain better estimates of the volcanic hazard. This is done in three steps: Firstly, the historical eruptive series is complemented with the available geological eruption data. The linking of these series is done assuming an inverse relationship between the eruption magnitudes and the occurrence rate of each magnitude class. Secondly, we perform a Weibull analysis of the distribution of repose time between successive eruptions. Thirdly, the linked eruption series are analyzed as a non-homogeneous Poisson process with a generalized Pareto distribution as intensity function. As an application, the method is tested on the eruption series of five active polygenetic Mexican volcanoes: Colima, Citlaltépetl, Nevado de Toluca, Popocatépetl and El Chichón, to obtain hazard estimates.

  5. Predicting hepatitis B monthly incidence rates using weighted Markov chains and time series methods.

    Science.gov (United States)

    Shahdoust, Maryam; Sadeghifar, Majid; Poorolajal, Jalal; Javanrooh, Niloofar; Amini, Payam

    2015-01-01

    Hepatitis B (HB) is a major global mortality. Accurately predicting the trend of the disease can provide an appropriate view to make health policy disease prevention. This paper aimed to apply three different to predict monthly incidence rates of HB. This historical cohort study was conducted on the HB incidence data of Hamadan Province, the west of Iran, from 2004 to 2012. Weighted Markov Chain (WMC) method based on Markov chain theory and two time series models including Holt Exponential Smoothing (HES) and SARIMA were applied on the data. The results of different applied methods were compared to correct percentages of predicted incidence rates. The monthly incidence rates were clustered into two clusters as state of Markov chain. The correct predicted percentage of the first and second clusters for WMC, HES and SARIMA methods was (100, 0), (84, 67) and (79, 47) respectively. The overall incidence rate of HBV is estimated to decrease over time. The comparison of results of the three models indicated that in respect to existing seasonality trend and non-stationarity, the HES had the most accurate prediction of the incidence rates.

  6. [Correlation coefficient-based principle and method for the classification of jump degree in hydrological time series].

    Science.gov (United States)

    Wu, Zi Yi; Xie, Ping; Sang, Yan Fang; Gu, Hai Ting

    2018-04-01

    The phenomenon of jump is one of the importantly external forms of hydrological variabi-lity under environmental changes, representing the adaption of hydrological nonlinear systems to the influence of external disturbances. Presently, the related studies mainly focus on the methods for identifying the jump positions and jump times in hydrological time series. In contrast, few studies have focused on the quantitative description and classification of jump degree in hydrological time series, which make it difficult to understand the environmental changes and evaluate its potential impacts. Here, we proposed a theatrically reliable and easy-to-apply method for the classification of jump degree in hydrological time series, using the correlation coefficient as a basic index. The statistical tests verified the accuracy, reasonability, and applicability of this method. The relationship between the correlation coefficient and the jump degree of series were described using mathematical equation by derivation. After that, several thresholds of correlation coefficients under different statistical significance levels were chosen, based on which the jump degree could be classified into five levels: no, weak, moderate, strong and very strong. Finally, our method was applied to five diffe-rent observed hydrological time series, with diverse geographic and hydrological conditions in China. The results of the classification of jump degrees in those series were closely accorded with their physically hydrological mechanisms, indicating the practicability of our method.

  7. 2D XXZ model ground state properties using an analytic Lanczos expansion

    International Nuclear Information System (INIS)

    Witte, N.S.; Hollenberg, L.C.L.; Weihong Zheng

    1997-01-01

    A formalism was developed for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the t-expansion, and spin-wave theory and series expansion methods. It was found that far from the isotropic point all moment methods give essentially very similar results, but near the isotopic point the plaquette expansion is generally better than the others. 20 refs., 6 tabs

  8. A design of a mode converter for electron cyclotron heating by the method of normal mode expansion

    International Nuclear Information System (INIS)

    Hoshino, Katsumichi; Kawashima, Hisato; Hata, Kenichiro; Yamamoto, Takumi

    1983-09-01

    Mode conversion of electromagnetic wave propagating in the over-size circular waveguide is attained by giving a periodical perturbation in the guide wall. Mode coupling equation is expressed by ''generalized telegraphist's equations'' which are derived from the Maxwell's equations using a normal mode expansion. A computer code to solve the coupling equations is developed and mode amplitude, conversion efficiency, etc. of a particular type of mode converter for the 60 GHz electron cyclotron heating are obtained. (author)

  9. Multistage-multiorifice flow fractionation (MS-MOFF): continuous size-based separation of microspheres using multiple series of contraction/expansion microchannels.

    Science.gov (United States)

    Sim, Tae Seok; Kwon, Kiho; Park, Jae Chan; Lee, Jeong-Gun; Jung, Hyo-Il

    2011-01-07

    Previously we introduced a novel hydrodynamic method using a multi-orifice microchannel for size-based particle separation, which is called a multi-orifice flow fractionation (MOFF). The MOFF has several advantages such as continuous, non-intrusive, and minimal power consumption. However, it has a limitation that the recovery yield is relatively low. Although the recovery may be increased by adjusting parameters such as the Reynolds number and central collecting region, poor purity inevitably followed. We newly designed and fabricated a microfluidic channel for multi-stage multi-orifice flow fractionation (MS-MOFF), which is made by combining three multi-orifice segments, and consists of 3 inlets, 3 filters, 3 multi-orifice segments and 5 outlets. The structure and dimensions of the MS-MOFF were determined by the hydrodynamic principles to have constant Reynolds numbers at each multi-orifice segment. Polystyrene microspheres of two different sizes (7 μm and 15 μm) were tested. With this device, we made an attempt to improve recovery and minimize loss of purity by collecting and re-separating non-selected particles of the first separation. The final recovery successfully increased from 73.2% to 88.7% while the final purity slightly decreased from 91.4% to 89.1% (for 15 μm). These values were never achievable with the single-stage MOFF (SS-MOFF) having only one multi-orifice segment in our previous work. The MS-MOFF channel will be useful for clinical applications, such as separation of circulating tumor cells (CTC) or rare cells from human blood samples.

  10. A Novel Generation Method for the PV Power Time Series Combining the Decomposition Technique and Markov Chain Theory

    DEFF Research Database (Denmark)

    Xu, Shenzhi; Ai, Xiaomeng; Fang, Jiakun

    2017-01-01

    Photovoltaic (PV) power generation has made considerable developments in recent years. But its intermittent and volatility of its output has seriously affected the security operation of the power system. In order to better understand the PV generation and provide sufficient data support...... for analysis the impacts, a novel generation method for PV power time series combining decomposition technique and Markov chain theory is presented in this paper. It digs important factors from historical data from existing PV plants and then reproduce new data with similar patterns. In detail, the proposed...... method first decomposes the PV power time series into ideal output curve, amplitude parameter series and random fluctuating component three parts. Then generating daily ideal output curve by the extraction of typical daily data, amplitude parameter series based on the Markov chain Monte Carlo (MCMC...

  11. New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

    Science.gov (United States)

    Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

    2014-01-01

    In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

  12. Development of a neutronics code based on analytic function expansion nodal method for pebble-type High Temperature Gas-cooled Reactor design

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo [Korea Advanced Institute of Science and Tehcnology, Daejeon (Korea, Republic of)

    2006-03-15

    There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis.

  13. Development of a neutronics code based on analytic function expansion nodal method for pebble-type High Temperature Gas-cooled Reactor design

    International Nuclear Information System (INIS)

    Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo

    2006-03-01

    There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis

  14. Evaluation of expansion algorithm of measurement range suited for 3D shape measurement using two pitches of projected grating with light source-stepping method

    Science.gov (United States)

    Sakaguchi, Toshimasa; Fujigaki, Motoharu; Murata, Yorinobu

    2015-03-01

    Accurate and wide-range shape measurement method is required in industrial field. The same technique is possible to be used for a shape measurement of a human body for the garment industry. Compact 3D shape measurement equipment is also required for embedding in the inspection system. A shape measurement by a phase shifting method can measure the shape with high spatial resolution because the coordinates can be obtained pixel by pixel. A key-device to develop compact equipment is a grating projector. Authors developed a linear LED projector and proposed a light source stepping method (LSSM) using the linear LED projector. The shape measurement euipment can be produced with low-cost and compact without any phase-shifting mechanical systems by using this method. Also it enables us to measure 3D shape in very short time by switching the light sources quickly. A phase unwrapping method is necessary to widen the measurement range with constant accuracy for phase shifting method. A general phase unwrapping method with difference grating pitches is often used. It is one of a simple phase unwrapping method. It is, however, difficult to apply the conventional phase unwrapping algorithm to the LSSM. Authors, therefore, developed an expansion unwrapping algorithm for the LSSM. In this paper, an expansion algorithm of measurement range suited for 3D shape measurement using two pitches of projected grating with the LSSM was evaluated.

  15. A Fourier-series-based kernel-independent fast multipole method

    International Nuclear Information System (INIS)

    Zhang Bo; Huang Jingfang; Pitsianis, Nikos P.; Sun Xiaobai

    2011-01-01

    We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.

  16. Low-derivative operators of the Standard Model effective field theory via Hilbert series methods

    Energy Technology Data Exchange (ETDEWEB)

    Lehman, Landon; Martin, Adam [Department of Physics, University of Notre Dame,Nieuwland Science Hall, Notre Dame, IN 46556 (United States)

    2016-02-12

    In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N{sub f}=1 operators.

  17. ROS evaluation for a series of CNTs and their derivatives using an ESR method with DMPO

    International Nuclear Information System (INIS)

    Tsuruoka, S; Noguchi, T; Endo, M; Tristan, F; Terrones, M; Takeuchi, K; Koyama, K; Usui, Y; Matsumoto, H; Saito, N; Porter, D W; Castranova, V

    2013-01-01

    Carbon nanotubes (CNTs) are important materials in advanced industries. It is a concern that pulmonary exposure to CNTs may induce carcinogenic responses. It has been recently reported that CNTs scavenge ROS though non-carbon fibers generate ROS. A comprehensive evaluation of ROS scavenging using various kinds of CNTs has not been demonstrated well. The present work specifically investigates ROS scavenging capabilities with a series of CNTs and their derivatives that were physically treated, and with the number of commercially available CNTs. CNT concentrations were controlled at 0.2 through 0.6 wt%. The ROS scavenging rate was measured by ESR with DMPO. Interestingly, the ROS scavenging rate was not only influenced by physical treatments, but was also dependent on individual manufacturing methods. Ratio of CNTs to DMPO/ hydrogen peroxide is a key parameter to obtain appropriate ROS quenching results for comparison of CNTs. The present results suggest that dangling bonds are not a sole factor for scavenging, and electron transfer on the CNT surface is not clearly determined to be the sole mechanism to explain ROS scavenging.

  18. ROS evaluation for a series of CNTs and their derivatives using an ESR method with DMPO.

    Science.gov (United States)

    Tsuruoka, S; Takeuchi, K; Koyama, K; Noguchi, T; Endo, M; Tristan, F; Terrones, M; Matsumoto, H; Saito, N; Usui, Y; Porter, D W; Castranova, V

    Carbon nanotubes (CNTs) are important materials in advanced industries. It is a concern that pulmonary exposure to CNTs may induce carcinogenic responses. It has been recently reported that CNTs scavenge ROS though non-carbon fibers generate ROS. A comprehensive evaluation of ROS scavenging using various kinds of CNTs has not been demonstrated well. The present work specifically investigates ROS scavenging capabilities with a series of CNTs and their derivatives that were physically treated, and with the number of commercially available CNTs. CNT concentrations were controlled at 0.2 through 0.6 wt%. The ROS scavenging rate was measured by ESR with DMPO. Interestingly, the ROS scavenging rate was not only influenced by physical treatments, but was also dependent on individual manufacturing methods. Ratio of CNTs to DMPO/ hydrogen peroxide is a key parameter to obtain appropriate ROS quenching results for comparison of CNTs. The present results suggest that dangling bonds are not a sole factor for scavenging, and electron transfer on the CNT surface is not clearly determined to be the sole mechanism to explain ROS scavenging.

  19. Low-derivative operators of the Standard Model effective field theory via Hilbert series methods

    International Nuclear Information System (INIS)

    Lehman, Landon; Martin, Adam

    2016-01-01

    In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N_f=1 operators.

  20. From divergent power series to analytic functions theory and application of multisummable power series

    CERN Document Server

    Balser, Werner

    1994-01-01

    Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

  1. Heat transfer characteristics of UF6 in a container heated from outer surface. Pt. 1. Thermal hydraulic analysis method taking account of phase change and volume expansion

    International Nuclear Information System (INIS)

    Wataru, Masumi; Gomi, Yoshio; Yamakawa, Hidetsugu; Tsumune, Daisuke

    1995-01-01

    Natural UF6 is transported in a steel container from foreign countries to the enrichment plant in Japan. If the container meets fire accident, it is heated by fire (800degC) and rupture of the container may occur. For the safety point of view, it is necessary to know whether rupture occurs or not. Because UF6 has a radiological and chemical hazards, it is difficult to perform a demonstration test with UF6. So thermal calculation method has to be developed. The rupture is caused by UF6 gaseous pressure or volume expansion of liquid UF6. To know time history of internal pressure and temperature distribution in the container, it is important to evaluate thermal phenomena of UF6. When UF6 is heated, it changes from solid to liquid or gas at low temperature (64degC) and then its volume expands little by little. In this study, thermal calculation method has been developed taking phase change and thermal expansion of UF6 into account. In the calculation, a two-dimensional model is adopted and natural convection of liquid UF6 is analyzed. As a result of this study, numerical solutions have been obtained taking phase change and volume expansion into account. (author)

  2. The hyperspherical-harmonics expansion method and the integral-equation approach to solving the few-body problem in momentum space

    International Nuclear Information System (INIS)

    Liu, F.-Q.; Lim, T.K.

    1988-01-01

    The Faddeev and Faddeev-Yakubovsky equations for three- and four-body systems are solved by applying the hyperspherical-harmonics expansion to them in momentum space. This coupling of two popular approaches to the few-body problem together with the use of the so-called Raynal-Revai transformation, which relates hyperspherical functions, allows the few-body equations to be written as one-dimensional coupled integral equations. Numerical solutions for these are achieved through standard matrix methods; these are made straightforward, because a second transformation renders potential multipoles easily calculable. For sample potentials and a restricted size of matrix in each case, the binding energies extracted match those previously obtained in solving the Schroedinger equation through the hyperspherical-harmonics expansion in coordinate space. 9 refs

  3. Nonperturbative path integral expansion II

    International Nuclear Information System (INIS)

    Kaiser, H.J.

    1976-05-01

    The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)

  4. Forecasts for the Canadian Lynx time series using method that bombine neural networks, wavelet shrinkage and decomposition

    Directory of Open Access Journals (Sweden)

    Levi Lopes Teixeira

    2015-12-01

    Full Text Available Time series forecasting is widely used in various areas of human knowledge, especially in the planning and strategic direction of companies. The success of this task depends on the forecasting techniques applied. In this paper, a hybrid approach to project time series is suggested. To validate the methodology, a time series already modeled by other authors was chosen, allowing the comparison of results. The proposed methodology includes the following techniques: wavelet shrinkage, wavelet decomposition at level r, and artificial neural networks (ANN. Firstly, a time series to be forecasted is submitted to the proposed wavelet filtering method, which decomposes it to components of trend and linear residue. Then, both are decomposed via level r wavelet decomposition, generating r + 1 Wavelet Components (WCs for each one; and then each WC is individually modeled by an ANN. Finally, the predictions for all WCs are linearly combined, producing forecasts to the underlying time series. For evaluating purposes, the time series of Canadian Lynx has been used, and all results achieved by the proposed method were better than others in existing literature.

  5. Advances in time series methods and applications the A. Ian McLeod festschrift

    CERN Document Server

    Stanford, David; Yu, Hao

    2016-01-01

    This volume reviews and summarizes some of A. I. McLeod's significant contributions to time series analysis. It also contains original contributions to the field and to related areas by participants of the festschrift held in June 2014 and friends of Dr. McLeod. Covering a diverse range of state-of-the-art topics, this volume well balances applied and theoretical research across fourteen contributions by experts in the field. It will be of interest to researchers and practitioners in time series, econometricians, and graduate students in time series or econometrics, as well as environmental statisticians, data scientists, statisticians interested in graphical models, and researchers in quantitative risk management.

  6. Thermal expansion of coking coals

    Energy Technology Data Exchange (ETDEWEB)

    Orlik, M.; Klimek, J. (Vyzkumny a Zkusebni Ustav Nova Hut, Ostrava (Czechoslovakia))

    1992-12-01

    Analyzes expansion of coal mixtures in coke ovens during coking. Methods for measuring coal expansion on both a laboratory and pilot plant scale are comparatively evaluated. The method, developed, tested and patented in Poland by the Institute for Chemical Coal Processing in Zabrze (Polish standard PN-73/G-04522), is discussed. A laboratory device developed by the Institute for measuring coal expansion is characterized. Expansion of black coal from 10 underground mines in the Ostrava-Karvina coal district and from 9 coal mines in the Upper Silesia basin in Poland is comparatively evaluated. Investigations show that coal expansion reaches a maximum for coal types with a volatile matter ranging from 20 to 25%. With increasing volatile matter in coal, its expansion decreases. Coal expansion increases with increasing swelling index. Coal expansion corresponds with coal dilatation. With increasing coal density its expansion increases. Coal mixtures should be selected in such a way that their expansion does not cause a pressure exceeding 40 MPa. 11 refs.

  7. Quantum Coherent States and Path Integral Method to Stochastically Determine the Anisotropic Volume Expansion in Lithiated Silicon Nanowires

    Directory of Open Access Journals (Sweden)

    Donald C. Boone

    2017-10-01

    Full Text Available This computational research study will analyze the multi-physics of lithium ion insertion into a silicon nanowire in an attempt to explain the electrochemical kinetics at the nanoscale and quantum level. The electron coherent states and a quantum field version of photon density waves will be the joining theories that will explain the electron-photon interaction within the lithium-silicon lattice structure. These two quantum particles will be responsible for the photon absorption rate of silicon atoms that are hypothesized to be the leading cause of breaking diatomic silicon covalent bonds that ultimately leads to volume expansion. It will be demonstrated through the combination of Maxwell stress tensor, optical amplification and path integrals that a stochastic analyze using a variety of Poisson distributions that the anisotropic expansion rates in the <110>, <111> and <112> orthogonal directions confirms the findings ascertained in previous works made by other research groups. The computational findings presented in this work are similar to those which were discovered experimentally using transmission electron microscopy (TEM and simulation models that used density functional theory (DFT and molecular dynamics (MD. The refractive index and electric susceptibility parameters of lithiated silicon are interwoven in the first principle theoretical equations and appears frequently throughout this research presentation, which should serve to demonstrate the importance of these parameters in the understanding of this component in lithium ion batteries.

  8. Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

    Science.gov (United States)

    Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.

    1998-01-01

    We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

  9. Most probable dimension value and most flat interval methods for automatic estimation of dimension from time series

    International Nuclear Information System (INIS)

    Corana, A.; Bortolan, G.; Casaleggio, A.

    2004-01-01

    We present and compare two automatic methods for dimension estimation from time series. Both methods, based on conceptually different approaches, work on the derivative of the bi-logarithmic plot of the correlation integral versus the correlation length (log-log plot). The first method searches for the most probable dimension values (MPDV) and associates to each of them a possible scaling region. The second one searches for the most flat intervals (MFI) in the derivative of the log-log plot. The automatic procedures include the evaluation of the candidate scaling regions using two reliability indices. The data set used to test the methods consists of time series from known model attractors with and without the addition of noise, structured time series, and electrocardiographic signals from the MIT-BIH ECG database. Statistical analysis of results was carried out by means of paired t-test, and no statistically significant differences were found in the large majority of the trials. Consistent results are also obtained dealing with 'difficult' time series. In general for a more robust and reliable estimate, the use of both methods may represent a good solution when time series from complex systems are analyzed. Although we present results for the correlation dimension only, the procedures can also be used for the automatic estimation of generalized q-order dimensions and pointwise dimension. We think that the proposed methods, eliminating the need of operator intervention, allow a faster and more objective analysis, thus improving the usefulness of dimension analysis for the characterization of time series obtained from complex dynamical systems

  10. New methods to minimize the preventive maintenance cost of series-parallel systems using ant colony optimization

    International Nuclear Information System (INIS)

    Samrout, M.; Yalaoui, F.; Cha-hat telet, E.; Chebbo, N.

    2005-01-01

    This article is based on a previous study made by Bris, Chatelet and Yalaoui [Bris R, Chatelet E, Yalaoui F. New method to minimise the preventive maintenance cost of series-parallel systems. Reliab Eng Syst Saf 2003;82:247-55]. They use genetic algorithm to minimize preventive maintenance cost problem for the series-parallel systems. We propose to improve their results developing a new method based on another technique, the Ant Colony Optimization (ACO). The resolution consists in determining the solution vector of system component inspection periods, T P . Those calculations were applied within the programming tool Matlab. Thus, highly interesting results and improvements of previous studies were obtained

  11. A Time-Series Water Level Forecasting Model Based on Imputation and Variable Selection Method

    OpenAIRE

    Jun-He Yang; Ching-Hsue Cheng; Chia-Pan Chan

    2017-01-01

    Reservoirs are important for households and impact the national economy. This paper proposed a time-series forecasting model based on estimating a missing value followed by variable selection to forecast the reservoir's water level. This study collected data from the Taiwan Shimen Reservoir as well as daily atmospheric data from 2008 to 2015. The two datasets are concatenated into an integrated dataset based on ordering of the data as a research dataset. The proposed time-series forecasting m...

  12. Comparison of different Methods for Univariate Time Series Imputation in R

    OpenAIRE

    Moritz, Steffen; Sardá, Alexis; Bartz-Beielstein, Thomas; Zaefferer, Martin; Stork, Jörg

    2015-01-01

    Missing values in datasets are a well-known problem and there are quite a lot of R packages offering imputation functions. But while imputation in general is well covered within R, it is hard to find functions for imputation of univariate time series. The problem is, most standard imputation techniques can not be applied directly. Most algorithms rely on inter-attribute correlations, while univariate time series imputation needs to employ time dependencies. This paper provides an overview of ...

  13. Resonant state expansions

    International Nuclear Information System (INIS)

    Lind, P.

    1993-02-01

    The completeness properties of the discrete set of bound state, virtual states and resonances characterizing the system of a single nonrelativistic particle moving in a central cutoff potential is investigated. From a completeness relation in terms of these discrete states and complex scattering states one can derive several Resonant State Expansions (RSE). It is interesting to obtain purely discrete expansion which, if valid, would significantly simplify the treatment of the continuum. Such expansions can be derived using Mittag-Leffler (ML) theory for a cutoff potential and it would be nice to see if one can obtain the same expansions starting from an eigenfunction theory that is not restricted to a finite sphere. The RSE of Greens functions is especially important, e.g. in the continuum RPA (CRPA) method of treating giant resonances in nuclear physics. The convergence of RSE is studied in simple cases using square well wavefunctions in order to achieve high numerical accuracy. Several expansions can be derived from each other by using the theory of analytic functions and one can the see how to obtain a natural discretization of the continuum. Since the resonance wavefunctions are oscillating with an exponentially increasing amplitude, and therefore have to be interpreted through some regularization procedure, every statement made about quantities involving such states is checked by numerical calculations.Realistic nuclear wavefunctions, generated by a Wood-Saxon potential, are used to test also the usefulness of RSE in a realistic nuclear calculation. There are some fundamental differences between different symmetries of the integral contour that defines the continuum in RSE. One kind of symmetry is necessary to have an expansion of the unity operator that is idempotent. Another symmetry must be used if we want purely discrete expansions. These are found to be of the same form as given by ML. (29 refs.)

  14. From greedy to lazy expansions and their driving dynamics

    NARCIS (Netherlands)

    Dajani, K.; Kraaikamp, C.

    2001-01-01

    In this paper we study the ergodic properties of non-greedy series expansions to non-integer bases β > 1. It is shown that the so-called 'lazy' expansion is isomorphic to the 'greedy' expansion. Furthermore, a class of expansions to base β > 1, β =2 Z, 'in between' the lazy and the greedy

  15. Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

    Science.gov (United States)

    Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

    2014-01-01

    In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

  16. Planar ESPAR Array Design with Nonsymmetrical Pattern by Means of Finite-Element Method, Domain Decomposition, and Spherical Wave Expansion

    Directory of Open Access Journals (Sweden)

    Jesús García

    2012-01-01

    Full Text Available The application of a 3D domain decomposition finite-element and spherical mode expansion for the design of planar ESPAR (electronically steerable passive array radiator made with probe-fed circular microstrip patches is presented in this work. A global generalized scattering matrix (GSM in terms of spherical modes is obtained analytically from the GSM of the isolated patches by using rotation and translation properties of spherical waves. The whole behaviour of the array is characterized including all the mutual coupling effects between its elements. This procedure has been firstly validated by analyzing an array of monopoles on a ground plane, and then it has been applied to synthesize a prescribed radiation pattern optimizing the reactive loads connected to the feeding ports of the array of circular patches by means of a genetic algorithm.

  17. Kato expansion in quantum canonical perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)

    2016-06-15

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  18. Kato expansion in quantum canonical perturbation theory

    International Nuclear Information System (INIS)

    Nikolaev, Andrey

    2016-01-01

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  19. A cluster expansion approach to exponential random graph models

    International Nuclear Information System (INIS)

    Yin, Mei

    2012-01-01

    The exponential family of random graphs are among the most widely studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated using cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region

  20. Application of the Laplace transform method for computational modelling of radioactive decay series

    Energy Technology Data Exchange (ETDEWEB)

    Oliveira, Deise L.; Damasceno, Ralf M.; Barros, Ricardo C. [Univ. do Estado do Rio de Janeiro (IME/UERJ) (Brazil). Programa de Pos-graduacao em Ciencias Computacionais

    2012-03-15

    It is well known that when spent fuel is removed from the core, it is still composed of considerable amount of radioactive elements with significant half-lives. Most actinides, in particular plutonium, fall into this category, and have to be safely disposed of. One solution is to store the long-lived spent fuel as it is, by encasing and burying it deep underground in a stable geological formation. This implies estimating the transmutation of these radioactive elements with time. Therefore, we describe in this paper the application of the Laplace transform technique in matrix formulation to analytically solve initial value problems that mathematically model radioactive decay series. Given the initial amount of each type of radioactive isotopes in the decay series, the computer code generates the amount at a given time of interest, or may plot a graph of the evolution in time of the amount of each type of isotopes in the series. This computer code, that we refer to as the LTRad{sub L} code, where L is the number of types of isotopes belonging to the series, was developed using the Scilab free platform for numerical computation and can model one segment or the entire chain of any of the three radioactive series existing on Earth today. Numerical results are given to typical model problems to illustrate the computer code efficiency and accuracy. (orig.)

  1. Application of the Laplace transform method for computational modelling of radioactive decay series

    International Nuclear Information System (INIS)

    Oliveira, Deise L.; Damasceno, Ralf M.; Barros, Ricardo C.

    2012-01-01

    It is well known that when spent fuel is removed from the core, it is still composed of considerable amount of radioactive elements with significant half-lives. Most actinides, in particular plutonium, fall into this category, and have to be safely disposed of. One solution is to store the long-lived spent fuel as it is, by encasing and burying it deep underground in a stable geological formation. This implies estimating the transmutation of these radioactive elements with time. Therefore, we describe in this paper the application of the Laplace transform technique in matrix formulation to analytically solve initial value problems that mathematically model radioactive decay series. Given the initial amount of each type of radioactive isotopes in the decay series, the computer code generates the amount at a given time of interest, or may plot a graph of the evolution in time of the amount of each type of isotopes in the series. This computer code, that we refer to as the LTRad L code, where L is the number of types of isotopes belonging to the series, was developed using the Scilab free platform for numerical computation and can model one segment or the entire chain of any of the three radioactive series existing on Earth today. Numerical results are given to typical model problems to illustrate the computer code efficiency and accuracy. (orig.)

  2. Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

    Science.gov (United States)

    Jia, Weile; Lin, Lin

    2017-10-01

    Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

  3. Dating of the middle Palaeolithic site of Payre (Ardeche): new radiometric data (U-series and ESR methods)

    International Nuclear Information System (INIS)

    Masaoudi, H.; Falgueres, Ch.; Bahain, J.J.; Moncel, M.H.

    1997-01-01

    The site of Payre is located in Ardeche. Several archaeological layers containing lithic artefacts of Middle Palaeolithic were found. These artefacts lie associated with carbonate formations which are good chronostratigraphic markers. The U-series and ESR methods on bones and stalagmitic floors placed the human occupation between isotopic marine stages 7 and 4. (authors)

  4. Combining Different Conceptual Change Methods within Four-Step Constructivist Teaching Model: A Sample Teaching of Series and Parallel Circuits

    Science.gov (United States)

    Ipek, Hava; Calik, Muammer

    2008-01-01

    Based on students' alternative conceptions of the topics "electric circuits", "electric charge flows within an electric circuit", "how the brightness of bulbs and the resistance changes in series and parallel circuits", the current study aims to present a combination of different conceptual change methods within a four-step constructivist teaching…

  5. Low Thermal Expansion Glass Ceramics

    CERN Document Server

    Bach, Hans

    2005-01-01

    This book appears in the authoritative series reporting the international research and development activities conducted by the Schott group of companies. This series provides an overview of Schott's activities for scientists, engineers, and managers from all branches of industry worldwide in which glasses and glass ceramics are of interest. Each volume begins with a chapter providing a general idea of the current problems, results, and trends relating to the subjects treated. This new extended edition describes the fundamental principles, the manufacturing process, and applications of low thermal expansion glass ceramics. The composition, structure, and stability of polycrystalline materials having a low thermal expansion are described, and it is shown how low thermal expansion glass ceramics can be manufactured from appropriately chosen glass compositions. Examples illustrate the formation of this type of glass ceramic by utilizing normal production processes together with controlled crystallization. Thus g...

  6. Low thermal expansion glass ceramics

    CERN Document Server

    1995-01-01

    This book is one of a series reporting on international research and development activities conducted by the Schott group of companies With the series, Schott aims to provide an overview of its activities for scientists, engineers, and managers from all branches of industry worldwide where glasses and glass ceramics are of interest Each volume begins with a chapter providing a general idea of the current problems, results, and trends relating to the subjects treated This volume describes the fundamental principles, the manufacturing process, and applications of low thermal expansion glass ceramics The composition, structure, and stability of polycrystalline materials having a low thermal expansion are described, and it is shown how low thermal expansion glass ceramics can be manufactured from appropriately chosen glass compositions Examples illustrate the formation of this type of glass ceramic by utilizing normal production processes together with controlled crystallization Thus glass ceramics with thermal c...

  7. Light-Cone Expansion of the Dirac Sea in the Presence of Chiral and Scalar Potentials

    OpenAIRE

    Finster, Felix

    1998-01-01

    We study the Dirac sea in the presence of external chiral and scalar/pseudoscalar potentials. In preparation, a method is developed for calculating the advanced and retarded Green's functions in an expansion around the light cone. For this, we first expand all Feynman diagrams and then explicitly sum up the perturbation series. The light-cone expansion expresses the Green's functions as an infinite sum of line integrals over the external potential and its partial derivatives. The Dirac sea is...

  8. A summation procedure for expansions in orthogonal polynomials

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Grinstein, F.F.

    1977-01-01

    Approximants to functions defined by formal series expansions in orthogonal polynomials are introduced. They are shown to be convergent even out of the elliptical domain where the original expansion converges

  9. Simulation of ion behavior in an open three-dimensional Paul trap using a power series method

    Energy Technology Data Exchange (ETDEWEB)

    Herbane, Mustapha Said, E-mail: mherbane@hotmail.com [King Khalid University, Faculty of Science, Department of Physics, P.O. Box 9004, Abha (Saudi Arabia); Berriche, Hamid [King Khalid University, Faculty of Science, Department of Physics, P.O. Box 9004, Abha (Saudi Arabia); Laboratoire des Interfaces et Matériaux Avancés, Physics Department, College of Science, University of Monastir, 5019 Monastir (Tunisia); Abd El-hady, Alaa [King Khalid University, Faculty of Science, Department of Physics, P.O. Box 9004, Abha (Saudi Arabia); Department of Physics, Faculty of Science, Zagazig University, Zagazig 44519 (Egypt); Al Shahrani, Ghadah [King Khalid University, Faculty of Science, Department of Physics, P.O. Box 9004, Abha (Saudi Arabia); Ban, Gilles; Fléchard, Xavier; Liénard, Etienne [LPC CAEN-ENSICAEN, 6 Boulevard du Marechal Juin, 14050 Caen Cedex (France)

    2014-07-01

    Simulations of the dynamics of ions trapped in a Paul trap with terms in the potential up to the order 10 have been carried out. The power series method is used to solve numerically the equations of motion of the ions. The stability diagram has been studied and the buffer gas cooling has been implemented by a Monte Carlo method. The dipole excitation was also included. The method has been applied to an existing trap and it has shown good agreement with the experimental results and previous simulations using other methods. - Highlights: • Paul trap with potentials up to the order 10. • Series solution of the ions equations of motion. • Hard sphere model for the simulation of the buffer gas cooling and simulation of the dipolar excitation.

  10. Statistical time series methods for damage diagnosis in a scale aircraft skeleton structure: loosened bolts damage scenarios

    International Nuclear Information System (INIS)

    Kopsaftopoulos, Fotis P; Fassois, Spilios D

    2011-01-01

    A comparative assessment of several vibration based statistical time series methods for Structural Health Monitoring (SHM) is presented via their application to a scale aircraft skeleton laboratory structure. A brief overview of the methods, which are either scalar or vector type, non-parametric or parametric, and pertain to either the response-only or excitation-response cases, is provided. Damage diagnosis, including both the detection and identification subproblems, is tackled via scalar or vector vibration signals. The methods' effectiveness is assessed via repeated experiments under various damage scenarios, with each scenario corresponding to the loosening of one or more selected bolts. The results of the study confirm the 'global' damage detection capability and effectiveness of statistical time series methods for SHM.

  11. Time-series-based hybrid mathematical modelling method adapted to forecast automotive and medical waste generation: Case study of Lithuania.

    Science.gov (United States)

    Karpušenkaitė, Aistė; Ruzgas, Tomas; Denafas, Gintaras

    2018-05-01

    The aim of the study was to create a hybrid forecasting method that could produce higher accuracy forecasts than previously used 'pure' time series methods. Mentioned methods were already tested with total automotive waste, hazardous automotive waste, and total medical waste generation, but demonstrated at least a 6% error rate in different cases and efforts were made to decrease it even more. Newly developed hybrid models used a random start generation method to incorporate different time-series advantages and it helped to increase the accuracy of forecasts by 3%-4% in hazardous automotive waste and total medical waste generation cases; the new model did not increase the accuracy of total automotive waste generation forecasts. Developed models' abilities to forecast short- and mid-term forecasts were tested using prediction horizon.

  12. On summation of perturbation expansions

    International Nuclear Information System (INIS)

    Horzela, A.

    1985-04-01

    The problem of the restoration of physical quantities defined by divergent perturbation expansions is analysed. The Pad'e and Borel summability is proved for alternating perturbation expansions with factorially growing coefficients. The proof is based on the methods of the classical moments theory. 17 refs. (author)

  13. Multipotent Mesenchymal Stromal Stem Cell Expansion by Plating Whole Bone Marrow at a Low Cellular Density: A More Advantageous Method for Clinical Use

    Directory of Open Access Journals (Sweden)

    Katia Mareschi

    2012-01-01

    Full Text Available Mesenchymal stem cells (MSCs are a promising source for cell therapy due to their pluripotency and immunomodulant proprieties. As the identification of “optimal” conditions is important to identify a standard procedure for clinical use. Percoll, Ficoll and whole bone marrow directly plated were tested from the same sample as separation methods. The cells were seeded at the following densities: 100 000, 10 000, 1000, 100, 10 cells/cm2. After reaching confluence, the cells were detached, pooled and re-plated at 1000, 500, 100, and 10 cells/cm2. Statistical analyses were performed. Cumulative Population Doublings (PD did not show significant differences for the separation methods and seeding densities but only for the plating density. Some small quantity samples plated in T25 flasks at plating densities of 10 and 100 cells/cm2 did not produce any expansion. However, directly plated whole bone marrow resulted in a more advantageous method in terms of CFU-F number, cellular growth and minimal manipulation. No differences were observed in terms of gross morphology, differentiation potential or immunophenotype. These data suggest that plating whole bone marrow at a low cellular density may represent a good procedure for MSC expansion for clinical use.

  14. Multipotent Mesenchymal Stromal Stem Cell Expansion by Plating Whole Bone Marrow at a Low Cellular Density: A More Advantageous Method for Clinical Use

    Science.gov (United States)

    Mareschi, Katia; Rustichelli, Deborah; Calabrese, Roberto; Gunetti, Monica; Sanavio, Fiorella; Castiglia, Sara; Risso, Alessandra; Ferrero, Ivana; Tarella, Corrado; Fagioli, Franca

    2012-01-01

    Mesenchymal stem cells (MSCs) are a promising source for cell therapy due to their pluripotency and immunomodulant proprieties. As the identification of “optimal” conditions is important to identify a standard procedure for clinical use. Percoll, Ficoll and whole bone marrow directly plated were tested from the same sample as separation methods. The cells were seeded at the following densities: 100 000, 10 000, 1000, 100, 10 cells/cm2. After reaching confluence, the cells were detached, pooled and re-plated at 1000, 500, 100, and 10 cells/cm2. Statistical analyses were performed. Cumulative Population Doublings (PD) did not show significant differences for the separation methods and seeding densities but only for the plating density. Some small quantity samples plated in T25 flasks at plating densities of 10 and 100 cells/cm2 did not produce any expansion. However, directly plated whole bone marrow resulted in a more advantageous method in terms of CFU-F number, cellular growth and minimal manipulation. No differences were observed in terms of gross morphology, differentiation potential or immunophenotype. These data suggest that plating whole bone marrow at a low cellular density may represent a good procedure for MSC expansion for clinical use. PMID:23715383

  15. A Phenology-Based Method for Monitoring Woody and Herbaceous Vegetation in Mediterranean Forests from NDVI Time Series

    OpenAIRE

    David Helman; Itamar M. Lensky; Naama Tessler; Yagil Osem

    2015-01-01

    We present an efficient method for monitoring woody (i.e., evergreen) and herbaceous (i.e., ephemeral) vegetation in Mediterranean forests at a sub pixel scale from Normalized Difference Vegetation Index (NDVI) time series derived from the Moderate Resolution Imaging Spectroradiometer (MODIS). The method is based on the distinct development periods of those vegetation components. In the dry season, herbaceous vegetation is absent or completely dry in Mediterranean forests. Thus the mean NDVI ...

  16. Trend analysis of time-series data: A novel method for untargeted metabolite discovery

    NARCIS (Netherlands)

    Peters, S.; Janssen, H.-G.; Vivó-Truyols, G.

    2010-01-01

    A new strategy for biomarker discovery is presented that uses time-series metabolomics data. Data sets from samples analysed at different time points after an intervention are searched for compounds that show a meaningful trend following the intervention. Obviously, this requires new data-analytical

  17. THE EFFECT OF DECOMPOSITION METHOD AS DATA PREPROCESSING ON NEURAL NETWORKS MODEL FOR FORECASTING TREND AND SEASONAL TIME SERIES

    Directory of Open Access Journals (Sweden)

    Subanar Subanar

    2006-01-01

    Full Text Available Recently, one of the central topics for the neural networks (NN community is the issue of data preprocessing on the use of NN. In this paper, we will investigate this topic particularly on the effect of Decomposition method as data processing and the use of NN for modeling effectively time series with both trend and seasonal patterns. Limited empirical studies on seasonal time series forecasting with neural networks show that some find neural networks are able to model seasonality directly and prior deseasonalization is not necessary, and others conclude just the opposite. In this research, we study particularly on the effectiveness of data preprocessing, including detrending and deseasonalization by applying Decomposition method on NN modeling and forecasting performance. We use two kinds of data, simulation and real data. Simulation data are examined on multiplicative of trend and seasonality patterns. The results are compared to those obtained from the classical time series model. Our result shows that a combination of detrending and deseasonalization by applying Decomposition method is the effective data preprocessing on the use of NN for forecasting trend and seasonal time series.

  18. Chromatic Derivatives, Chromatic Expansions and Associated Spaces

    OpenAIRE

    Ignjatovic, Aleksandar

    2009-01-01

    This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess the best features of both the Taylor and the Shannon expansions. This makes chromatic derivatives and ...

  19. Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

    Directory of Open Access Journals (Sweden)

    Q. Zhang

    2018-02-01

    Full Text Available River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1 fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2 the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β or other equivalent scaling parameters (e.g., Hurst exponent – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1 they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0 to Brown noise (β  =  2 and (2 their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among

  20. Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

    Science.gov (United States)

    Zhang, Qian; Harman, Ciaran J.; Kirchner, James W.

    2018-02-01

    River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling - in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of