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.

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.

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.)

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.

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)

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.

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.

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

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

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.

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)

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.

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.

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)

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.

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.

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)

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 ...

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)

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.

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.

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

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.

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

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

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...

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

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

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)

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.

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.

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,…

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.

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.

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.

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.

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

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.

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.

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)

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)

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.

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

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.

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.

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.

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.

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

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.)

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}.

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.

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

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.

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

[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.

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

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.)

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

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.

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.)

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.

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

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.

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

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.

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)

More on zeta-function regularization of high-temperature expansions

International Nuclear Information System (INIS)

Actor, A.

1987-01-01

A recent paper using the Riemann ζ-function to regularize the (divergent) coefficients occurring in the high-temperature expansions of one-loop thermodynamic potentials is extended. This method proves to be a powerful tool for converting Dirichlet-type series Σ m a m (x i )/m s into power series in the dimensionless parameters x i . The coefficients occurring in the power series are (proportional to) ζ-functions evaluated away from their poles - this is where the regularization occurs. High-temperature expansions are just one example of this highly-nontrivial rearrangement of Dirichlet series into power series form. We discuss in considerable detail series in which a m (x i ) is a product of trigonometric, algebraic and Bessel function factors. The ζ-function method is carefully explained, and a large number of new formulae are provided. The means to generalize these formulae are also provided. Previous results on thermodynamic potentials are generalized to include a nonzero constant term in the gauge potential (time component) which can be used to probe the electric sector of temperature gauge theories. (author)

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.

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.

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.

[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.

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.)

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.

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.

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.

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

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.

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.

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

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

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)

Coupling-parameter expansion in thermodynamic perturbation theory.

Science.gov (United States)

Ramana, A Sai Venkata; Menon, S V G

2013-02-01

An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.

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

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.

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.

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

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.

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.

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.

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

Science.gov (United States)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral

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)

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.

Convergent Power Series of sech⁡(x and Solutions to Nonlinear Differential Equations

Directory of Open Access Journals (Sweden)

U. Al Khawaja

2018-01-01

Full Text Available It is known that power series expansion of certain functions such as sech⁡(x diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS to obtain a power series representation of sech⁡(x that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2. A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.

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

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.

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

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.

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...

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

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

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.

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.

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...

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...

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.

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.

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

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.

Dressed skeleton expansion and the coupling scale ambiguity problem

International Nuclear Information System (INIS)

Lu, Hung Jung.

1992-09-01

Perturbative expansions in quantum field theories are usually expressed in powers of a coupling constant. In principle, the infinite sum of the expansion series is independent of the renormalization scale of the coupling constant. In practice, there is a remnant dependence of the truncated series on the renormalization scale. This scale ambiguity can severely restrict the predictive power of theoretical calculations. The dressed skeleton expansion is developed as a calculational method which avoids the coupling scale ambiguity problem. In this method, physical quantities are expressed as functional expansions in terms of a coupling vertex function. The arguments of the vertex function are given by the physical momenta of each process. These physical momenta effectively replace the unspecified renormalization scale and eliminate the ambiguity problem. This method is applied to various field theoretical models and its main features and limitations are explored. For quantum chromodynamics, an expression for the running coupling constant of the three-gluon vertex is obtained. The effective coupling scale of this vertex is shown to be essentially given by μ 2 ∼ Q min 2 Q med 2 /Q max 2 where Q min 2 Q med 2 /Q max 2 are respectively the smallest, the next-to-smallest and the largest scale among the three gluon virtualities. This functional form suggests that the three-gluon vertex becomes non-perturbative at asymmetric momentum configurations. Implications for four-jet physics is discussed

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.

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

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.

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

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.

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.

A mutually profitable alliance - Asymptotic expansions and numerical computations

Science.gov (United States)

Euvrard, D.

Problems including the flow past a wing airfoil at Mach 1, and the two-dimensional flow past a partially immersed body are used to show the advantages of coupling a standard numerical method for the whole domain where everything is of the order of 1, with an appropriate asymptotic expansion in the vicinity of some singular point. Cases more closely linking the two approaches are then considered. In the localized finite element method, the asymptotic expansion at infinity becomes a convergent series and the problem reduces to a variational form. Combined analytical and numerical methods are used in the singularity distribution method and in the various couplings of finite elements and a Green integral representation to design a subroutine to compute the Green function and its derivatives.

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.

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

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 ...

Computation of solar perturbations with Poisson series

Science.gov (United States)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

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.

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

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.

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.

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

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

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.

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

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...

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...

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

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.

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.

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

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

Transmutation of a trans-series: the Gross-Witten-Wadia phase transition

Science.gov (United States)

Ahmed, Anees; Dunne, Gerald V.

2017-11-01

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g 2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms `condense' at the transition point to match with the double-scaling limit trans-series. We also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.

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 ...

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

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

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.

A new separable expansion for the two-body problem

International Nuclear Information System (INIS)

Haberzettl, H.

1988-07-01

We derive a new separable expansion of the two-body T matrix which represents the T matrix as a series of diagonal separable terms. The representation is exact half-on-shell at all energies even when truncated to one single term; moreover, the truncated expansion satisfies the full off-shell unitarity relation. The approach does not take recourse to some complete set of functions but rather uses properties of the Lippmann-Schwinger equation itself to arrive at the expansion. It is based on the W-matrix representation of the two-body T matrix introduced by Bartnik, Haberzettl, and Sandhas. That representation provides a splitting of the T matrix in one single separable term which contains all bound state poles and scatttering cuts and in a nonsingular, real remainder which vanishes half-on-shell. The method presented here yields a separable expansion of this remainder in which all its properties are preserved term by term. Any given n-term approximation can easily be refined to an (n+1)-term expansion by simply adding a new term. At each stage the amount of additional numerical work is constant. The method is applicable to any kind of short range potential, local, nonlocal or energy dependent. (orig.)

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.

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)

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)

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 ...

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 ...

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

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)

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

Convergent WKB Series--How Can It be ?

International Nuclear Information System (INIS)

Ezawa, Hiroshi; Nakamura, Toru; Watanabe, Keiji

2008-01-01

Schroedinger equation for a polynomial potential with the highest order term having an even power and a positive coefficient is solved for high eigenvalues E n in two different ways after Liouville transformation, (a) converting the differential equation into integral equation and solving it iteratively and (b) by the WKB method. While the series solution in powers of 1/√(E n ) from (b) is known to diverge, we show that the one from (a) converges. We show then that asymptotic re-expansion of the convergent series from (a) agrees with the divergent series from (b). Actually, we have been able to show the agreement only up to order (1/√(E n )) 5 , but we believe that it holds to all orders. If this is true, the divergent WKB series can be reorganized into a convergent series, which is in fact obtained by the method of iteration (a)

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.

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)

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

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

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

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.

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.

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.

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)

Optimisation of expansion liquefaction processes using mixed refrigerant N_2–CH_4

International Nuclear Information System (INIS)

Ding, He; Sun, Heng; He, Ming

2016-01-01

Highlights: • A refrigerant composition matching method for N_2–CH_4 expansion processes. • Efficiency improvements for propane pre-cooled N_2–CH_4 expansion processes. • The process shows good adaptability to varying natural gas compositions. - Abstract: An expansion process with a pre-cooling system is simulated and optimised by Aspen HYSYS and MATLAB"™. Taking advantage of higher specific refrigeration effect of methane and easily reduced refrigeration temperature of nitrogen, the designed process adopts N_2–CH_4 as a mixed refrigerant. Based on the different thermodynamic properties and sensitivity difference of N_2 and CH_4 over the same heat transfer temperature range, this work proposes a novel method of matching refrigerant composition which aims at single-stage or multi-stage series expansion liquefaction processes with pre-cooling systems. This novel method is applied successfully in propane pre-cooled N_2–CH_4 expansion process, and the unit power consumption is reduced to 7.09 kWh/kmol, which is only 5.35% higher than the global optimised solutions obtained by genetic algorithm. This novel method can fulfil the accomplishments of low energy consumption and high liquefaction rate, and thus decreases the gap between the mixed refrigerant and expansion processes in energy consumption. Furthermore, the high exergy efficiency of the process indicates good adaptability to varying natural gas compositions.

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.

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

The Hubble series: convergence properties and redshift variables

International Nuclear Information System (INIS)

Cattoen, Celine; Visser, Matt

2007-01-01

In cosmography, cosmokinetics and cosmology, it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available; for instance, we have supernova data at least back to redshift z ∼ 1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift. Based on a combination of mathematical and physical reasonings, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z > 1, corresponding to a universe less than half of its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parametrization y = z/(1 + z). In terms of the y-redshift, we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang (y = 1), but that y-based expansions must break down for y < -1, now corresponding to a universe more than twice its current size

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

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.

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.

Quantum field theory in the presence of a medium: Green's function expansions

Energy Technology Data Exchange (ETDEWEB)

Kheirandish, Fardin [Department of Physics, Islamic Azad University, Shahreza-Branch, Shahreza (Iran, Islamic Republic of); Salimi, Shahriar [Department of Physics, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

2011-12-15

Starting from a Lagrangian and using functional-integration techniques, series expansions of Green's function of a real scalar field and electromagnetic field, in the presence of a medium, are obtained. The parameter of expansion in these series is the susceptibility function of the medium. Relativistic and nonrelativistic Langevin-type equations are derived. Series expansions for Lifshitz energy in finite temperature and for an arbitrary matter distribution are derived. Covariant formulations for both scalar and electromagnetic fields are introduced. Two illustrative examples are given.

Wigner-Kirkwood expansion of the phase-space density for half infinite nuclear matter

International Nuclear Information System (INIS)

Durand, M.; Schuck, P.

1987-01-01

The phase space distribution of half infinite nuclear matter is expanded in a ℎ-series analogous to the low temperature expansion of the Fermi function. Besides the usual Wigner-Kirkwood expansion, oscillatory terms are derived. In the case of a Woods-Saxon potential, a smallness parameter is defined, which determines the convergence of the series and explains the very rapid convergence of the Wigner-Kirkwood expansion for average (nuclear) binding energies

Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes

Science.gov (United States)

Liu, Zhangjun; Liu, Zixin; Peng, Yongbo

2017-11-01

Conventional Karhunen-Loeve expansions for simulation of stochastic processes often encounter the challenge of dealing with hundreds of random variables. For breaking through the barrier, a random function embedded Karhunen-Loeve expansion method is proposed in this paper. The updated scheme has a similar form to the conventional Karhunen-Loeve expansion, both involving a summation of a series of deterministic orthonormal basis and uncorrelated random variables. While the difference from the updated scheme lies in the dimension reduction of Karhunen-Loeve expansion through introducing random functions as a conditional constraint upon uncorrelated random variables. The random function is expressed as a single-elementary-random-variable orthogonal function in polynomial format (non-Gaussian variables) or trigonometric format (non-Gaussian and Gaussian variables). For illustrative purposes, the simulation of seismic ground motion is carried out using the updated scheme. Numerical investigations reveal that the Karhunen-Loeve expansion with random functions could gain desirable simulation results in case of a moderate sample number, except the Hermite polynomials and the Laguerre polynomials. It has the sound applicability and efficiency in simulation of stochastic processes. Besides, the updated scheme has the benefit of integrating with probability density evolution method, readily for the stochastic analysis of nonlinear structures.

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.

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.

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...

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

International Nuclear Information System (INIS)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

Highlights: • Paraxial beams are represented in a series expansion in terms of Bessel wave functions. • The coefficients of the series expansion can be analytically determined by using the pattern in the focal plane. • In particular, Gaussian beams and apertured wave fields have been critically examined. • This representation of the wave field is adequate for scattering problems with shaped beams. - Abstract: The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Generalized heat kernel coefficients for a new asymptotic expansion

International Nuclear Information System (INIS)

Osipov, Alexander A.; Hiller, Brigitte

2003-01-01

The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified

Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free Approach

OpenAIRE

Cyril Grunspan

2011-01-01

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in terms of a power series in call price.

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.

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

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

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)

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.

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

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.

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.

An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Moh’d Khier Al-Srihin

2017-01-01

Full Text Available In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.

The Laplace series solution for local fractional Korteweg-de Vries equation

Directory of Open Access Journals (Sweden)

Ye Shan-Shan

2016-01-01

Full Text Available In this paper, we consider a new application of the local fractional Laplace series expansion method to handle the local fractional Korteweg-de Vries equation. The obtained solution with non-differentiable type shows that the technology is accurate and efficient.

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.

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

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

Fourier expansions and multivariable Bessel functions concerning radiation programmes

International Nuclear Information System (INIS)

Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.

1996-01-01

The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)

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).

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...

Linked cluster expansion in the SU(2) lattice Higgs model at strong gauge coupling

International Nuclear Information System (INIS)

Wagner, C.E.M.

1989-01-01

A linked cluster expansion is developed for the β=0 limit of the SU(2) Higgs model. This method, when combined with strong gauge coupling expansions, is used to obtain the phase transition surface and the behaviour of scalar and vector masses in the lattice regularized theory. The method, in spite of the low order of truncation of the series applied, gives a reasonable agreement with Monte Carlo data for the phase transition surface and a qualitatively good picture of the behaviour of Higgs, glueball and gauge vector boson masses, in the strong coupling limit. Some limitations of the method are discussed, and an intuitive picture of the different behaviour for small and large bare self-coupling λ is given. (orig.)

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.

Does query expansion limit our learning? A comparison of social-based expansion to content-based expansion for medical queries on the internet.

Science.gov (United States)

Pentoney, Christopher; Harwell, Jeff; Leroy, Gondy

2014-01-01

Searching for medical information online is a common activity. While it has been shown that forming good queries is difficult, Google's query suggestion tool, a type of query expansion, aims to facilitate query formation. However, it is unknown how this expansion, which is based on what others searched for, affects the information gathering of the online community. To measure the impact of social-based query expansion, this study compared it with content-based expansion, i.e., what is really in the text. We used 138,906 medical queries from the AOL User Session Collection and expanded them using Google's Autocomplete method (social-based) and the content of the Google Web Corpus (content-based). We evaluated the specificity and ambiguity of the expansion terms for trigram queries. We also looked at the impact on the actual results using domain diversity and expansion edit distance. Results showed that the social-based method provided more precise expansion terms as well as terms that were less ambiguous. Expanded queries do not differ significantly in diversity when expanded using the social-based method (6.72 different domains returned in the first ten results, on average) vs. content-based method (6.73 different domains, on average).

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

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)

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.)

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.

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

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.

Operator expansion in quantum chromodynamics beyond perturbation theory

International Nuclear Information System (INIS)

Novikov, V.A.; Shifman, M.A.; Vainshtejn, A.I.; Zakharov, V.I.

1980-01-01

The status of operator expansion at short distances is descussed within the frameworks of nonperturbatue QCD. The question of instanton effects is investigated in various aspects. Two-point functions induced by the gluonic currents are considered. It is shown that certain gluonic correlations vanish in the field of definite duality. It is proved that there does exist a very special relation between the expansion coefficients required by consistancy between instanton calculations and the general operator expansion. At last a certain modification of the naive version of operator expansion is proposed, which allows one to go beyond the critical power and construct, if necessary, an infinite series

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.

The delta expansion in zero dimensions

International Nuclear Information System (INIS)

Cho, H.T.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.

1989-01-01

The recently introduced δ-expansion (or logarithmic-expansion) technique for obtaining nonperturbative information about quantum field theories is reviewed in the zero-dimensional context. There, it is easy to study questions of analytic continuation that arise in the construction of the Feynman rules that generate the δ series. It is found that for six- and higher-point Green's functions, a cancellation occurs among the most divergent terms, and that divergences that arise from summing over an infinite number of internal lines are illusory. The numerical accuracy is studied in some detail: The δ series converges inside a circle of radius one for positive bare mass squared, and diverges if the bare mass squared is negative, but in all cases, low-order Pade approximants are extremely accurate. These general features are expected to hold in higher dimensions, such as four

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

The Exponential Model for the Spectrum of a Time Series: Extensions and Applications

DEFF Research Database (Denmark)

Proietti, Tommaso; Luati, Alessandra

The exponential model for the spectrum of a time series and its fractional extensions are based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion form the cepstrum of the time series. After deriving the cepstrum of important classes of time...

Cluster expansion of the solvation free energy difference: Systematic improvements in the solvation of single ions

Science.gov (United States)

Pliego, Josefredo R.

2017-07-01

The cluster expansion method has been used in the imperfect gas theory for several decades. This paper proposes a cluster expansion of the solvation free energy difference. This difference, which results from a change in the solute-solvent potential energy, can be written as the logarithm of a finite series. Similar to the Mayer function, the terms in the series are related to configurational integrals, which makes the integrand relevant only for configurations of the solvent molecules close to the solute. In addition, the terms involve interaction of solute with one, two, and so on solvent molecules. The approach could be used for hybrid quantum mechanical and molecular mechanics methods or mixed cluster-continuum approximation. A simple form of the theory was applied for prediction of pKa in methanol; the results indicated that three explicit methanol molecules and the dielectric continuum lead to a root of mean squared error (RMSE) of only 1.3 pKa units, whereas the pure continuum solvation model based on density method leads to a RMSE of 6.6 pKa units.

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)

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.

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.

From Taylor series to Taylor models

International Nuclear Information System (INIS)

Berz, Martin

1997-01-01

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on the set of Taylor models, arbitrary order integrators with rigorous remainder treatment are developed. The integrators can meet pre-specified accuracy requirements in a mathematically strict way, and are a stepping stone towards fully rigorous estimates of stability of repetitive systems

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.

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.

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...

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.

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.

Analytical model of cracking due to rebar corrosion expansion in concrete considering the structure internal force

Science.gov (United States)

Lin, Xiangyue; Peng, Minli; Lei, Fengming; Tan, Jiangxian; Shi, Huacheng

2017-12-01

Based on the assumptions of uniform corrosion and linear elastic expansion, an analytical model of cracking due to rebar corrosion expansion in concrete was established, which is able to consider the structure internal force. And then, by means of the complex variable function theory and series expansion technology established by Muskhelishvili, the corresponding stress component functions of concrete around the reinforcement were obtained. Also, a comparative analysis was conducted between the numerical simulation model and present model in this paper. The results show that the calculation results of both methods were consistent with each other, and the numerical deviation was less than 10%, proving that the analytical model established in this paper is reliable.

Linked cluster expansions for open quantum systems on a lattice

Science.gov (United States)

Biella, Alberto; Jin, Jiasen; Viyuela, Oscar; Ciuti, Cristiano; Fazio, Rosario; Rossini, Davide

2018-01-01

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Padé analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.

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.

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.

The Thermal Expansion Of Feldspars

Science.gov (United States)

Hovis, G. L.; Medford, A.; Conlon, M.

2009-12-01

Hovis and others (1) investigated the thermal expansion of natural and synthetic AlSi3 feldspars and demonstrated that the coefficient of thermal expansion (α) decreases significantly, and linearly, with increasing room-temperature volume (VRT). In all such feldspars, therefore, chemical expansion limits thermal expansion. The scope of this work now has been broadened to include plagioclase and Ba-K feldspar crystalline solutions. X-ray powder diffraction data have been collected between room temperature and 925 °C on six plagioclase specimens ranging in composition from anorthite to oligoclase. When combined with thermal expansion data for albite (2,3,4) a steep linear trend of α as a function of VRT emerges, reflecting how small changes in composition dramatically affect expansion behavior. The thermal expansion data for five synthetic Ba-K feldspars ranging in composition from 20 to 100 mole percent celsian, combined with data for pure K-feldspar (3,4), show α-VRT relationships similar in nature to the plagioclase series, but with a slope and intercept different from the latter. Taken as a group all Al2Si2 feldspars, including anorthite and celsian from the present study along with Sr- (5) and Pb-feldspar (6) from other workers, show very limited thermal expansion that, unlike AlSi3 feldspars, has little dependence on the divalent-ion (or M-) site occupant. This apparently is due to the necessitated alternation of Al and Si in the tetrahedral sites of these minerals (7), which in turn locks the tetrahedral framework and makes the M-site occupant nearly irrelevant to expansion behavior. Indeed, in feldspar series with coupled chemical substitution it is the change away from a 1:1 Al:Si ratio that gives feldspars greater freedom to expand. Overall, the relationships among α, chemical composition, and room-temperature volume provide useful predictive tools for estimating feldspar thermal expansion and give insight into the controls of expansion behavior in

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

A convergence theorem for asymptotic expansions of Feynman amplitudes

International Nuclear Information System (INIS)

Mabouisson, A.P.C.

1999-06-01

The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to ∞, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)

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

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

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.

An exact power series formula of the outage probability with noise and interference over generalized fading channels

KAUST Repository

Rached, Nadhir B.

2016-12-24

In this paper, we develop a generalized momentbased approach for the evaluation of the outage probability (OP) in the presence of co-channel interference and additive white Gaussian noise. The proposed method allows the evaluation of the OP of the signal-to-interference-plus-noise ratio by a power series expansion in the threshold value. Its main advantage is that it does not require a particular distribution for the interference channels. The only necessary ingredients are a power series expansion for the cumulative distribution function of the desired user power and the cross-moments of the interferers\\' powers. These requirements are easily met in many practical fading models, for which the OP might not be obtained in closed-form expression. For a sake of illustration, we consider the application of our method to the Rician fading environment. Under this setting, we carry out a convergence study of the proposed power series and corroborate the validity of our method for different values of fading parameters and various numbers of co-channel interferers.

Regulation of gas infrastructure expansion

International Nuclear Information System (INIS)

De Joode, J.

2012-01-01

The topic of this dissertation is the regulation of gas infrastructure expansion in the European Union (EU). While the gas market has been liberalised, the gas infrastructure has largely remained in the regulated domain. However, not necessarily all gas infrastructure facilities - such as gas storage facilities, LNG import terminals and certain gas transmission pipelines - need to be regulated, as there may be scope for competition. In practice, the choice of regulation of gas infrastructure expansion varies among different types of gas infrastructure facilities and across EU Member States. Based on a review of economic literature and on a series of in-depth case studies, this study explains these differences in choices of regulation from differences in policy objectives, differences in local circumstances and differences in the intrinsic characteristics of the infrastructure projects. An important conclusion is that there is potential for a larger role for competition in gas infrastructure expansion.

Specific heat of Ginzburg-Landau fields in the n-1 expansion

International Nuclear Information System (INIS)

Bray, A.J.

1975-01-01

The n -1 expansion for the specific heat C/subv/ of the n-component Ginzburg-Landau model is discussed in terms of an n -1 expansion for the irreducible polarization. In the low-temperature limit, each successive term of the latter expansion diverges more strongly than the last, invalidating a truncation of this series at any finite order in 1/n. The most divergent terms in each order are identified and summed. The results provide justification for the usual truncated expansions for C/subv/

Thermal expansion in 3d-metal Prussian Blue Analogs-A survey study

International Nuclear Information System (INIS)

Adak, Sourav; Daemen, Luke L.; Hartl, Monika; Williams, Darrick; Summerhill, Jennifer; Nakotte, Heinz

2011-01-01

We present a comprehensive study of the structural properties and the thermal expansion behavior of 17 different Prussian Blue Analogs (PBAs) with compositions M II 3 [(M') III (CN) 6 ] 2 .nH 2 O and M II 2 [Fe II (CN) 6 ].nH 2 O, where M II =Mn, Fe, Co, Ni, Cu and Zn, (M') III =Co, Fe and n is the number of water molecules, which range from 5 to 18 for these compounds. The PBAs were synthesized via standard chemical precipitation methods, and temperature-dependent X-ray diffraction studies were performed in the temperature range between -150 deg. C (123 K) and room-temperature. The vast majority of the studied PBAs were found to crystallize in cubic structures of space groups Fm3-bar m, F4-bar 3m and Pm3-bar m. The temperature dependence of the lattice parameters was taken to compute an average coefficient of linear thermal expansion in the studied temperature range. Of the 17 compounds, 9 display negative values for the average coefficient of linear thermal expansion, which can be as large as 39.7x 1 0 -6 K -1 for Co 3 [Co(CN) 6 ] 2 .12H 2 O. All of the M II 3 [Co III (CN) 6 ] 2 .nH 2 O compounds show negative thermal expansion behavior, which correlates with the Irving-Williams series for metal complex stability. The thermal expansion behavior for the PBAs of the M II 3 [Fe III (CN) 6 ] 2 .nH 2 O family are found to switch between positive (for M=Mn, Co, Ni) and negative (M=Cu, Zn) behavior, depending on the choice of the metal cation (M). On the other hand, all of the M II 2 [Fe II (CN) 6 ].nH 2 O compounds show positive thermal expansion behavior. - Graphical Abstract: The structure of Prussian Blue analogs (PBAs) consists of two types of metal centered octahedral units connected by cyanide ligand. Lattice and interstitial water molecules are present in these framework structures. All the PBAs of the M 3 [Co(CN) 6 ] 2 .nH 2 O family show negative thermal expansion (NTE) behavior. The lattice parameters and magnitude of NTE correlates inversely with the Irving

Light-cone expansion of the Dirac sea in the presence of chiral and scalar potentials

Science.gov (United States)

Finster, Felix

2000-10-01

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 decomposed into a causal and a noncausal contribution. The causal contribution has a light-cone expansion which is closely related to the light-cone expansion of the Green's functions; it describes the singular behavior of the Dirac sea in terms of nested line integrals along the light cone. The noncausal contribution, on the other hand, is, to every order in perturbation theory, a smooth function in position space.

Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations

Directory of Open Access Journals (Sweden)

Bahman Ghazanfari

2013-08-01

Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.

Stochastic Neural Field Theory and the System-Size Expansion

KAUST Repository

Bressloff, Paul C.

2010-01-01

We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N → ∞) we recover standard activity-based or voltage-based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N) can be truncated to form a closed system of equations for the first-and second-order moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean-field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately determine exponentially small transitions. © by SIAM.

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

Expansions of general stationary stochastic optical fields: general formalism

International Nuclear Information System (INIS)

Martinez-Herrero, R.; Mejias, P.M.

1985-01-01

A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed

On the analyticity of Laguerre series

International Nuclear Information System (INIS)

Weniger, Ernst Joachim

2008-01-01

The transformation of a Laguerre series f(z) = Σ ∞ n=0 λ (α) n L (α) n (z) to a power series f(z) = Σ ∞ n=0 γ n z n is discussed. Since many nonanalytic functions can be expanded in terms of generalized Laguerre polynomials, success is not guaranteed and such a transformation can easily lead to a mathematically meaningless expansion containing power series coefficients that are infinite in magnitude. Simple sufficient conditions based on the decay rates and sign patterns of the Laguerre series coefficients λ (α) n as n → ∞ can be formulated which guarantee that the resulting power series represents an analytic function. The transformation produces a mathematically meaningful result if the coefficients λ (α) n either decay exponentially or factorially as n → ∞. The situation is much more complicated-but also much more interesting-if the λ (α) n decay only algebraically as n → ∞. If the λ (α) n ultimately have the same sign, the series expansions for the power series coefficients diverge, and the corresponding function is not analytic at the origin. If the λ (α) n ultimately have strictly alternating signs, the series expansions for the power series coefficients still diverge, but are summable to something finite, and the resulting power series represents an analytic function. If algebraically decaying and ultimately alternating Laguerre series coefficients λ (α) n possess sufficiently simple explicit analytical expressions, the summation of the divergent series for the power series coefficients can often be accomplished with the help of analytic continuation formulae for hypergeometric series p+1 F p , but if the λ (α) n have a complicated structure or if only their numerical values are available, numerical summation techniques have to be employed. It is shown that certain nonlinear sequence transformations-in particular the so-called delta transformation (Weniger 1989 Comput. Phys. Rep. 10 189-371 (equation (8.4-4)))-are able to

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.

From Taylor series to Taylor models

International Nuclear Information System (INIS)

Berz, M.

1997-01-01

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on the set of Taylor models, arbitrary order integrators with rigorous remainder treatment are developed. The integrators can meet pre-specified accuracy requirements in a mathematically strict way, and are a stepping stone towards fully rigorous estimates of stability of repetitive systems. copyright 1997 American Institute of Physics

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

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

Spherical harmonic expansion of short-range screened Coulomb interactions

Energy Technology Data Exchange (ETDEWEB)

Angyan, Janos G [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Gerber, Iann [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Marsman, Martijn [Institut fuer Materialphysik and Center for Computational Materials Science, Universitaet Wien, Sensengasse 8, A-1090, Vienna (Austria)

2006-07-07

Spherical harmonic expansions of the screened Coulomb interaction kernel involving the complementary error function are required in various problems in atomic, molecular and solid state physics, like for the evaluation of Ewald-type lattice sums or for range-separated hybrid density functionals. A general analytical expression is derived for the kernel, which is non-separable in the radial variables. With the help of series expansions a separable approximate form is proposed, which is in close analogy with the conventional multipole expansion of the Coulomb kernel in spherical harmonics. The convergence behaviour of these expansions is studied and illustrated by the electrostatic potential of an elementary charge distribution formed by products of Slater-type atomic orbitals.

Asymptotic series and functional integrals in quantum field theory

International Nuclear Information System (INIS)

Shirkov, D.V.

1979-01-01

Investigations of the methods for analyzing ultra-violet and infrared asymptotics in the quantum field theory (QFT) have been reviewed. A powerful method of the QFT analysis connected with the group property of renormalized transformations has been created at the first stage. The result of the studies of the second period is the constructive solution of the problem of outgoing the framework of weak coupling. At the third stage of studies essential are the asymptotic series and functional integrals in the QFT, which are used for obtaining the asymptotic type of the power expansion coefficients in the coupling constant at high values of the exponents for a number of simple models. Further advance to higher values of the coupling constant requires surmounting the difficulties resulting from the asymptotic character of expansions and a constructive application in the region of strong coupling (g >> 1)

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.

Application of eigen value expansion to feature extraction from MRI images

International Nuclear Information System (INIS)

Kinosada, Yasutomi; Takeda, Kan; Nakagawa, Tsuyoshi

1991-01-01

The eigen value expansion technique was utilized for feature extraction of magnetic resonance (MR) images. The eigen value expansion is an orthonormal transformation method which decomposes a set of images into some statistically uncorrelated images. The technique was applied to MR images obtained with various imaging parameters at the same anatomical site. It generated one mean image and another set of images called bases for the images. Each basis corresponds to a feature in the images. A basis is, therefore, utilized for the feature extraction from MR images and a weighted sum of bases is also used for the feature enhancement. Furthermore, any MR image with specific feature can be obtained from a linear combination of the mean image and all of the bases. Images of hemorrhaged brain with a spin echo sequence and a series of cinematic cerebro spinal fluid flow images with ECG gated gradient refocused echo sequence were employed to estimate the ability of the feature extraction and the contrast enhancement. Results showed us that proposed application of an eigen value expansion technique to the feature extraction of MR images is good enough to clinical use and superior to other feature extraction methods such as producing a calculated MR image with a given TR and TE or the matched-filter method in processing speed and reproducibility of results. (author)

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.

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.

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

On the convergence of quantum resonant-state expansion

International Nuclear Information System (INIS)

Brown, J. M.; Bahl, A.; Jakobsen, P.; Moloney, J. V.; Kolesik, M.

2016-01-01

Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonant expansion, good approximations can be obtained in a compact spatial domain.

On the convergence of quantum resonant-state expansion

Energy Technology Data Exchange (ETDEWEB)

Brown, J. M.; Bahl, A. [College of Optical Sciences, University of Arizona, 1630 East University Boulevard, Tucson, Arizona 85721 (United States); Jakobsen, P. [Department of Mathematics and Statistics, University of Tromsø, Tromsø (Norway); Moloney, J. V.; Kolesik, M. [College of Optical Sciences, University of Arizona, 1630 East University Boulevard, Tucson, Arizona 85721 (United States); Arizona Center for Mathematical Sciences, University of Arizona, Tucson, Arizona 85721 (United States)

2016-03-15

Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonant expansion, good approximations can be obtained in a compact spatial domain.

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

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.

Studying the method of linearization of exponential calibration curves

International Nuclear Information System (INIS)

Bunzh, Z.A.

1989-01-01

The results of study of the method for linearization of exponential calibration curves are given. The calibration technique and comparison of the proposed method with piecewise-linear approximation and power series expansion, are given

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.

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.

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.

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

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)

The 1/ N Expansion of Tensor Models Beyond Perturbation Theory

Science.gov (United States)

Gurau, Razvan

2014-09-01

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.

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.

Strong-coupling expansion for the ground-state energy in the Vertical BarxVertical Bar/sup α/ potential

International Nuclear Information System (INIS)

Bender, C.M.; Mead, L.R.; Simmons, L.M. Jr.

1981-01-01

Using lattice techniques we examine the strong-coupling expansion for the ground-state energy of a gVertical BarxVertical Bar/sup α/ (α>0) potential in quantum mechanics. We are particularly interested in studying the effectiveness of various Pade-type methods for extrapolating the lattice series back to the continuum. We have computed the lattice series out to 12th order for all α and we identify three regions. When α or =2 the lattice series has a finite radius of convergence; here, completely-off-diagonal Pade extrapolants work best. As α increases beyond 2 it becomes more difficult to obtain good continuum results, apparently because the sign pattern of the lattice series seems to fluctuate randomly. The onset of randomness occurs earlier in the lattice series as α→infinity

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

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. ?

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.

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)

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

Science.gov (United States)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

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)

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)

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)

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.

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.

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...

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.

APPLING REMOTE SENSING TECHNIQUE TO MONITORING SPATIAL EXPANSION OF IMPORTANT CITIES IN CHINA-INDOCHINA PENINSULA ECONOMIC CORRIDOR

Directory of Open Access Journals (Sweden)

J. Li

2017-09-01

Full Text Available Since twentieth Century, the process of economic globalization has made great progress, and Southeast Asia has developed rapidly under the background of international industrial transferring. In this paper, the 6 important nodes cities in China - Indochina Peninsula along the economic corridor are took as study area. The main data is time series Landsat data. The method of object-oriented random forest classification was used to extract the classification results of study area from 2000 to 2015. The urban expansion of the node cities was evaluated by calculating the expansion speed of the impervious surface and the landscape pattern metrics. The results indicated that the method of object oriented random forest classification can effectively extract the urban impervious surface. the overall accuracy is over 81 %, and the Kappa coefficient is over 0.82. In the past 15 years, the expansion speed of Vientiane city was fastest in 6 countries. The area of urban impervious surface expanded 8 times than that of 2000.The pattern of expansion is summarized as “gather first-diffuse then”, “diffuse first-gather then” and “gather”. Overall, the process of urbanization of these cities are still in the rising period.

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.

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)

δ expansion for local gauge theories. I. A one-dimensional model

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.; Milton, K.A.; Moshe, M.; Pinsky, S.S.; Simmons, L.M. Jr.

1992-01-01

The principles of the δ perturbation theory were first proposed in the context of self-interacting scalar quantum field theory. There it was shown how to expand a (φ 2 ) 1+δ theory as a series in powers of δ and how to recover nonperturbative information about a φ 4 field theory from the δ expansion at δ=1. The purpose of this series of papers is to extend the notions of δ perturbation theory from boson theories to theories having a local gauge symmetry. In the case of quantum electrodynamics one introduces the parameter δ by generalizing the minimal coupling terms to bar ψ(∂-ieA) δ ψ and expanding in powers of δ. This interaction preserves local gauge invariance for all δ. While there are enormous benefits in using the δ expansion (obtaining nonperturbative results), gauge theories present new technical difficulties not encountered in self-interacting boson theories because the expression (∂-ieA) δ contains a derivative operator. In the first paper of this series a one-dimensional model whose interaction term has the form bar ψ[d/dt-igφ(t)] δ ψ is considered. The virtue of this model is that it provides a laboratory in which to study fractional powers of derivative operators without the added complexity of γ matrices. In the next paper of this series we consider two-dimensional electrodynamics and show how to calculate the anomaly in the δ expansion

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

General post-Minkowskian expansion of time transfer functions

Energy Technology Data Exchange (ETDEWEB)

Teyssandier, Pierre; Poncin-Lafitte, Christophe Le [Departement Systemes de Reference Temps et Espace, CNRS/UMR 8630, Observatoire de Paris, 61 avenue de l' Observatoire, F-75014 Paris (France)

2008-07-21

Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

General post-Minkowskian expansion of time transfer functions

International Nuclear Information System (INIS)

Teyssandier, Pierre; Poncin-Lafitte, Christophe Le

2008-01-01

Modeling most of the tests of general relativity requires us to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling us to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant G (general post-Minkowskian expansion). Our method is self-sufficient in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function is necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation

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)

Conformal Dimensions via Large Charge Expansion.

Science.gov (United States)

Banerjee, Debasish; Chandrasekharan, Shailesh; Orlando, Domenico

2018-02-09

We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series.

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

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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

Comparison of the methods for discrete approximation of the fractional-order operator

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Zborovjan Martin

2003-12-01

Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.

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

Travelling Wave Solutions of Coupled Burger’s Equations of Time-Space Fractional Order by Novel (Gʹ/G-Expansion Method

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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.

Correlations between Socioeconomic Drivers and Indicators of Urban Expansion: Evidence from the Heavily Urbanised Shanghai Metropolitan Area, China

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Jinghui Li

2017-07-01

Full Text Available Rapid urban expansion resulting in increased impervious surfaces causes a series of urban environmental problems, e.g., the urban heat island and urban forest fragmentation. Urban expansion is a serious threat to human quality of life and living environments. It has been studied from a variety of aspects, but its driving factors and time series expansion characteristics (i.e., expansion intensity, pattern and direction need to be better explained in order to devise more effective management strategies. This study examined how social and economic factors are linked in driving urban expansion. Based on multi-temporal aerial images, a rapid urban expansion period, 2000–2010, in Shanghai was analysed. The urban area expanded from 1770.36 to 2855.44 km2 in the period, with a mean annual expansion rate of 108.51 km2. Urban expansion in 2000–2005 (40.42% was much faster than in 2005–2010 (14.86%, and its direction was southeast, southwest and south. The main pattern was edge expansion in both sub-periods. Social factors, especially population density, significantly affected urban expansion. These findings can help understand the urban expansion process and its driving factors, which has important implications for urban planning and management in Shanghai and similar cities.

Principles of Thermal Expansion in Feldspars

Science.gov (United States)

Hovis, Guy; Medford, Aaron; Conlon, Maricate; Tether, Allison; Romanoski, Anthony

2010-05-01

Following the recent thermal expansion work of Hovis et al. (1) on AlSi3 feldspars, we have investigated the thermal expansion of plagioclase, Ba-K, and Ca-K feldspar crystalline solutions. X-ray powder diffraction data were collected between room temperature and 925 °C on six natural plagioclase specimens ranging in composition from anorthite to oligoclase, the K-exchanged equivalents of these plagioclase specimens, and five synthetic Ba-K feldspars with compositions ranging from 25 to 99 mol % BaAl2Si2O8. The resulting thermal expansion coefficients (α) for volume have been combined with earlier results for end-member Na- and K-feldspars (2,3). Unlike AlSi3 feldspars, Al2Si2 feldspars, including anorthite and celsian from the present study plus Sr- and Pb-feldspar from other workers (4,5), show essentially constant and very limited thermal expansion, regardless of divalent cation size. In the context of structures where the Lowenstein rule (6) requires Al and Si to alternate among tetrahedra, the proximity of bridging Al-O-Si oxygen ions to divalent neighbors (ranging from 0 to 2) produces short Ca-O (or Ba-O) bonds (7,8) that apparently are the result of local charge-balance requirements (9). Gibbs et al. (10) suggest that short bonds such as these have a partially covalent character. This in turn stiffens the structure. Thus, for feldspar series with coupled substitution the change away from a purely divalent M-site occupant gives the substituting (less strongly bonded) monovalent cations increasingly greater influence on thermal expansion. Overall, then, thermal expansion in the feldspar system is well represented on a plot of α against room-temperature volume, where one sees a quadrilateral bounded by data for (A) AlSi3 feldspars whose expansion behavior is controlled largely by the size of the monovalent alkali-site occupant, (B) Al2Si2 feldspars whose expansion is uniformly limited by partially-covalent bonds between divalent M-site occupants and

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.

On q-extension of Laurent expansion with applications

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Ahmed Salem

2014-01-01

Full Text Available In this article, Cauchy’s integral formula for nth q-derivative of analytic functions is established and used to introduce a new proof to q-Taylor series by means of using the residue calculus in the complex analysis. Some theorems related to this formula are presented. A q-extension of a Laurent expansion is derived and proved by means of using Cauchy’s integral formula for a function, which is analytic on a ring-shaped region bounded by two concentric circles. Three illustrative examples are presented to be as applications for a q-Laurent expansion.

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)

on some properties of the alternating sylvester series and alternating

African Journals Online (AJOL)

DJFLEX

. (iii) above is known in literature as the alternating Sylvester series while (iv) is known as the alternating Engel expansion (Kalpazidou and Ganatsiou (1991)). We are interested in studying the properties of these alternating series. Theorem 2: ...

Research progress on expansive soil cracks under changing environment.

Science.gov (United States)

Shi, Bei-xiao; Zheng, Cheng-feng; Wu, Jin-kun

2014-01-01

Engineering problems shunned previously rise to the surface gradually with the activities of reforming the natural world in depth, the problem of expansive soil crack under the changing environment becoming a control factor of expansive soil slope stability. The problem of expansive soil crack has gradually become a research hotspot, elaborates the occurrence and development of cracks from the basic properties of expansive soil, and points out the role of controlling the crack of expansive soil strength. We summarize the existing research methods and results of expansive soil crack characteristics. Improving crack measurement and calculation method and researching the crack depth measurement, statistical analysis method, crack depth and surface feature relationship will be the future direction.

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

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

Isotropic Negative Thermal Expansion Metamaterials.

Science.gov (United States)

Wu, Lingling; Li, Bo; Zhou, Ji

2016-07-13

Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.

The resonance expansion for the Green's function of the Schroedinger and wave equations

International Nuclear Information System (INIS)

Albeverio, S.; Aix-Marseille-2 Univ., 13 - Marseille; Hoeegh-Krohn, R.; Oslo Univ.

1984-01-01

We give a survey of some recent mathematical work on resonances, in particular on perturbation series, low energy expansions and on resonances for point interactions. Expansions of the kernels of esup(-it)√sup(H+) and esup(-itH) in terms of resonances are also given (where Hsub(+) is the positive part of the Hamiltonian). (orig.)

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

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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.

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)

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

Thermal expansion: Metallic elements and alloys. [Handbook

Science.gov (United States)

Touloukian, Y. S.; Kirby, R. K.; Taylor, R. E.; Desai, P. D.

1975-01-01

The introductory sections of the work are devoted to the theory of thermal expansion of solids and to methods for the measurement of the linear thermal expansion of solids (X-ray methods, high speed methods, interferometry, push-rod dilatometry, etc.). The bulk of the work is devoted to numerical data on the thermal linear expansion of all the metallic elements, a large number of intermetallics, and a large number of binary alloy systems and multiple alloy systems. A comprehensive bibliography is provided along with an index to the materials examined.

Quantum-statistical mechanics of an atom-dimer mixture: Lee-Yang cluster expansion approach

International Nuclear Information System (INIS)

Ohkuma, Takahiro; Ueda, Masahito

2006-01-01

We use the Lee-Yang cluster expansion method to study quantum-statistical properties of a mixture of interconvertible atoms and dimers, where the dimers form in a two-body bound state of the atoms. We point out an infinite series of cluster diagrams whose summation leads to the Bose-Einstein condensation of the dimers below a critical temperature. Our theory captures some important features of a cold atom-dimer mixture such as interconversion of atoms and dimers and properties of the mixture at the unitarity limit

Impact factors on expansion of built-up areas in Zhejiang Province, China

Science.gov (United States)

Liu, Dong; Zhu, Qiankun; Li, Yan; Gong, Fang

2017-10-01

Built-up areas are the results of human activities. Not only are they the real reflection of human and society activities, but also one of the most important input parameters for the simulation of biogeochemical cycle. Therefore, it is very necessary to map the distribution of built-up areas and monitor their changes by using new technologies and methods at high spatiotemporal resolution. By combining technologies of GIS (Geographic Information System) and RS (Remote Sensing), this study mainly explored the expansion and driving factors of built-up areas at the beginning of the 21st century in Zhejiang Province, China. Firstly, it introduced the mapping processes of LULC (Land Use and Land Cover) based on the method which combined object-oriented method and binary decision tree. Then, it analyzed the expansion features of built-up areas in Zhejiang from 2000 to 2005 and 2005 to 2010. In addition to these, potential driving factors on the expansion of built-up areas were also explored, which contained physical geographical factors, railways, highways, rivers, urban centers, elevation, and slop. Results revealed that the expansions of built-up areas in Zhejiang from 2000 to 2005 and from 2005 to 2010 were very obvious and they showed high levels of variation in spatial heterogeneity. Except those, increased built-up areas with distance to railways, highways, rivers, and urban centers could be fitted with power function (y = a*xb ), with minimum R2 of 0.9507 for urban centers from 2000 to 2005; the increased permillages of built-up areas to mean elevation and mean slop could be fitted with exponential functions (y = a*ebx), with minimum R2 of 0.6657 for mean slop from 2005 to 2010. Besides, government policy could also impact expansion of built-up areas. In a nutshell, a series of conclusions were obtained through this study about the spatial features and driving factors of evolution of built-up areas in Zhejiang from 2000 to 2010.

Systematic and controllable negative, zero, and positive thermal expansion in cubic Zr(1-x)Sn(x)Mo2O8.

Science.gov (United States)

Tallentire, Sarah E; Child, Felicity; Fall, Ian; Vella-Zarb, Liana; Evans, Ivana Radosavljević; Tucker, Matthew G; Keen, David A; Wilson, Claire; Evans, John S O

2013-08-28

We describe the synthesis and characterization of a family of materials, Zr1-xSnxMo2O8 (0 thermal expansion coefficient can be systematically varied from negative to zero to positive values. These materials allow tunable expansion in a single phase as opposed to using a composite system. Linear thermal expansion coefficients, αl, ranging from -7.9(2) × 10(-6) to +5.9(2) × 10(-6) K(-1) (12-500 K) can be achieved across the series; contraction and expansion limits are of the same order of magnitude as the expansion of typical ceramics. We also report the various structures and thermal expansion of "cubic" SnMo2O8, and we use time- and temperature-dependent diffraction studies to describe a series of phase transitions between different ordered and disordered states of this material.

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.

Estimation of pure autoregressive vector models for revenue series ...

African Journals Online (AJOL)

This paper aims at applying multivariate approach to Box and Jenkins univariate time series modeling to three vector series. General Autoregressive Vector Models with time varying coefficients are estimated. The first vector is a response vector, while others are predictor vectors. By matrix expansion each vector, whether ...

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)

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)

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.

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

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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.

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)

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)

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

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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.

On Clebsch-Gordan expansion for 0(2h+1,1)

International Nuclear Information System (INIS)

Dobrev, V.; Petkova, V.; Petrova, S.; Mack, G.; Todorov, I.

1974-01-01

The direct-product expansion of two unitary representations of the supplementary series of 0(2h+1.1) is studied in detail. Invariant bi-linear forms are written down for arbitrary symmetric tensor representations and necessary and sufficient conditions are found for their positivity. Normalized Clebsh-Gordon kernels are evaluated explicitly and the Plancherel formula is verified. The results are applied elsewhere for the diagonalization of conformal covariant dynamical equations for the Euclidean Green functions. They are related to the derivation of covariant operator product expansions

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.

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.

Higher-order semiclassical energy expansions for potentials with ...

Indian Academy of Sciences (India)

global behavior of eigenfunctions and energy spectra of quantum mechanical systems are very important. ... where p, q and r are positive integers and contourC encloses points +1 and -1 on the real axis. Also these ... Derivation of AEE which is a relationship between quantum number k and the power series expansion of ...

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

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.

On the divergence of gradient expansions for kinetic energy functionals in the potential functional theory

International Nuclear Information System (INIS)

Sergeev, Alexey; Jovanovic, Raka; Kais, Sabre; Alharbi, Fahhad H

2016-01-01

We consider the density of a fermionic system as a functional of the potential, in one-dimensional case, where it is approximated by the Thomas–Fermi term plus semiclassical corrections through the gradient expansion. We compare this asymptotic series with the exact answer for the case of the harmonic oscillator and the Morse potential. It is found that the leading (Thomas–Fermi) term is in agreement with the exact density, but the subdominant term does not agree in terms of the asymptotic behavior because of the presence of oscillations in the exact density, but their absence in the gradient expansion. However, after regularization of the density by convolution with a Gaussian, the agreement can be established even in the subdominant term. Moreover, it is found that the expansion is always divergent, and its terms grow proportionally to the factorial function of the order, similar to the well-known divergence of perturbation series in field theory and the quantum anharmonic oscillator. Padé–Hermite approximants allow summation of the series, and one of the branches of the approximants agrees with the density. (paper)

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.

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)

Volterra Series Based Distortion Effect

DEFF Research Database (Denmark)

Agerkvist, Finn T.

2010-01-01

A large part of the characteristic sound of the electric guitar comes from nonlinearities in the signal path. Such nonlinearities may come from the input- or output-stage of the amplier, which is often equipped with vacuum tubes or a dedicated distortion pedal. In this paper the Volterra series...... expansion for non linear systems is investigated with respect to generating good distortion. The Volterra series allows for unlimited adjustment of the level and frequency dependency of each distortion component. Subjectively relevant ways of linking the dierent orders are discussed....

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

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.

Markov Trends in Macroeconomic Time Series

NARCIS (Netherlands)

R. Paap (Richard)

1997-01-01

textabstractMany macroeconomic time series are characterised by long periods of positive growth, expansion periods, and short periods of negative growth, recessions. A popular model to describe this phenomenon is the Markov trend, which is a stochastic segmented trend where the slope depends on the

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

Perturbative expansion and the initial value problem of the K.d.V. equations

International Nuclear Information System (INIS)

Turchetti, G.

1980-01-01

For the potential K.d.V. equation is considered a perturbation expansion in which the initial condition is imposed on the zeroth order term. The N soliton solutions turn out to be rational functions in the expansion parameter so that the perturbation series can be exactly summed by the [N-1/N] Pade approximants; moreover the [n-1/n] and [n/n] Pade approximants for n [pt

Some properties and expansions associated with the q -digamma ...

African Journals Online (AJOL)

This paper is devoted to derive some properties and expansions associated with the q-digamma function. The Newton series which is consisting of terms of forward difference operator, is established for the q-digamma function. The maltiplication formula of the q-gamma function is used to present some recurrence relations ...

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

Belief propagation and loop series on planar graphs

International Nuclear Information System (INIS)

Chertkov, Michael; Teodorescu, Razvan; Chernyak, Vladimir Y

2008-01-01

We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R) [cond-mat/0601487]; 2006 J. Stat. Mech. P06009 [cond-mat/0603189]) is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation (Fisher 1961 Phys. Rev. 124 1664), to evaluating the partition function of the dimer-matching model on an auxiliary planar graph. Thus, the truncated series can be easily re-summed, using the Pfaffian formula of Kasteleyn (1961 Physics 27 1209). This allows us to identify a big class of computationally tractable planar models reducible to a dimer model via the Belief Propagation (gauge) transformation. The Pfaffian representation can also be extended to the full Loop Series, in which case the expansion becomes a sum of Pfaffian contributions, each associated with dimer matchings on an extension to a subgraph of the original graph. Algorithmic consequences of the Pfaffian representation, as well as relations to quantum and non-planar models, are discussed

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.

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.

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.

Physiological and behavioral responses of poultry exposed to gas-filled high expansion foam.

Science.gov (United States)

McKeegan, D E F; Reimert, H G M; Hindle, V A; Boulcott, P; Sparrey, J M; Wathes, C M; Demmers, T G M; Gerritzen, M A

2013-05-01

Disease control measures require poultry to be killed on farms to minimize the risk of disease being transmitted to other poultry and, in some cases, to protect public health. We assessed the welfare implications for poultry of the use of high-expansion gas-filled foam as a potentially humane, emergency killing method. In laboratory trials, broiler chickens, adult laying hens, ducks, and turkeys were exposed to air-, N2-, or CO2-filled high expansion foam (expansion ratio 300:1) under standardized conditions. Birds were equipped with sensors to measure cardiac and brain activity, and measurements of oxygen concentration in the foam were carried out. Initial behavioral responses to foam were not pronounced but included headshakes and brief bouts of wing flapping. Both N2- and CO2-filled foam rapidly induced ataxia/loss of posture and vigorous wing flapping in all species, characteristic of anoxic death. Immersion in air-filled, high expansion foam had little effect on physiology or behavior. Physiological responses to both N2- and CO2-filled foam were characterized by a pronounced bradyarrythymia and a series of consistent changes in the appearance of the electroencephalogram. These were used to determine an unequivocal time to loss of consciousness in relation to submersion. Mean time to loss of consciousness was 30 s in hens and 18 s in broilers exposed to N2-filled foam, and 16 s in broilers, 1 s in ducks, and 15 s in turkeys exposed to CO2-filled foam. Euthanasia achieved with anoxic foam was particularly rapid, which is explained by the very low oxygen concentrations (below 1%) inside the foam. Physiological observations and postmortem examination showed that the mode of action of high expansion, gas-filled foam is anoxia, not occlusion of the airway. These trials provide proof-of-principle that submersion in gas-filled, high expansion foam provides a rapid and highly effective method of euthanasia, which may have potential to provide humane emergency killing

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 ...

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.)

Extended gamma sources modelling using multipole expansion: Application to the Tunisian gamma source load planning

International Nuclear Information System (INIS)

Loussaief, Abdelkader

2007-01-01

In this work we extend the use of multipole moments expansion to the case of inner radiation fields. A series expansion of the photon flux was established. The main advantage of this approach is that it offers the opportunity to treat both inner and external radiation field cases. We determined the expression of the inner multipole moments in both spherical harmonics and in cartesian coordinates. As an application we applied the analytical model to a radiation facility used for small target irradiation. Theoretical, experimental and simulation studies were performed, in air and in a product, and good agreement was reached.Conventional dose distribution study for gamma irradiation facility involves the use of isodose maps. The establishment of these maps requires the measurement of the absorbed dose in many points, which makes the task expensive experimentally and very long by simulation. However, a lack of points of measurement can distort the dose distribution cartography. To overcome these problems, we present in this paper a mathematical method to describe the dose distribution in air. This method is based on the multipole expansion in spherical harmonics of the photon flux emitted by the gamma source. The determination of the multipole coefficients of this development allows the modeling of the radiation field around the gamma source. (Author)

Analytical method for solving radioactive transformations

International Nuclear Information System (INIS)

Vukadin, Z.

1999-01-01

The exact method of solving radioactive transformations is presented. Nonsingular Bateman coefficients, which can be computed using recurrence formulas, greatly reduce computational time and eliminate singularities that often arise in problems involving nuclide transmutations. Depletion function power series expansion enables high accuracy of the performed calculations, specially in a case of a decay constants with closely spaced values. Generality and simplicity of the method make the method useful for many practical applications. (author)

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)

Stochastic models for time series

CERN Document Server

Doukhan, Paul

2018-01-01

This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit ...

The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

International Nuclear Information System (INIS)

Finster, Felix; Grotz, Andreas

2010-01-01

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

Science.gov (United States)

Finster, Felix; Grotz, Andreas

2010-07-01

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

Maxwell superalgebras and Abelian semigroup expansion

Directory of Open Access Journals (Sweden)

P.K. Concha

2014-09-01

Full Text Available The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2 leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N. Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.

Maxwell superalgebras and Abelian semigroup expansion

Energy Technology Data Exchange (ETDEWEB)

Concha, P.K.; Rodríguez, E.K. [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Dipartimento di Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria, 1, 10125 Torino (Italy)

2014-09-15

The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM{sup (N)} recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N). Moreover, we show that new minimal Maxwell superalgebras type sM{sub m+2} and their N-extended generalization can be obtained using the S-expansion procedure.

On the binary expansions of algebraic numbers

Energy Technology Data Exchange (ETDEWEB)

Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl

2003-07-01

Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.

A simple method for calculation of Glauber's amplitude

International Nuclear Information System (INIS)

Omboo, Z.

1983-01-01

A method of calculating the terms of Glauber series expansions for elastic scattering of composed systems are presented. The inclusion of general scattering diagram simplifies essentially the calculation procedure. In this case the complicated combinatorical problem of reduction of similar terms in Glauber series is solved easily and determinant corresponding to various terms of the series decreases at least by a factor of two, if numbers of constituents of scattered systems are equal. If these numbers are not equal, the determinant order is equal to the smallest one

OPEC production: Capital limitations, environmental movements may interfere with expansion plans

International Nuclear Information System (INIS)

Ismail, I.A.H.

1994-01-01

Obtaining capital is a critical element in the production expansion plans of OPEC member countries. Another issue that may impact the plans is the environmental taxes that may reduce the call on OPEC oil by 5 million b/d in 2000 and about 16 million b/d in the year 2010. This concluding part of a two-part series discusses the expansion possibilities of non-Middle East OPEC members, OPEC's capital requirements, and environmental concerns. Non-Middle East OPEC includes Algeria, Gabon, Indonesia, Libya, Nigeria, and Venezuela

Considering FACTS in Optimal Transmission Expansion Planning

Directory of Open Access Journals (Sweden)

K. Soleimani

2017-10-01

Full Text Available The expansion of power transmission systems is an important part of the expansion of power systems that requires enormous investment costs. Since the construction of new transmission lines is very expensive, it is necessary to choose the most efficient expansion plan that ensures system security with a minimal number of new lines. In this paper, the role of Flexible AC Transmission System (FACTS devices in the effective operation and expansion planning of transmission systems is examined. Effort was taken to implement a method based on sensitivity analysis to select the optimal number and location of FACTS devices, lines and other elements of the transmission system. Using this method, the transmission expansion plan for a 9 and a 39 bus power system was performed with and without the presence of FACTS with the use of DPL environment in Digsilent software 15.1. Results show that the use of these devices reduces the need for new transmission lines and minimizes the investment cost.

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

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...

High-energy expansion for nuclear multiple scattering

International Nuclear Information System (INIS)

Wallace, S.J.

1975-01-01

The Watson multiple scattering series is expanded to develop the Glauber approximation plus systematic corrections arising from three (1) deviations from eikonal propagation between scatterings, (2) Fermi motion of struck nucleons, and (3) the kinematic transformation which relates the many-body scattering operators of the Watson series to the physical two-body scattering amplitude. Operators which express effects ignored at the outset to obtain the Glauber approximation are subsequently reintroduced via perturbation expansions. Hence a particular set of approximations is developed which renders the sum of the Watson series to the Glauber form in the center of mass system, and an expansion is carried out to find leading order corrections to that summation. Although their physical origins are quite distinct, the eikonal, Fermi motion, and kinematic corrections produce strikingly similar contributions to the scattering amplitude. It is shown that there is substantial cancellation between their effects and hence the Glauber approximation is more accurate than the individual approximations used in its derivation. It is shown that the leading corrections produce effects of order (2kR/subc/) -1 relative to the double scattering term in the uncorrected Glauber amplitude, hk being momentum and R/subc/ the nuclear char []e radius. The leading order corrections are found to be small enough to validate quatitative analyses of experimental data for many intermediate to high energy cases and for scattering angles not limited to the very forward region. In a Gaussian model, the leading corrections to the Glauber amplitude are given as convenient analytic expressions

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.

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.

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.

Logarithmic compression methods for spectral data

Science.gov (United States)

Dunham, Mark E.

2003-01-01

A method is provided for logarithmic compression, transmission, and expansion of spectral data. A log Gabor transformation is made of incoming time series data to output spectral phase and logarithmic magnitude values. The output phase and logarithmic magnitude values are compressed by selecting only magnitude values above a selected threshold and corresponding phase values to transmit compressed phase and logarithmic magnitude values. A reverse log Gabor transformation is then performed on the transmitted phase and logarithmic magnitude values to output transmitted time series data to a user.

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.

Thermal expansion of NZP-family alkali-metal (Na, K) zirconium phosphates

International Nuclear Information System (INIS)

Orlova, A.I.; Kemenov, D.V.; Pet'kov, V.I.; Samojlov, S.G.; Kazantsev, G.N.

2000-01-01

By means of high-temperature X-ray diffraction one investigated into thermal expansion of alkali-zirconium phosphates crystallizing in NaZr 2 (PO 4 ) 3 structure type within 20-700 deg C temperature range. One synthesized phosphates of A x Zr 2.25-0.25x (PO 4 ) 3 type two series where A-Na (x = 0.5; 1.0; 2.0; 3.0; 4.0; 5.0) and K (x = 1.0; 3.0; 5.0). One calculated for them a and c parameters of the elementary cells and α a and α c linear expansion temperature coefficients. Anisotropy of thermal expansion the maximum one for AZr 2 (PO 4 ) 3 and Na 5 Zr(PO 4 ) 3 phosphates was determined. K 5 Zr(PO 4 ) 3 compound was characterized by the minimum thermal expansion at the near-zero anisotropy of Na 5 Zr(PO 4 ) 3 [ru

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.

Generalizing Integrals Involving X [superscript X] and Series Involving N [superscript N

Science.gov (United States)

Osler, Thomas J.; Tsay, Jeffrey

2005-01-01

In this paper, the authors evaluate the series and integrals presented by P. Glaister. The authors show that this function has the Maclauren series expansion. The authors derive the series from the integral in two ways. The first derivation uses the technique employed by Glaister. The second derivation uses a change in variable in the integral.

Effective potential of the three-dimensional Ising model: The pseudo-ɛ expansion study

Science.gov (United States)

Sokolov, A. I.; Kudlis, A.; Nikitina, M. A.

2017-08-01

The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for the critical values of g6, g8, g10, R6 =g6 / g42, R8 =g8 / g43 and R10 =g10 / g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ɛ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6* = 1.6488 and R6* = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ɛ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8* = 0.868, the number being close to the lattice estimate R8* = 0.871 and compatible with the result of 3D RG analysis R8* = 0.857. Pseudo-ɛ expansions for R10* and g10* are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

Energy expansion planning by considering electrical and thermal expansion simultaneously

International Nuclear Information System (INIS)

Abbasi, Ali Reza; Seifi, Ali Reza

2014-01-01

Highlights: • This paper focused on the expansion planning optimization of energy systems. • Employing two form of energy: the expansion of electrical and thermal energies. • The main objective is to minimize the costs. • A new Modified Honey Bee Mating Optimization (MHBMO) algorithm is applied. - Abstract: This study focused on the expansion planning optimization of energy systems employing two forms of energy: the expansion of electrical and thermal energies simultaneously. The main objective of this investigation is confirming network adequacy by adding new equipment to the network, over a given planning horizon. The main objective of the energy expansion planning (EEP) is to minimize the real energy loss, voltage deviation and the total cost of installation equipments. Since the objectives are different and incommensurable, it is difficult to solve the problem by the conventional approaches that may optimize a single objective. So, the meta-heuristic algorithm is applied to this problem. Here, Honey Bee Mating Optimization algorithm (HBMO) as a new evolutionary optimization algorithm is utilized. In order to improve the total ability of HBMO for the global search and exploration, a new modification process is suggested such a way that the algorithm will search the total search space globally. Also, regarding the uncertainties of the new complicated energy systems, in this paper for the first time, the EEP problem is investigated in a stochastic environment by the use of probabilistic load flow technique based on Point Estimate Method (PEM). In order to evaluate the feasibility and effectiveness of the proposed algorithm, two modified test systems are used as case studies

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.

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...

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

Multi-load Optimal Design of Burner-inner-liner Under Performance Index Constraint by Second-Order Polynomial Taylor Series Method

Directory of Open Access Journals (Sweden)

Tu Gaoqiao

2016-01-01

Full Text Available Using maximum expansion pressure of n-decane, the aeroengine burner-inner-liner combustion pressure load is computed. Aerodynamic loads are obtained from internal gas pressure load and gas momentum. Multi-load second-order Taylor series equations are established using multi-variant polynomials and their sensitivities. Optimal designs are carried out using various performance index constraints. When 0.25 to 0.8 rectifications of different design variants are implemented, they converge under 5×10‒4 d-norm difference ratio.

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.

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...

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).

216-B-3 expansion ponds closure plan

International Nuclear Information System (INIS)

1994-10-01

This document describes the activities for clean closure under the Resource Conservation and Recovery Act of 1976 (RCRA) of the 216-B-3 Expansion Ponds. The 216-B-3 Expansion Ponds are operated by the US Department of Energy, Richland Operations Office (DOE-RL) and co-operated by Westinghouse Hanford Company (Westinghouse Hanford). The 216-B-3 Expansion Ponds consists of a series of three earthen, unlined, interconnected ponds that receive waste water from various 200 East Area operating facilities. The 3A, 3B, and 3C ponds are referred to as Expansion Ponds because they expanded the capability of the B Pond System. Waste water (primarily cooling water, steam condensate, and sanitary water) from various 200 East Area facilities is discharged to the Bypass pipe (Project X-009). Water discharged to the Bypass pipe flows directly into the 216-B-3C Pond. The ponds were operated in a cascade mode, where the Main Pond overflowed into the 3A Pond and the 3A Pond overflowed into the 3C Pond. The 3B Pond has not received waste water since May 1985; however, when in operation, the 3B Pond received overflow from the 3A Pond. In the past, waste water discharges to the Expansion Ponds had the potential to have contained mixed waste (radioactive waste and dangerous waste). The radioactive portion of mixed waste has been interpreted by the US Department of Energy (DOE) to be regulated under the Atomic Energy Act of 1954; the dangerous waste portion of mixed waste is regulated under RCRA

216-B-3 expansion ponds closure plan

Energy Technology Data Exchange (ETDEWEB)

1994-10-01

This document describes the activities for clean closure under the Resource Conservation and Recovery Act of 1976 (RCRA) of the 216-B-3 Expansion Ponds. The 216-B-3 Expansion Ponds are operated by the US Department of Energy, Richland Operations Office (DOE-RL) and co-operated by Westinghouse Hanford Company (Westinghouse Hanford). The 216-B-3 Expansion Ponds consists of a series of three earthen, unlined, interconnected ponds that receive waste water from various 200 East Area operating facilities. The 3A, 3B, and 3C ponds are referred to as Expansion Ponds because they expanded the capability of the B Pond System. Waste water (primarily cooling water, steam condensate, and sanitary water) from various 200 East Area facilities is discharged to the Bypass pipe (Project X-009). Water discharged to the Bypass pipe flows directly into the 216-B-3C Pond. The ponds were operated in a cascade mode, where the Main Pond overflowed into the 3A Pond and the 3A Pond overflowed into the 3C Pond. The 3B Pond has not received waste water since May 1985; however, when in operation, the 3B Pond received overflow from the 3A Pond. In the past, waste water discharges to the Expansion Ponds had the potential to have contained mixed waste (radioactive waste and dangerous waste). The radioactive portion of mixed waste has been interpreted by the US Department of Energy (DOE) to be regulated under the Atomic Energy Act of 1954; the dangerous waste portion of mixed waste is regulated under RCRA.

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.

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

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

Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

CSIR Research Space (South Africa)

Fedotov, I

2006-07-01

Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...

Node-Expansion Operators for the UCT Algorithm

Science.gov (United States)

Yajima, Takayuki; Hashimoto, Tsuyoshi; Matsui, Toshiki; Hashimoto, Junichi; Spoerer, Kristian

Recent works on the MCTS and UCT framework in the domain of Go focused on introducing knowledge to the playout and on pruning variations from the tree, but so far node expansion has not been investigated. In this paper we show that delaying expansion according to the number of the siblings delivers a gain of more than 92% when compared to normal expansion. We propose three improvements; one that uses domain knowledge and two that are domain-independent methods. Experimental results show that all advanced operators significantly improve the UCT performance when compared to the basic delaying expansion. From the results we may conclude that the new expansion operators are an appropriate means to improve the UCT algorithm.

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

An integral nodal variational method for multigroup criticality calculations

International Nuclear Information System (INIS)

Lewis, E.E.; Tsoulfanidis, N.

2003-01-01

An integral formulation of the variational nodal method is presented and applied to a series of benchmark critically problems. The method combines an integral transport treatment of the even-parity flux within the spatial node with an odd-parity spherical harmonics expansion of the Lagrange multipliers at the node interfaces. The response matrices that result from this formulation are compatible with those in the VARIANT code at Argonne National Laboratory. Either homogeneous or heterogeneous nodes may be employed. In general, for calculations requiring higher-order angular approximations, the integral method yields solutions with comparable accuracy while requiring substantially less CPU time and memory than the standard spherical harmonics expansion using the same spatial approximations. (author)

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

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.

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.

Glass ceramics for sealing to high-thermal-expansion metals

International Nuclear Information System (INIS)

Wilder, J.A. Jr.

1980-10-01

Glass ceramics were studied, formulated in the Na 2 O CaO.P 2 O 5 , Na 2 O.BaOP 2 O 5 , Na 2 O.Al 2 O 3 .P 2 O 5 , and Li 2 O.BaO.P 2 O 5 systems to establish their suitability for sealing to high thermal expansion metals, e.g. aluminum, copper, and 300 series stainless steels. Glass ceramics in Na 2 O.CaO.P 2 O 5 and Na 2 O.BaO.P 2 O 5 systems have coefficients of thermal expansion in the range 140 x 10 -1 per 0 C less than or equal to α less than or equal to 225 x 10 -7 per 0 C and fracture toughness values generally greater than those of phosphate glasses; they are suitable for fabricating seals to high thermal expansion metals. Crystal phases include NaPo 3 , (NaPO 3 ) 3 , NaBa(PO 3 ) 3 , and NaCa(PO 3 ) 3 . Glass ceramics formed in the Na 2 O.Al 2 O 3 .P 2 O 5 systems have coefficients of thermal expansion greater than 240 x 10 -7 per 0 C, but they have extensive microcracking. Due to their low thermal expansion values (α less than or equal to 120 x 10 -7 per 0 C), glass ceramics in the Li 2 O.BaO.P 2 O 5 system are unsuitable for sealing to high thermal expansion metals

Instanton expansions for mass deformed N=4 super Yang-Mills theories

International Nuclear Information System (INIS)

Minahan, J.A.; Nemeschansky, D.; Warner, N.P.

1998-01-01

We derive modular anomaly equations from the Seiberg-Witten-Donagi curves for softly broken N=4 SU(n) gauge theories. From these equations we can derive recursion relations for the pre-potential in powers of m 2 , where m is the mass of the adjoint hypermultiplet. Given the perturbative contribution of the pre-potential and the presence of ''gaps'', we can easily generate the m 2 expansion in terms of polynomials of Eisenstein series, at least for relatively low rank groups. This enables us to determine efficiently the instanton expansion up to fairly high order for these gauge groups, e.g. eighth order for SU(3). We find that after taking a derivative, the instanton expansion of the pre-potential has integer coefficients. We also postulate the form of the modular anomaly equations, the recursion relations and the form of the instanton expansions for the SO(2n) and E n gauge groups, even though the corresponding Seiberg-Witten-Donagi curves are unknown at this time. (orig.)

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)

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.

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

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}

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

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

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.

Analytical method for solving radioactive transformations

International Nuclear Information System (INIS)

Vudakin, Z.

1999-01-01

Analytical method for solving radioactive transformations is presented in this paper. High accuracy series expansion of the depletion function and nonsingular Bateman coefficients are used to overcome numerical difficulties when applying well-known Bateman solution of a simple radioactive decay. Generality and simplicity of the method are found to be useful in evaluating nuclide chains with one hundred or more nuclides in the chain. Method enables evaluation of complete chain, without elimination of short-lives nuclides. It is efficient and accurate

A non-uniform expansion mechanical safety model of the stent.

Science.gov (United States)

Yang, J; Huang, N; Du, Q

2009-01-01

Stents have a serial unstable structure that readily leads to non-uniform expansion. Non-uniform expansion in turn creates a stent safety problem. We explain how a stent may be simplified to a serial unstable structure, and present a method to calculate the non-uniform expansion of the stent on the basis of the serial unstable structure. We propose a safety criterion based on the expansion displacement instead of the strain, and explain that the parameter Rd, the ratio of the maximum displacement of the elements to normal displacement, is meaningful to assess the safety level of the stent. We also examine how laser cutting influences non-uniform expansion. The examples illustrate how to calculate the parameter Rd to assess non-uniform expansion of the stent, and demonstrate how the laser cutting offset and strengthening coefficient of the material influence the stent expansion behaviour. The methods are valuable for assessing stent safety due to non-uniform expansion.

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.

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.

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

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.

Expansion analyses of strategic petroleum reserve in Bayou Choctaw : revised locations.

Energy Technology Data Exchange (ETDEWEB)

Ehgartner, Brian L.; Park, Byoung Yoon

2010-11-01

This report summarizes a series of three-dimensional simulations for the Bayou Choctaw Strategic Petroleum Reserve. The U.S. Department of Energy plans to leach two new caverns and convert one of the existing caverns within the Bayou Choctaw salt dome to expand its petroleum reserve storage capacity. An existing finite element mesh from previous analyses is modified by changing the locations of two caverns. The structural integrity of the three expansion caverns and the interaction between all the caverns in the dome are investigated. The impacts of the expansion on underground creep closure, surface subsidence, infrastructure, and well integrity are quantified. Two scenarios were used for the duration and timing of workover conditions where wellhead pressures are temporarily reduced to atmospheric pressure. The three expansion caverns are predicted to be structurally stable against tensile failure for both scenarios. Dilatant failure is not expected within the vicinity of the expansion caverns. Damage to surface structures is not predicted and there is not a marked increase in surface strains due to the presence of the three expansion caverns. The wells into the caverns should not undergo yield. The results show that from a structural viewpoint, the locations of the two newly proposed expansion caverns are acceptable, and all three expansion caverns can be safely constructed and operated.

On Taylor-Series Approximations of Residual Stress

Science.gov (United States)

Pruett, C. David

1999-01-01

Although subgrid-scale models of similarity type are insufficiently dissipative for practical applications to large-eddy simulation, in recently published a priori analyses, they perform remarkably well in the sense of correlating highly against exact residual stresses. Here, Taylor-series expansions of residual stress are exploited to explain the observed behavior and "success" of similarity models. Until very recently, little attention has been given to issues related to the convergence of such expansions. Here, we re-express the convergence criterion of Vasilyev [J. Comput. Phys., 146 (1998)] in terms of the transfer function and the wavenumber cutoff of the grid filter.

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

Applications of the large mass expansion

International Nuclear Information System (INIS)

Fleischer, J.; Kotikov, A.V.; ); Veretin, O.L.

1998-01-01

The method of the large mass expansion (LME) is investigated for selfenergy and vertex functions in two-loop order. It has the technical advantage that in many cases the expansion coefficients can be expressed analytically. As long as only one non-zero external momentum squared, q 2 , is involved also the Taylor expansion (TE) w.r.t. small q 2 yields high precision results in a domain sufficient for most applications. In the case of only one non-zero mass M and only one external momentum squared, the expansion w.r.t. q 2 /M 2 is identical for the TE and the LME. In this case the combined techniques yield analytic expressions for many diagrams, which are quite easy to handle numerically. (author)

A Three Step Explicit Method for Direct Solution of Third Order ...

African Journals Online (AJOL)

This study produces a three step discrete Linear Multistep Method for Direct solution of third order initial value problems of ordinary differential equations of the form y'''= f(x,y,y',y''). Taylor series expansion technique was adopted in the development of the method. The differential system from the basis polynomial function to ...

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

Eisenstein series for infinite-dimensional U-duality groups

Science.gov (United States)

Fleig, Philipp; Kleinschmidt, Axel

2012-06-01

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.

On the area expansion of magnetic flux tubes in solar active regions

Energy Technology Data Exchange (ETDEWEB)

Dudík, Jaroslav [DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Dzifčáková, Elena [Astronomical Institute of the Academy of Sciences of the Czech Republic, Fričova 298, 251 65 Ondřejov (Czech Republic); Cirtain, Jonathan W., E-mail: J.Dudik@damtp.cam.ac.uk, E-mail: elena@asu.cas.cz [NASA Marshall Space Flight Center, VP 62, Huntsville, AL 35812 (United States)

2014-11-20

We calculated the three-dimensional (3D) distribution of the area expansion factors in a potential magnetic field, extrapolated from the high-resolution Hinode/SOT magnetogram of the quiescent active region NOAA 11482. Retaining only closed loops within the computational box, we show that the distribution of area expansion factors show significant structure. Loop-like structures characterized by locally lower values of the expansion factor are embedded in a smooth background. These loop-like flux tubes have squashed cross-sections and expand with height. The distribution of the expansion factors show an overall increase with height, allowing an active region core characterized by low values of the expansion factor to be distinguished. The area expansion factors obtained from extrapolation of the Solar Optical Telescope magnetogram are compared to those obtained from an approximation of the observed magnetogram by a series of 134 submerged charges. This approximation retains the general flux distribution in the observed magnetogram, but removes the small-scale structure in both the approximated magnetogram and the 3D distribution of the area expansion factors. We argue that the structuring of the expansion factor can be a significant ingredient in producing the observed structuring of the solar corona. However, due to the potential approximation used, these results may not be applicable to loops exhibiting twist or to active regions producing significant flares.

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

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.

[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.

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.

Synthesis, microstructure and thermal expansion studies

Indian Academy of Sciences (India)

Abstract. We report on the synthesis, microstructure and thermal expansion studies on Ca0.5+/2Sr0.5+/2Zr4P6−2Si2O24 ( = 0.00 to 1.00) system which belongs to NZP family of low thermal expansion ceramics. The ceramics synthesized by co-precipitation method at lower calcination and the sintering temperatures ...

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

The bootstrap and edgeworth expansion

CERN Document Server

Hall, Peter

1992-01-01

This monograph addresses two quite different topics, in the belief that each can shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. Chapter 1 is about the bootstrap, witih almost no mention of Edgeworth expansion; Chapter 2 is about Edgeworth expansion, with scarcely a word about the bootstrap; and Chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properites of the bootstrap. The book is aimed a a graduate level audience who has some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter (entitled "Details of Mathematical Rogour"), and so a mathematically able reader without knowledge of the rigorous theory of probability will have no trouble understanding the first four-fifths of the book. The book simultaneously fills two gaps in the literature; it provides a very readable graduate level account of t...

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....

Simple spectral method for solving propagation problems in cylindrical geometry with fast Fourier transforms

International Nuclear Information System (INIS)

Feit, M.D.; Fleck, J.A. Jr.

1989-01-01

We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage

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.

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