Development of a neutronics code based on analytic function expansion nodal method for pebble-type High Temperature Gas-cooled Reactor design

International Nuclear Information System (INIS)

Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo

2006-03-01

There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis

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.

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

Analytic continuation in perturbative QCD

International Nuclear Information System (INIS)

Caprini, Irinel

2002-01-01

We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (author)

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

Science.gov (United States)

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

An analytical wall-function for recirculating and impinging turbulent heat transfer

International Nuclear Information System (INIS)

Suga, K.; Ishibashi, Y.; Kuwata, Y.

2013-01-01

Highlights: ► Improvement of the analytical wall-function is proposed. ► Strain parameter dependency is introduced to the prescribed eddy viscosity profile of the analytical wall-function. ► The model performance is evaluated in turbulent pipe, channel, back-step, abrupt expansion pipe and plane impinging flows. ► Generally improved heat transfer is obtained in all the test cases with the standard k-e model. -- Abstract: The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested

Edgeworth expansion for functionals of continuous diffusion processes

DEFF Research Database (Denmark)

Podolskij, Mark; Yoshida, Nakahiro

This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes....... Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations.......This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes...

An analytical calculation of the axial density profile for 1-d slab expansion

International Nuclear Information System (INIS)

Ho, D

1999-01-01

Obtaining an analytical expression for the axial density profile can provide us with a quick and convenient way to evaluate the density evolution for targets with different densities and dimensions. In this note, we show that such an analytical expression can be obtained based on the self-similar solutions and the method of characteristics for 1-D slab expansion

Analytic approximation for the modified Bessel function I -2/3(x)

Science.gov (United States)

Martin, Pablo; Olivares, Jorge; Maass, Fernando

2017-12-01

In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.

Precise analytic approximations for the Bessel function J1 (x)

Science.gov (United States)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

Analytical evaluation of the plasma dispersion function for a Fermi Dirac distribution

International Nuclear Information System (INIS)

Mamedov, B.A.

2012-01-01

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi—Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data. (physics of gases, plasmas, and electric discharges)

Analytic Hierarchy Process Expansion for Innovation Performance Measurement Framework

Directory of Open Access Journals (Sweden)

Song-Kyoo Kim

2013-01-01

Full Text Available Innovation is a top strategic priority for the majority of companies. The need for innovation becomes more and more evident in the current corporate world, and the purpose of innovation is to create business value. The Analytic Hierarchy Process (AHP is a structured technique for organizing and analyzing complex decisions. This paper is targeting the framework design of the innovation performance criteria and provides the general guidelines to evaluate the relationship between the criteria by using AHP expansion.

Discrete expansions of continuum functions. General concepts

International Nuclear Information System (INIS)

Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

1979-01-01

Different discrete expansions of the continuum wave functions are considered: pole expansion (according to the Mittag-Lefler theorem), Weinberg states. The general property of these groups of states is their completeness in the finite region of space. They satisfy the Schroedinger type equations and are matched with free solutions of the Schroedinger equation at the boundary. Convergence of expansions for the S matrix, the Green functions and the continuous-spectrum wave functions is studied. A new group of states possessing the best convergence is introduced

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.

Spherical cavity-expansion forcing function in PRONTO 3D for application to penetration problems

Energy Technology Data Exchange (ETDEWEB)

Warren, T.L.; Tabbara, M.R.

1997-05-01

In certain penetration events the primary mode of deformation of the target can be approximated by known analytical expressions. In the context of an analysis code, this approximation eliminates the need for modeling the target as well as the need for a contact algorithm. This technique substantially reduces execution time. In this spirit, a forcing function which is derived from a spherical-cavity expansion analysis has been implemented in PRONTO 3D. This implementation is capable of computing the structural and component responses of a projectile due to three dimensional penetration events. Sample problems demonstrate good agreement with experimental and analytical results.

Covariant spectator theory of $np$ scattering:\\\\ Effective range expansions and relativistic deuteron wave functions

Energy Technology Data Exchange (ETDEWEB)

Franz Gross, Alfred Stadler

2010-09-01

We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.

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)

Operator product expansion on the lattice: analytic Wilson coefficients

Science.gov (United States)

Perlt, Holger

2006-12-01

We present first results for Wilson coefficients of operators up to first order in the covariant deriva- tives for the case of Wilson fermions. They are derived from the off-shell Compton scattering amplitude Wµν (a, p, q) of massless quarks with momentum p. The Wilson coefficients are clas- sified according to the transformation of the corresponding operators under the hypercubic group H(4). We give selected examples for a special choice of the momentum transfer q. All Wil- son coefficients are given in closed analytic form and in an expansion in powers of a up to first corrections.

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)

Expansion of continuum functions on resonance wave functions and amplitudes

International Nuclear Information System (INIS)

Bang, J.; Gareev, F.A.; Gizzatkulov, M.H.; Goncharov, S.A.

1978-01-01

To overcome difficulties encountered with wave functions of continuum spectrum (for example, in a shell model with continuum) the pole expansion (by the Mittag-Leffler theorem) of wave functions, scattering amplitudes and the Green functions with positive energies are considered. It is shown that resonance functions (the Gamov functions) form a complete set over which the continuum functions could be expanded. The general view of these expansions for final potentials and for the Coulomb repulsion potential are obtained and discussed. It is shown that the application of the method to nuclear structure calculations leads to simple algebraic equations

An Analytical Diffusion–Expansion Model for Forbush Decreases Caused by Flux Ropes

Science.gov (United States)

Dumbović, Mateja; Heber, Bernd; Vršnak, Bojan; Temmer, Manuela; Kirin, Anamarija

2018-06-01

We present an analytical diffusion–expansion Forbush decrease (FD) model ForbMod, which is based on the widely used approach of an initially empty, closed magnetic structure (i.e., flux rope) that fills up slowly with particles by perpendicular diffusion. The model is restricted to explaining only the depression caused by the magnetic structure of the interplanetary coronal mass ejection (ICME). We use remote CME observations and a 3D reconstruction method (the graduated cylindrical shell method) to constrain initial boundary conditions of the FD model and take into account CME evolutionary properties by incorporating flux rope expansion. Several flux rope expansion modes are considered, which can lead to different FD characteristics. In general, the model is qualitatively in agreement with observations, whereas quantitative agreement depends on the diffusion coefficient and the expansion properties (interplay of the diffusion and expansion). A case study was performed to explain the FD observed on 2014 May 30. The observed FD was fitted quite well by ForbMod for all expansion modes using only the diffusion coefficient as a free parameter, where the diffusion parameter was found to correspond to an expected range of values. Our study shows that, in general, the model is able to explain the global properties of an FD caused by a flux rope and can thus be used to help understand the underlying physics in case studies.

The exponential function expansion of the intra-nodal cross sections for the spectral history gradient correction

International Nuclear Information System (INIS)

Cho, J. Y.; Noh, J. M.; Cheong, H. K.; Choo, H. K.

1998-01-01

In order to simplify the previous spectral history effect correction based on the polynomial expansion nodal method, a new spectral history effect correction is proposed. The new spectral history correction eliminates four microscopic depletion points out of total 13 depletion points in the previous correction by approximating the group cross sections with exponential function. The neutron flux to homogenize the group cross sections for the correction of the spectral history effect is calculated by the analytic function expansion nodal method in stead of the conventional polynomial expansion nodal method. This spectral history correction model is verified against the three MOX benchmark cores: a checkerboard type, a small core with 25 fuel assemblies, and a large core with 177 fuel assemblies. The benchmark results prove that this new spectral history correction model is superior to the previous one even with the reduced number of the local microscopic depletion points

Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications.

Science.gov (United States)

Chen, Jun; Hu, Lei; Deng, Jinxia; Xing, Xianran

2015-06-07

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is a consequence of a complex interplay among the lattice, phonons, and electrons. Interestingly, a large number of NTE materials have been found in various types of functional materials. In the last two decades good progress has been achieved to discover new phenomena and mechanisms of NTE. In the present review article, NTE is reviewed in functional materials of ferroelectrics, magnetics, multiferroics, superconductors, temperature-induced electron configuration change and so on. Zero thermal expansion (ZTE) of functional materials is emphasized due to the importance for practical applications. The NTE functional materials present a general physical picture to reveal a strong coupling role between physical properties and NTE. There is a general nature of NTE for both ferroelectrics and magnetics, in which NTE is determined by either ferroelectric order or magnetic one. In NTE functional materials, a multi-way to control thermal expansion can be established through the coupling roles of ferroelectricity-NTE, magnetism-NTE, change of electron configuration-NTE, open-framework-NTE, and so on. Chemical modification has been proved to be an effective method to control thermal expansion. Finally, challenges and questions are discussed for the development of NTE materials. There remains a challenge to discover a "perfect" NTE material for each specific application for chemists. The future studies on NTE functional materials will definitely promote the development of NTE materials.

Properties of power series of analytic in a bidisc functions of bounded $\\mathbf{L}$-index in joint variables

Directory of Open Access Journals (Sweden)

A. I. Bandura

2017-07-01

Full Text Available We generalized some criteria of boundedness of $\\mathbf{L}$-index in joint variables for analytic in a bidisc functions, where $\\mathbf{L}(z=(l_1(z_1,z_2,$ $l_{2}(z_1,z_2,$ $l_j:\\mathbb{D}^2\\to \\mathbb{R}_+$ is a continuous function, $j\\in\\{1,2\\},$ $\\mathbb{D}^2$ is a bidisc $\\{(z_1,z_2\\in\\mathbb{C}^2: |z_1|<1,|z_2|<1\\}.$ The propositions describe a behaviour of power series expansion on a skeleton of a bidisc. We estimated power series expansion by a dominating homogeneous polynomial with the degree that does not exceed some number depending only from radii of bidisc. Replacing universal quantifier by existential quantifier for radii of bidisc, we also proved sufficient conditions of boundedness of $\\mathbf{L}$-index in joint variables for analytic functions which are weaker than necessary conditions.

On q-extension of Laurent expansion with applications

Directory of Open Access Journals (Sweden)

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.

Analytic properties for the honeycomb lattice Green function at the origin

Science.gov (United States)

Joyce, G. S.

2018-05-01

The analytic properties of the honeycomb lattice Green function are investigated, where is a complex variable which lies in a plane. This double integral defines a single-valued analytic function provided that a cut is made along the real axis from w  =  ‑3 to . In order to analyse the behaviour of along the edges of the cut it is convenient to define the limit function where . It is shown that and can be evaluated exactly for all in terms of various hypergeometric functions, where the argument function is always real-valued and rational. The second-order linear Fuchsian differential equation satisfied by is also used to derive series expansions for and which are valid in the neighbourhood of the regular singular points and . Integral representations are established for and , where with . In particular, it is proved that where J 0(z) and Y 0(z) denote Bessel functions of the first and second kind, respectively. The results derived in the paper are utilized to evaluate the associated logarithmic integral where w lies in the cut plane. A new set of orthogonal polynomials which are connected with the honeycomb lattice Green function are also briefly discussed. Finally, a link between and the theory of Pearson random walks in a plane is established.

Analytic hierarchy process helps select site for limestone quarry expansion in Barbados.

Science.gov (United States)

Dey, Prasanta Kumar; Ramcharan, Eugene K

2008-09-01

Site selection is a key activity for quarry expansion to support cement production, and is governed by factors such as resource availability, logistics, costs, and socio-economic-environmental factors. Adequate consideration of all the factors facilitates both industrial productivity and sustainable economic growth. This study illustrates the site selection process that was undertaken for the expansion of limestone quarry operations to support cement production in Barbados. First, alternate sites with adequate resources to support a 25-year development horizon were identified. Second, technical and socio-economic-environmental factors were then identified. Third, a database was developed for each site with respect to each factor. Fourth, a hierarchical model in analytic hierarchy process (AHP) framework was then developed. Fifth, the relative ranking of the alternate sites was then derived through pair wise comparison in all the levels and through subsequent synthesizing of the results across the hierarchy through computer software (Expert Choice). The study reveals that an integrated framework using the AHP can help select a site for the quarry expansion project in Barbados.

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

Czech Academy of Sciences Publication Activity Database

Abbas, G.; Ananthanarayan, B.; Caprini, I.; Fischer, Jan

2013-01-01

Roč. 87, č. 1 (2013), "014008-1"-"014008-14" ISSN 1550-7998 R&D Projects: GA MŠk(CZ) LG13031 Institutional support: RVO:68378271 Keywords : perturbative expansion * Borel transformation * Adler function Subject RIV: BE - Theoretical Physics Impact factor: 4.864, year: 2013

Analytical and numerical studies of positive ion beam expansion for surface treatment applications

Science.gov (United States)

Lounes-Mahloul, Soumya; Bendib, Abderrezeg; Oudini, Noureddine

2018-01-01

The aim of this work is to study the expansion in vacuum, of a positive ion beam with the use of one dimensional (1D) analytic model and a two dimensional Particle-In-Cell (2D-PIC) simulation. The ion beam is extracted and accelerated from preformed plasma by an extraction system composed of two polarized parallel perforated grids. The results obtained with both approaches reveal the presence of a potential barrier downstream the extraction system which tends to reflect the ion flux. The dependence of the critical distance for which all extracted ions are reflected, is investigated as a function of the extracted ion beam current density. In particular, it is shown that the 1D model recovers the well-known Child-Langmuir law and that the 2D simulation presents a significant discrepancy with respect to the 1D prediction. Indeed, for a given value of current density, the transverse effects lead to a greater critical distance.

Oblique photon expansion of QED structure functions

International Nuclear Information System (INIS)

Chahine, C.

1986-01-01

In the oblique photon expansion, the collinear part of photon emission is summed up to all orders in perturbation theory. The number of oblique or non-collinear photons is the expansion order. Unlike in perturbation theory, every term of the expansion is both infrared finite and gauge invariant. The zero oblique photon contribution to the electromagnetic structure tensor in QED is computed in detail. The behaviors of the structure functions F1 and F2 are discussed in the soft and ultra-soft limits

Parabolic cyclinder functions : examples of error bounds for asymptotic expansions

NARCIS (Netherlands)

R. Vidunas; N.M. Temme (Nico)

2002-01-01

textabstractSeveral asymptotic expansions of parabolic cylinder functions are discussedand error bounds for remainders in the expansions are presented. Inparticular Poincaré-type expansions for large values of the argument$z$ and uniform expansions for large values of the parameter areconsidered.

Some elements of a theory of multidimensional complex variables. I - General theory. II - Expansions of analytic functions and application to fluid flows

Science.gov (United States)

Martin, E. Dale

1989-01-01

The paper introduces a new theory of N-dimensional complex variables and analytic functions which, for N greater than 2, is both a direct generalization and a close analog of the theory of ordinary complex variables. The algebra in the present theory is a commutative ring, not a field. Functions of a three-dimensional variable were defined and the definition of the derivative then led to analytic functions.

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.

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.

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.

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

Graph approach to the gradient expansion of density functionals

International Nuclear Information System (INIS)

Kozlowski, P.M.; Nalewajski, R.F.

1986-01-01

A graph representation of terms in the gradient expansion of the kinetic energy density functional is presented. They briefly discuss the implications of the virial theorem for the graph structure and relations between possible graphs at a given order of expansion

Implementation of a state-to-state analytical framework for the calculation of expansion tube flow properties

Science.gov (United States)

James, C. M.; Gildfind, D. E.; Lewis, S. W.; Morgan, R. G.; Zander, F.

2018-03-01

Expansion tubes are an important type of test facility for the study of planetary entry flow-fields, being the only type of impulse facility capable of simulating the aerothermodynamics of superorbital planetary entry conditions from 10 to 20 km/s. However, the complex flow processes involved in expansion tube operation make it difficult to fully characterise flow conditions, with two-dimensional full facility computational fluid dynamics simulations often requiring tens or hundreds of thousands of computational hours to complete. In an attempt to simplify this problem and provide a rapid flow condition prediction tool, this paper presents a validated and comprehensive analytical framework for the simulation of an expansion tube facility. It identifies central flow processes and models them from state to state through the facility using established compressible and isentropic flow relations, and equilibrium and frozen chemistry. How the model simulates each section of an expansion tube is discussed, as well as how the model can be used to simulate situations where flow conditions diverge from ideal theory. The model is then validated against experimental data from the X2 expansion tube at the University of Queensland.

Discrete expansions of continuum wave functions

International Nuclear Information System (INIS)

Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

1980-01-01

Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)

Conformal four point functions and the operator product expansion

International Nuclear Information System (INIS)

Dolan, F.A.; Osborn, H.

2001-01-01

Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z,x which are simply related to u,v. The operator product expansion analysis is applied to the explicit expressions for the four point function found for free scalar, fermion and vector field theories in four dimensions. The results for four point functions obtained by using the AdS/CFT correspondence are also analysed in terms of functions related to those appearing in the operator product discussion

Analytic Solutions of Special Functional Equations

Directory of Open Access Journals (Sweden)

Octav Olteanu

2013-07-01

Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.

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.

Development of a code in three-dimensional cylindrical geometry based on analytic function expansion nodal (AFEN) method

International Nuclear Information System (INIS)

Lee, Joo Hee

2006-02-01

There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)

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.)

Nonlocal Symmetries, Consistent Riccati Expansion, and Analytical Solutions of the Variant Boussinesq System

Science.gov (United States)

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun

2017-07-01

Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Unitarity or asymptotic completeness equations and analytic structure of the S matrix and Green functions

International Nuclear Information System (INIS)

Iagolnitzer, D.

1983-11-01

Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense

Computing the zeros of analytic functions

CERN Document Server

Kravanja, Peter

2000-01-01

Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

Foundations of predictive analytics

CERN Document Server

Wu, James

2012-01-01

Drawing on the authors' two decades of experience in applied modeling and data mining, Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications, such as consumer behavior modeling, risk and marketing analytics, and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods, from distributions to cumulant and copula functions to Cornish--Fisher expansion and o

An integral equation for the continuation of perturbative expansions

International Nuclear Information System (INIS)

Ciulli, S.

1984-01-01

It is shown how a procedure for analytic continuation, based on methods of functional analysis, can be used to extend the results of a perturbative calculation to yield nonperturbative information which could not be obtained directly from a perturbative expansion

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations

Science.gov (United States)

García, Isaac A.; Llibre, Jaume; Maza, Susanna

2018-06-01

In this work we consider real analytic functions , where , Ω is a bounded open subset of , is an interval containing the origin, are parameters, and ε is a small parameter. We study the branching of the zero-set of at multiple points when the parameter ε varies. We apply the obtained results to improve the classical averaging theory for computing T-periodic solutions of λ-families of analytic T-periodic ordinary differential equations defined on , using the displacement functions defined by these equations. We call the coefficients in the Taylor expansion of in powers of ε the averaged functions. The main contribution consists in analyzing the role that have the multiple zeros of the first non-zero averaged function. The outcome is that these multiple zeros can be of two different classes depending on whether the zeros belong or not to the analytic set defined by the real variety associated to the ideal generated by the averaged functions in the Noetheriang ring of all the real analytic functions at . We bound the maximum number of branches of isolated zeros that can bifurcate from each multiple zero z 0. Sometimes these bounds depend on the cardinalities of minimal bases of the former ideal. Several examples illustrate our results and they are compared with the classical theory, branching theory and also under the light of singularity theory of smooth maps. The examples range from polynomial vector fields to Abel differential equations and perturbed linear centers.

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)

The Analytical Diffusion-Expansion Model for Forbush Decreases Caused by Flux Ropes

Science.gov (United States)

Dumbovic, M.; Temmer, M.

2017-12-01

Identification and tracking of interplanetary coronal mass ejections (ICMEs) throughout the heliosphere is a growingly important aspect of space weather research. One of the "signatures" of ICME passage is the corresponding Forbush decrease (FD), a short term decrease in the galactic cosmic ray flux. These depressions are observed at the surface of the Earth for over 50 years, by several spacecraft in interplanetary space in the past couple of decades, and recently also on Mars' surface with Curiosity rover. In order to use FDs as ICME signatures efficiently, it is important to model ICME interaction with energetic particles by taking into account ICME evolution and constraining the model with observational data. We present an analytical diffusion-expansion FD model ForbMod which is based on the widely used approach of the initially empty, closed magnetic structure (i.e. flux rope) which fills up slowly with particles by perpendicular diffusion. The model is restricted to explain only the depression caused by the magnetic structure of the ICME and not of the associated shock. We use remote CME observations and a 3D reconstruction method (the Graduated Cylindrical Shell method) to constrain initial and boundary conditions of the FD model and take into account CME evolutionary properties by incorporating flux rope expansion. Several options of flux rope expansion are regarded as the competing mechanism to diffusion which can lead to different FD characteristics. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 745782.

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

Energy Technology Data Exchange (ETDEWEB)

Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece); School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Hadjinicolaou, Maria [School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Karahalios, George T. [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece)

2016-08-15

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

International Nuclear Information System (INIS)

Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

2016-01-01

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

Science.gov (United States)

Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

2016-08-01

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions

Multipole expansion of vertex functions with two final particles

International Nuclear Information System (INIS)

Daumens, Michel

1977-01-01

The expansions of the usual vertex functions are generalized to the vertex functions with two final particles. For four vector functions, expressions are similar to those of Chew, Goldberger, Low and Nambu, and of Adler and the consequences of the isobaric model are studied [fr

Analytic structure of the wave function for a hydrogen atom in an analytic potential

International Nuclear Information System (INIS)

Hill, R.N.

1984-01-01

The rate of convergence of an approximate method for solving Schroedinger's equation depends on the ability of the approximating sequence to mimic the analytic structure of the unknown exact wave function. Thus a knowledge of the analytic structure of the wave function can be of great value when approximation schemes are designed. Consider the Schroedinger equation [- 1/2 del 2 -r -1 +V(r)]Psi(r) = EPsi(r) for a hydrogen atom in a potential V(r). The general theory of elliptic partial differential equations implies that Psi is analytic at regular points, but no general theory is available at singular points. The present paper investigates the Coulomb singular point at r = 0 and shows that, if V(r) = V 1 (x, y, z)+rV 2 (x, y, z) where V 1 and V 2 are analytic functions of x, y, z at x = y = z = 0, then the wave function has the form Psi(r) = Psi 1 (x, y, z)+rPsi 2 (x, y, z) where Psi 1 and Psi 2 are analytic functions of x, y, z at x = y = z = 0

Expansion of passive safety function

International Nuclear Information System (INIS)

Inai, Nobuhiko; Nei, Hiromichi; Kumada, Toshiaki.

1995-01-01

Expansion of the use of passive safety functions is proposed. Two notions are presented. One is that, in the design of passive safety nuclear reactors where aversion of active components is stressed, some active components are purposely introduced, by which a system is built in such a way that it behaves in an apparently passive manner. The second notion is that, instead of using a passive safety function alone, a passive safety function is combined with some active components, relating the passivity in the safety function with enhanced controllability in normal operation. The nondormant system which the authors propose is one example of the first notion. This is a system in which a standby safety system is a portion of the normal operation system. An interpretation of the nondormant system via synergetics is made. As an example of the second notion, a PIUS density lock aided with active components is proposed and is discussed

Analytical solution of Mori's equation with secant hyperbolic memory

International Nuclear Information System (INIS)

Tankeshwar, K.; Pathak, K.N.

1993-07-01

The equation of motion of the auto-correlation function has been solved analytically using a secant-hyperbolic form of the memory function. The analytical results obtained for the long time expansion together with the short time expansion provide a good description over the whole time domain as judged by their comparison with the numerical solution of Mori's equation of motion. We also find that the time evolution of the auto-correlation function is determined by a single parameter τ which is related to the frequency sum rules up to the fourth order. The auto-correlation function has been found to show simple decaying or oscillatory behaviour depending on whether the parameter τ is greater than or less than some critical values. Similarities as well as differences in time evolution of the auto-correlation have been discussed for exponential, secant-hyperbolic and Gaussian approaches of the memory function. (author). 16 refs, 5 figs

Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of the S U (Nc) conformal anomaly and studies of the conformal symmetry limit

Science.gov (United States)

Cvetič, Gorazd; Kataev, A. L.

2016-07-01

We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.

Measuring myokines with cardiovascular functions: pre-analytical variables affecting the analytical output.

Science.gov (United States)

Lombardi, Giovanni; Sansoni, Veronica; Banfi, Giuseppe

2017-08-01

In the last few years, a growing number of molecules have been associated to an endocrine function of the skeletal muscle. Circulating myokine levels, in turn, have been associated with several pathophysiological conditions including the cardiovascular ones. However, data from different studies are often not completely comparable or even discordant. This would be due, at least in part, to the whole set of situations related to the preparation of the patient prior to blood sampling, blood sampling procedure, processing and/or store. This entire process constitutes the pre-analytical phase. The importance of the pre-analytical phase is often not considered. However, in routine diagnostics, the 70% of the errors are in this phase. Moreover, errors during the pre-analytical phase are carried over in the analytical phase and affects the final output. In research, for example, when samples are collected over a long time and by different laboratories, a standardized procedure for sample collecting and the correct procedure for sample storage are acknowledged. In this review, we discuss the pre-analytical variables potentially affecting the measurement of myokines with cardiovascular functions.

Analytical approximations to seawater optical phase functions of scattering

Science.gov (United States)

Haltrin, Vladimir I.

2004-11-01

This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.

Trinucleon wave functions from separable expansions of the N-N interaction

International Nuclear Information System (INIS)

Birrell, N.D.

1976-09-01

This work is intended to determine whether a separable expansion for the N-N interaction can be used to obtain trinucleon wave functions of high quality. The expansions used in the study are the Unitary Pole expansion of Harms, Afnan and Read, and the expansion of Adhikari and Sloan. We first compare the calculation of the RSC potential Triton binding energy with the two methods, and find that the results agree quite closely. However, while it is found necessary to use t-matrix perturbation theory to obtain the UPE result, such is not the case with the ASE, thus offering a considerable improvement on the previously used method. We then proceed to calculate the L-S coupling probabilities for the wave function, and in so doing, discover a source of inaccuracy in the work of other authors. We also find that the UPE and ASE give probabilities in good agreement with one another. The calculation of the He 3 charge form factor turns out to be the most critical judge of the accuracy of the wave function. Although both expansions give quite satisfactory results for the charge form factor, those obtained with the ASE are exceptionally pleasing. We finally apply both methods to the OBEP of Holinde and Machleidt, and find that the UPE is quite unsuitable for such application. The ASE, however, once again gives very good results, indicating the high quality of the trinucleon wave function obtained with it. (author)

A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d-Finite Functions

Directory of Open Access Journals (Sweden)

Agata Bezubik

2006-03-01

Full Text Available This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.

Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions

NARCIS (Netherlands)

J.L. López; N.M. Temme (Nico)

2010-01-01

textabstractExpansions in terms of Bessel functions are considered of the Kummer function ${}_1F_1(a;c,z)$ (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic

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

Two-dimensional analytic weighting functions for limb scattering

Science.gov (United States)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

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.

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)

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

Analytical Model for the End-Bearing Capacity of Tapered Piles Using Cavity Expansion Theory

Directory of Open Access Journals (Sweden)

Suman Manandhar

2012-01-01

Full Text Available On the basis of evidence from model tests on increasing the end-bearing behavior of tapered piles at the load-settlement curve, this paper proposes an analytical spherical cavity expansion theory to evaluate the end-bearing capacity. The angle of tapering is inserted in the proposed model to evaluate the end-bearing capacity. The test results of the proposed model in different types of sands and different relative densities show good effects compared to conventional straight piles. The end-bearing capacity increases with increases in the tapering angle. The paper then propounds a model for prototypes and real-type pile tests which predicts and validates to evaluate the end-bearing capacity.

Jacobian elliptic function expansion solutions of nonlinear stochastic equations

International Nuclear Information System (INIS)

Wei Caimin; Xia Zunquan; Tian Naishuo

2005-01-01

Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

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

Causality and analyticity in optics

International Nuclear Information System (INIS)

Nussenzveig, H.M.

In order to provide an overall picture of the broad range of optical phenomena that are directly linked with the concepts of causality and analyticity, the following topics are briefly reviewed, emphasizing recent developments: 1) Derivation of dispersion relations for the optical constants of general linear media from causality. Application to the theory of natural optical activity. 2) Derivation of sum rules for the optical constants from causality and from the short-time response function (asymptotic high-frequency behavior). Average spectral behavior of optical media. Applications. 3) Role of spectral conditions. Analytic properties of coherence functions in quantum optics. Reconstruction theorem.4) Phase retrieval problems. 5) Inverse scattering problems. 6) Solution of nonlinear evolution equations in optics by inverse scattering methods. Application to self-induced transparency. Causality in nonlinear wave propagation. 7) Analytic continuation in frequency and angular momentum. Complex singularities. Resonances and natural-mode expansions. Regge poles. 8) Wigner's causal inequality. Time delay. Spatial displacements in total reflection. 9) Analyticity in diffraction theory. Complex angular momentum theory of Mie scattering. Diffraction as a barrier tunnelling effect. Complex trajectories in optics. (Author) [pt

Finite-temperature correlation function for the one-dimensional quantum Ising model:The virial expansion

Science.gov (United States)

Reyes, S. A.; Tsvelik, A. M.

2006-06-01

We rewrite the exact expression for the finite-temperature two-point correlation function for the magnetization as a partition function of some field theory. This removes singularities and provides a convenient form to develop a virial expansion (expansion in powers of the soliton density).

Asymptotic Expansions of Generalized Nevanlinna Functions and their Spectral Properties

NARCIS (Netherlands)

Derkach, Vladimir; Hassi, Seppo; de Snoo, Hendrik

2007-01-01

Asymptotic expansions of generalized Nevanlinna functions Q are investigated by means of a factorization model involving a part of the generalized zeros and poles of nonpositive type of the function Q. The main results in this paper arise from the explicit construction of maximal Jordan chains in

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)

The linear potential propagator via wave function expansion

International Nuclear Information System (INIS)

Nassar, Antonio B.; Cattani, Mauro S.D.

2002-01-01

We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developed formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities. (author)

Exponential Expansion in Evolutionary Economics

DEFF Research Database (Denmark)

Frederiksen, Peter; Jagtfelt, Tue

2013-01-01

This article attempts to solve current problems of conceptual fragmentation within the field of evolutionary economics. One of the problems, as noted by a number of observers, is that the field suffers from an assemblage of fragmented and scattered concepts (Boschma and Martin 2010). A solution...... to this problem is proposed in the form of a model of exponential expansion. The model outlines the overall structure and function of the economy as exponential expansion. The pictographic model describes four axiomatic concepts and their exponential nature. The interactive, directional, emerging and expanding...... concepts are described in detail. Taken together it provides the rudimentary aspects of an economic system within an analytical perspective. It is argued that the main dynamic processes of the evolutionary perspective can be reduced to these four concepts. The model and concepts are evaluated in the light...

Nodewise analytical calculation of the transfer function

International Nuclear Information System (INIS)

Makai, Mihaly

1994-01-01

The space dependence of neutron noise has so far been mostly investigated in homogeneous core models. Application of core diagnostic methods to locate a malfunction requires however that the transfer function be calculated for real, inhomogeneous cores. A code suitable for such purpose must be able to handle complex arithmetic and delta-function source. Further requirements are analytical dependence in one spatial variable and fast execution. The present work describes the TIDE program written to fulfil the above requirements. The core is subdivided into homogeneous, square assemblies. An analytical solution is given, which is a generalisation of the inhomogeneous response matrix method. (author)

Towards an analytic solution of QCD: The glueball mass gap

International Nuclear Information System (INIS)

West, G.B.

1987-01-01

Certain general features and beliefs concerning quantum chromodynamics are reviewed with he view to seeing whether the theory sense and whether its physical spectrum can be determined. A typical Green's function is represented as an expansion around the minima of the action, each term of which is divergent and requires renormalization. It is shown that even after renormalization, each of the series generated by expansion around a minimum is divergent and requires a summability procedure to make sense. The causality and analyticity of the resulting Green's function is then discussed. The ideas thus developed are shown to determine the position of the first singularity of the Green's function

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)

Patterns of coordinated cortical remodeling during adolescence and their associations with functional specialization and evolutionary expansion.

Science.gov (United States)

Sotiras, Aristeidis; Toledo, Jon B; Gur, Raquel E; Gur, Ruben C; Satterthwaite, Theodore D; Davatzikos, Christos

2017-03-28

During adolescence, the human cortex undergoes substantial remodeling to support a rapid expansion of behavioral repertoire. Accurately quantifying these changes is a prerequisite for understanding normal brain development, as well as the neuropsychiatric disorders that emerge in this vulnerable period. Past accounts have demonstrated substantial regional heterogeneity in patterns of brain development, but frequently have been limited by small samples and analytics that do not evaluate complex multivariate imaging patterns. Capitalizing on recent advances in multivariate analysis methods, we used nonnegative matrix factorization (NMF) to uncover coordinated patterns of cortical development in a sample of 934 youths ages 8-20, who completed structural neuroimaging as part of the Philadelphia Neurodevelopmental Cohort. Patterns of structural covariance (PSCs) derived by NMF were highly reproducible over a range of resolutions, and differed markedly from common gyral-based structural atlases. Moreover, PSCs were largely symmetric and showed correspondence to specific large-scale functional networks. The level of correspondence was ordered according to their functional role and position in the evolutionary hierarchy, being high in lower-order visual and somatomotor networks and diminishing in higher-order association cortex. Furthermore, PSCs showed divergent developmental associations, with PSCs in higher-order association cortex networks showing greater changes with age than primary somatomotor and visual networks. Critically, such developmental changes within PSCs were significantly associated with the degree of evolutionary cortical expansion. Together, our findings delineate a set of structural brain networks that undergo coordinated cortical thinning during adolescence, which is in part governed by evolutionary novelty and functional specialization.

Analytic behavior of the QED polarizability function at finite temperature

International Nuclear Information System (INIS)

Bernal, A.; Perez, A.

2012-01-01

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.

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

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)

Nucleon structure functions from lattice operator product expansion

Energy Technology Data Exchange (ETDEWEB)

Chambers, A.J.; Somfleth, K.; Young, R.D.; Zanotti, J.M. [Adelaide Univ., SA (Australia). CSSM, Dept. of Physics; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2017-03-15

Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

Nucleon structure functions from lattice operator product expansion

International Nuclear Information System (INIS)

Chambers, A.J.; Somfleth, K.; Young, R.D.; Zanotti, J.M.; Perlt, H.; Schiller, A.

2017-03-01

Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

Analytic continuation and perturbative expansions in QCD

Czech Academy of Sciences Publication Activity Database

Caprini, I.; Fischer, Jan

2002-01-01

Roč. 24, - (2002), s. 127-135 ISSN 1434-6044 R&D Projects: GA MPO RP-4210/69 Institutional research plan: CEZ:AV0Z1010920 Keywords : perturbative expansion * quantum chromodynamics * infrared ambiguity * essential singularities Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 6.162, year: 2002

Approximation of Analytic Functions by Bessel's Functions of Fractional Order

Directory of Open Access Journals (Sweden)

Soon-Mo Jung

2011-01-01

Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.

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.

On a generalized oscillator system: interbasis expansions

Energy Technology Data Exchange (ETDEWEB)

Kibler, M [Lyon-1 Univ., 69 - Villeurbanne (France). Inst. de Physique Nucleaire; Mardoyan, L G; Pogosyan, G S [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics

1997-12-31

This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The Schroedinger equation for this generalized oscillator system is separable in spherical, cylindrical, and spheroidal (prolate and oblate) coordinates. The quantum mechanical spectrum of this system is worked out in some details. The problem of interbasis expansions of the wave functions is completely solved. The coefficients for the expansion of the cylindrical basis in terms of the spherical basis, and vice-versa, are found to be analytic continuations (to real values of their arguments) of Clebsch-Gordan coefficients for the group SU(2). The interbasis expansion coefficients for the prolate and oblate spheroidal bases in terms of the spherical or the cylindrical bases are shown to satisfy three-term recursion relations. Finally, a connection between the generalized oscillator system (projected on the z-line) and the Morse system (in one dimension) are discussed. 41 refs.,.

On a generalized oscillator system: interbasis expansions

International Nuclear Information System (INIS)

Kibler, M.; Mardoyan, L.G.; Pogosyan, G.S.

1996-01-01

This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The Schroedinger equation for this generalized oscillator system is separable in spherical, cylindrical, and spheroidal (prolate and oblate) coordinates. The quantum mechanical spectrum of this system is worked out in some details. The problem of interbasis expansions of the wave functions is completely solved. The coefficients for the expansion of the cylindrical basis in terms of the spherical basis, and vice-versa, are found to be analytic continuations (to real values of their arguments) of Clebsch-Gordan coefficients for the group SU(2). The interbasis expansion coefficients for the prolate and oblate spheroidal bases in terms of the spherical or the cylindrical bases are shown to satisfy three-term recursion relations. Finally, a connection between the generalized oscillator system (projected on the z-line) and the Morse system (in one dimension) are discussed. 41 refs.,

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.

Asymptotic expansions of Mathieu functions in wave mechanics

International Nuclear Information System (INIS)

Hunter, G.; Kuriyan, M.

1976-01-01

Solutions of the radial Schroedinger equation containing a polarization potential r -4 are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states

Analytical extraction of leaky modes in circular slab waveguides with arbitrary refractive index profile.

Science.gov (United States)

Sarrafi, P; Zareian, N; Mehrany, K

2007-12-20

Circular slab waveguides are conformally transformed into straight inhomogeneous waveguides, whereupon electromagnetic fields in the core are expanded in terms of Legendre polynomial basis functions. Thereafter, different analytical expression of electromagnetic fields in the cladding region, viz. Wentzel-Kramers-Brillouin solution, modified Airy function expansion, and the exact field solution for circular waveguides, i.e., Hankel function of complex order, are each matched to the polynomial expansion of the transverse electric field within the guide. This field matching process renders different boundary conditions to be satisfied by the set of orthogonal Legendre polynomial basis functions. In this fashion, the governing wave equation is converted into an algebraic and easy to solve eigenvalue problem, which is associated with a matrix whose elements are analytically given. Various numerical examples are presented and the accuracy of each of the abovementioned different boundary conditions is assessed. Furthermore, the computational efficiency and the convergence rate of the proposed method with increasing number of basis functions are briefly discussed.

A general analytical solution for the stochastic Milne problem using Karhunen–Loeve (K–L) expansion

International Nuclear Information System (INIS)

Hussein, A.; Selim, M.M.

2013-01-01

This paper considers the solution of the stochastic integro-differential equation of Milne problem with random operator. The Pomraning–Eddington method is implemented to get a closed form solution deterministically. Relying on the spectral properties of the covariance function, the Karhunen–Loeve (K–L) expansion is used to represent the input stochastic process in the deterministic solution. This leads to an explicit expression for the solution process as a multivariate functional of a set of uncorrelated random variables. By using different distributions for these variables, the work is realized through computing the mean and the variance of the solution. The numerical results are found in agreement with those obtained in the literature. -- Highlights: •The solution of the stochastic Milne problem is considered. •We dealt with the random cross-section itself not with the optical transformation of it. •Pomraning–Eddington method together with the (K–L) expansion were implemented. •The solution process is obtained as a functional of a set of uncorrelated random variables. •Good results are obtained for different distributions of these variables

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

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

Science.gov (United States)

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

2009-06-08

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

On the analytic continuation of functions defined by Legendre series

International Nuclear Information System (INIS)

Grinstein, F.F.

1981-07-01

An infinite diagonal sequence of Punctual Pade Approximants is considered for the approximate analytical continuation of a function defined by a formal Legendre series. The technique is tested in the case of two series with exactly known analytical sum: the generating function for Legendre polynomials and the Coulombian scattering amplitude. (author)

Multi-criteria Generation-Expansion Planning with Carbon dioxide emissions and Nuclear Safety considerations

International Nuclear Information System (INIS)

Lee, Hun Gyu; Kim, Young Chang

2010-01-01

A multiple criteria decision making (MCDM) method is developed to aid decision makers in Generation Expansion planning and management. Traditionally, the prime objective of an electric utility's generation-expansion planning has been to determine the minimum cost supply plans that meet expected demands over a planning horizon (typically 10 to 30 years). Today, however, the nature of decision environments has changed substantially. Increased policy attention is given to solve the multiple tradeoff function including environmental and social factors as well as economic one related to nuclear power expansion. In order to deal with this MCDM problem, the Analytic Hierarchy Process (AHP) Model is applied

Multipole expansion of vertex functions in an arbitrary frame

International Nuclear Information System (INIS)

Daumens, Michel

1977-01-01

Vertex functions are expanded on the bases of tensor spherical harmonics and tensor multipoles. The coefficients of the expansions are rotational invariant form factors. The relations with those defined in particular frames by Durand, De Celles and Marr, and by De Rafael are exhibited. Finally multipolar form factors are built which are irreducible under pure Lorentz transformations [fr

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

Science.gov (United States)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

A new way of obtaining analytic approximations of Chandrasekhar's H function

International Nuclear Information System (INIS)

Vukanic, J.; Arsenovic, D.; Davidovic, D.

2007-01-01

Applying the mean value theorem for definite integrals in the non-linear integral equation for Chandrasekhar's H function describing conservative isotropic scattering, we have derived a new, simple analytic approximation for it, with a maximal relative error below 2.5%. With this new function as a starting-point, after a single iteration in the corresponding integral equation, we have obtained a new, highly accurate analytic approximation for the H function. As its maximal relative error is below 0.07%, it significantly surpasses the accuracy of other analytic approximations

Local properties of analytic functions and non-standard analysis

International Nuclear Information System (INIS)

O'Brian, N.R.

1976-01-01

This is an expository account which shows how the methods of non-standard analysis can be applied to prove the Nullstellensatz for germs of analytic functions. This method of proof was discovered originally by Abraham Robinson. The necessary concepts from model theory are described in some detail and the Nullstellensatz is proved by investigating the relation between the set of infinitesimal elements in the complex n-plane and the spectrum of the ring of germs of analytic functions. (author)

Asymptotic expansion of a partition function related to the sinh-model

CERN Document Server

Borot, Gaëtan; Kozlowski, Karol K

2016-01-01

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integra...

Coefficient inequality for certain subclass of analytic functions

Directory of Open Access Journals (Sweden)

D. Vamshee Krishna

2013-03-01

Full Text Available The objective of this paper is to an obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for the function $f$, belonging to a certain subclass of analytic functions, using Toeplitz determinants.

Exact asymptotic expansion for the resistance between the center node and a node on the cobweb network boundary

Directory of Open Access Journals (Sweden)

R. Kenna

2014-09-01

Full Text Available We analyze the resistance between two nodes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M x N cobweb network with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.

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)

Analytical studies on the Benney-Luke equation in mathematical physics

Science.gov (United States)

Islam, S. M. Rayhanul; Khan, Kamruzzaman; Woadud, K. M. Abdul Al

2018-04-01

The enhanced (G‧/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney-Luke equation by using the enhanced (G‧/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.

Resonant state expansion applied to three-dimensional open optical systems

OpenAIRE

Doost, M. B.; Langbein, W.; Muljarov, E. A.

2014-01-01

The resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the valid...

Momentum autocorrelation function of a classic diatomic chain

Energy Technology Data Exchange (ETDEWEB)

Yu, Ming B., E-mail: mingbyu@gmail.com

2016-10-23

A classical harmonic diatomic chain is studied using the recurrence relations method. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical contributions are derived as even-order Bessel function expansions with coefficients given in terms of integrals of elliptic functions in real axis and a contour parallel to the imaginary axis, respectively. - Highlights: • Momentum autocorrelation function of a classic diatomic chain is studied. • It is derived as even-order Bessel function expansion using the convolution theorem. • The expansion coefficients are integrals of elliptic functions. • Addition theorem is used to reduce complex elliptic function to complex sum of real ones.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

Science.gov (United States)

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

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.

Executive Function and Reading Comprehension: A Meta-Analytic Review

Science.gov (United States)

Follmer, D. Jake

2018-01-01

This article presents a meta-analytic review of the relation between executive function and reading comprehension. Results (N = 6,673) supported a moderate positive association between executive function and reading comprehension (r = 0.36). Moderator analyses suggested that correlations between executive function and reading comprehension did not…

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.

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

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.

Functional perturbative RG and CFT data in the ε-expansion

Energy Technology Data Exchange (ETDEWEB)

Codello, A. [Southern Denmark Univ., Odense (Denmark). CP3-Origins; INFN-Sezione di Bologna, Bologna (Italy); Safari, M. [INFN-Sezione di Bologna, Bologna (Italy); Bologna Univ. (Italy). Dipt di Fisica e Astronomia; Vacca, G.P. [INFN-Sezione di Bologna, Bologna (Italy); Zanusso, O. [INFN-Sezione di Bologna, Bologna (Italy); Jena Univ. (Germany). Theoretisch-Physikalisches Inst.

2018-01-15

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the ε-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models φ{sup 2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks. (orig.)

Instability of a planar expansion wave.

Science.gov (United States)

Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G

2005-10-01

An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.

Auto-Baecklund Transformation and Analytic Solutions of (2+1)-Dimensional Boussinesq Equation

International Nuclear Information System (INIS)

Liu Guanting

2008-01-01

Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Baecklund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass wp function. Some of them are novel.

A two-parameter family of double-power-law biorthonormal potential-density expansions

Science.gov (United States)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Analytic functions of several complex variables

CERN Document Server

Gunning, Robert C

2009-01-01

The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resol

Adiabatic supernova expansion into the circumstellar medium

International Nuclear Information System (INIS)

Band, D.L.; Liang, E.P.

1987-01-01

We perform one dimensional numerical simulations with a Lagrangian hydrodynamics code of the adiabatic expansion of a supernova into the surrounding medium. The early expansion follows Chevalier's analytic self-similar solution until the reverse shock reaches the ejecta core. We follow the expansion as it evolves towards the adiabatic blast wave phase. Some memory of the earlier phases of expansion is retained in the interior even when the outer regions expand as a blast wave. We find the results are sensitive to the initial configuration of the ejecta and to the placement of gridpoints. 6 refs., 2 figs

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

Science.gov (United States)

Zylka, Christian; Vojta, Guenter

1993-01-01

The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

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

Aft-body loading function for penetrators based on the spherical cavity-expansion approximation.

Energy Technology Data Exchange (ETDEWEB)

Longcope, Donald B., Jr.; Warren, Thomas Lynn; Duong, Henry

2009-12-01

In this paper we develop an aft-body loading function for penetration simulations that is based on the spherical cavity-expansion approximation. This loading function assumes that there is a preexisting cavity of radius a{sub o} before the expansion occurs. This causes the radial stress on the cavity surface to be less than what is obtained if the cavity is opened from a zero initial radius. This in turn causes less resistance on the aft body as it penetrates the target which allows for greater rotation of the penetrator. Results from simulations are compared with experimental results for oblique penetration into a concrete target with an unconfined compressive strength of 23 MPa.

Nucleon Structure Functions from Operator Product Expansion on the Lattice.

Science.gov (United States)

Chambers, A J; Horsley, R; Nakamura, Y; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A; Somfleth, K; Young, R D; Zanotti, J M

2017-06-16

Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.

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

Algebraic and analyticity properties of the n-point function in quantum field theory

International Nuclear Information System (INIS)

Bros, Jacques

1970-01-01

The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author) [fr

Promoting Efficacy Research on Functional Analytic Psychotherapy

Science.gov (United States)

Maitland, Daniel W. M.; Gaynor, Scott T.

2012-01-01

Functional Analytic Psychotherapy (FAP) is a form of therapy grounded in behavioral principles that utilizes therapist reactions to shape target behavior. Despite a growing literature base, there is a paucity of research to establish the efficacy of FAP. As a general approach to psychotherapy, and how the therapeutic relationship produces change,…

Functional differential equation approach to the large N expansion and mean field perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.

1985-01-01

An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

Neural substrate expansion for the restoration of brain function

Directory of Open Access Journals (Sweden)

Han-Chiao Isaac Chen

2016-01-01

Full Text Available Restoring neurological and cognitive function in individuals who have suffered brain damage is one of the principal objectives of modern translational neuroscience. Electrical stimulation approaches, such as deep-brain stimulation, have achieved the most clinical success, but they ultimately may be limited by the computational capacity of the residual cerebral circuitry. An alternative strategy is brain substrate expansion, in which the computational capacity of the brain is augmented through the addition of new processing units and the reconstitution of network connectivity. This latter approach has been explored to some degree using both biological and electronic means but thus far has not demonstrated the ability to reestablish the function of large-scale neuronal networks. In this review, we contend that fulfilling the potential of brain substrate expansion will require a significant shift from current methods that emphasize direct manipulations of the brain (e.g., injections of cellular suspensions and the implantation of multi-electrode arrays to the generation of more sophisticated neural tissues and neural-electric hybrids in vitro that are subsequently transplanted into the brain. Drawing from neural tissue engineering, stem cell biology, and neural interface technologies, this strategy makes greater use of the manifold techniques available in the laboratory to create biocompatible constructs that recapitulate brain architecture and thus are more easily recognized and utilized by brain networks.

Small-x behavior of the structure function F2 and its slope ∂lnF2/∂ln(1/x) for ''frozen'' and analytic strong-coupling constants

International Nuclear Information System (INIS)

Cvetic, G.; Kniehl, B.A.; Kotikov, A.V.

2009-06-01

Using the leading-twist approximation of the Wilson operator product expansion with ''frozen'' and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F 2 and its slope ∂lnF 2 /∂ln(1/x) at small values of x, obtained for a at initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA. (orig.)

Security of Semi-Device-Independent Random Number Expansion Protocols.

Science.gov (United States)

Li, Dan-Dan; Wen, Qiao-Yan; Wang, Yu-Kun; Zhou, Yu-Qian; Gao, Fei

2015-10-27

Semi-device-independent random number expansion (SDI-RNE) protocols require some truly random numbers to generate fresh ones, with making no assumptions on the internal working of quantum devices except for the dimension of the Hilbert space. The generated randomness is certified by non-classical correlation in the prepare-and-measure test. Until now, the analytical relations between the amount of the generated randomness and the degree of non-classical correlation, which are crucial for evaluating the security of SDI-RNE protocols, are not clear under both the ideal condition and the practical one. In the paper, first, we give the analytical relation between the above two factors under the ideal condition. As well, we derive the analytical relation under the practical conditions, where devices' behavior is not independent and identical in each round and there exists deviation in estimating the non-classical behavior of devices. Furthermore, we choose a different randomness extractor (i.e., two-universal random function) and give the security proof.

Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion

International Nuclear Information System (INIS)

Oladyshkin, S.; Nowak, W.

2012-01-01

We discuss the arbitrary polynomial chaos (aPC), which has been subject of research in a few recent theoretical papers. Like all polynomial chaos expansion techniques, aPC approximates the dependence of simulation model output on model parameters by expansion in an orthogonal polynomial basis. The aPC generalizes chaos expansion techniques towards arbitrary distributions with arbitrary probability measures, which can be either discrete, continuous, or discretized continuous and can be specified either analytically (as probability density/cumulative distribution functions), numerically as histogram or as raw data sets. We show that the aPC at finite expansion order only demands the existence of a finite number of moments and does not require the complete knowledge or even existence of a probability density function. This avoids the necessity to assign parametric probability distributions that are not sufficiently supported by limited available data. Alternatively, it allows modellers to choose freely of technical constraints the shapes of their statistical assumptions. Our key idea is to align the complexity level and order of analysis with the reliability and detail level of statistical information on the input parameters. We provide conditions for existence and clarify the relation of the aPC to statistical moments of model parameters. We test the performance of the aPC with diverse statistical distributions and with raw data. In these exemplary test cases, we illustrate the convergence with increasing expansion order and, for the first time, with increasing reliability level of statistical input information. Our results indicate that the aPC shows an exponential convergence rate and converges faster than classical polynomial chaos expansion techniques.

Computing derivative-based global sensitivity measures using polynomial chaos expansions

International Nuclear Information System (INIS)

Sudret, B.; Mai, C.V.

2015-01-01

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSMs) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis. - Highlights: • Derivative-based global sensitivity measures (DGSM) have been developed for screening purpose. • Polynomial chaos expansions (PC) are used as a surrogate model of the original computational model. • From a PC expansion the DGSM can be computed analytically. • The paper provides the derivatives of Hermite, Legendre and Laguerre polynomials for this purpose

A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation

International Nuclear Information System (INIS)

Chang, K.S.; Kim, B.S.; Park, C.H.; Ryu, K.S.

2003-01-01

We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L p into L p-ci r cumflexprime (1< p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies an integral equation related to the generalized Schroedinger equation. The resulting theorems extend the theory of operator-valued function space integrals substantially and previous theorems about these integrals are generalized by our results

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

Energy Technology Data Exchange (ETDEWEB)

Izacard, Olivier, E-mail: izacard@llnl.gov [Lawrence Livermore National Laboratory, 7000 East Avenue, L-637, Livermore, California 94550 (United States)

2016-08-15

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it

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.

Semi-analytical solution to arbitrarily shaped beam scattering

Science.gov (United States)

Wang, Wenjie; Zhang, Huayong; Sun, Yufa

2017-07-01

Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

CERN Document Server

Dixon, Lance J.; Henn, Johannes M.

2012-01-01

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two function...

The influence of medium elasticity on the prediction of histotripsy-induced bubble expansion and erythrocyte viability

Science.gov (United States)

Bader, Kenneth B.

2018-05-01

Histotripsy is a form of therapeutic ultrasound that liquefies tissue mechanically via acoustic cavitation. Bubble expansion is paramount in the efficacy of histotripsy therapy, and the cavitation dynamics are strongly influenced by the medium elasticity. In this study, an analytic model to predict histotripsy-induced bubble expansion in a fluid was extended to include the effects of medium elasticity. Good agreement was observed between the predictions of the analytic model and numerical computations utilizing highly nonlinear excitations (shock-scattering histotripsy) and purely tensile pulses (microtripsy). No bubble expansion was computed for either form of histotripsy when the elastic modulus was greater than 20 MPa and the peak negative pressure was less than 50 MPa. Strain in the medium due to the expansion of a single bubble was also tabulated. The viability of red blood cells was calculated as a function of distance from the bubble wall based on empirical data of impulsive stretching of erythrocytes. Red blood cells remained viable at distances further than 44 µm from the bubble wall. As the medium elasticity increased, the distance over which bubble expansion-induced strain influenced red blood cells was found to decrease sigmoidally. These results highlight the relationship between tissue elasticity and the efficacy of histotripsy. In addition, an upper medium elasticity limit was identified, above which histotripsy may not be effective for tissue liquefaction.

Estimates of radiation over clouds and dust aerosols: Optimized number of terms in phase function expansion

International Nuclear Information System (INIS)

Ding Shouguo; Xie Yu; Yang Ping; Weng Fuzhong; Liu Quanhua; Baum, Bryan; Hu Yongxiang

2009-01-01

The bulk-scattering properties of dust aerosols and clouds are computed for the community radiative transfer model (CRTM) that is a flagship effort of the Joint Center for Satellite Data Assimilation (JCSDA). The delta-fit method is employed to truncate the forward peaks of the scattering phase functions and to compute the Legendre expansion coefficients for re-constructing the truncated phase function. Use of more terms in the expansion gives more accurate re-construction of the phase function, but the issue remains as to how many terms are necessary for different applications. To explore this issue further, the bidirectional reflectances associated with dust aerosols, water clouds, and ice clouds are simulated with various numbers of Legendre expansion terms. To have relative numerical errors smaller than 5%, the present analyses indicate that, in the visible spectrum, 16 Legendre polynomials should be used for dust aerosols, while 32 Legendre expansion terms should be used for both water and ice clouds. In the infrared spectrum, the brightness temperatures at the top of the atmosphere are computed by using the scattering properties of dust aerosols, water clouds and ice clouds. Although small differences of brightness temperatures compared with the counterparts computed with 4, 8, 128 expansion terms are observed at large viewing angles for each layer, it is shown that 4 terms of Legendre polynomials are sufficient in the radiative transfer computation at infrared wavelengths for practical applications.

Analytic properties of the whistler dispersion function

International Nuclear Information System (INIS)

Daniell, G.J.

1986-01-01

The analytic properties of the dispersion function of a whistler are investigated in the complex frequency plane. It possesses a pole and a branch point at a frequency equal to the minimum value of the electron gyrofrequency along the path of propagation. An integral equation relates the dispersion function to the distribution of magnetospheric electrons along the path and the solution of this equation is obtained. It is found that the electron density in the equatorial plane is very simply related to the dispersion function. A discussion of approximate formulae to represent the dispersion shows how particular terms can be related to attributes of the electron density distribution, and a new approximate formula is proposed. (author)

A new approach to stochastic transport via the functional Volterra expansion

International Nuclear Information System (INIS)

Ziya Akcasu, A.; Corngold, N.

2005-01-01

In this paper we present a new algorithm (FDA) for the calculation of the mean and the variance of the flux in stochastic transport when the transport equation contains a spatially random parameter θ(r), such as the density of the medium. The approach is based on the renormalized functional Volterra expansion of the flux around its mean. The attractive feature of the approach is that it explicitly displays the functional dependence of the flux on the products of θ(r i ), and hence enables one to take ensemble averages directly to calculate the moments of the flux in terms of the correlation functions of the underlying random process. The renormalized deterministic transport equation for the mean flux has been obtained to the second order in θ(r), and a functional relationship between the variance and the mean flux has been derived to calculate the variance to this order. The feasibility and accuracy of FDA has been demonstrated in the case of stochastic diffusion, using the diffusion equation with a spatially random diffusion coefficient. The connection of FDA with the well-established approximation schemes in the field of stochastic linear differential equations, such as the Bourret approximation, developed by Van Kampen using cumulant expansion, and by Terwiel using projection operator formalism, which has recently been extended to stochastic transport by Corngold. We hope that FDA's potential will be explored numerically in more realistic applications of the stochastic transport. (authors)

Instability of a planar expansion wave

International Nuclear Information System (INIS)

Velikovich, A.L.; Zalesak, S.T.; Metzler, N.; Wouchuk, J.G.

2005-01-01

An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent γ. At γ>3, the mass modulation amplitude δm in a rippled expansion wave exhibits a power-law growth with time ∝t β , where β=(γ-3)/(γ-1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme γ-1 -1/2 , and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low γ. Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results

The boundary value problem for discrete analytic functions

KAUST Repository

Skopenkov, Mikhail

2013-06-01

This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.

Self-adaptive numerical integrator for analytic functions

International Nuclear Information System (INIS)

Garribba, S.; Quartapelle, L.; Reina, G.

1978-01-01

A new adaptive algorithm for the integration of analytical functions is presented. The algorithm processes the integration interval by generating local subintervals whose length is controlled through a feedback loop. The control is obtained by means of a relation derived on an analytical basis and valid for an arbitrary integration rule: two different estimates of an integral are used to compute the interval length necessary to obtain an integral estimate with accuracy within the assigned error bounds. The implied method for local generation of subintervals and an effective assumption of error partition among subintervals give rise to an adaptive algorithm provided with a highly accurate and very efficient integration procedure. The particular algorithm obtained by choosing the 6-point Gauss-Legendre integration rule is considered and extensive comparisons are made with other outstanding integration algorithms

Proper Analytic Point Spread Function for Lateral Modulation

Science.gov (United States)

Sumi, Chikayoshi; Shimizu, Kunio; Matsui, Norihiko

2010-07-01

For ultrasonic lateral modulation for the imaging and measurement of tissue motion, better envelope shapes of the point spread function (PSF) than of a parabolic function are searched for within analytic functions or windows on the basis of the knowledge of the ideal shape of PSF previously obtained, i.e., having a large full width at half maximum and short feet. Through simulation of displacement vector measurement, better shapes are determined. As a better shape, a new window is obtained from a Turkey window by changing Hanning windows by power functions with an order larger than the second order. The order of measurement accuracies obtained is as follows, the new window > rectangular window > power function with a higher order > parabolic function > Akaike window.

An analytical approximation for the prediction of transients with temperature feedback

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro (IFRJ), RJ (Brazil); Martinez, Aquilino S. [COPPE/UFRJ, RJ (Brazil). Programa de Engenharia Nuclear

2010-05-15

In the present paper a new analytical solution for the point kinetics equation system with temperature feedback is presented. This solution is based on the expansion of the neutron density in terms of the generation time of prompt neutrons (Nahla, 2009) and presents the advantage of being explicit in time and having a simple functional form in comparison with other existing formulations in supercritical transients. (orig.)

An analytical approximation for the prediction of transients with temperature feedback

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.

2010-01-01

In the present paper a new analytical solution for the point kinetics equation system with temperature feedback is presented. This solution is based on the expansion of the neutron density in terms of the generation time of prompt neutrons (Nahla, 2009) and presents the advantage of being explicit in time and having a simple functional form in comparison with other existing formulations in supercritical transients. (orig.)

Optimal separable bases and series expansions

International Nuclear Information System (INIS)

Poirier, B.

1997-01-01

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

Analytical method for reconstruction pin to pin of the nuclear power density distribution

International Nuclear Information System (INIS)

Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.

2013-01-01

An accurate and efficient method for reconstructing pin to pin of the nuclear power density distribution, involving the analytical solution of the diffusion equation for two-dimensional neutron energy groups in homogeneous nodes, is presented. The boundary conditions used for analytic as solution are the four currents or fluxes on the surface of the node, which are obtained by Nodal Expansion Method (known as NEM) and four fluxes at the vertices of a node calculated using the finite difference method. The analytical solution found is the homogeneous distribution of neutron flux. Detailed distributions pin to pin inside a fuel assembly are estimated by the product of homogeneous flux distribution by local heterogeneous form function. Furthermore, the form functions of flux and power are used. The results obtained with this method have a good accuracy when compared with reference values. (author)

Analytical method for reconstruction pin to pin of the nuclear power density distribution

Energy Technology Data Exchange (ETDEWEB)

Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: ppessoa@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@imp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil)

2013-07-01

An accurate and efficient method for reconstructing pin to pin of the nuclear power density distribution, involving the analytical solution of the diffusion equation for two-dimensional neutron energy groups in homogeneous nodes, is presented. The boundary conditions used for analytic as solution are the four currents or fluxes on the surface of the node, which are obtained by Nodal Expansion Method (known as NEM) and four fluxes at the vertices of a node calculated using the finite difference method. The analytical solution found is the homogeneous distribution of neutron flux. Detailed distributions pin to pin inside a fuel assembly are estimated by the product of homogeneous flux distribution by local heterogeneous form function. Furthermore, the form functions of flux and power are used. The results obtained with this method have a good accuracy when compared with reference values. (author)

Linear circuit transfer functions an introduction to fast analytical techniques

CERN Document Server

Basso, Christophe P

2016-01-01

Linear Circuit Transfer Functions: An introduction to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical Circuits Techniques. Building on their existing knowledge of classical loop/nodal analysis, the book improves and expands their skills to unveil transfer functions in a swift and efficient manner. Starting with simple examples, the author explains step-by-step how expressing circuits time constants in different configurations leads to writing transfer functions in a compact and insightful way. By learning how to organize numerators and denominators in the fastest possible way, readers will speed-up analysis and predict the frequency resp nse of simple to complex circuits. In some cases, they will be able to derive the final expression by inspection, without writing a line of algebra. Key features: * Emphasizes analysis through employing time constant-based methods discussed in other text books but not widely us...

On the modular structure of the genus-one Type II superstring low energy expansion

International Nuclear Information System (INIS)

D’Hoker, Eric; Green, Michael B.; Vanhove, Pierre

2015-01-01

The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure modulus of the world-sheet torus. These modular functions are associated with world-sheet vacuum Feynman diagrams and given by multiple sums over the discrete momenta on the torus. In this paper we exhibit exact differential and algebraic relations for a certain infinite class of such modular functions by showing that they satisfy Laplace eigenvalue equations with inhomogeneous terms that are polynomial in non-holomorphic Eisenstein series. Furthermore, we argue that the set of modular functions that contribute to the coefficients of interactions up to order D 10 R 4 are linear sums of functions in this class and quadratic polynomials in Eisenstein series and odd Riemann zeta values. Integration over the complex structure results in coefficients of the low energy expansion that are rational numbers multiplying monomials in odd Riemann zeta values.

On the modular structure of the genus-one Type II superstring low energy expansion

Energy Technology Data Exchange (ETDEWEB)

D’Hoker, Eric [Department of Physics and Astronomy,University of California, Los Angeles, CA 90095 (United States); Green, Michael B. [Department of Applied Mathematics and Theoretical Physics,Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Vanhove, Pierre [Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 route de Chartres,F-91440 Bures-sur-Yvette (France); Institut de physique théorique, Université Paris Saclay, CEA, CNRS,F-91191 Gif-sur-Yvette (France)

2015-08-11

The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure modulus of the world-sheet torus. These modular functions are associated with world-sheet vacuum Feynman diagrams and given by multiple sums over the discrete momenta on the torus. In this paper we exhibit exact differential and algebraic relations for a certain infinite class of such modular functions by showing that they satisfy Laplace eigenvalue equations with inhomogeneous terms that are polynomial in non-holomorphic Eisenstein series. Furthermore, we argue that the set of modular functions that contribute to the coefficients of interactions up to order D{sup 10}R{sup 4} are linear sums of functions in this class and quadratic polynomials in Eisenstein series and odd Riemann zeta values. Integration over the complex structure results in coefficients of the low energy expansion that are rational numbers multiplying monomials in odd Riemann zeta values.

An assessment of the expansion strategy followed by Avianca Airlines: Period 2008-2012

Directory of Open Access Journals (Sweden)

Mauricio Emboaba Moreira

2017-04-01

Full Text Available Purpose: This article aims to apply to the case of Avianca Airlines the Analytical Model for the Assessment of Airline Expansion Strategies developed by Moreira (2014 in order to explain the rationale of the expansion strategy followed by this airline and indicate other possible expansion strategies.  Design/methodology/approach: This article is a case study in the sense that it aims to arrive to broad generalizations based on the collected evidences, focusing on one of the most traditional airlines in the world. This article is a positivist case study, based in the positivist understanding; because it is supported by objective facts of the situation which are informed by the researcher’s interpretive understanding according to it is recommended for this type of study. Findings: The application of the Analytical Model for the Assessment of Airline Expansion Strategies above referred was successful, considering that the model was able to explain a wide range of complex aspects of the Avianca’s development. Thus, being one of the oldest airlines in continued operation in the world, the expansion process of this airline is connected to many political, sociological and economic facets - ie., its general environment - of its mother country, Colombia. The analytical model offered the opportunity to explore these issues in a detailed manner, adding a broader comprehension of this airline that goes beyond its operating and economic analysis. Originality/value: They reside on the fact that this is the first time that this analytical model is applied to study extensively an actual situation. Besides, airlines in Latin America have not been widely covered by the academia and this is an opportunity to begin to fill this gap. Furthermore, the referred analytical model is applicable to organizations or firms that operate in other industries if the proper adjustments are made. Implications: The implications for the academic research are to understand that

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

Energy Technology Data Exchange (ETDEWEB)

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu [Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)

2015-08-15

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

International Nuclear Information System (INIS)

th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Samin, Adib; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Lahti, Erik; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Zhang, Jinsuo

2015-01-01

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes

Expansion of a function about a displaced centre

International Nuclear Information System (INIS)

Rashid, M.A.

1981-07-01

We review the progress recently made in obtaining closed form expressions for the expansion of general orbitals about a displaced centre and establish the equivalence between different expansions. We also examine how these expressions do have the desired limit as the displacement approaches zero. (author)

Power system generation expansion planning using the maximum principle and analytical production cost model

International Nuclear Information System (INIS)

Lee, K.Y.; Park, Y.M.

1991-01-01

Historically, the electric utility demand in most countries has increased rapidly, with a doubling of approximately 10 years in the case of developing countries. In order to meet this growth in demand, the planners of expansion policies were concerned with obtaining expansion pans which dictate what new generation facilities to add and when to add them. This paper reports that, however, the practical planning problem is extremely difficult and complex, and required many hours of the planner's time even though the alternatives examined were extremely limited. In this connection, increased motivation for more sophisticated techniques of valuating utility expansion policies has been developed during the past decade. Among them, the long-range generation expansion planning is to select the most economical and reliable generation expansion plans in order to meet future power demand over a long period of time subject to a multitude of technical, economical, and social constraints

Hadronic wave functions at short distances and the operator product expansion

International Nuclear Information System (INIS)

Brodsky, S.J.; Lepage, G.P.

1980-01-01

The operator product expansion, of appropriate products of quark fields, is used to find the anamalous dimensions which control the short distance behavior of hadronic wave functions. This vehavior in turn controls the high-Q 2 limit of hadronic form factors. In particular, we relate each anamalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal αsub(s)(Q 2 )/Q 2 fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements. (orig.)

Analytical and numerical comparisons of the α parameter obtained from several expressions versus reactivity

International Nuclear Information System (INIS)

Minguez, E.

1983-01-01

A review of the analytical expressions between α-parameter and reactivity (rho) has been done in this article. Finally, several lineal approximations have been obtained for two important points of values. The analytical expansion has been made using only one family of precursors from delayed neutrons; diffusion equation in one energy groups; neutron flux separability with known spatial function. Numerical results have been obtained using typical data from fast and thermal reactors; considering and homogeneous media of Pu 239 in the first case, and U-235 in the second one. (author)

Voigt equivalent widths and spectral-bin single-line transmittances: Exact expansions and the MODTRAN®5 implementation

Science.gov (United States)

Berk, Alexander

2013-03-01

Exact expansions for Voigt line-shape total, line-tail and spectral bin equivalent widths and for Voigt finite spectral bin single-line transmittances have been derived in terms of optical depth dependent exponentially-scaled modified Bessel functions of integer order and optical depth independent Fourier integral coefficients. The series are convergent for the full range of Voigt line-shapes, from pure Doppler to pure Lorentzian. In the Lorentz limit, the expansion reduces to the Ladenburg and Reiche function for the total equivalent width. Analytic expressions are derived for the first 8 Fourier coefficients for pure Lorentzian lines, for pure Doppler lines and for Voigt lines with at most moderate Doppler dependence. A strong-line limit sum rule on the Fourier coefficients is enforced to define an additional Fourier coefficient and to optimize convergence of the truncated expansion. The moderate Doppler dependence scenario is applicable to and has been implemented in the MODTRAN5 atmospheric band model radiative transfer software. Finite-bin transmittances computed with the truncated expansions reduce transmittance residuals compared to the former Rodgers-Williams equivalent width based approach by ∼2 orders of magnitude.

Derivation of the density functional theory from the cluster expansion.

Science.gov (United States)

Hsu, J Y

2003-09-26

The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.

Large momentum expansion of two-loop self-energy diagrams with arbitrary masses

International Nuclear Information System (INIS)

Davydychev, A.I.; Smirnov, V.A.; Tausk, J.B.

1993-01-01

For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the coefficients of the expansion are calculated analytically. For some two-loop diagrams occurring in the Standard Model, comparison with results of numerical integration shows that our expansion works well in the region above the highest physical threshold. (orig.)

Analytical calculation of the average scattering cross sections using fourier series

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro, Nilopolis, RJ (Brazil)], e-mail: dpalmaster@gmail.com; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear], e-mail: asilva@con.ufrj.br, e-mail: agoncalves@con.ufrj.br, e-mail: aquilino@lmp.ufrj.br, e-mail: fernando@con.ufrj.br

2009-07-01

The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)

Analytical calculation of the average scattering cross sections using fourier series

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da

2009-01-01

The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)

Analytic properties of the relativistic Thomas-Fermi equation and the total energy of atomic ions

International Nuclear Information System (INIS)

March, N.H.; Senatore, G.

1985-06-01

The analytic properties of solutions of the relativistic Thomas-Fermi equation which tend to zero at infinity are first examined, the neutral atom solution being a member of this class. A new length is shown to enter the theory, proportional to the square root of the fine structure constant. This information is used to develop a perturbation expansion around the neutral atom solution, corresponding to positive atomic ions with finite but large radii. The limiting law relating ionic radius to the degree of ionization is thereby displayed in functional form, and solved explicitly to lowest order in the fine structure constant. To embrace this knowledge of heavy positive ions, as well as results from the one-electron Dirac equation, a proposal is then advanced as to the analytic form of the relativistic total energy E(Z,N) of an atomic ion with nuclear charge Ze and total number of electrons N. The fact that, for N>1, the nucleus is known only to bind Z+n electrons, where n is 1 or 2, indicates non-analyticity in the complex Z plane, represented by a circle of radius Z approx.= N. Such non-analyticity is also a property of the non-relativistic energy derived from the many-electron Schroedinger equation. The relativistic theory, however, must also embody a second type of non-analyticity associated with the known property for N=1 that the Dirac equation predicts electron-positron pair production when the electronic binding energy becomes equal to twice the electron rest mass energy. This corresponds to a second circle of non-analyticity in E(Z,N), and hence to a Taylor-Laurent expansion of this quantity in the atomic number Z. The relation of this expansion to the Layzer-Bahcall series is finally discussed. (author)

Application of modified analytical function for approximation and computer simulation of diffraction profile

International Nuclear Information System (INIS)

Marrero, S. I.; Turibus, S. N.; Assis, J. T. De; Monin, V. I.

2011-01-01

Data processing of the most of diffraction experiments is based on determination of diffraction line position and measurement of broadening of diffraction profile. High precision and digitalisation of these procedures can be resolved by approximation of experimental diffraction profiles by analytical functions. There are various functions for these purposes both simples, like Gauss function, but no suitable for wild range of experimental profiles and good approximating functions but complicated for practice using, like Vougt or PersonVII functions. Proposed analytical function is modified Cauchy function which uses two variable parameters allowing describing any experimental diffraction profile. In the presented paper modified function was applied for approximation of diffraction lines of steels after various physical and mechanical treatments and simulation of diffraction profiles applied for study of stress gradients and distortions of crystal structure. (Author)

An analytical study of physical models with inherited temporal and spatial memory

Science.gov (United States)

Jaradat, Imad; Alquran, Marwan; Al-Khaled, Kamel

2018-04-01

Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β\\in(0,1]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor's formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor's series method to obtain closed-form solutions of various physical models with inherited time and space memory.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

International Nuclear Information System (INIS)

Freericks, J. K.; Krishnamurthy, H. R.; Kato, Yasuyuki; Kawashima, Naoki; Trivedi, Nandini

2009-01-01

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator-to-superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

The Navier-Stokes equations an elementary functional analytic approach

CERN Document Server

Sohr, Hermann

2001-01-01

The primary objective of this monograph is to develop an elementary and self­ contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier­ Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin­ earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...

Functional expansion for evolution operators in a system of many fermions with many conditions

International Nuclear Information System (INIS)

Barrios, S.C.

1985-01-01

We present a mean field expansion for many body system, using integral functionals. The problem is formulated as a initial conditions one and it is studied the effective dynamics of the body density with given initial conditions. (M.W.O.) [pt

Functional Commutant Lifting and Interpolation on Generalized Analytic Polyhedra

Czech Academy of Sciences Publication Activity Database

Ambrozie, Calin-Grigore

2008-01-01

Roč. 34, č. 2 (2008), s. 519-543 ISSN 0362-1588 R&D Projects: GA ČR(CZ) GA201/06/0128 Institutional research plan: CEZ:AV0Z10190503 Keywords : intertwining lifting * interpolation * analytic functions Subject RIV: BA - General Mathematics Impact factor: 0.327, year: 2008

Integral simulation of the creation and expansion of a transonic argon plasma

International Nuclear Information System (INIS)

Peerenboom, K S C; Goedheer, W J; Van Dijk, J; Van der Mullen, J J A M

2010-01-01

A transonic argon plasma is studied in an integral simulation where both the plasma creation and expansion are incorporated in the same model. This integral approach allows for simulation of expanding plasmas where the Mach number is not known a priori. Results of this integral simulation are validated with semi-analytical models. Inside the creation region the results for the electron temperature, the heavy particle temperature and the electron density are compared with a global model of the creation region. In the expansion region, the simulation results of the compressible flow field are compared with predictions for the shock position. Both the results inside the creation region as well as in the expansion region are in good agreement with the semi-analytical models.

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

Science.gov (United States)

Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

2018-05-01

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure

Fine structure and analytical quantum-defect wave functions

International Nuclear Information System (INIS)

Kostelecky, V.A.; Nieto, M.M.; Truax, D.R.

1988-01-01

We investigate the domain of validity of previously proposed analytical wave functions for atomic quantum-defect theory. This is done by considering the fine-structure splitting of alkali-metal and singly ionized alkaline-earth atoms. The Lande formula is found to be naturally incorporated. A supersymmetric-type integer is necessary for finite results. Calculated splittings correctly reproduce the principal features of experimental values for alkali-like atoms

Analytic properties of the Ruelle ζ-function for mean field models of phase transition

International Nuclear Information System (INIS)

Hallerberg, Sarah; Just, Wolfram; Radons, Guenter

2005-01-01

We evaluate by analytical means the Ruelle ζ-function for a spin model with global coupling. The implications of the ferromagnetic phase transitions for the analytical properties of the ζ-function are discussed in detail. In the paramagnetic phase the ζ-function develops a single branch point. In the low-temperature regime two branch points appear which correspond to the ferromagnetic state and the metastable state. The results are typical for any Ginsburg-Landau-type phase transition

Generalization of the Z expansion scheme in atoms

Energy Technology Data Exchange (ETDEWEB)

Horak, Z J; Maca, F [Czechoslovak Academy of Sciences, Praha, (Czechoslovakia). Inst. of Solid State Physics

1979-03-01

A perturbation theory is described which recovers the ordinary Z-expansion scheme in the limit Z ..-->.. infinity. It introduces nonintegral principal quantum numbers and orbitals of analytical form which is more realistic than hydrogen-like orbitals.

Reciprocal expansion of modified Bessel function in simple fractions and obtaining general summation relationships containing its zeros

Science.gov (United States)

Sherstyukov, V. B.; Sumin, E. V.

2017-12-01

Modified Bessel functions of the first kind Iv (z) (Infeld functions) where v > -1 are considered. Due to the constraint on the parameter v, all zeros of the function Iv (z) except z = 0 are simple, located on the imaginary axis by symmetric pairs and form an infinite countable set. On the basis on previous research of the authors dealing with general Bessel functions of the first kind Jv (z), a question about reciprocal expansion 1/Iv (z) in series of simple fractions of a certain structure (Krein’s series) is studied. The general formulas to calculate of special infinite sums containing degrees of Infeld function zeros are an important consequence of obtained expansion in simple fractions of the value 1/Iv (z) with any v > -1. The possibility of concrete definition of established summation relationships at different values of parameters and their connection with analogous relationships for the Bessel functions of the first kind Jv (z) is discussed.

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

Science.gov (United States)

Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus

2017-10-01

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

Observations on the summability of confluent hypergeometric functions and on semiclassical quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Silverstone, H.J.; Nakai, S.; Harris, J.G.

1985-09-01

Asymptotic expansions for Airy functions and more generally confluent hypergeometric functions, which are of fundamental importance in semiclassical quantum mechanics, are summable. The Stokes lines of the expansions are cuts of the Borel sums of the power series occurring in the expansions. At a Stokes line on which the function is continuous, the asymptotic expansions change discontinuously, but their composite sums do not: a fact that greatly clarifies the role of the Stokes line. On a Stokes line itself, it is still possible to evaluate the asymptotic expansion by Borel summation via analytic continuation, and as a consequence complex expansions may have real sums, and vice versa. This observation has important implications for the significance and use of asymptotic expansions recently derived for the resonances of the LoSurdo-Stark effect and for the energy eigenvalues of H/sub 2/ /sup +/. For both of these problems the physical values of the expansion parameters, the electric field strength and the reciprocal of the internuclear distance, lie on Stokes lines.

Some classes of analytic functions involving Noor integral operator

Science.gov (United States)

Patel, J.; Cho, N. E.

2005-12-01

The object of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions defined by using the Noor integral operator. The integral preserving properties in connection with the operator are also considered. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

Local extremal problems for bounded analytic functions without zeros

International Nuclear Information System (INIS)

Prokhorov, D V; Romanova, S V

2006-01-01

In the class B(t), t>0, of all functions f(z,t)=e -t +c 1 (t)z+c 2 (t)z 2 +... that are analytic in the unit disc U and such that 0 0. We suggest an algorithm for determining those t>0 for which the canonical functions provide the local maximum of Re c n (t) in B(t). We describe the set of functionals Lf)=Σ k=0 n λ k c k for which the canonical functions provide the maximum of Re L(f) in B(t) for small and large values of t. The proofs are based on optimization methods for solutions of control systems of differential equations

Local extremal problems for bounded analytic functions without zeros

Science.gov (United States)

Prokhorov, D. V.; Romanova, S. V.

2006-08-01

In the class B(t), t>0, of all functions f(z,t)=e^{-t}+c_1(t)z+c_2(t)z^2+\\dots that are analytic in the unit disc U and such that 00. We suggest an algorithm for determining those t>0 for which the canonical functions provide the local maximum of \\operatorname{Re}c_n(t) in B(t). We describe the set of functionals L(f)=\\sum_{k=0}^n\\lambda_kc_k for which the canonical functions provide the maximum of \\operatorname{Re}L(f) in B(t) for small and large values of t. The proofs are based on optimization methods for solutions of control systems of differential equations.

Fuel Thermal Expansion (FTHEXP)

International Nuclear Information System (INIS)

Reymann, G.A.

1978-07-01

A model is presented which deals with dimensional changes in LWR fuel pellets caused by changes in temperature. It is capable of dealing with any combination of UO 2 and PuO 2 in solid, liquid or mixed phase states, and includes expansion due to the solid-liquid phase change. The function FTHEXP models fuel thermal expansion as a function of temperature, fraction of PuO 2 , and the fraction of fuel which is molten

Impact of two-stage turbocharging architectures on pumping losses of automotive engines based on an analytical model

International Nuclear Information System (INIS)

Galindo, J.; Serrano, J.R.; Climent, H.; Varnier, O.

2010-01-01

Present work presents an analytical study of two-stage turbocharging configuration performance. The aim of this work is to understand the influence of different two-stage-architecture parameters to optimize the use of exhaust manifold gases energy and to aid decision making process. An analytical model giving the relationship between global compression ratio and global expansion ratio is developed as a function of basic engine and turbocharging system parameters. Having an analytical solution, the influence of different variables, such as expansion ratio between HP and LP turbine, intercooler efficiency, turbochargers efficiency, cooling fluid temperature and exhaust temperature are studied independently. Engine simulations with proposed analytical model have been performed to analyze the influence of these different parameters on brake thermal efficiency and pumping mean effective pressure. The results obtained show the overall performance of the two-stage system for the whole operative range and characterize the optimum control of the elements for each operative condition. The model was also used to compare single-stage and two-stage architectures performance for the same engine operative conditions. Benefits and limits in terms of breathing capabilities and brake thermal efficiency of each type of system have been presented and analyzed.

Thermal expansion of an amorphous alloy. Reciprocal-space versus real-space distribution functions

International Nuclear Information System (INIS)

Louzguine-Luzgin, Dmitri V.; Inoue, Akihisa

2007-01-01

This paper describes the relation between the change in the position of the first X-ray diffraction maximum in reciprocal space and the first maximum of the distribution function in real space for the Ge 50 Al 40 Cr 10 amorphous alloy. It is also shown that the first diffraction maximum of the interference function carries the most significant information about the interatomic distances in real space while the subsequent peaks of the interference function are responsible for the shoulders of the main peak of the real-space distribution function. The results are used to support validity of the method previously used to monitor thermal expansion of the glassy alloys using an X-ray diffraction profile

Operator expansions in the minimal subtraction scheme. II. Explicit formulas for coefficient functions

International Nuclear Information System (INIS)

Chetyrkin, K.G.

1989-01-01

It is shown in an arbitrary model that the coefficient functions of the operator expansion (renormalized in the minimal subtraction scheme) are finite. Explicit formulas convenient for calculating them in practice are obtained. The gluing method and the formalism of the R* operation are used to transform the formulas in such a way that the coefficient functions can be expressed in terms of ordinary diagrams containing neither nonstandard propagators nor an additional loop integration. An important feature of the representation for the coefficient functions is that the R* operation, which subtracts simultaneously the ultraviolet and infrared divergences, guarantees the existence of the coefficient functions in the limit when the dimensional regularization is lifted without any restrictions

On Analytical Solutions of f(R) Modified Gravity Theories in FLRW Cosmologies

Science.gov (United States)

Domazet, Silvije; Radovanović, Voja; Simonović, Marko; Štefančić, Hrvoje

2013-02-01

A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R), which leads to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.

Analytical results for a hole in an antiferromagnet

International Nuclear Information System (INIS)

Li, Y.M.; d'Ambrumenil, N.; Su, Z.B.

1996-04-01

The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite. Our results also suggest that the hole motion is polaronic in nature with a bandwidth proportional to t 2 /J exp[-c(t/J) 2 ] (c is a constant) for J/t >or approx 0.5. The connection of the long-wavelength approximation to the first-order approximation in the cumulant expansion is also clarified. (author). 23 refs, 2 figs

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)

Analytical treatment of the runaway-effect

International Nuclear Information System (INIS)

Kaeppeler, H.J.

1980-09-01

In the analytical treatment of the runaway-effect there appear the integrals Isub(m)(α). For m = 1, 2 and 3, series expansions for these integrals can be found in the literature. Furthermore, asymptotic solutions for Isub(m)(α) are known. It is shown here that the solutions for Isub(m)(α) can be approximated by the modified Bessel Function Ksub(n)(αsup(ν)) in such a way that for α → 0 the exact limiting value for Isub(m)(α) follows and that for α → infinite essentially the known asymptotic solutions for Isub(m)(α) follow. The maximum error for this approximation in the order of percent is considered justifiable for the application considered. (orig.)

Pre-Calculus Instructional Guide for Elementary Functions, Analytic Geometry.

Science.gov (United States)

Montgomery County Public Schools, Rockville, MD.

This is a guide for use in semester-long courses in Elementary Functions and Analytic Geometry. A list of entry-level skills and a list of approved textbooks is provided. Each of the 18 units consists of: (1) overview, suggestions for teachers, and suggested time; (2) list of objectives; (3) cross-references guide to approved textbooks; (4) sample…

Binding assays with streptavidin-functionalized superparamagnetic nanoparticles and biotinylated analytes using fluxgate magnetorelaxometry

International Nuclear Information System (INIS)

Heim, Erik; Ludwig, Frank; Schilling, Meinhard

2009-01-01

Binding assays based on the magnetorelaxation of superparamagnetic nanoparticles as markers are presented utilizing a differential fluxgate system. As ligand and receptor, streptavidin and biotin, respectively, are used. Superparamagnetic nanoparticles are functionalized with streptavidin and bound to two types of biotinylated analytes: agarose beads and bovine serum (BSA) proteins. The size difference of the two analytes causes a different progress of the reaction. As a consequence, the analysis of the relaxation signal is carried out dissimilarly for the two analytes. In addition, we studied the reaction kinetics of the two kinds of analytes with the fluxgate system.

Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

International Nuclear Information System (INIS)

Olesov, A V

2014-01-01

New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles

Partition function for a singular background

International Nuclear Information System (INIS)

McKenzie-Smith, J.J.; Naylor, W.

2005-01-01

We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the local Born approximation (LBA)

Partition function for a singular background

Energy Technology Data Exchange (ETDEWEB)

McKenzie-Smith, J.J. [Financial Risk Management Ltd, 15 Adam Street, London WC2N 6AH (United Kingdom)]. E-mail: julian.mckenzie-smith@frmhedge.com; Naylor, W. [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)]. E-mail: naylor@yukawa.kyoto-u.ac.jp

2005-03-17

We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the local Born approximation (LBA)

An advanced complex analysis problem book topological vector spaces, functional analysis, and Hilbert spaces of analytic functions

CERN Document Server

Alpay, Daniel

2015-01-01

This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Analytic function theory of several variables elements of Oka’s coherence

CERN Document Server

Noguchi, Junjiro

2016-01-01

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps). The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appear...

Wilson expansion in the minimal subtraction scheme

International Nuclear Information System (INIS)

Smirnov, V.A.

1989-01-01

The small distance expansion of the product of composite fields is constructed for an arbitrary renormalization procedure of the type of minimal subtraction scheme. Coefficient functions of the expansion are expressed explicitly through the Green functions of composite fields. The expansion has the explicity finite form: the ultraviolet (UV) divergences of the coefficient functions and composite fields are removed by the initial renormalization procedure while the infrared (IR) divergences in massless diagrams with nonvanishing contribution into the coefficient functions are removed by the R-operation which is the IR part of the R-operation. The latter is the generalization of the dimensional renormalization in the case when both UV and IR divergences are present. To derive the expansion, a ''pre-subtracting operator'' is introduced and formulas of the counter-term technique are exploited

Analytic solution of field distribution and demagnetization function of ideal hollow cylindrical field source

Science.gov (United States)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-09-01

The Halbach type hollow cylindrical permanent magnet array (HCPMA) is a volume compact and energy conserved field source, which have attracted intense interests in many practical applications. Here, using the complex variable integration method based on the Biot-Savart Law (including current distributions inside the body and on the surfaces of magnet), we derive analytical field solutions to an ideal multipole HCPMA in entire space including the interior of magnet. The analytic field expression inside the array material is used to construct an analytic demagnetization function, with which we can explain the origin of demagnetization phenomena in HCPMA by taking into account an ideal magnetic hysteresis loop with finite coercivity. These analytical field expressions and demagnetization functions provide deeper insight into the nature of such permanent magnet array systems and offer guidance in designing optimized array system.

Analytic Evolution of Singular Distribution Amplitudes in QCD

Energy Technology Data Exchange (ETDEWEB)

Tandogan Kunkel, Asli [Old Dominion Univ., Norfolk, VA (United States)

2014-08-01

Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standard method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.

Semi-analytical wave functions in relativistic average atom model for high-temperature plasmas

International Nuclear Information System (INIS)

Guo Yonghui; Duan Yaoyong; Kuai Bin

2007-01-01

The semi-analytical method is utilized for solving a relativistic average atom model for high-temperature plasmas. Semi-analytical wave function and the corresponding energy eigenvalue, containing only a numerical factor, are obtained by fitting the potential function in the average atom into hydrogen-like one. The full equations for the model are enumerated, and more attentions are paid upon the detailed procedures including the numerical techniques and computer code design. When the temperature of plasmas is comparatively high, the semi-analytical results agree quite well with those obtained by using a full numerical method for the same model and with those calculated by just a little different physical models, and the result's accuracy and computation efficiency are worthy of note. The drawbacks for this model are also analyzed. (authors)

Virial Expansion Bounds

Science.gov (United States)

Tate, Stephen James

2013-10-01

In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.

Equifinality in Functional Analytic Psychotherapy: Different Strokes for Different Folks

Science.gov (United States)

Darrow, Sabrina M.; Dalto, Georgia; Follette, William C.

2012-01-01

Functional Analytic Psychotherapy (FAP) is an interpersonal behavior therapy that relies on a therapist's ability to contingently respond to in-session client behavior. Valued behavior change in clients results from the therapist shaping more effective client interpersonal behaviors by providing effective social reinforcement when these behaviors…

Functional Analytic Multisensory Environmental Therapy for People with Dementia

OpenAIRE

Staal, Jason A.

2012-01-01

This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET) for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment thera...

α′-Expansion of open string disk integrals via Mellin transformations

Directory of Open Access Journals (Sweden)

Ellis Ye Yuan

2015-02-01

Full Text Available Open string disk integrals are represented as contour integrals of a product of Beta functions using Mellin transformations. This makes the mathematical problem of computing the α′-expansion around the field-theory limit similar to that of the ϵ-expansion in Feynman loop integrals around the four-dimensional limit. More explicitly, the formula in Mellin space obtained directly from the standard Koba–Nielsen-like representation is valid in a region of values of α′ that does not include α′=0. Analytic continuation is therefore needed since contours are pinched by poles as α′→0. Deforming contours that get pinched by poles generates a set of (n−3! multi-dimensional residues left behind which contain all the field theory information. Some analogies between the field theory formulas obtained by this method and those derived recently from using the scattering equations are commented at the end.

Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean

Energy Technology Data Exchange (ETDEWEB)

Petrov, P.S., E-mail: petrov@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Prants, S.V., E-mail: prants@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Petrova, T.N., E-mail: petrova.tn@dvfu.ru [Far Eastern Federal University, 8 Sukhanova str., 690950, Vladivostok (Russian Federation)

2017-06-21

The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic equations are solved explicitly, and the analytical expressions for the modal coefficients are obtained using a Lie-algebraic technique. - Highlights: • A group-theoretical approach is applied to a problem of sound propagation in a shallow sea with variable bottom slope. • An analytical solution of this problem is obtained in the form of modal expansion with analytical expressions of the coefficients. • Our result is the only analytical solution of the 3D sound propagation problem with no translational invariance. • This solution can be used for the validation of the numerical propagation models.

On genus expansion of superpolynomials

Energy Technology Data Exchange (ETDEWEB)

Mironov, Andrei, E-mail: mironov@itep.ru [Lebedev Physics Institute, Moscow 119991 (Russian Federation); ITEP, Moscow 117218 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Morozov, Alexei, E-mail: morozov@itep.ru [ITEP, Moscow 117218 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Sleptsov, Alexei, E-mail: sleptsov@itep.ru [ITEP, Moscow 117218 (Russian Federation); Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk 454001 (Russian Federation); KdVI, University of Amsterdam (Netherlands); Smirnov, Andrey, E-mail: asmirnov@math.columbia.edu [ITEP, Moscow 117218 (Russian Federation); Columbia University, Department of Mathematics, New York (United States)

2014-12-15

Recently it was shown that the (Ooguri–Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present paper we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are β-deformed to Hamiltonians of the Calogero–Moser–Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials. However, even for the thin knots the beta-deformation is non-innocent: already in the simplest examples it seems inconsistent with the positivity of colored superpolynomials in non-(anti)symmetric representations, which also happens in I. Cherednik's (DAHA-based) approach to the torus knots.

Heavy-quark QCD vacuum polarisation function. Analytical results at four loops

International Nuclear Information System (INIS)

Kniehl, B.A.; Kotikov, A.V.

2006-07-01

The first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are found in fully analytical form by evaluating the missing massive four-loop tadpole master integrals. (orig.)

Optimization of nonlinear wave function parameters

International Nuclear Information System (INIS)

Shepard, R.; Minkoff, M.; Chemistry

2006-01-01

An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules

A New Class of Analytic Functions Defined by Using Salagean Operator

Directory of Open Access Journals (Sweden)

R. M. El-Ashwah

2013-01-01

Full Text Available We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

Plasma expansion into vacuum with charge separation effect

International Nuclear Information System (INIS)

Murakami, Masakatsu

2008-01-01

Plasma expansion into vacuum and resultant ion acceleration are studied theoretically. A new self-similar solution is found to describe free expansion of a finite plasma mass into vacuum with a full account of charge separation effects. It is argued that the normalized plasma size Λ R/λ D plays the dominant role in determining the whole ion energy spectrum and thus the maximum ion kinetic energy, where R and λ D are the plasma scale length and the Debye length, respectively. The analytical model is compared with experiments to show excellent agreement

The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group

International Nuclear Information System (INIS)

Keitel, Jan; Bartosch, Lorenz

2012-01-01

We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model. (paper)

On the Equisummability of Hermite and Fourier Expansions

Indian Academy of Sciences (India)

We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.

Adler function for light quarks in analytic perturbation theory

International Nuclear Information System (INIS)

Milton, K. A.; Solovtsov, I. L.; Solovtsova, O. P.

2001-01-01

The method of analytic perturbation theory, which avoids the problem of ghost-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the 'light' Adler function corresponding to the nonstrange vector channel of the inclusive decay of the τ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the 'experimental' Adler function down to the lowest energy scale

A generalization of the Z expansion scheme in atoms

International Nuclear Information System (INIS)

Horak, Z.J.; Maca, F.

1979-01-01

A perturbation theory is described which recovers the ordinary Z-expansion scheme in the limit Z → infinity. It introduces nonintegral principal quantum numbers and orbitals of analytical form which is more realistic than hydrogen-like orbitals. (Auth.)

Asymptotic expansions close to the singularity in Gowdy spacetimes[04.20.Dw Singularities and cosmic censorship;

Energy Technology Data Exchange (ETDEWEB)

Ringstroem, Hans [Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany)

2004-02-07

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In a paper by Grubisic and Moncrief, a formal expansion of solutions in the direction towards the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analytic solutions with the maximum number of free functions and the desired asymptotics at the singularity. The condition of real analyticity was subsequently removed by Rendall. In a previous paper, we proved that one can put a condition on initial data that leads to asymptotic expansions. However, control of up to and including three derivatives in L{sup 2} was necessary, and the condition was rather technical. The main point of the present paper is to demonstrate the existence of certain monotone quantities and to illustrate how these can be used to weaken the assumptions to one derivative in the sup norm. Furthermore, we demonstrate that the false spikes do not appear in the disc model. Finally, we show that knowledge concerning the behaviour of the solution (as time tends to the singularity) for one fixed spatial point in some situations can be used to conclude that there are smooth expansions in the neighbourhood of that spatial point.

The General Analytic Solution of a Functional Equation of Addition Type

OpenAIRE

Braden, H. W.; Buchstaber, V. M.

1995-01-01

The general analytic solution to the functional equation $$ \\phi_1(x+y)= { { \\biggl|\\matrix{\\phi_2(x)&\\phi_2(y)\\cr\\phi_3(x)&\\phi_3(y)\\cr}\\biggr|} \\over { \\biggl|\\matrix{\\phi_4(x)&\\phi_4(y)\\cr\\phi_5(x)&\\phi_5(y)\\cr}\\biggr|} } $$ is characterised. Up to the action of the symmetry group, this is described in terms of Weierstrass elliptic functions. We illustrate our theory by applying it to the classical addition theorems of the Jacobi elliptic functions and the functional equations $$ \\phi_1(x+...

Analytic trigonometry

CERN Document Server

Bruce, William J; Maxwell, E A; Sneddon, I N

1963-01-01

Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions

Expansion Under Climate Change: The Genetic Consequences.

Science.gov (United States)

Garnier, Jimmy; Lewis, Mark A

2016-11-01

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically, the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

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.

Semigroups of analytic functions in analysis and applications

International Nuclear Information System (INIS)

Goryainov, Victor V

2012-01-01

This survey considers problems of analysis and certain related areas in which semigroups of analytic functions with respect to the operation of composition appear naturally. The main attention is devoted to holomorphic maps of a disk (or a half-plane) into itself. The role of fixed points is highlighted, both in the description of the structure of semigroups and in applications. Interconnections of the problem of fractional iteration with certain problems in the theory of random branching processes are pointed out, as well as with certain questions of non-commutative probability. The role of the infinitesimal description of semigroups of conformal maps in the development of the parametric method in the theory of univalent functions is shown. Bibliography: 94 titles.

Geometric theory of functions of a complex variable

CERN Document Server

Goluzin, G M

1969-01-01

This book is based on lectures on geometric function theory given by the author at Leningrad State University. It studies univalent conformal mapping of simply and multiply connected domains, conformal mapping of multiply connected domains onto a disk, applications of conformal mapping to the study of interior and boundary properties of analytic functions, and general questions of a geometric nature dealing with analytic functions. The second Russian edition upon which this English translation is based differs from the first mainly in the expansion of two chapters and in the addition of a long survey of more recent developments. The book is intended for readers who are already familiar with the basics of the theory of functions of one complex variable.

Partition function expansion on region graphs and message-passing equations

International Nuclear Information System (INIS)

Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong

2011-01-01

Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)

Emergence of Data Analytics in the Information Systems Curriculum

Science.gov (United States)

Jafar, Musa J.; Babb, Jeffry; Abdullat, Amjda

2017-01-01

As a phenomenon of interest, impact, and import, there is little doubt that the pervasive expansion of data is upon us as Information Systems educators. Concerns and topics such as Data Science, Data Analytics, Machine Learning, Business Analytics, and Business Intelligence are now ubiquitous and often situated as being the "next big…

Recovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinates

Science.gov (United States)

Salman, Yehonatan

2017-09-01

The aim of this paper is to introduce a new inversion procedure for recovering functions, defined on R2 , from the spherical mean transform, which integrates functions on a prescribed family Λ of circles, where Λ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by Norton (J Acoust Soc Am 67:1266-1273, 1980) for recovering functions in case where Λ consists of circles with centers on a circle. However, at some point we will have to modify the method in [24] by using expansion in elliptical coordinates, rather than spherical coordinates, in order to solve the more generalized elliptical case. We will rely on a recent result obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the eigenfunction expansion of the Bessel function in elliptical coordinates.

Elements of a function analytic approach to probability.

Energy Technology Data Exchange (ETDEWEB)

Ghanem, Roger Georges (University of Southern California, Los Angeles, CA); Red-Horse, John Robert

2008-02-01

We first provide a detailed motivation for using probability theory as a mathematical context in which to analyze engineering and scientific systems that possess uncertainties. We then present introductory notes on the function analytic approach to probabilistic analysis, emphasizing the connections to various classical deterministic mathematical analysis elements. Lastly, we describe how to use the approach as a means to augment deterministic analysis methods in a particular Hilbert space context, and thus enable a rigorous framework for commingling deterministic and probabilistic analysis tools in an application setting.

Thermodynamics of atomic and ionized hydrogen: analytical results versus equation-of-state tables and Monte Carlo data.

Science.gov (United States)

Alastuey, A; Ballenegger, V

2012-12-01

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some

Evaluation of Analytical Modeling Functions for the Phonation Onset Process

Directory of Open Access Journals (Sweden)

Simon Petermann

2016-01-01

Full Text Available The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO, called the voice onset time (VOT, is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1 reliability of the fit function for a correct approximation of VO; (2 consistency represented by the standard deviation of VOT; and (3 accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.

DNA breathing dynamics: analytic results for distribution functions of relevant Brownian functionals.

Science.gov (United States)

Bandyopadhyay, Malay; Gupta, Shamik; Segal, Dvira

2011-03-01

We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size x₀, we derive analytical expressions for (i) the distribution P(t{f}|x₀) of the first-passage time t{f}, characterizing the bubble lifetime, (ii) the distribution P(A|x₀) of the area A until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution P(M) of the maximum bubble size M attained before the first-passage time, and (iv) the joint probability distribution P(M,t{m}) of the maximum bubble size M and the time t{m} of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numericalsimulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.

On a Monge-Amp\\`ere operator for plurisubharmonic functions with analytic singularities

OpenAIRE

Andersson, Mats; Błocki, Zbigniew; Wulcan, Elizabeth

2017-01-01

We study continuity properties of generalized Monge-Amp\\`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Amp\\`ere measure of such a function on a compact K\\"ahler manifold.

Thermal expansion and density measurements of molten and solid materials at high temperatures by the gamma attenuation technique

International Nuclear Information System (INIS)

Drotning, W.D.

1979-05-01

An apparatus is described for the measurement of the density and thermal expansion of molten materials to 3200 0 K using the gamma attenuation technique. The precision of the experimental technique was analytically examined for both absolute and relative density determinations. Three analytical expressions used to reduce data for liquid density determinations were evaluated for their precision. Each allows use of a different set of input data parameters, which can be chosen based on experimental considerations. Using experimentally reasonable values for the precision of the parameters yields a similar resultant density precision from the three methods, on the order of 0.2%. The analytical method for measurements of the linear thermal expansion of solids by the gamma method is also described. To demonstrate the use of the technique on reasonably well-characterized systems, data are presented for (1) the density and thermal expansion of molten tin, lead, and aluminum to 1300 0 K, (2) the thermal expansion of solid aluminum to the melting point, and (3) the thermal expansion of a low melting point glass through the transition temperature and melting region. The data agree very well with published results using other methods where such published data exist

Wrapping interactions and the genus expansion of the 2-point function of composite operators

International Nuclear Information System (INIS)

Sieg, Christoph; Torrielli, Alessandro

2005-01-01

We perform a systematic analysis of wrapping interactions for a general class of theories with color degrees of freedom, including N=4 SYM. Wrapping interactions arise in the genus expansion of the 2-point function of composite operators as finite size effects that start to appear at a certain order in the coupling constant at which the range of the interaction is equal to the length of the operators. We analyze in detail the relevant genus expansions, and introduce a strategy to single out the wrapping contributions, based on adding spectator fields. We use a toy model to demonstrate our procedure, performing all computations explicitly. Although completely general, our treatment should be particularly useful for applications to the recent problem of wrapping contributions in some checks of the AdS/CFT correspondence

Logarithmic residues of analytic Banach algebra valued functions possessing a simply meromorphic inverse

NARCIS (Netherlands)

H. Bart (Harm); T. Ehrhardt; B. Silbermann

2001-01-01

textabstractA logarithmic residue is a contour integral of a logarithmic derivative (left or right) of an analytic Banach algebra valued function. For functions possessing a meromorphic inverse with simple poles only, the logarithmic residues are identified as the sums of idempotents. With the help

Analytic and numeric Green's functions for a two-dimensional electron gas in an orthogonal magnetic field

International Nuclear Information System (INIS)

Cresti, Alessandro; Grosso, Giuseppe; Parravicini, Giuseppe Pastori

2006-01-01

We have derived closed analytic expressions for the Green's function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green's functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green's function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of the Green's function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green's function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems

Analyticity without Differentiability

Science.gov (United States)

Kirillova, Evgenia; Spindler, Karlheinz

2008-01-01

In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…

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

International Nuclear Information System (INIS)

Sai Venkata Ramana, A.

2014-01-01

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

Mayer expansions for Euclidean lattice field theory: Convergence properties and relation with perturbation theory

International Nuclear Information System (INIS)

Pordt, A.

1985-10-01

The author describes the Mayer expansion in Euclidean lattice field theory by comparing it with the statistical mechanics of polymer systems. In this connection he discusses the Borel summability and the analyticity of the activities on the lattice. Furthermore the relations between renormalization and the Mayer expansion are considered. (HSI)

Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

Directory of Open Access Journals (Sweden)

Te-Wen Tu

2015-01-01

Full Text Available An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

Science.gov (United States)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

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.

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.

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

Energy Technology Data Exchange (ETDEWEB)

Ringholm, Magnus; Ruud, Kenneth [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Bast, Radovan [Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, AlbaNova University Center, S-10691 Stockholm (Sweden); PDC Center for High Performance Computing, Royal Institute of Technology, S-10044 Stockholm (Sweden); Oggioni, Luca [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Department of Physics G. Occhialini, University of Milano Bicocca, Piazza della scienza 3, 20126 Milan (Italy); Ekström, Ulf [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo (Norway)

2014-10-07

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube

International Nuclear Information System (INIS)

Eraslan, Ahmet N.; Akis, Tolga

2006-01-01

Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states are investigated. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected significantly by the material nonhomogeneity. Different modes of plasticization may take place unlike the homogeneous case. It is also shown mathematically that the nonhomogeneous elastoplastic solution presented here reduces to that of a homogeneous one by appropriate choice of the material parameters

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

Science.gov (United States)

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers

Directory of Open Access Journals (Sweden)

Belkacem Meziane

2008-01-01

Full Text Available A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These solutions are shown to evolve in accordance with the driving frequency of the permanent solution that we recently reported to illustrate the system. The procedure amounts to analytically construct the signal Fourier transform by applying an iterative algorithm that reconstitutes the first few terms of its development.

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

Analytic Approximation to Radiation Fields from Line Source Geometry

International Nuclear Information System (INIS)

Michieli, I.

2000-01-01

Line sources with slab shields represent typical source-shield configuration in gamma-ray attenuation problems. Such shielding problems often lead to the generalized Secant integrals of the specific form. Besides numerical integration approach, various expansions and rational approximations with limited applicability are in use for computing the value of such integral functions. Lately, the author developed rapidly convergent infinite series representation of generalized Secant Integrals involving incomplete Gamma functions. Validity of such representation was established for zero and positive values of integral parameter a (a=0). In this paper recurrence relations for generalized Secant Integrals are derived allowing us simple approximate analytic calculation of the integral for arbitrary a values. It is demonstrated how truncated series representation can be used, as the basis for such calculations, when possibly negative a values are encountered. (author)

Revised Line Profile Function for Hydrogenic Species

Directory of Open Access Journals (Sweden)

Sapar A.

2012-09-01

Full Text Available Analytical series expansions for the hydrogenic spectral line profile functions are derived starting from the three single expressions, obtained by integrating twice the convolution of the Holtsmark, Lorentz and Doppler line profile functions. We get well converging series expansions for the line wings and centers by reducing the number of arguments in the profile function by one, introducing the module of the Holtsmark and Lorentz profiles as a new argument. In the intermediate part of the line, the parabolic cylinder functions expressed via the confluent hypergeometric series, are used. The multi-component Stark splitting of the hydrogenic spectral lines and the modeled stochastic electron transitions in the electric field of the adjacent ions generate wide Doppler plateaux at the line centers, with the characteristic widths estimated from the fit to the characteristic width of the Holtsmark profile. This additional Doppler broadening of the line profile function removes the central dip typical to the Holtsmark profile.

A multiyear DG-incorporated framework for expansion planning of distribution networks using binary chaotic shark smell optimization algorithm

International Nuclear Information System (INIS)

Ahmadigorji, Masoud; Amjady, Nima

2016-01-01

In this paper, a new model for MEPDN (multiyear expansion planning of distribution networks) is proposed. By solving this model, the optimal expansion scheme of primary (i.e. medium voltage) distribution network including the reinforcement pattern of primary feeders as well as location and size of DG (distributed generators) during an ascertained planning period is determined. Furthermore, the time-based feature of proposed model allows it to specify the investments/reinforcements time (i.e. year). Moreover, a minimum load shedding-based analytical approach for optimizing the network's reliability is introduced. The associated objective function of proposed model is minimizing the total investment and operation costs. To solve the formulated MEPDN model as a complex multi-dimensional optimization problem, a new evolutionary algorithm-based solution method called BCSSO (Binary Chaotic Shark Smell Optimization) is presented. The effectiveness of the proposed MEPDN model and solution approach is illustrated by applying them on two widely-used test cases including 12-bus and 33-bus distribution network and comparing the acquired results with the results of other solution methods. - Highlights: • A multiyear expansion planning model for distribution network is presented. • A new evolutionary algorithm-based solution approach is proposed. • A minimum load shedding-based analytical method for EENS minimization is suggested. • The efficacy of the proposed solution approach is broadly investigated.

Remark on the Operator-valued Interpolation for Multivariable Bounded Analytic Functions

Czech Academy of Sciences Publication Activity Database

Ambrozie, Calin-Grigore

2004-01-01

Roč. 53, č. 6 (2004), s. 1551-1576 ISSN 0022-2518 R&D Projects: GA ČR(CZ) GA201/03/0041 Institutional research plan: CEZ:AV0Z1019905 Keywords : von Neumann inequality * interpolation * analytic functions Subject RIV: BA - General Mathematics Impact factor: 0.784, year: 2004

POLYGALACTURONASE INVOLVED IN EXPANSION1 functions in cell elongation and flower development in Arabidopsis.

Science.gov (United States)

Xiao, Chaowen; Somerville, Chris; Anderson, Charles T

2014-03-01

Pectins are acidic carbohydrates that comprise a significant fraction of the primary walls of eudicotyledonous plant cells. They influence wall porosity and extensibility, thus controlling cell and organ growth during plant development. The regulated degradation of pectins is required for many cell separation events in plants, but the role of pectin degradation in cell expansion is poorly defined. Using an activation tag screen designed to isolate genes involved in wall expansion, we identified a gene encoding a putative polygalacturonase that, when overexpressed, resulted in enhanced hypocotyl elongation in etiolated Arabidopsis thaliana seedlings. We named this gene POLYGALACTURONASE INVOLVED IN EXPANSION1 (PGX1). Plants lacking PGX1 display reduced hypocotyl elongation that is complemented by transgenic PGX1 expression. PGX1 is expressed in expanding tissues throughout development, including seedlings, roots, leaves, and flowers. PGX1-GFP (green fluorescent protein) localizes to the apoplast, and heterologously expressed PGX1 displays in vitro polygalacturonase activity, supporting a function for this protein in apoplastic pectin degradation. Plants either overexpressing or lacking PGX1 display alterations in total polygalacturonase activity, pectin molecular mass, and wall composition and also display higher proportions of flowers with extra petals, suggesting PGX1's involvement in floral organ patterning. These results reveal new roles for polygalacturonases in plant development.

Semi-analytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity-waveguide structures

DEFF Research Database (Denmark)

de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper

2015-01-01

We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained, ......-trivial spectrum with a peak and a dip is found, which is reproduced only when including both the two relevant QNMs in the theory. In both cases, we find relative errors below 1% in the bandwidth of interest.......We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained......, and for two types of two-dimensional PhCs, with one and two cavities side-coupled to an extended waveguide, the theory is validated against numerically exact computations. For the single cavity, a slightly asymmetric spectrum is found, which the QNM theory reproduces, and for two cavities a non...

Fekete-Szegö Inequalities of a Subclass of Multivalent Analytic Functions

Directory of Open Access Journals (Sweden)

Selvaraj C.

2016-07-01

Full Text Available The main object of this paper is to study Fekete-Szegö problem for a certain subclass of p - valent analytic functions. Fekete-Szegö inequality of several classes are obtained as special cases from our results. Applications of the result are also obtained on the class defined by convolution.

The Zernike expansion--an example of a merit function for 2D/3D registration based on orthogonal functions.

Science.gov (United States)

Dong, Shuo; Kettenbach, Joachim; Hinterleitner, Isabella; Bergmann, Helmar; Birkfellner, Wolfgang

2008-01-01

Current merit functions for 2D/3D registration usually rely on comparing pixels or small regions of images using some sort of statistical measure. Problems connected to this paradigm the sometimes problematic behaviour of the method if noise or artefacts (for instance a guide wire) are present on the projective image. We present a merit function for 2D/3D registration which utilizes the decomposition of the X-ray and the DRR under comparison into orthogonal Zernike moments; the quality of the match is assessed by an iterative comparison of expansion coefficients. Results in a imaging study on a physical phantom show that--compared to standard cross--correlation the Zernike moment based merit function shows better robustness if histogram content in images under comparison is different, and that time expenses are comparable if the merit function is constructed out of a few significant moments only.

Exact mean-energy expansion of Ginibre's gas for coupling constants Γ =2 ×(oddinteger)

Science.gov (United States)

Salazar, R.; Téllez, G.

2017-12-01

Using the approach of a Vandermonde determinant to the power Γ =Q2/kBT expansion on monomial functions, a way to find the excess energy Uexc of the two-dimensional one-component plasma (2DOCP) on hard and soft disks (or a Dyson gas) for odd values of Γ /2 is provided. At Γ =2 , the present study not only corroborates the result for the particle-particle energy contribution of the Dyson gas found by Shakirov [Shakirov, Phys. Lett. A 375, 984 (2011), 10.1016/j.physleta.2011.01.004] by using an alternative approach, but also provides the exact N -finite expansion of the excess energy of the 2DOCP on the hard disk. The excess energy is fitted to the ansatz of the form Uexc=K1N +K2√{N }+K3+K4/N +O (1 /N2) to study the finite-size correction, with Ki coefficients and N the number of particles. In particular, the bulk term of the excess energy is in agreement with the well known result of Jancovici for the hard disk in the thermodynamic limit [Jancovici, Phys. Rev. Lett. 46, 386 (1981), 10.1103/PhysRevLett.46.386]. Finally, an expression is found for the pair correlation function which still keeps a link with the random matrix theory via the kernel in the Ginibre ensemble [Ginibre, J. Math. Phys. 6, 440 (1965), 10.1063/1.1704292] for odd values of Γ /2 . A comparison between the analytical two-body density function and histograms obtained with Monte Carlo simulations for small systems and Γ =2 ,6 ,10 ,... shows that the approach described in this paper may be used to study analytically the crossover behavior from systems in the fluid phase to small crystals.

The propagator for the step potential and delta function potential using the path decomposition expansion

Energy Technology Data Exchange (ETDEWEB)

Yearsley, James M [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)

2008-07-18

We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and the Brownian motion definition of the path integral. The derivation exploits properties of the Catalan numbers, which enumerate certain classes of lattice paths.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

Science.gov (United States)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

Energy Technology Data Exchange (ETDEWEB)

Bolzoni, Paolo; Moch, Sven-Olaf [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Somogyi, Gabor [Zurich Univ. (Switzerland). Inst. fuer Theoretische Physik; Trocsanyi, Zoltan [Debrecen Univ. (Hungary); Hungarian Academy of Sciences, Debrecen (Hungary). Inst. of Nuclear Research

2009-05-15

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4-2{epsilon} dimensions to obtain the coefficients of their Laurent expansions around {epsilon}=0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in {epsilon} both numerically and analytically by complex integration over the Mellin-Barnes contours. (orig.)

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

International Nuclear Information System (INIS)

Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gabor; Trocsanyi, Zoltan

2009-01-01

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 - 2ε dimensions to obtain the coefficients of their Laurent expansions around ε = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in ε both numerically and analytically by complex integration over the Mellin-Barnes contours.

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

Science.gov (United States)

Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gábor; Trócsányi, Zoltán

2009-08-01

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 - 2epsilon dimensions to obtain the coefficients of their Laurent expansions around epsilon = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in epsilon both numerically and analytically by complex integration over the Mellin-Barnes contours.

Analytic integration of real-virtual counterterms in NNLO jet cross sections II

International Nuclear Information System (INIS)

Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gabor; Trocsanyi, Zoltan; Hungarian Academy of Sciences, Debrecen

2009-05-01

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4-2ε dimensions to obtain the coefficients of their Laurent expansions around ε=0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in ε both numerically and analytically by complex integration over the Mellin-Barnes contours. (orig.)

Analytical and functional similarity of Amgen biosimilar ABP 215 to bevacizumab.

Science.gov (United States)

Seo, Neungseon; Polozova, Alla; Zhang, Mingxuan; Yates, Zachary; Cao, Shawn; Li, Huimin; Kuhns, Scott; Maher, Gwendolyn; McBride, Helen J; Liu, Jennifer

ABP 215 is a biosimilar product to bevacizumab. Bevacizumab acts by binding to vascular endothelial growth factor A, inhibiting endothelial cell proliferation and new blood vessel formation, thereby leading to tumor vasculature normalization. The ABP 215 analytical similarity assessment was designed to assess the structural and functional similarity of ABP 215 and bevacizumab sourced from both the United States (US) and the European Union (EU). Similarity assessment was also made between the US- and EU-sourced bevacizumab to assess the similarity between the two products. The physicochemical properties and structural similarity of ABP 215 and bevacizumab were characterized using sensitive state-of-the-art analytical techniques capable of detecting small differences in product attributes. ABP 215 has the same amino acid sequence and exhibits similar post-translational modification profiles compared to bevacizumab. The functional similarity assessment employed orthogonal assays designed to interrogate all expected biological activities, including those known to affect the mechanisms of action for ABP 215 and bevacizumab. More than 20 batches of bevacizumab (US) and bevacizumab (EU), and 13 batches of ABP 215 representing unique drug substance lots were assessed for similarity. The large dataset allows meaningful comparisons and garners confidence in the overall conclusion for the analytical similarity assessment of ABP 215 to both US- and EU-sourced bevacizumab. The structural and purity attributes, and biological properties of ABP 215 are demonstrated to be highly similar to those of bevacizumab.

Using analytic derivatives to assess the impact of phase function Fourier decomposition technique on the accuracy of a radiative transfer model

International Nuclear Information System (INIS)

Sanghavi, Suniti; Natraj, Vijay

2013-01-01

Fourier decomposition of the phase function is essential to decouple the azimuthal component of the radiative transfer equation for multiple scattering calculations. This decomposition can be carried out by means of a direct numerical method based on the definition of the Fourier transform (numFT), or by an expansion of the phase function in terms of spherical Legendre polynomials (sphFT). numFT requires interpolation of the phase function between discrete angles, leading to spurious errors in the final computations. This error is difficult to quantify by means of intensity-only computations, since it is hard to determine the absolute accuracy of any given approach. We show that a linearization (analytic computation of derivatives) of the intensity with respect to parameters governing the phase function can be compared against results using the finite difference method, thereby providing a self-consistency test for characterizing and quantifying the error. We have applied this approach to two linearized versions of the Matrix Operator Method, which are identical in all respects except that one uses numFT while the other uses sphFT. In both cases, we compute the derivatives of the intensity with respect to aerosol parameters governing scattering in the simulated atmosphere. Comparison of the derivatives against their finite difference estimates shows a reduction of error by several orders of magnitude when Legendre polynomials are employed. We have also examined the effect of the angular resolution of the phase function on the error due to the numFT technique. A general reduction of error is seen with increasing angular resolution, indicating that interpolation is indeed the major error source. Also, we have pointed out a related source of error in numFT computations that occurs when Fourier decomposition is carried out on the composite phase function of a layer consisting of more than one scatterer. We conclude that an expansion of the phase function in terms of

On a class of analytic functions generated by fractional integral operator

Directory of Open Access Journals (Sweden)

Ibrahim Rabha W.

2017-01-01

Full Text Available In this note, we improve the idea of the Tsallis entropy in a complex domain. This improvement is contingent on the fractional operator in a complex domain (type Alexander. We clarify some new classes of analytic functions, which are planned in view of the geometry function theory. This category of entropy is called fractional entropy; accordingly, we demand them fractional entropic geometry classes. Other geometric properties are established in the sequel. Our exhibition is supported by the Maxwell Lemma and Jack Lemma.

Thermal expansion of L-ascorbic acid

Science.gov (United States)

Nicolaï, B.; Barrio, M.; Tamarit, J.-Ll.; Céolin, R.; Rietveld, I. B.

2017-04-01

The specific volume of vitamin C has been investigated by X-ray powder diffraction as a function of temperature from 110 K up to complete degradation around 440 K. Its thermal expansion is relatively small in comparison with other organic compounds with an expansivity α v of 1.2(3) × 10-4 K-1. The structure consists of strongly bound molecules in the ac plane through a dense network of hydrogen bonds. The thermal expansion is anisotropic. Along the b axis, the expansion has most leeway and is about 10 times larger than in the other directions.

An Example of a Hakomi Technique Adapted for Functional Analytic Psychotherapy

Science.gov (United States)

Collis, Peter

2012-01-01

Functional Analytic Psychotherapy (FAP) is a model of therapy that lends itself to integration with other therapy models. This paper aims to provide an example to assist others in assimilating techniques from other forms of therapy into FAP. A technique from the Hakomi Method is outlined and modified for FAP. As, on the whole, psychotherapy…

To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2007-01-01

We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'

Hypersonic expansion of the Fokker--Planck equation

International Nuclear Information System (INIS)

Fernandez-Feria, R.

1989-01-01

A systematic study of the hypersonic limit of a heavy species diluted in a much lighter gas is made via the Fokker--Planck equation governing its velocity distribution function. In particular, two different hypersonic expansions of the Fokker--Planck equation are considered, differing from each other in the momentum equation of the heavy gas used as the basis of the expansion: in the first of them, the pressure tensor is neglected in that equation while, in the second expansion, the pressure tensor term is retained. The expansions are valid when the light gas Mach number is O(1) or larger and the difference between the mean velocities of light and heavy components is small compared to the light gas thermal speed. They can be applied away from regions where the spatial gradient of the distribution function is very large, but it is not restricted with respect to the temporal derivative of the distribution function. The hydrodynamic equations corresponding to the lowest order of both expansions constitute two different hypersonic closures of the moment equations. For the subsequent orders in the expansions, closed sets of moment equations (hydrodynamic equations) are given. Special emphasis is made on the order of magnitude of the errors of the lowest-order hydrodynamic quantities. It is shown that if the heat flux vanishes initially, these errors are smaller than one might have expected from the ordinary scaling of the hypersonic closure. Also it is found that the normal solution of both expansions is a Gaussian distribution at the lowest order

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Siafarikas Panayiotis D

2004-01-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the and spaces, p∈ℕ, . The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

Goal-Oriented Probability Density Function Methods for Uncertainty Quantification

Science.gov (United States)

2015-12-11

approximations or data-driven approaches. We investigated the accuracy of analytical tech- niques based Kubo -Van Kampen operator cumulant expansions for...analytical techniques based Kubo -Van Kampen operator cumulant expansions for Langevin equations driven by fractional Brownian motion and other noises

Analytic Lorentz integral transform of an arbitrary response function and its application to the inversion problem

International Nuclear Information System (INIS)

Barnea, N.; Liverts, E.

2010-01-01

In this paper we present an analytic expression for the Lorentz integral transform of an arbitrary response function expressed as a polynomial times a decaying exponent. The resulting expression is applied to the inversion problem of the Lorentz integral transform, simplifying the inversion procedure and improving the accuracy of the procedure. We have presented analytic formulae for a family of basis function often used in the inversion of the LIT function. These formulae allow for an efficient and accurate inversion. The quality and the stability of the resulting inversions were demonstrated through two different examples yielding outstanding results. (author)

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 new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

Science.gov (United States)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

Lace expansion for dummies

NARCIS (Netherlands)

Bolthausen, Erwin; Van Der Hofstad, Remco; Kozma, Gady

2018-01-01

We show Green's function asymptotic upper bound for the two-point function of weakly self-Avoiding walk in d >4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier

Interpolation and sampling in spaces of analytic functions

CERN Document Server

Seip, Kristian

2004-01-01

The book is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for H^\\infty, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem. The book aims at clarifying how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szegő condition. The book is based on six lectures given by the author at the University of Michigan. This is reflected in the exposition, which is a blend of informal explanations with technical details. The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiari...

Approximate, analytic solutions of the Bethe equation for charged particle range

OpenAIRE

Swift, Damian C.; McNaney, James M.

2009-01-01

By either performing a Taylor expansion or making a polynomial approximation, the Bethe equation for charged particle stopping power in matter can be integrated analytically to obtain the range of charged particles in the continuous deceleration approximation. Ranges match reference data to the expected accuracy of the Bethe model. In the non-relativistic limit, the energy deposition rate was also found analytically. The analytic relations can be used to complement and validate numerical solu...

Federalism. Theory and Neo-Functionalism: Elements for an analytical framework

DEFF Research Database (Denmark)

Dosenrode, Søren

2010-01-01

-McKayian way, is able to explain the cases of ‘big bang’ integration (USA, Australia, Canada), but not an ‘organic’ integration process. Neo-functionalism, on the other hand, is not able to explain this relatively fast form of integration, but it is – in its new version - able to analyze and explain......The purpose of this article is to propose a draft for an analytical frame for analyzing regional integration consisting of federalism theory and neo-functionalism. It starts out discussing the concept of regional integration setting up a stagiest model for categorizing it.Then follows an analysis...... of federalism theory and neo-functionalism. One argument of this article is to understand federalism theory as a regional integration theory. Another is to look at federalism theory as complementary to neo-functionalism when trying to explain regional integration. Federalism theory, in an extended Riker...

Thermal expansion of doped lanthanum gallates

Indian Academy of Sciences (India)

Administrator

Since the components are in intimate mechanical contact, any stress generated due to their thermal expansion mis- match during thermal cycling could lead to catastrophic failure of the cell. The functional materials must have similar thermal expansions to avoid mechanical stresses. Hence it is useful to study the thermal ...

Functional analytic methods in complex analysis and applications to partial differential equations

International Nuclear Information System (INIS)

Mshimba, A.S.A.; Tutschke, W.

1990-01-01

The volume contains 24 lectures given at the Workshop on Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations held in Trieste, Italy, between 8-19 February 1988, at the ICTP. A separate abstract was prepared for each of these lectures. Refs and figs

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 ...

An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

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Ryoichi Chiba

2018-01-01

Full Text Available An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of n layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at n-1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

Innovative analytical tools to characterize prebiotic carbohydrates of functional food interest.

Science.gov (United States)

Corradini, Claudio; Lantano, Claudia; Cavazza, Antonella

2013-05-01

Functional foods are one of the most interesting areas of research and innovation in the food industry. A functional food or functional ingredient is considered to be any food or food component that provides health benefits beyond basic nutrition. Recently, consumers have shown interest in natural bioactive compounds as functional ingredients in the diet owing to their various beneficial effects for health. Water-soluble fibers and nondigestible oligosaccharides and polysaccharides can be defined as functional food ingredients. Fructooligosaccharides (FOS) and inulin are resistant to direct metabolism by the host and reach the caecocolon, where they are used by selected groups of beneficial bacteria. Furthermore, they are able to improve physical and structural properties of food, such as hydration, oil-holding capacity, viscosity, texture, sensory characteristics, and shelf-life. This article reviews major innovative analytical developments to screen and identify FOS, inulins, and the most employed nonstarch carbohydrates added or naturally present in functional food formulations. High-performance anion-exchange chromatography with pulsed electrochemical detection (HPAEC-PED) is one of the most employed analytical techniques for the characterization of those molecules. Mass spectrometry is also of great help, in particularly matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS), which is able to provide extensive information regarding the molecular weight and length profiles of oligosaccharides and polysaccharides. Moreover, MALDI-TOF-MS in combination with HPAEC-PED has been shown to be of great value for the complementary information it can provide. Some other techniques, such as NMR spectroscopy, are also discussed, with relevant examples of recent applications. A number of articles have appeared in the literature in recent years regarding the analysis of inulin, FOS, and other carbohydrates of interest in the field and

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

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

Low-temperature expansions and correlation functions of the Z3-chiral Potts model

International Nuclear Information System (INIS)

Han, N.S.; Honecker, A.

1993-04-01

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z 3 -chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z n -spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z 3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length. (orig.)

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

International Nuclear Information System (INIS)

Doha, E H; Ahmed, H M

2004-01-01

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

An analytically resolved model of a potato's thermal processing using Heun functions

Science.gov (United States)

Vargas Toro, Agustín.

2014-05-01

A potato's thermal processing model is solved analytically. The model is formulated using the equation of heat diffusion in the case of a spherical potato processed in a furnace, and assuming that the potato's thermal conductivity is radially modulated. The model is solved using the method of the Laplace transform, applying Bromwich Integral and Residue Theorem. The temperatures' profile in the potato is presented as an infinite series of Heun functions. All computations are performed with computer algebra software, specifically Maple. Using the numerical values of the thermal parameters of the potato and geometric and thermal parameters of the processing furnace, the time evolution of the temperatures in different regions inside the potato are presented analytically and graphically. The duration of thermal processing in order to achieve a specified effect on the potato is computed. It is expected that the obtained analytical results will be important in food engineering and cooking engineering.

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

International Nuclear Information System (INIS)

Anteneodo, C; Vallejos, R O

2010-01-01

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ* respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ* in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ* by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

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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.

Operator expansion at short distance in QCD

Energy Technology Data Exchange (ETDEWEB)

Hubschmid, W [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik; Mallik, S [Karlsruhe Univ. (T.H.) (Germany, F.R.). Inst. fuer Theoretische Kernphysik

1982-11-01

We present a method of calculating coefficients of gluon operators in the operator product expansion of two-point functions at short distance. It is based on a short-distance expansion of the singular part of the quark propagator in the gluon field, the latter being treated as external. We verify in full generality that the spin zero, gluon operator of dimension six does not contribute to the two-point functions of quark bilinears.

Decisions through data: analytics in healthcare.

Science.gov (United States)

Wills, Mary J

2014-01-01

The amount of data in healthcare is increasing at an astonishing rate. However, in general, the industry has not deployed the level of data management and analysis necessary to make use of those data. As a result, healthcare executives face the risk of being overwhelmed by a flood of unusable data. In this essay I argue that, in order to extract actionable information, leaders must take advantage of the promise of data analytics. Small data, predictive modeling expansion, and real-time analytics are three forms of data analytics. On the basis of my analysis for this study, I recommend all three for adoption. Recognizing the uniqueness of each organization's situation, I also suggest that practices, hospitals, and healthcare systems examine small data and conduct real-time analytics and that large-scale organizations managing populations of patients adopt predictive modeling. I found that all three solutions assist in the collection, management, and analysis of raw data to improve the quality of care and decrease costs.

Characterization of dilation-analytic operators

Energy Technology Data Exchange (ETDEWEB)

Balslev, E; Grossmann, A; Paul, T

1986-01-01

Dilation analytic vectors and operators are characterized in a new representation of quantum mechanical states through functions analytic on the upper half-plane. In this space H/sub o/-bounded operators are integral operators and criteria for dilation analyticity are given in terms of analytic continuation outside of the half-plane for functions and for kernels. A sufficient condition is given for an integral operator in momentum space to be dilation-analytic.

Analytic continuation of massless two-loop four-point functions

International Nuclear Information System (INIS)

Gehrmann, T.; Remiddi, E.

2002-01-01

We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like 1→3 decay to Minkowskian regions relevant to all 1→3 and 2→2 reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron-positron annihilation. (author)

Functional analytic multisensory environmental therapy for people with dementia.

Science.gov (United States)

Staal, Jason A

2012-01-01

This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET) for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment therapy. The aim of the treatment is to provide a safe and effective framework for reducing the behavioral disturbance of the disease process, increasing elder well-being, and to promote transfer of positive effects to other environments outside of the multisensory treatment room.

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

Analytical functions in non-canonical two dimensional algebras; Funzioni analitiche nelle algebre a due componenti

Energy Technology Data Exchange (ETDEWEB)

Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione

1997-10-01

Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.

Intimacy Is a Transdiagnostic Problem for Cognitive Behavior Therapy: Functional Analytical Psychotherapy Is a Solution

Science.gov (United States)

Wetterneck, Chad T.; Hart, John M.

2012-01-01

Problems with intimacy and interpersonal issues are exhibited across most psychiatric disorders. However, most of the targets in Cognitive Behavioral Therapy are primarily intrapersonal in nature, with few directly involved in interpersonal functioning and effective intimacy. Functional Analytic Psychotherapy (FAP) provides a behavioral basis for…

The threshold expansion of the 2-loop sunrise self-mass master amplitudes

International Nuclear Information System (INIS)

Caffo, M.; Czyz, H.; Remiddi, E.

2001-01-01

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained analytically for arbitrary masses

ANALYTIC CAUSATIVES IN JAVANESE: A LEXICAL- FUNCTIONAL APPROACH

Directory of Open Access Journals (Sweden)

Agus Subiyanto

2014-01-01

Full Text Available Analytic  causatives  are  the  type  of  causatives  formed  by  separate predicates  expressing the cause and the effect, that is, the causing notion  is  realized  by  a  word  separate  from  the  word  denoting  the caused activity. This paper aims to discuss the forms and syntactic structure  of  analytic  causatives  in  Javanese.  To  discuss  the syntactic structure, the theory of lexical functional grammar (LFG is  employed.  The  data  used  in  this  study  is  the  „ngoko‟  level  of Javanese of the Surakarta dialect. By using a negation marker and modals  as  the  syntactic  operators to test mono-  or bi-clausality  of analytic  causatives,  the  writer  found  that  analytic  causatives  in Javanese form biclausal constructions. These constructions have an X-COMP  structure,  in  that  the  SUBJ  of  the  second  verb  is controlled  by  the  OBJ  of  the  causative  verb  (Ngawe  „make‟.  In terms  of  the  constituent  structure,  analytic  causatives  have  two kinds of structures, which are V-cause OBJ X-COMP and V-cause X-COMP OBJ. Kausatif  analitik  adalah  tipe  kausatif  yang  dibentuk  oleh  dua predikat  atau  dua  kata  terpisah  untuk  mengungkapkan  makna sebab dan akibat, yakni makna sebab direalisasikan oleh kata yang berbeda  dengan  kata  yang  menyatakan  makna  akibat.  Tulisan  ini membahas  bentuk  dan  struktur  sintaksis  kausatif  analitik  dalam bahasa Jawa. Untuk menjelaskan struktur sintaksis digunakan teori Tata  Bahasa  Leksikal  Fungsional.  Data  yang  digunakan  dalam penelitian  ini  adalah  bahasa  Jawa  dialek  Surakarta  ragam  ngoko. Dengan  menggunakan  alat  uji  pemarkah  negasi  dan  penggunaaan modalitas,  penulis  menemukan  bahwa  kausatif  analitik  dalam bahasa Jawa membentuk struktur biklausa. Konstruksi ini memiliki struktur  X

Cognitive-analytical therapy for a patient with functional neurological symptom disorder-conversion disorder (psychogenic myopia: A case study

Directory of Open Access Journals (Sweden)

Hamid Nasiri

2015-01-01

Full Text Available Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-old boy with the diagnosed functional neurological symptom disorder (psychogenic myopia was put under a cognitive-analytical treatment. The outcome of this treatment modality was proved successful.

Cognitive-analytical therapy for a patient with functional neurological symptom disorder-conversion disorder (psychogenic myopia): A case study.

Science.gov (United States)

Nasiri, Hamid; Ebrahimi, Amrollah; Zahed, Arash; Arab, Mostafa; Samouei, Rahele

2015-05-01

Functional neurological symptom disorder commonly presents with symptoms and defects of sensory and motor functions. Therefore, it is often mistaken for a medical condition. It is well known that functional neurological symptom disorder more often caused by psychological factors. There are three main approaches namely analytical, cognitive and biological to manage conversion disorder. Any of such approaches can be applied through short-term treatment programs. In this case, study a 12-year-old boy with the diagnosed functional neurological symptom disorder (psychogenic myopia) was put under a cognitive-analytical treatment. The outcome of this treatment modality was proved successful.

The Analytic Solution of Schroedinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

International Nuclear Information System (INIS)

Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu

2009-01-01

The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)

Separable expansions for virtual states and resonances

International Nuclear Information System (INIS)

Adhikari, S.K.; Fonseca, A.C.; Tomio, L.

1983-01-01

Finite rank expansions for two- and three-body t matrices are analytically continued to the unphysical sheet of the complex energy plane associated with the lowest two-body scattering threshold in order to obtain the position and residue of the virtual state and resonance poles. The present method is applied to study the 1 S 0 virtual state of two nucleons, the Efimov virtual states of three identical bosons, and the doublet virtual state of three nucleons

Analytical expressions for the correlation function of a hard sphere dimer fluid

Science.gov (United States)

Kim, Soonho; Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.

Analytical expression for the correlation function of a hard sphere chain fluid

Science.gov (United States)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Convergence and analytic properties of manifestly finite perturbation theory

International Nuclear Information System (INIS)

Mtingwa, S.K.

1979-01-01

The author discusses more carefully the ultraviolet convergence properties of Feynman diagrams in recently proposed manifestly finite perturbation expansions. Speccifically, he refines one of the constraints on the γ's-the noncanonical dimensions-such that, when satisfied, any general product-type interaction of massive scalar, fermion and vector fields yields finite perturbation expansions requiring no conventional renormalization procedure. Moreover, the analytic properties of the Feynman integrals in the theory are discussed and concluded with remarks on the necessity of a modified Kaellen-Lehmann representation

Interpersonal Mindfulness Informed by Functional Analytic Psychotherapy: Findings from a Pilot Randomized Trial

Science.gov (United States)

Bowen, Sarah; Haworth, Kevin; Grow, Joel; Tsai, Mavis; Kohlenberg, Robert

2012-01-01

Functional Analytic Psychotherapy (FAP; Kohlenberg & Tsai, 1991) aims to improve interpersonal relationships through skills intended to increase closeness and connection. The current trial assessed a brief mindfulness-based intervention informed by FAP, in which an interpersonal element was added to a traditional intrapersonal mindfulness…

Convergence of high-intensity expansions for atomic ionization

International Nuclear Information System (INIS)

Antunes Neto, H.S.; Davidovich, L.

1984-01-01

It is shown that a frequently used nonperturbative approximation for atomic ionization rates is cancelled out when corrections are taken into account. This explains the strong gauge dependence of previous results. A convergent and gauge invariant expansion is obtained. Numerical results show that its first term, which may be calculated analytically in many cases, describes very well the time-dependent behaviour of the ionization probability, for very strong fields. (Author) [pt

On analyticity of linear waves scattered by a layered medium

Science.gov (United States)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Logarithmic residues of analytic Banach algebra valued functions possessing a simply meromorphic inverse

OpenAIRE

Bart, Harm; Ehrhardt, T.; Silbermann, B.

2001-01-01

textabstractA logarithmic residue is a contour integral of a logarithmic derivative (left or right) of an analytic Banach algebra valued function. For functions possessing a meromorphic inverse with simple poles only, the logarithmic residues are identified as the sums of idempotents. With the help of this observation, the issue of left versus right logarithmic residues is investigated, both for connected and nonconnected underlying Cauchy domains. Examples are given to elucidate the subject ...

Eigenfunction expansion for fractional Brownian motions

International Nuclear Information System (INIS)

Maccone, C.

1981-01-01

The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

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.

ORBITALES. A program for the calculation of wave functions with an analytical central potential

International Nuclear Information System (INIS)

Yunta Carretero; Rodriguez Mayquez, E.

1974-01-01

In this paper is described the objective, basis, carrying out in FORTRAN language and use of the program ORBITALES. This program calculate atomic wave function in the case of ths analytical central potential (Author) 8 refs

A Micro-Test Structure for the Thermal Expansion Coefficient of Metal Materials

Directory of Open Access Journals (Sweden)

Qingying Ren

2017-02-01

Full Text Available An innovative micro-test structure for detecting the thermal expansion coefficient (TEC of metal materials is presented in this work. Throughout this method, a whole temperature sensing moveable structures are supported by four groups of cascaded chevrons beams and packed together. Thermal expansion of the metal material causes the deflection of the cascaded chevrons, which leads to the capacitance variation. By detecting the capacitance value at different temperatures, the TEC value of the metal materials can be calculated. A finite element model has been established to verify the relationship between the TEC of the material and the displacement of the structure on horizontal and vertical directions, thus a function of temperature for different values of TEC can be deduced. In order to verify the analytical model, a suspended-capacitive micro-test structure has been fabricated by MetalMUMPs process and tested in a climate chamber. Test results show that in the temperature range from 30 °C to 80 °C, the TEC of the test material is 13.4 × 10−6 °C−1 with a maximum relative error of 0.8% compared with the given curve of relationship between displacement and temperature.

Analytical Propagation of Uncertainty in Life Cycle Assessment Using Matrix Formulation

DEFF Research Database (Denmark)

Imbeault-Tétreault, Hugues; Jolliet, Olivier; Deschênes, Louise

2013-01-01

with Monte Carlo results. The sensitivity and contribution of input parameters to output uncertainty were also analytically calculated. This article outlines an uncertainty analysis of the comparison between two case study scenarios. We conclude that the analytical method provides a good approximation...... on uncertainty calculation. This article shows the importance of the analytical method in uncertainty calculation, which could lead to a more complete uncertainty analysis in LCA practice....... uncertainty assessment is not a regular step in LCA. An analytical approach based on Taylor series expansion constitutes an effective means to overcome the drawbacks of the Monte Carlo method. This project aimed to test the approach on a real case study, and the resulting analytical uncertainty was compared...

Functional Analytic Multisensory Environmental Therapy for People with Dementia

Directory of Open Access Journals (Sweden)

Jason A. Staal

2012-01-01

Full Text Available This paper introduces Functional Analytic Multisensory Environmental Therapy (FAMSET for use with elders with dementia while using a multisensory environment/snoezelen room. The model introduces behavioral theory and practice to the multisensory environment treatment, addressing assessment, and, within session techniques, integrating behavioral interventions with emotion-oriented care. A modular approach is emphasized to delineate different treatment phases for multisensory environment therapy. The aim of the treatment is to provide a safe and effective framework for reducing the behavioral disturbance of the disease process, increasing elder well-being, and to promote transfer of positive effects to other environments outside of the multisensory treatment room.

Ex Vivo Expansion of Functional Human UCB-HSCs/HPCs by Coculture with AFT024-hkirre Cells

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Muti ur Rehman Khan

2014-01-01

Full Text Available Kiaa1867 (human Kirre, hKirre has a critical role in brain development and/or maintenance of the glomerular slit diaphragm in kidneys. Murine homolog of this gene, mKirre expressed in OP9 and AFT024 cells could support hematopoietic stem cells/hematopoietic progenitor cells (HSC/HPC expansion in vitro. HKirre is also expressed in human FBMOB-hTERT cell line and fetal liver fibroblast-like cells but its function has remained unclear. In this paper, we cloned a hKirre gene from human fetal liver fibroblast-like cells and established a stably overexpressing hKirre-AFT024 cell line. Resultant cells could promote self-renewal and ex vivo expansion of HSCs/HPCs significantly higher than AFT024-control cells transformed with mock plasmid. The Expanded human umbilical cord blood (hUCB CD34+ cells retained the capacity of multipotent differentiation as long as 8 weeks and successfully repopulated the bone marrow of sublethally irradiated NOD/SCID mice, which demonstrated the expansion of long-term primitive transplantable HSCs/HPCs. Importantly, hkirre could upregulate the expressions of Wnt-5A, BMP4, and SDF-1 and downregulate TGF-β with other hematopoietic growth factors. By SDS-PAGE and Western Blot analysis, a ~89 kDa protein in total lysate of AFT024-hKirre was identified. Supernatants from AFT024-hkirre could also support CD34+CD38− cells expansion. These results demonstrated that the AFT024-hKirre cells have the ability to efficiently expand HSCs/HPCs.

The Expansion and Functional Diversification of the Mammalian Ribonuclease A Superfamily Epitomizes the Efficiency of Multigene Families at Generating Biological Novelty

Science.gov (United States)

Goo, Stephen M.; Cho, Soochin

2013-01-01

The ribonuclease (RNase) A superfamily is a vertebrate-specific gene family. Because of a massive expansion that occurred during the early mammalian evolution, extant mammals in general have much more RNase genes than nonmammalian vertebrates. Mammalian RNases have been associated with diverse physiological functions including digestion, cytotoxicity, angiogenesis, male reproduction, and host defense. However, it is still uncertain when their expansion occurred and how a wide array of functions arose during their evolution. To answer these questions, we generate a compendium of all RNase genes identified in 20 complete mammalian genomes including the platypus, Ornithorhynchus anatinus. Using this, we delineate 13 ancient RNase gene lineages that arose before the divergence between the monotreme and the other mammals (∼220 Ma). These 13 ancient gene lineages are differentially retained in the 20 mammals, and the rate of protein sequence evolution is highly variable among them, which suggest that they have undergone extensive functional diversification. In addition, we identify 22 episodes of recent expansion of RNase genes, many of which have signatures of adaptive functional differentiation. Exemplifying this, bursts of gene duplication occurred for the RNase1, RNase4, and RNase5 genes of the little brown bat (Myotis lucifugus), which might have contributed to the species’ effective defense against heavier pathogen loads caused by its communal roosting behavior. Our study illustrates how host-defense systems can generate new functions efficiently by employing a multigene family, which is crucial for a host organism to adapt to its ever-changing pathogen environment. PMID:24162010

Min-Max Spaces and Complexity Reduction in Min-Max Expansions

Energy Technology Data Exchange (ETDEWEB)

Gaubert, Stephane, E-mail: Stephane.Gaubert@inria.fr [Ecole Polytechnique, INRIA and CMAP (France); McEneaney, William M., E-mail: wmceneaney@ucsd.edu [University of California San Diego, Dept. of Mech. and Aero. Eng. (United States)

2012-06-15

Idempotent methods have been found to be extremely helpful in the numerical solution of certain classes of nonlinear control problems. In those methods, one uses the fact that the value function lies in the space of semiconvex functions (in the case of maximizing controllers), and approximates this value using a truncated max-plus basis expansion. In some classes, the value function is actually convex, and then one specifically approximates with suprema (i.e., max-plus sums) of affine functions. Note that the space of convex functions is a max-plus linear space, or moduloid. In extending those concepts to game problems, one finds a different function space, and different algebra, to be appropriate. Here we consider functions which may be represented using infima (i.e., min-max sums) of max-plus affine functions. It is natural to refer to the class of functions so represented as the min-max linear space (or moduloid) of max-plus hypo-convex functions. We examine this space, the associated notion of duality and min-max basis expansions. In using these methods for solution of control problems, and now games, a critical step is complexity-reduction. In particular, one needs to find reduced-complexity expansions which approximate the function as well as possible. We obtain a solution to this complexity-reduction problem in the case of min-max expansions.

An accurate solution of parabolic equations by expansion in ultraspherical polynomials

International Nuclear Information System (INIS)

Doha, E.H.

1986-11-01

An ultraspherical expansion technique is applied to obtain numerically the solution of the third boundary value problem for linear parabolic partial differential equation in one-space variable. The differential equation with its boundary and initial conditions is reduced to a system of ordinary differential equations for the coefficients of the expansion. This system may be solved analytically or numerically in a step-by-step manner. The method in its present form may be considered as a generalization of that of Dew and Scraton. The extension of the method to the polar-type equations is also considered. (author). 12 refs, 1 tab

Negative thermal expansion in Sc2(WO4)3

International Nuclear Information System (INIS)

Evans, J.S.O.; Mary, T.A.; Sleight, A.W.

1998-01-01

Sc 2 (WO 4 ) 3 has been found to show the highly unusual property of negative thermal expansion over a temperature range of 10 to 1,073 K. Powder neutron diffraction data from 10 to 450 K shows an essentially linear decrease in cell volume as a function of temperature. The intrinsic linear coefficient of thermal expansion from this data is -2.2 x 10 -6 K -1 . The linear coefficient of thermal expansion measured on a ceramic bar of Sc 2 (WO 4 ) 3 can be as negative as -11 x 10 -6 K -1 due to microstructure changes as a function of temperature. Rietveld refinement as a function of temperature suggests that the intrinsic negative thermal expansion can be related to transverse vibrations of bridging oxygen atoms in the structure. The anharmonic nature of these vibrations leads to a coupled tilting of the quasi-rigid framework polyhedra. This tilting in turn causes the structure to become more dense with increasing temperature

Analytic continuation of scattering data as a method of obtaining characteristics of bound states

International Nuclear Information System (INIS)

Blokhintsev, L.; Savin, D.

2014-01-01

An asymptotic normalization coefficient (ANC) determines the asymptotics of a wave function of a nucleus a in a binary channel b + c. ANCs are proportional to nuclear vertex constants (NVCs), which are on-shell matrix elements of the virtual processes a ↔ b+c. The method of the analytic continuation of the effective range function is applied to obtain the asymptotic normalization coefficients for 6 Li nucleus in the α+ d channel. Several sets of scattering phases obtained from the phase-shift analyses as well as from Faddeev calculations are used as an input. Since the α+d system possesses the low-lying inelastic threshold due to the dissociation of a deuteron, the approach used is generalized to include inelastic channels. The sensitivity of the obtained values of asymptotic normalization coefficients to the elastic channels coupling and to account of the inelastic channel is investigated. In summary, we can say that employing the analytic continuation of the effective range expansion to determine the ANCs and NVCs for the 6 Li → α + d channel turns out to be successful

Tailored functional materials with controlled thermal expansion and excellent thermal conductivity

International Nuclear Information System (INIS)

Korb, G.; Sebo, P.

1997-01-01

Engineering materials are mainly used for structures. Therefore high-strength, stiffness and sufficient toughness are of prime importance. For a long time engineers thought first in terms of metals. Material scientists developed alloys tailored to the needs of industry. Ceramics are known to be brittle and therefore not suitable in the first place for structural application under stress. Polymers with their low modulus became attractive when reinforced with high-strength fibres. Composites processed by polymer, metal or ceramic matrices and high-strength reinforcements have been introduced into many sectors of industry. Engineering materials for structural applications fulfil a function: they withstand high stresses, temperatures, fatigue, creep etc. But usually we do not call them functional materials. Functional materials serve applications apart from classical engineering fields. Electricity conducting materials, semi conductors, memory alloys and many others are called functional materials. Because of the fact that the basic physical properties cannot be changed in single-phase materials, the combination of two and more materials with different properties lead to components with new and tailored properties. A few techniques for preparation are described as powder metallurgy, infiltration of prepegs and compaction of precoated fibres/particles. The lecture is focusing on carbon fibre/particle reinforced Metal Matrix Materials. The achievable properties, in particular the thermal conductivity originating from the base materials is depending on the orientation of the fibres and interfacial contacts in the composite. The carefully controlled expansion behaviour is the most important property to use the material as a heat sink in electronic assemblies. (author)

Separable expansions for local potentials with Coulomb interactions

International Nuclear Information System (INIS)

Adhikari, S.K.

1976-01-01

If two particles are interacting via a short range potential and a repulsive Coulomb potential the t matrix can be written as a sum of the Coulomb and the ''nuclear'' t matrices. In order to solve the three-nucleon problem with Coulomb interactions usually we need a separable representation of this ''nuclear'' t matrix. A recently proposed method for finding a separable expansion for local potentials is here extended to find a rapidly convergent separable expansion, with analytic form factors, for the ''nuclear'' part of the t matrix of a local potential, in the presence of Coulomb interactions. The method is illustrated for a two-term Malfliet-Tjon potential. In each rank the ''nuclear'' phase shift is close to the corresponding phase shift when the Coulomb interaction is switched off

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

DEFF Research Database (Denmark)

Pan, E.; Chen, J.Y.; Bevis, M.

2015-01-01

to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core...... the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both...... the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth...

On Learning Ring-Sum-Expansions

DEFF Research Database (Denmark)

Fischer, Paul; Simon, H. -U.

1992-01-01

The problem of learning ring-sum-expansions from examples is studied. Ring-sum-expansions (RSE) are representations of Boolean functions over the base {#123;small infinum, (+), 1}#125;, which reflect arithmetic operations in GF(2). k-RSE is the class of ring-sum-expansions containing only monomials...... of length at most k:. term-RSE is the class of ring-sum-expansions having at most I: monomials. It is shown that k-RSE, k>or=1, is learnable while k-term-RSE, k>2, is not learnable if RPnot=NP. Without using a complexity-theoretical hypothesis, it is proven that k-RSE, k>or=1, and k-term-RSE, k>or=2 cannot...... be learned from positive (negative) examples alone. However, if the restriction that the hypothesis which is output by the learning algorithm is also a k-RSE is suspended, then k-RSE is learnable from positive (negative) examples only. Moreover, it is proved that 2-term-RSE is learnable by a conjunction...

Residual stresses associated with the hydraulic expansion of steam generator tubing into tubesheets

International Nuclear Information System (INIS)

Middlebrooks, W.B.; Harrod, D.L.; Gold, R.E.

1991-01-01

Westinghouse has used three different processes for the full depth expansion of tubes into the tube sheets of recirculating nuclear steam generators: mechanical rolling, explosive expansion and hydraulic expansion. Each process aims at expanding tubes tightly to tube sheets, leaving the smallest possible secondary side crevice depth, and minimizing the residual stress in the expanded tubes, all for the purpose of mitigating the effect of corrosion phenomena. The hydraulic expansion process was qualified and has been implemented since 1978, and more than 1.1 million tube ends have been hydraulically expanded into production units. In this paper, the results of the recent analytical studies related to the residual stress in the expanded tubes are summarized. The method of hydraulic expansion is explained, and some important parameters are given. Finite element method, theoretical incremental analysis, tube sheet yielding and residual stress, contact pressure, sensitivity analysis and temperature effect in the central region of tube sheets, and the residual stress in the transition zone are described. (K.I.)

Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

CERN Document Server

Rassias, Michael

2014-01-01

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

A characterization of dilation-analytic operators

International Nuclear Information System (INIS)

Balslev, E.; Grossmann, A.; Paul, T.

1986-01-01

Dilation analytic vectors and operators are characterized in a new representation of quantum mechanical states through functions analytic on the upper half-plane. In this space H o -bounded operators are integral operators and criteria for dilation analyticity are given in terms of analytic continuation outside of the half-plane for functions and for kernels. A sufficient condition is given for an integral operator in momentum space to be dilation-analytic

Analysis of water hammer in pipelines by partial fraction expansion of transfer function in frequency domain

International Nuclear Information System (INIS)

Lee, Jun Shin; Lee, Wook Ryun; Oh, Ki Yong; Kim, Bong Ki

2010-01-01

Understanding water hammer is very important to the prevention of excessive pressure build-up in pipelines. Many researchers have studied this phenomenon, drawing effective solutions through the time- and frequency-domain approaches. For the purposes of enhancing the advantages of the frequency-domain approach and, thereby, rendering investigations of the dynamic characteristics of pipelines more effective, we propose partial fraction expansion of the transfer function between the unsteady flow source and a given section. We simulate the proposed approach using a vibration element inserted into a simple pipeline, deducing much useful physical information pertaining to pipeline design. We conclude that locating the resonance of the vibration element between the first and second resonances of the pipeline can mitigate the excessive pressure build-up attendant on the occurrence of water hammer. Our method of partial fraction expansion is expected to be useful and effective in analyses of unsteady flows in pipelines

Radial core expansion reactivity feedback in advanced LMRs: uncertainties and their effects on inherent safety

International Nuclear Information System (INIS)

Wigeland, R.A.; Moran, T.J.

1988-01-01

An analytical model for calculating radial core expansion, based on the thermal and elastic bowing of a single subassembly at the core periphery, is used to quantify the effect of uncertainties on this reactivity feedback mechanism. This model has been verified and validated with experimental and numerical results. The impact of these uncertainties on the safety margins in unprotected transients is investigated with SASSYS/SAS4A, which includes this model for calculating the reactivity feedback from radial core expansion. The magnitudes of these uncertainties are not sufficient to preclude the use of radial core expansion reactivity feedback in transient analysis

Functional and Structural Characterization of a Receptor-Like Kinase Involved in Germination and Cell Expansion in Arabidopsis

Science.gov (United States)

Wu, Zhen; Liang, Shan; Song, Wen; Lin, Guangzhong; Wang, Weiguang; Zhang, Heqiao; Han, Zhifu; Chai, Jijie

2017-01-01

Leucine-rich repeat receptor-like kinases (LRR-RLKs) are widespread in different plant species and play important roles in growth and development. Germination inhibition is vital for the completion of seed maturation and cell expansion is a fundamental cellular process driving plant growth. Here, we report genetic and structural characterizations of a functionally uncharacterized LRR-RLK, named GRACE (Germination Repression and Cell Expansion receptor-like kinase). Overexpression of GRACE in Arabidopsis exhibited delayed germination, enlarged cotyledons, rosette leaves and stubbier petioles. Conversely, these phenotypes were reversed in the T-DNA insertion knock-down mutant grace-1 plants. A crystal structure of the extracellular domain of GRACE (GRACE-LRR) determined at the resolution of 3.0 Å revealed that GRACE-LRR assumed a right-handed super-helical structure with an island domain (ID). Structural comparison showed that structure of the ID in GRACE-LRR is strikingly different from those observed in other LRR-RLKs. This structural observation implies that GRACE might perceive a new ligand for signaling. Collectively, our data support roles of GRACE in repressing seed germination and promoting cell expansion of Arabidopsis, presumably by perception of unknown ligand(s). PMID:29213277

Computation of the modified Bessel function of the third kind of imaginary orders: uniform Airy-type asymptotic expansion

NARCIS (Netherlands)

A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

2002-01-01

textabstractThe use of a uniform Airy-type asymptotic expansion for the computation of the modified Bessel functions of the third kind of imaginary orders ($K_{ia}(x)$) near the transition point $x=a$, is discussed. In [2], an algorithm for the evaluation of $K_{ia}(x)$ was presented, which made use

Cluster expansion for vacuum confining fields

International Nuclear Information System (INIS)

Simonov, Yu.A.

1987-01-01

Colored particle Green functions in vacuum background random fields are written as path integrals. Averaging over random fields is done using the cluster (cumulant) expansion. The existence of a finite correlation length for vacuum background fields is shown to produce the linear confinement, in agreement with the results, obtained with the help of averaged Hamiltonians. A modified form of cluster expansion for nonabelian fields is introduced using the path-ordered cumulants

Stochastic quantization and 1/N expansion

International Nuclear Information System (INIS)

Brunelli, J.C.; Mendes, R.S.

1992-10-01

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the non linear sigma model in two dimensions is worked out as an example. (author). 19 refs., 5 figs

Calculation of Resonance Interaction Effects Using a Rational Approximation to the Symmetric Resonance Line Shape Function

International Nuclear Information System (INIS)

Haeggblom, H.

1968-08-01

The method of calculating the resonance interaction effect by series expansions has been studied. Starting from the assumption that the neutron flux in a homogeneous mixture is inversely proportional to the total cross section, the expression for the flux can be simplified by series expansions. Two types of expansions are investigated and it is shown that only one of them is generally applicable. It is also shown that this expansion gives sufficient accuracy if the approximate resonance line shape function is reasonably representative. An investigation is made of the approximation of the resonance shape function with a Gaussian function which in some cases has been used to calculate the interaction effect. It is shown that this approximation is not sufficiently accurate in all cases which can occur in practice. Then, a rational approximation is introduced which in the first order approximation gives the same order of accuracy as a practically exact shape function. The integrations can be made analytically in the complex plane and the method is therefore very fast compared to purely numerical integrations. The method can be applied both to statistically correlated and uncorrelated resonances

Calculation of Resonance Interaction Effects Using a Rational Approximation to the Symmetric Resonance Line Shape Function

Energy Technology Data Exchange (ETDEWEB)

Haeggblom, H

1968-08-15

The method of calculating the resonance interaction effect by series expansions has been studied. Starting from the assumption that the neutron flux in a homogeneous mixture is inversely proportional to the total cross section, the expression for the flux can be simplified by series expansions. Two types of expansions are investigated and it is shown that only one of them is generally applicable. It is also shown that this expansion gives sufficient accuracy if the approximate resonance line shape function is reasonably representative. An investigation is made of the approximation of the resonance shape function with a Gaussian function which in some cases has been used to calculate the interaction effect. It is shown that this approximation is not sufficiently accurate in all cases which can occur in practice. Then, a rational approximation is introduced which in the first order approximation gives the same order of accuracy as a practically exact shape function. The integrations can be made analytically in the complex plane and the method is therefore very fast compared to purely numerical integrations. The method can be applied both to statistically correlated and uncorrelated resonances.

Semiclassical expansions on and near caustics

International Nuclear Information System (INIS)

Meetz, K.

1984-09-01

We show that the standard WKB expansion can be generalized so that it reproduces the behavior of the wave function on and near a caustic in two-dimensional space time. The expansion is related to the unfolding polynomials of the elementary catastrophes occurring in two dimensions: the fold and the cusp catastrophe. The method determines control parameters and transport coefficients in a self-consistent way from differential equations and does not refer to the asymptotic expansion of Feynman path integrals. The lowest order equations are solved explicitly in terms of the multivalued classical action. The result is a generalized semiclassical approximation on and beyond a caustic. (orig.)

Cumulus Cell Expansion, Its Role in Oocyte Biology and Perspectives of Measurement: A Review

Directory of Open Access Journals (Sweden)

Nevoral J.

2015-01-01

Full Text Available Cumulus expansion of the cumulus-oocyte complex is necessary for meiotic maturation and acquiring developmental competence. Cumulus expansion is based on extracellular matrix synthesis by cumulus cells. Hyaluronic acid is the most abundant component of this extracellular matrix. Cumulus expansion takes place during meiotic oocyte maturation under in vivo and in vitro conditions. Quantification and measurement of cumulus expansion intensity is one possible method of determining oocyte quality and optimizing conditions for in vitro cultivation. Currently, subjective methods of expanded area and more exact cumulus expansion measurement by hyaluronic acid assessment are available. Among the methods of hyaluronic acid measurement is the use of radioactively labelled synthesis precursors. Alternatively, immunological and analytical methods, including enzyme-linked immunosorbent assay (ELISA, spectrophotometry, and high-performance liquid chromatography (HPLC in UV light, could be utilized. The high sensitivity of these methods could provide a precise analysis of cumulus expansion without the use of radioisotopes. Therefore, the aim of this review is to summarize and compare available approaches of cumulus expansion measurement, respecting special biological features of expanded cumuli, and to suggest possible solutions for exact cumulus expansion analysis.

New calibration methodology for calorimetric determination of isobaric thermal expansivity of liquids as a function of temperature and pressure

Energy Technology Data Exchange (ETDEWEB)

Navia, Paloma; Troncoso, Jacobo [Departamento de Fisica Aplicada, Facultad de Ciencias de Ourense, Campus As Lagoas, 32004 Ourense (Spain); Romani, Luis [Departamento de Fisica Aplicada, Facultad de Ciencias de Ourense, Campus As Lagoas, 32004 Ourense (Spain)], E-mail: romani@uvigo.es

2008-11-15

A new method for determining isobaric thermal expansivity of liquids as a function of temperature and pressure through calorimetric measurements against pressure is described. It is based on a previously reported measurement technique, but due to the different kind of calorimeter and experimental set up, a new calibration procedure was developed. Two isobaric thermal expansivity standards are needed; in this work, with a view on the quality of the available literature data, hexane and water are chosen. The measurements were carried out in the temperature and pressure intervals (278.15 to 348.15) K and (0.5 to 55) MPa for a set of liquids, and experimental values are compared with the available literature data in order to evaluate the precision of the experimental procedure. The analysis of the results reveals that the proposed methodology is highly accurate for isobaric thermal expansivity determination, and it allows obtaining a precise characterisation of the temperature and pressure dependence of this thermodynamic coefficient.

New calibration methodology for calorimetric determination of isobaric thermal expansivity of liquids as a function of temperature and pressure

International Nuclear Information System (INIS)

Navia, Paloma; Troncoso, Jacobo; Romani, Luis

2008-01-01

A new method for determining isobaric thermal expansivity of liquids as a function of temperature and pressure through calorimetric measurements against pressure is described. It is based on a previously reported measurement technique, but due to the different kind of calorimeter and experimental set up, a new calibration procedure was developed. Two isobaric thermal expansivity standards are needed; in this work, with a view on the quality of the available literature data, hexane and water are chosen. The measurements were carried out in the temperature and pressure intervals (278.15 to 348.15) K and (0.5 to 55) MPa for a set of liquids, and experimental values are compared with the available literature data in order to evaluate the precision of the experimental procedure. The analysis of the results reveals that the proposed methodology is highly accurate for isobaric thermal expansivity determination, and it allows obtaining a precise characterisation of the temperature and pressure dependence of this thermodynamic coefficient

The {β}-expansion formalism in perturbative QCD and its extension

Energy Technology Data Exchange (ETDEWEB)

Kataev, A.L. [Institute for Nuclear Research of the Academy of Sciences of Russia,60th October Anniversary Prospect 7a, 117312, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutskii per. 9, 141700, Dolgoprudny, Moscow Region (Russian Federation); Mikhailov, S.V. [Bogoliubov Laboratory of Theoretical Physics, JINR,Joliot-Curie 6, 141980 Dubna (Russian Federation)

2016-11-11

We discuss the {β}-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ R-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the {β}-expansion. We illustrate this feature considering the nonsinglet Adler function D{sup NS} in the third order of perturbation. We propose a generalization of the {β}-expansion for the renormalization group covariant quantities — the {β,γ}-expansion.

On the analytical evaluation of the partition function for unit hypercubes in four dimensions

International Nuclear Information System (INIS)

Hari Dass, N.D.

1984-10-01

The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU 2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)

Experimental design and multiple response optimization. Using the desirability function in analytical methods development.

Science.gov (United States)

Candioti, Luciana Vera; De Zan, María M; Cámara, María S; Goicoechea, Héctor C

2014-06-01

A review about the application of response surface methodology (RSM) when several responses have to be simultaneously optimized in the field of analytical methods development is presented. Several critical issues like response transformation, multiple response optimization and modeling with least squares and artificial neural networks are discussed. Most recent analytical applications are presented in the context of analytLaboratorio de Control de Calidad de Medicamentos (LCCM), Facultad de Bioquímica y Ciencias Biológicas, Universidad Nacional del Litoral, C.C. 242, S3000ZAA Santa Fe, ArgentinaLaboratorio de Control de Calidad de Medicamentos (LCCM), Facultad de Bioquímica y Ciencias Biológicas, Universidad Nacional del Litoral, C.C. 242, S3000ZAA Santa Fe, Argentinaical methods development, especially in multiple response optimization procedures using the desirability function. Copyright © 2014 Elsevier B.V. All rights reserved.

One year of operation of Mammoth Pacific`s MP1-100 turbine with metastable, supersaturated expansions

Energy Technology Data Exchange (ETDEWEB)

Mines, G.L. [Idaho National Engineering Lab., Idaho Falls, ID (United States)

1997-12-31

The Idaho National Engineering and Environmental Laboratory`s Heat Cycle Research project is developing a technology base that will increase the use of moderate-temperature hydrothermal resources to generate electrical power. One of the concepts under investigation is the use of a metastable, supersaturated turbine expansion. This expansion process supports a supersaturated vapor. If brought to equilibrium conditions, liquid condensate would be present in the expanding vapor. Analytical studies show that a plant designed to operate with this expansion will have an improvement in the brine effectiveness of up to 8% provided there is no adverse impact on turbine performance. Determining the impact of this expansion on turbine performance is focus of the project investigations being reported.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

OpenAIRE

Pan, E.; Chen, J.Y.; Bevis, M.; Bordoni, Andrea; Barletta, Valentina Roberta; Tabrizi, A. Molavi

2015-01-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in ...

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.

Numerical Investigation of magnetohydrodynamic flow through Sudden expansion pipes in Liquid Metal Blankets

Energy Technology Data Exchange (ETDEWEB)

Feng, Jingchao; He, Qingyun; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; Ye, Minyou

2016-11-01

In fusion liquid metal blanket, sudden expansions and sudden contractions are very common geometries. Changing of the cross-section causes 3-D magnetohydrodynamic (MHD) effects, which will affect the flow pattern, current distribution and pressure drop. In this paper the numerical code based on OpenFOAM platform developed by University of Science and Technology of China was used to investigate and optimize the sudden expansion pipe. The code has been validated by the recommended benchmark cases including Shercliff, Hunt, ALEX experiments (rectangular duct and round pipe) and KIT experiment cases. The obtained numerical results agreed well with those of all the benchmark cases. Previous and valuable analytical and experimental works have been done by L. Buhler, et. el. Based on these works, in the present paper, further investigation of different expansion lengths between the upstream pipe and downstream pipe at high Hartmann number and Reynolds number were conducted. Besides, different expansion ratios with a specific expansion length were conducted. The numerical results showed that with the increasing of expansion length, the 3D MHD effects gradually weakened. Especially, the 3D pressure drop decreases with the increasing of expansion length. Whereas, the expansion ratio factor shows no obvious influences on the total MHD pressure drop but greatly influence the local pressure distribution. These numerical simulations can be used to evaluate the MHD flow inside the expansion and contraction pipes.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

Science.gov (United States)

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Analytical study of Yang–Mills theory in the infrared from first principles

Energy Technology Data Exchange (ETDEWEB)

Siringo, Fabio, E-mail: fabio.siringo@ct.infn.it

2016-06-15

Pure Yang–Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the coupling becomes small and the one-loop approximation is under full control.

Strain expansion-reduction approach

Science.gov (United States)

Baqersad, Javad; Bharadwaj, Kedar

2018-02-01

Validating numerical models are one of the main aspects of engineering design. However, correlating million degrees of freedom of numerical models to the few degrees of freedom of test models is challenging. Reduction/expansion approaches have been traditionally used to match these degrees of freedom. However, the conventional reduction/expansion approaches are only limited to displacement, velocity or acceleration data. While in many cases only strain data are accessible (e.g. when a structure is monitored using strain-gages), the conventional approaches are not capable of expanding strain data. To bridge this gap, the current paper outlines a reduction/expansion technique to reduce/expand strain data. In the proposed approach, strain mode shapes of a structure are extracted using the finite element method or the digital image correlation technique. The strain mode shapes are used to generate a transformation matrix that can expand the limited set of measurement data. The proposed approach can be used to correlate experimental and analytical strain data. Furthermore, the proposed technique can be used to expand real-time operating data for structural health monitoring (SHM). In order to verify the accuracy of the approach, the proposed technique was used to expand the limited set of real-time operating data in a numerical model of a cantilever beam subjected to various types of excitations. The proposed technique was also applied to expand real-time operating data measured using a few strain gages mounted to an aluminum beam. It was shown that the proposed approach can effectively expand the strain data at limited locations to accurately predict the strain at locations where no sensors were placed.

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.

Temperature expansions for magnetic systems

International Nuclear Information System (INIS)

Cangemi, D.; Dunne, G.

1996-01-01

We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the proper-time method for the background field effects, and zeta function regularization for developing the expansions. We emphasize the essential difference between even and odd dimensions, focusing on 2+1 and 3+1 dimensions. We concentrate on the high temperature limit, but we also discuss the T=0 limit with nonzero chemical potential. Copyright copyright 1996 Academic Press, Inc

Cosmological models constructed by van der Waals fluid approximation and volumetric expansion

Science.gov (United States)

Samanta, G. C.; Myrzakulov, R.

The universe modeled with van der Waals fluid approximation, where the van der Waals fluid equation of state contains a single parameter ωv. Analytical solutions to the Einstein’s field equations are obtained by assuming the mean scale factor of the metric follows volumetric exponential and power-law expansions. The model describes a rapid expansion where the acceleration grows in an exponential way and the van der Waals fluid behaves like an inflation for an initial epoch of the universe. Also, the model describes that when time goes away the acceleration is positive, but it decreases to zero and the van der Waals fluid approximation behaves like a present accelerated phase of the universe. Finally, it is observed that the model contains a type-III future singularity for volumetric power-law expansion.

Analytical determination of Kondo and Fano resonances of electron Green's function in a single-level quantum dot

International Nuclear Information System (INIS)

Nguyen Bich Ha; Nguyen Van Hop

2009-01-01

The Kondo and Fano resonances in the two-point Green's function of the single-level quantum dot were found and investigated in many previous works by means of different numerical calculation methods. In this work we present the derivation of the analytical expressions of resonance terms in the expression of the two-point Green's function. For that purpose the system of Dyson equations for the two-point nonequilibrium Green's functions in the complex-time Keldysh formalism was established in the second order with respect to the tunneling coupling constants and the mean field approximation. This system of Dyson equations was solved exactly and the analytical expressions of the resonance terms are derived. The conditions for the existence of Kondo or Fano resonances are found.

Functional perturbative RG and CFT data in the ϵ -expansion

DEFF Research Database (Denmark)

Codello, A.; Safari, M.; Vacca, G. P.

2018-01-01

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straight......We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified...... several results for the whole family of renormalizable multi-critical models ϕ2 n. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks....

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

Science.gov (United States)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Predicted range expansion of Chinese tallow tree (Triadica sebifera) in forestlands of the southern United States

Science.gov (United States)

Hsiao-Hsuan Wang; William Grant; Todd Swannack; Jianbang Gan; William Rogers; Tomasz Koralewski; James Miller; John W. Taylor Jr.

2011-01-01

We present an integrated approach for predicting future range expansion of an invasive species (Chinese tallow tree) that incorporates statistical forecasting and analytical techniques within a spatially explicit, agent-based, simulation framework.

Satellite orbits perturbed by direct solar radiation pressure: general expansion of the disturbing function

International Nuclear Information System (INIS)

Hughes, S.

1977-01-01

An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method (Astr. J.; 67:300 (1962)). The Kaula inclination functions are replaced by an equivalent set of modified Allan (Proc. R. Soc. A.; 288:60 (1965)) inclination functions. The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, Cel. Mech.; 13:89 (1976)), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonance with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure. (author)

Repair for scattering expansion truncation errors in transport calculations

International Nuclear Information System (INIS)

Emmett, M.B.; Childs, R.L.; Rhoades, W.A.

1980-01-01

Legendre expansion of angular scattering distributions is usually limited to P 3 in practical transport calculations. This truncation often results in non-trivial errors, especially alternating negative and positive lateral scattering peaks. The effect is especially prominent in forward-peaked situations such as the within-group component of the Compton Scattering of gammas. Increasing the expansion to P 7 often makes the peaks larger and narrower. Ward demonstrated an accurate repair, but his method requires special cross section sets and codes. The DOT IV code provides fully-compatible, but heuristic, repair of the erroneous scattering. An analytical Klein-Nishina estimator, newly available in the MORSE code, allows a test of this method. In the MORSE calculation, particle scattering histories are calculated in the usual way, with scoring by an estimator routine at each collision site. Results for both the conventional P 3 estimator and the analytical estimator were obtained. In the DOT calculation, the source moments are expanded into the directional representation at each iteration. Optionally a sorting procedure removes all negatives, and removes enough small positive values to restore particle conservation. The effect of this is to replace the alternating positive and negative values with positive values of plausible magnitude. The accuracy of those values is examined herein

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

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.

FPSPH DFPSPF, Line Shape Function for Doppler Broadened Resonance Cross-Sections Calculation

International Nuclear Information System (INIS)

Ribon, P.

1982-01-01

1 - Description of problem or function: In the computation of Doppler- broadened resonance cross sections, use is made of the symmetric and anti-symmetric line shape functions. These functions usually denoted as Psi and Phi (Psi and Chi in Anglo-Saxon formalism) are defined in terms of the real and imaginary parts of the error function for complex arguments. They are the product of the convolution of a Gaussian function with the symmetric and anti-symmetric Breit-Wigner functions, respectively. FPSPH and DFPSPH compute these functions. 2 - Method of solution: For (1+x 2 ) > 20 Beta 2 , the calculation is based upon the asymptotic expansion: Psi+(i*Phi) = 1/(1-ix)*(1-t+3t 2 -3.5t 3 +3.5+7t 4 ---), with: t = 1/(2z 2 ); z = (1-ix)/Beta. The half-plane (Beta,x) is split in several parts, and use is made of PADE approximants. For 1 + x 2 2 , the calculation is based upon the relation with the erf function: Psi + i*Phi = SQRT(Pi)/Beta*(e (z 2 ) )*(1-erf(z)) (z = (1-ix)/Beta, and erf(z) being calculated from its analytic expansion: erf(z) = 2/SQRT(Pi)*z*e (-z 2 ) *(1+z 2 /3+z 4 /(3*5) + z 6 /(3*5*7)+---). PADE approximants are used to compute the expansion and e z 2

Unified treatment for accurate and fast evaluation of the Fermi–Dirac functions

International Nuclear Information System (INIS)

Guseinov, I. I.; Mamedov, B. A.

2010-01-01

A new analytical approach to the computation of the Fermi-Dirac (FD) functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed. (general)

Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory

International Nuclear Information System (INIS)

Zhang, Xing; Herbert, John M.

2014-01-01

We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H 3 near its D 3h geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state

Extended Plefka expansion for stochastic dynamics

International Nuclear Information System (INIS)

Bravi, B; Sollich, P; Opper, M

2016-01-01

We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry. (paper)

Extended Plefka expansion for stochastic dynamics

Science.gov (United States)

Bravi, B.; Sollich, P.; Opper, M.

2016-05-01

We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry.

Detection of hydrodynamic expansion in ultrashort pulse laser ellipsometric pump-probe experiments

International Nuclear Information System (INIS)

Morikami, Hidetoshi; Yoneda, Hitoki; Ueda, Ken-ichi; More, Richard M.

2004-01-01

In ultrashort-pulse laser interaction with solid target materials, the target rapidly heats, melts, evaporates, and begins to expand as a vapor or plasma. The onset of hydrodynamic expansion following surface evaporation is a switching point, where the dominant physics changes from temperature dependence of the solid dielectric function to refraction by the dense vapor cloud. We propose and demonstrate a method to analyze reflection data to identify this onset of target expansion. We use two of the Stokes parameters obtained from ellipsometric pump-probe measurements to determine a dielectric function with an assumption of no expansion. We use this dielectric function to predict the full set of reflectivity measurements. If there is a sharply defined target interface, this method reproduces the experimental data. When the plasma expansion is no longer negligible, the prediction deviates from the experimental measurements. This comparison shows when the plasma expansion is no longer negligible

Intermediate algebra & analytic geometry

CERN Document Server

Gondin, William R

1967-01-01

Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

Thermal expansion studies on Hafnium titanate (HfTiO4)

International Nuclear Information System (INIS)

Panneerselvam, G.; Subramanian, G.G.S.; Antony, M.P.

2006-01-01

The lattice thermal expansion characteristics of hafnium titanate (HfTiO 4 ) have been studied by measuring the lattice parameter as a function of temperature by high temperature X-ray diffraction technique (HT-XRD) in the temperature range 298-1973K. Percentage linear thermal expansion and mean linear thermal expansion coefficients were computed from the lattice parameter data. The thermal expansion of HfTiO 4 is highly anisotropic. The expansivity along 'a' axis is large; as compared to the expansivity along 'b' axis which is negative below 1073 K. The percentage linear thermal expansion in the temperature range 298-1973 K along a, b and c axis are 2.74, 0.901 and 1.49 respectively. Thermal expansion values obtained in the present study are in reasonable agreement with the existing thermal expansion data. (author)

Ion beam driven expansion of super-range multilayer plane targets

International Nuclear Information System (INIS)

Piriz, A.R.

1987-08-01

The expansion of a multilayer plane target driven by an ion beam which has a range shorter than the thickness of the slab is described by means of a simple analytic model. The effect of a two-layer structure is studied and criteria for the optimization of the kinetic energy of the unheated part of the slab, the payload, are set. (author). 14 refs, 3 figs

Fission gas retention and axial expansion of irradiated metallic fuel

International Nuclear Information System (INIS)

Fenske, G.R.; Emerson, J.E.; Savoie, F.E.; Johanson, E.W.

1986-05-01

Out-of-reactor experiments utilizing direct electrical heating and infrared heating techniques were performed on irradiated metallic fuel. The results indicate accelerated expansion can occur during thermal transients and that the accelerated expansion is driven by retained fission gases. The results also demonstrate gas retention and, hence, expansion behavior is a function of axial position within the pin

An analytic distribution function for a mass-less cored stellar system in a cuspy dark-matter halo

NARCIS (Netherlands)

Breddels, Maarten A.; Helmi, Amina

2013-01-01

We demonstrate the existence of a distribution function that can be used to represent spherical mass-less cored stellar systems having constant mildly tangential velocity anisotropy embedded in cuspy dark-matter halos. In particular, we derived analytically the functional form of the distribution

Symmetries and modelling functions for diffusion processes

International Nuclear Information System (INIS)

Nikitin, A G; Spichak, S V; Vedula, Yu S; Naumovets, A G

2009-01-01

A constructive approach to the theory of diffusion processes is proposed, which is based on application of both symmetry analysis and the method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error function expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment in experimental results obtained for surface diffusion of lithium on the molybdenum (1 1 2) surface precovered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems.

Advances in functional brain imaging technology and developmental neuro-psychology: their applications in the Jungian analytic domain.

Science.gov (United States)

Petchkovsky, Leon

2017-06-01

Analytical psychology shares with many other psychotherapies the important task of repairing the consequences of developmental trauma. The majority of analytic patients come from compromised early developmental backgrounds: they may have experienced neglect, abuse, or failures of empathic resonance from their carers. Functional brain imagery techniques including Quantitative Electroencephalogram (QEEG), and functional Magnetic Resonance Imagery (fMRI), allow us to track mental processes in ways beyond verbal reportage and introspection. This independent perspective is useful for developing new psychodynamic hypotheses, testing current ones, providing diagnostic markers, and monitoring treatment progress. Jung, with the Word Association Test, grasped these principles 100 years ago. Brain imaging techniques have contributed to powerful recent advances in our understanding of neurodevelopmental processes in the first three years of life. If adequate nurturance is compromised, a range of difficulties may emerge. This has important implications for how we understand and treat our psychotherapy clients. The paper provides an overview of functional brain imaging and advances in developmental neuropsychology, and looks at applications of some of these findings (including neurofeedback) in the Jungian psychotherapy domain. © 2017, The Society of Analytical Psychology.

Green function iterative solution of ground state wave function for Yukawa potential

International Nuclear Information System (INIS)

Zhang Zhao

2003-01-01

The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP

Application of system reliability analytical method, GO-FLOW

International Nuclear Information System (INIS)

Matsuoka, Takeshi; Fukuto, Junji; Mitomo, Nobuo; Miyazaki, Keiko; Matsukura, Hiroshi; Kobayashi, Michiyuki

1999-01-01

The Ship Research Institute proceed a developmental study on GO-FLOW method with various advancing functionalities for the system reliability analysis method occupying main parts of PSA (Probabilistic Safety Assessment). Here was attempted to intend to upgrade functionality of the GO-FLOW method, to develop an analytical function integrated with dynamic behavior analytical function, physical behavior and probable subject transfer, and to prepare a main accident sequence picking-out function. In 1997 fiscal year, in dynamic event-tree analytical system, an analytical function was developed by adding dependency between headings. In simulation analytical function of the accident sequence, main accident sequence of MRX for improved ship propulsion reactor became possible to be covered perfectly. And, input data for analysis was prepared with a function capable easily to set by an analysis operator. (G.K.)

Analytic properties of finite-temperature self-energies

International Nuclear Information System (INIS)

Weldon, H. Arthur

2002-01-01

The analytic properties in the energy variable k 0 of finite-temperature self-energies are investigated. A typical branch cut results from n particles being emitted into the heat bath and n ' being absorbed from the heat bath. There are three main results: First, in addition to the branch points at which the cuts terminate, there are also branch points attached to the cuts along their length. Second, branch points at k 0 =±k are ubiquitous and for massive particles they are essential singularities. Third, in a perturbative expansion using free particle propagators or in a resummed expansion in which the propagator pole occurs at a real energy, the self-energy will have a branch point at the pole location

Analytic derivatives for perturbatively corrected ''double hybrid'' density functionals: Theory, implementation, and applications

International Nuclear Information System (INIS)

Neese, Frank; Schwabe, Tobias; Grimme, Stefan

2007-01-01

A recently proposed new family of density functionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new ''double hybrid'' functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with ∼500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2

Analytic and numerical studies of Scyllac equilibrium

International Nuclear Information System (INIS)

Barnes, D.C.; Brackbill, J.U.; Dagazian, R.Y.; Freidberg, J.P.; Schneider, W.; Betancourt, O.; Garabedian, P.

1976-01-01

The results of both numerical and analytic studies of the Scyllac equilibria are presented. Analytic expansions are used to derive equilibrium equations appropriate to noncircular cross sections, and compute the stellarator fields which produce toroidal force balance. Numerical algorithms are used to solve both the equilibrium equations and the full system of dynamical equations in three dimensions. Numerical equilibria are found for both l = 1,0 and l= 1,2 systems. It is found that the stellarator fields which produce equilibria in the l = 1.0 system are larger for diffuse than for sharp boundary plasma profiles, and that the stability of the equilibria depends strongly on the harmonic content of the stellarator fields

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Panayiotis D. Siafarikas

2004-07-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the ℓp1 and ℓp2 spaces, p∈ℕ, p≥1. The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

Analytical representation of time correlation functions and application to relaxation problems; Representation analytique des fonctions de correlation temporelle et application a des problemes de relaxation

Energy Technology Data Exchange (ETDEWEB)

Dupuis, M [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires, departement de physico-chimie, services des isotopes stables

1971-07-01

Two analytical representations of the Laplace transform of the time autocorrelation of a dynamical variable, namely the moment expansion and Mori's continued fraction expansion, are investigated from the point of view of structure and convergence properties, and the relation between them is established. The general theory is applied first to a dynamical model exactly solvable, the isotopic impurity in a linear chain of coupled harmonic oscillators, and then to two stochastic models recently introduced by Gordon for the rotational diffusion of molecules. In the latter case, the continued fraction expansion yields simple analytical expressions for the infrared absorption band shapes, showing that these models contain all the features of observed shapes in compressed gases, liquids and solutions. (author) [French] Deux representations analytiques de la transformee de Laplace de la fonction d'autocorrelation temporelle d'une variable dynamique, le developpement en moments et le developpement en fraction continue recemment introduit par Mori, sont etudiees du point de vue de leurs proprietes de structure et de convergence, en meme temps que la relation qui existe entre elles est etablie. La theorie generale est appliquee, d'une part, a un modele dynamique exactement soluble, celui d'une particule isotopique dans une chaine lineaire d'oscillateurs harmoniques couples, et, d'autre part, a deux modeles stochastiques recemment proposes par Gordon pour la diffusion rotationnelle des molecules. Dans ce dernier cas, la voie de la fraction continue fournit des expressions analytiques simples pour les formes de bande d'absorption infrarouge, montrant que ces modeles possedent les caracteristiques des formes observees dans les gaz comprimes, les liquides ou les solutions. (auteur)

Cut contribution to momentum autocorrelation function of an impurity in a classical diatomic chain

Science.gov (United States)

Yu, Ming B.

2018-02-01

A classic diatomic chain with a mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity is a sum of contributions from two pairs of resonant poles and three branch cuts. The former results in cosine function and the latter in acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are integrals of elliptic functions in the real axis for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral is carried out for the calculation of optical branch: ∫0 ϕ dθ/√((1 - r 1 2 sin2 θ)(1 - r 2 2 sin2 θ)) = igsn -1 (sin ϕ) ( r 2 2 > r 1 2 > 1, g is a constant).

Anisotropic thermal expansion in flexible materials

Science.gov (United States)

Romao, Carl P.

2017-10-01

A definition of the Grüneisen parameters for anisotropic materials is derived based on the response of phonon frequencies to uniaxial stress perturbations. This Grüneisen model relates the thermal expansion in a given direction (αi i) to one element of the elastic compliance tensor, which corresponds to the Young's modulus in that direction (Yi i). The model is tested through ab initio prediction of thermal expansion in zinc, graphite, and calcite using density functional perturbation theory, indicating that it could lead to increased accuracy for structurally complex systems. The direct dependence of αi i on Yi i suggests that materials which are flexible along their principal axes but rigid in other directions will generally display both positive and negative thermal expansion.

Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method

Directory of Open Access Journals (Sweden)

Grzymkowski R.

2013-03-01

Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method

Directory of Open Access Journals (Sweden)

R. Grzymkowski

2013-01-01

Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

Self-force calculations with matched expansions and quasinormal mode sums

International Nuclear Information System (INIS)

Casals, Marc; Dolan, Sam; Ottewill, Adrian C.; Wardell, Barry

2009-01-01

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of 'matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the 'quasilocal' and 'distant past' regimes, and which may be matched together within the normal neighborhood. We perform our calculation in a static region of the spherically symmetric Nariai spacetime (dS 2 xS 2 ), in which scalar-field perturbations are governed by a radial equation with a Poeschl-Teller potential (frequently used as an approximation to the Schwarzschild radial potential) whose solutions are known in closed form. The key new ingredients in our study are (i) very high order quasilocal expansions and (ii) expansion of the distant past Green function in quasinormal modes. In combination, these tools enable a detailed study of the properties of the scalar-field Green function. We demonstrate that the Green function is singular whenever x and x ' are connected by a null geodesic, and apply asymptotic methods to determine the structure of the Green function near the null wave front. We show that the singular part of the Green function undergoes a transition each time the null wave front passes through a caustic point, following a repeating fourfold sequence δ(σ), 1/πσ, -δ(σ), -1/πσ, etc., where σ is Synge's world function. The matched-expansion method provides insight into the nonlocal properties of the self-force. We show that the self-force generated by the segment of the worldline lying outside the normal neighborhood is not negligible. We apply the matched-expansion method to compute the scalar self-force acting on

Residual stresses associated with the hydraulic expansion of steam generator tubing into tubesheets

International Nuclear Information System (INIS)

Middlebrooks, W.B.; Harrod, D.L.; Gold, R.E.

1993-01-01

Various methods are being used to expand heat transfer tubes into the thick tubesheets of nuclear steam generators. The residual stresses in the as-expanded tubes and methods for reducing these stresses are important because of the role which residual stresses play in stress corrosion cracking and stress assisted corrosion of the tubing. Of the various expansion processes, the hydraulic expansion process is most amenable to analytical study. This paper presents results on the residual stresses and strains in hydraulically expanded tubes and the tubesheet as computed by two different finite element codes with three different finite element models and by a theoretical incremental analysis method. The calculations include a sensitivity analysis to assess the effects of the expansion variables and the effect of stress relief heat treatments. (orig.)

On the stress-free lattice expansion of porous cordierite

International Nuclear Information System (INIS)

Bruno, Giovanni; Efremov, Alexander M.; Clausen, Bjorn; Balagurov, Anatoly M.; Simkin, Valeriy N.; Wheaton, Bryan R.; Webb, James E.; Brown, Donald W.

2010-01-01

An extensive investigation of the lattice expansion (up to 1200 deg. C) of porous synthetic cordierite (obtained by firing a mixture of talc, clay, alumina and silica) was carried out using time-of-flight neutron diffraction at LANSCE, Los Alamos, NM, USA and FNLP, Dubna, Russia. An extruded rod and several powders, with different particle size (dispersity), were studied, with the aim of monitoring the variation of the (lattice) micro-strain as a function of temperature and its influence on the microscopic and macroscopic thermal expansion. Results show a different expansion of the a- and b-axes of the orthorhombic cell (in the rod above 800 deg. C). While the finest powder seems to contract more along the c-axis, thus hinting at the presence of smaller stress, the integral peak width increases as a function of temperature in the intermediate range (300-700 deg. C). This could be explained by the integrity factor modeling in terms of micro-cracking. In polycrystalline cordierite, the model implies tension along the a- and b-axes (positive thermal expansion) accompanied by compression along the c-axis (negative thermal expansion) and a stress release upon cooling, via a thermal micro-cracking mechanism. The calculations of the cordierite macroscopic thermal expansion having as input crystal axial expansions assumed to be stress-free allowed us to conclude that even a fine powder (5 μm particle size) cannot be considered completely stress-free. This conclusion is supported by microstructural observations.

Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

Energy Technology Data Exchange (ETDEWEB)

Souza Batista, C.L. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Dingping Li [Perugia Univ. (Italy). Dipt. di Fisica

1996-07-01

We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory, are physically equivalent. (author). 31 refs., 2 tabs.

Dimensional expansion for the Ising limit of quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Boettcher, S.

1993-01-01

A recently proposed technique, called dimensional expansion, uses the space-time dimension D as an expansion parameter to extract nonperturbative results in quantum field theory. Here we apply dimensional-expansion methods to examine the Ising limit of a self-interacting scalar field theory. We compute the first few coefficients in the dimensional expansion of γ 2n , the renormalized 2n-point Green's function at zero momentum, for n=2, 3, 4, and 5. Because the exact results for γ 2n are known at D=1 we can compare the predictions of the dimensional expansion at this value of D. We find typical accuracies of less than 5%. The radius of convergence of the dimensional expansion for γ 2n appears to be 2n/(n-1). As a function of the space-time dimension D, γ 2n appears to rise monotonically with increasing D and we conjecture that it becomes infinite at D=2n/(n-1). We presume that for values of D greater than this critical value γ 2n vanishes identically because the corresponding φ 2n scalar quantum field theory is free for D>2n/(n-1)

Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn Sham density functional theory

International Nuclear Information System (INIS)

Gonis, Antonios; Daene, Markus W.; Nicholson, Don M.; Stocks, George Malcolm

2012-01-01

We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.

Analytical expression for the nonsinglet structure functions at small x in the double logarithmic approximation

International Nuclear Information System (INIS)

Lublinsky, Michael

2004-01-01

A simple analytic expression for the nonsinglet structure function f NS is given. The expression is derived from the result of Ermolaev, Manaenkov, and Ryskin obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD

Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD.

Science.gov (United States)

Dixon, Lance J; Luo, Ming-Xing; Shtabovenko, Vladyslav; Yang, Tong-Zhi; Zhu, Hua Xing

2018-03-09

The energy-energy correlation (EEC) between two detectors in e^{+}e^{-} annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions

Science.gov (United States)

Nguyen, Thuong T.; Székely, Eszter; Imbalzano, Giulio; Behler, Jörg; Csányi, Gábor; Ceriotti, Michele; Götz, Andreas W.; Paesani, Francesco

2018-06-01

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.

Renormalizations and operator expansion in sigma model

International Nuclear Information System (INIS)

Terentyev, M.V.

1988-01-01

The operator expansion (OPE) is studied for the Green function at x 2 → 0 (n(x) is the dynamical field ofσ-model) in the framework of the two-dimensional σ-model with the O(N) symmetry group at large N. As a preliminary step we formulate the renormalization scheme which permits introduction of an arbitrary intermediate scale μ 2 in the framework of 1/N expansion and discuss factorization (separation) of small (p μ) momentum region. It is shown that definition of composite local operators and coefficient functions figuring in OPE is unambiguous only in the leading order in 1/N expansion when dominant are the solutions with extremum of action. Corrections of order f(μ 2 )/N (here f(μ 2 ) is the effective interaction constant at the point μ 2 ) in composite operators and coefficient functions essentially depend on factorization method of high and low momentum regions. It is shown also that contributions to the power corrections of order m 2 x 2 f(μ 2 )/N in the Green function (here m is the dynamical mass-scale factor in σ-model) arise simultaneously from two sources: from the mean vacuum value of the composite operator n ∂ 2 n and from the hard particle contributions in the coefficient function of unite operator. Due to the analogy between σ-model and QCD the obtained result indicates theoretical limitations to the sum rule method in QCD. (author)

An analytic solution of the static problem of inclined risers conveying fluid

KAUST Repository

Alfosail, Feras; Nayfeh, Ali H.; Younis, Mohammad I.

2016-01-01

We use the method of matched asymptotic expansion to develop an analytic solution to the static problem of clamped–clamped inclined risers conveying fluid. The inclined riser is modeled as an Euler–Bernoulli beam taking into account its self

Scale breaking parton fragmentation functions, analytical parametrizations and comparison with charged multiplicities in e+e- annihilation

International Nuclear Information System (INIS)

Perlt, H.

1980-01-01

Scale breaking quark and gluon fragmentation functions obtained by solving numerically Altarelli-Parisi type equations are presented. Analytical parametrizations are given for the fragmentation of u and d quarks into pions. The calculated Q 2 dependent fragmentation functions are compared with experimental data. With these scale breaking fragmentation functions the average charged multiplicity is calculated in e + e - annihilation, which rises with energy more than logarithmically and is in good agreement with experiment. (author)

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.)

Analytic description of four-wave mixing in silicon-on-insulator waveguides

DEFF Research Database (Denmark)

Friis, Søren Michael Mørk; Koefoed, Jacob Gade; Guo, Kai

2018-01-01

and becomes a nonlinear differential equation that we solve analytically without further approximations. The signal and idler equations have no known solutions for arbitrary pump power evolution, but we calculate approximate field expressions based on a Magnus expansion, which has been used to study time...

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

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2013-01-01

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

An algebraic approach to the analytic bootstrap

Energy Technology Data Exchange (ETDEWEB)

Alday, Luis F. [Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Zhiboedov, Alexander [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA 02138 (United States)

2017-04-27

We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. We analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O(N) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O(N) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents.

Generalized 3D Zernike functions for analytic construction of band-limited line-detecting wavelets

OpenAIRE

Janssen, Augustus J. E. M.

2015-01-01

We consider 3D versions of the Zernike polynomials that are commonly used in 2D in optics and lithography. We generalize the 3D Zernike polynomials to functions that vanish to a prescribed degree $\\alpha\\geq0$ at the rim of their supporting ball $\\rho\\leq1$. The analytic theory of the 3D generalized Zernike functions is developed, with attention for computational results for their Fourier transform, Funk and Radon transform, and scaling operations. The Fourier transform of generalized 3D Zern...

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

Directory of Open Access Journals (Sweden)

Sun Huan

2016-01-01

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

An alternative analytical formulation for the Voigt function applied to resonant effects in nuclear processes

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Goncalves, Alessandro da C; Martinez, Aquilino S.

2011-01-01

The Voigt function H(a,v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.

An alternative analytical formulation for the Voigt function applied to resonant effects in nuclear processes

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P., E-mail: dpalmaster@gmail.com [CNEN-Comissao Nacional de Energia Nuclear, 22290-901, Rio de Janeiro (Brazil); Goncalves, Alessandro da C; Martinez, Aquilino S. [COPPE/UFRJ-Programa de Engenharia Nuclear, 21941-972, Rio de Janeiro (Brazil)

2011-10-21

The Voigt function H(a,v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.

Thin foil expansion into a vacuum

International Nuclear Information System (INIS)

Mora, P.

2005-01-01

Plasma expansion into a vacuum is an old problem which has been renewed recently in various contexts: expansion of ultra-cold plasmas, cluster expansion, of dust grains, expansion of thin foils. In this presentation I will first discuss the physics of the expansion of a thin foil irradiated by an ultra-short ultra-intense laser pulse. The expansion results in the formation of high energy ions. For an infinitely steep plasma-vacuum interface the fastest ions are located in the outer part of the expansion and their velocity is given by ν m ax∼ 2 C s (In ω p it) where c s (Zk B T e /m i )''1/2 is the ion-acoustic velocity ω p i=(n e 0Ze''2/m i e 0 )''1/2 is the ion plasma frequency, n e 0 is the electron density in the unperturbed plasma, Z is the ion charge number. In the above expression, t is either the pulse duration or the effective acceleration time (in particular t∼L/2c s , where L is the width of the foil, when the electron cooling is taken into account). A salient characteristic of the expansion is the occurrence of a double layer structure and a peak of the accelerating electric field at the ion front. I will explain the origin of the peak and predict its temporal behavior. This peak has been diagnosed in recent experiments. I will also discuss the effect of a 2-temperatures electron distribution function on the expansion, showing the dominant role of the hot electron component. Finally I will discuss the occurrence of ion spikes in the expansion when the initial density profile is smooth. The ion spike is due to a wave breaking which cannot be handled in a satisfactory way by a fluid code and requires a kinetic description. A. simple collisionless particle code has been used to treat the evolution of the spike after the wave breaking and the results will be shown. (Author)

Expansion and Functional Divergence of AP2 Group Genes in Spermatophytes Determined by Molecular Evolution and Arabidopsis Mutant Analysis

Directory of Open Access Journals (Sweden)

Pengkai Wang

2016-09-01

Full Text Available The APETALA2 (AP2 genes represent the AP2 group within a large group of DNA-binding proteins called AP2/EREBP. The AP2 gene is functional and necessary for flower development, stem cell maintenance, and seed development, whereas the other members of AP2 group redundantly affect flowering time. Here we study the phylogeny of AP2 group genes in spermatophytes. Spermatophyte AP2 group genes can be classified into AP2 and TOE types, six clades, and we found that the AP2 group homologs in gymnosperms belong to the AP2 type, whereas TOE types are absent, which indicates the AP2 type gene are more ancient and TOE type was split out of AP2 type and losing the major function. In Brassicaceae, the expansion of AP2 and TOE type lead to the gene number of AP2 group were up to six. Purifying selection appears to have been the primary driving force of spermatophyte AP2 group evolution, although positive selection occurred in the AP2 clade. The transition from exon to intron of AtAP2 in Arabidopsis mutant leads to the loss of gene function and the same situation was found in AtTOE2. Combining this evolutionary analysis and published research, the results suggest that typical AP2 group genes may first appear in gymnosperms and diverged in angiosperms, following expansion of group members and functional differentiation. In angiosperms, AP2 genes (AP2 clade inherited key functions from ancestors and other genes of AP2 group lost most function but just remained flowering time controlling in gene formation. In this study, the phylogenies of AP2 group genes in spermatophytes was analyzed, which supported the evidence for the research of gene functional evolution of AP2 group.

An accurate analytic description of neutrino oscillations in matter

Science.gov (United States)

Akhmedov, E. Kh.; Niro, Viviana

2008-12-01

A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.

Generalized 3D Zernike functions for analytic construction of band-limited line-detecting wavelets

NARCIS (Netherlands)

Janssen, A.J.E.M.

2015-01-01

We consider 3D versions of the Zernike polynomials that are commonly used in 2D in optics and lithography. We generalize the 3D Zernike polynomials to functions that vanish to a prescribed degree $\\alpha\\geq0$ at the rim of their supporting ball $\\rho\\leq1$. The analytic theory of the 3D generalized

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

International Nuclear Information System (INIS)

Wei Gaofeng; Dong Shihai

2008-01-01

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential

Analytical calculation of the vibrator-rotor transition in the sdg interacting boson model

International Nuclear Information System (INIS)

Wang Baolin

1992-01-01

Analytical calculation of the vibrator-rotor transition is given by utilizing the 1/N expansion technique in the sdg IBM. The phase transition of low-lying energy spectrum and E2 transition for Sm isotopes are calculated

Operator expansion in σ-model

International Nuclear Information System (INIS)

Terent'ev, M.V.

1986-01-01

The operator expansion is studied in two dimensional σ-model with O(N) symmetry group at large values of N for the Green function at x 2 → 0 (Here n(x) is the dynamical field of σ-model). As a preliminary step the renormalization scheme is formulated in framework of I/N expansion where the intermediate scale μ 2 is introdused and regions of large (p > μ) and small (p 2 )/N in composite operators (here f(μ 2 ) is the effective coupling constant at the point μ 2 ) and the corrections of order of m 2 x 2 f(μ 2 )/N in the coefficient functions (here m is the dynamical mass-scale factor of σ-model) decisively depend on the recipe of factorization of small and large momenta regions. Due to the analogy between σ-model and quantum chromodynamics (QCD) the obtained result indicates the theoretical limitations to the accuracy of sum rule method in QCD

First Steps in FAP: Experiences of Beginning Functional Analytic Psychotherapy Therapist with an Obsessive-Compulsive Personality Disorder Client

Science.gov (United States)

Manduchi, Katia; Schoendorff, Benjamin

2012-01-01

Practicing Functional Analytic Psychotherapy (FAP) for the first time can seem daunting to therapists. Establishing a deep and intense therapeutic relationship, identifying FAP's therapeutic targets of clinically relevant behaviors, and using contingent reinforcement to help clients emit more functional behavior in the therapeutic relationship all…

Quasineutral plasma expansion into infinite vacuum as a model for parallel ELM transport

Science.gov (United States)

Moulton, D.; Ghendrih, Ph; Fundamenski, W.; Manfredi, G.; Tskhakaya, D.

2013-08-01

An analytic solution for the expansion of a plasma into vacuum is assessed for its relevance to the parallel transport of edge localized mode (ELM) filaments along field lines. This solution solves the 1D1V Vlasov-Poisson equations for the adiabatic (instantaneous source), collisionless expansion of a Gaussian plasma bunch into an infinite space in the quasineutral limit. The quasineutral assumption is found to hold as long as λD0/σ0 ≲ 0.01 (where λD0 is the initial Debye length at peak density and σ0 is the parallel length of the Gaussian filament), a condition that is physically realistic. The inclusion of a boundary at x = L and consequent formation of a target sheath is found to have a negligible effect when L/σ0 ≳ 5, a condition that is physically plausible. Under the same condition, the target flux densities predicted by the analytic solution are well approximated by the ‘free-streaming’ equations used in previous experimental studies, strengthening the notion that these simple equations are physically reasonable. Importantly, the analytic solution predicts a zero heat flux density so that a fluid approach to the problem can be used equally well, at least when the source is instantaneous. It is found that, even for JET-like pedestal parameters, collisions can affect the expansion dynamics via electron temperature isotropization, although this is probably a secondary effect. Finally, the effect of a finite duration, τsrc, for the plasma source is investigated. As is found for an instantaneous source, when L/σ0 ≳ 5 the presence of a target sheath has a negligible effect, at least up to the explored range of τsrc = L/cs (where cs is the sound speed at the initial temperature).

On New Families of Integrals in Analytical Studies of Superconductors within the Conformal Transformation Method

Directory of Open Access Journals (Sweden)

Ryszard Gonczarek

2015-01-01

Full Text Available We show that, by applying the conformal transformation method, strongly correlated superconducting systems can be discussed in terms of the Fermi liquid with a variable density of states function. Within this approach, it is possible to formulate and carry out purely analytical study based on a set of fundamental equations. After presenting the mathematical structure of the s-wave superconducting gap and other quantitative characteristics of superconductors, we evaluate and discuss integrals inherent in fundamental equations describing superconducting systems. The results presented here extend the approach formulated by Abrikosov and Maki, which was restricted to the first-order expansion. A few infinite families of integrals are derived and allow us to express the fundamental equations by means of analytical formulas. They can be then exploited in order to find quantitative characteristics of superconducting systems by the method of successive approximations. We show that the results can be applied in studies of high-Tc superconductors and other superconducting materials of the new generation.

Mass spectra and wave functions of meson systems and the covariant oscillator quark model as an expansion basis

International Nuclear Information System (INIS)

Oda, Ryuichi; Ishida, Shin; Wada, Hiroaki; Yamada, Kenji; Sekiguchi, Motoo

1999-01-01

We examine mass spectra and wave functions of the nn-bar, cc-bar and bb-bar meson systems within the framework of the covariant oscillator quark model with the boosted LS-coupling scheme. We solve nonperturbatively an eigenvalue problem for the squared-mass operator, which incorporates the four-dimensional color-Coulomb-type interaction, by taking a set of covariant oscillator wave functions as an expansion basis. We obtain mass spectra of these meson systems, which reproduce quite well their experimental behavior. The resultant manifestly covariant wave functions, which are applicable to analyses of various reaction phenomena, are given. Our results seem to suggest that the present model may be considered effectively as a covariant version of the nonrelativistic linear-plus-Coulomb potential quark model. (author)

Heat kernel expansion in the background field formalism

CERN Document Server

Barvinsky, Andrei

2015-01-01

Heat kernel expansion and background field formalism represent the combination of two calculational methods within the functional approach to quantum field theory. This approach implies construction of generating functionals for matrix elements and expectation values of physical observables. These are functionals of arbitrary external sources or the mean field of a generic configuration -- the background field. Exact calculation of quantum effects on a generic background is impossible. However, a special integral (proper time) representation for the Green's function of the wave operator -- the propagator of the theory -- and its expansion in the ultraviolet and infrared limits of respectively short and late proper time parameter allow one to construct approximations which are valid on generic background fields. Current progress of quantum field theory, its renormalization properties, model building in unification of fundamental physical interactions and QFT applications in high energy physics, gravitation and...