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
Series expansions without diagrams
International Nuclear Information System (INIS)
Bhanot, G.; Creutz, M.; Horvath, I.; Lacki, J.; Weckel, J.
1994-01-01
We discuss the use of recursive enumeration schemes to obtain low- and high-temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagrammatic approaches and is easily generalizable. We illustrate the approach using Ising and Potts models. We present low-temperature series results in up to five dimensions and high-temperature series in three dimensions. The method is general and can be applied to any discrete model
International Nuclear Information System (INIS)
Doha, E H; Ahmed, H M
2005-01-01
Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives D p q f(x), and for the moments x l D p q f(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described
A Power Series Expansion and Its Applications
Chen, Hongwei
2006-01-01
Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.
Thermal expansion coefficient determination by CBED
International Nuclear Information System (INIS)
Angelini, P.; Bentley, J.
1984-01-01
The present application of CBED involves measurements of thermal-expansion coefficients by measurement of changes in HOLZ line positions as a function of temperature. Previous work on this subject was performed on Si at a constant accelerating voltage of 100 kV between about 90 and 600 K. Diffraction patterns were recorded and line shifts correlated to lattice parameter changes. Differences were noted between values determined by CBED and accepted thermal expansion values. Significant HOLZ line interactions and splitting occurring in the (111) patterns were noted to contribute to the differences. Preliminary measurements have been made on Al, Al 2 O 3 , and single-crystal tau (Ni/sub 20.3/Ti/sub 2.7/B 6 ). An example of changes in HOLZ lines present in (114) patterns for Al are shown and the effect of temperature on the position of lines in the pattern illustrated
Generalized heat kernel coefficients for a new asymptotic expansion
International Nuclear Information System (INIS)
Osipov, Alexander A.; Hiller, Brigitte
2003-01-01
The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified
Thermal linear expansion coefficient of structural graphites
International Nuclear Information System (INIS)
Virgil'ev, Yu.S.
1995-01-01
The data now available on radiation induced changes of linear thermal expansion coefficients (CTE) for native structural carbon materials (SCM) irradiated with high fluences are summarized. For different types of native and foreign SCM dose dependences of CTE changes in the temperature range of 300...1600 K and at fluences up to (2...3)x10 22 n/cm 2 (E>0.18 meV) are compared. On the base of this comparison factors defined the CTE changes under neutron irradiation are revealed and the explanation of observed phenomena is offered. Large number of the factors revealed does not allowed to calculate CTE radiation induced changes. 39 refs.; 16 figs.; 5 tabs
Series expansion of the modified Einstein Procedure
Seema Chandrakant Shah-Fairbank
2009-01-01
This study examines calculating total sediment discharge based on the Modified Einstein Procedure (MEP). A new procedure based on the Series Expansion of the Modified Einstein Procedure (SEMEP) has been developed. This procedure contains four main modifications to MEP. First, SEMEP solves the Einstein integrals quickly and accurately based on a series expansion. Next,...
Energy coefficients for a propeller series
DEFF Research Database (Denmark)
Olsen, Anders Smærup
2004-01-01
The efficiency for a propeller is calculated by energy coefficients. These coefficients are related to four types of losses, i.e. the axial, the rotational, the frictional, and the finite blade number loss, and one gain, i.e. the axial gain. The energy coefficients are derived by use...... of the potential theory with the propeller modelled as an actuator disk. The efficiency based on the energy coefficients is calculated for a propeller series. The results show a good agreement between the efficiency based on the energy coefficients and the efficiency obtained by a vortex-lattice method....
Seal assembly for materials with different coefficients of thermal expansion
Minford, Eric [Laurys Station, PA
2009-09-01
Seal assembly comprising (a) two or more seal elements, each element having having a coefficient of thermal expansion; and (b) a clamping element having a first segment, a second segment, and a connecting segment between and attached to the first and second segments, wherein the two or more seal elements are disposed between the first and second segments of the clamping element. The connecting segment has a central portion extending between the first segment of the clamping element and the second segment of the clamping element, and the connecting segment is made of a material having a coefficient of thermal expansion. The coefficient of thermal expansion of the material of the connecting segment is intermediate the largest and smallest of the coefficients of thermal expansion of the materials of the two or more seal elements.
Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
Burmistrov, I.S.; Gornyi, I.V.; Kachorovskii, V.Y.; Katsnelson, M.I.; Mirlin, A.D.
2016-01-01
We explore thermodynamics of a quantum membrane, with a particular application to suspended graphene membrane and with a particular focus on the thermal expansion coefficient. We show that an interplay between quantum and classical anharmonicity-controlled fluctuations leads to unusual elastic
Operator product expansion on the lattice: analytic Wilson coefficients
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.
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
Linear thermal expansion coefficient measurement technology in hot cell
International Nuclear Information System (INIS)
Park, Dae Gyu; Choo, Yong Sun; Ahn, Sang Bok; Hong, Kwon Pyo; Lee, K. S.
1998-06-01
To establish linear thermal expansion coefficient measurement technology in hot cell, we reviewed and evaluated various measuring technology by paper and these were compared with the data produced with pre-installed dilatometer in hot cell. Detailed contents are as follows; - The theory of test. - Review of characteristics for various measurement technology and compatibility with hot cell. - Review of standard testing regulations(ASTM). - System calibration of pre-installed dilatometer. - Performance test of pre-installed dilatometer. (author). 12 refs., 15 tabs., 8 figs
The loop expansion as a divergent-power-series expansion
International Nuclear Information System (INIS)
Murai, N.
1981-01-01
The loop expansion should be divergent, possibly an asymptotic one, in the Euclidean path integral formulation. This consideration is important in applications of the symmetric and mass-independent renormalization. The [1,1] Pade approximant is calculated in a PHI 4 model. Its classical vacua may be not truely stable for nonzero coupling constant. (author)
Expansion of Sobolev functions in series in Laguerre polynomials
International Nuclear Information System (INIS)
Selyakov, K.I.
1985-01-01
The solution of the integral equation for the Sobolev functions is represented in the form of series in Laguerre polynomials. The coefficients of these series are simultaneously the coefficients of the power series for the Ambartsumyan-Chandrasekhar H functions. Infinite systems of linear algebraic equations with Toeplitz matrices are given for the coefficients of the series. Numerical results and approximate expressions are given for the case of isotropic scattering
Zero and low coefficient of thermal expansion polycrystalline oxides
International Nuclear Information System (INIS)
Skaggs, S.R.
1977-09-01
Polycrystalline oxide systems with zero to low coefficient of thermal expansion (CTE) investigated by the author include hafnia-titania and hafnia. The CTE for 30 to 40 mol% TiO 2 in HfO 2 is less than or equal to 1 x 10 -6 / 0 C, while for other compositions in the range 25 to 60 mol% it is approximately 4 x 10 -6 / 0 C. An investigation of the CTE of 99.999% HfO 2 yielded a value of 4.6 x 10 -6 / 0 C from room temperature to 1000 0 C. Correlation with data on HfO 2 by other investigators shows a definite relationship between the CTE and the amount of ZrO 2 present. Data are listed for comparison of the CTE of several other polycrystalline oxides investigated by Holcombe at Oak Ridge
Zero and low coefficient of thermal expansion polycrystalline oxides
International Nuclear Information System (INIS)
Skaggs, S.R.
1977-01-01
Polycrystalline oxide systems with zero to low coefficient of thermal expansion (CTE) investigated by the author include hafnia-titania and hafnia. The CTE for 30 to 40 mol percent TiO 2 in HfO 2 is less than or equal to 1 x 10 -6 / 0 C, while for other compositions in the range 25 to 60 mol percent approximately 4 x 10 -6 / 0 C. An investigation of the CTE of 99.999 percent HfO 2 yielded a value of 4.6 x 10 -6 / 0 C from room temperature to 1000 0 C. Correlation with data on HfO 2 by other investigators shows a definite relationship between the CTE and the amount of ZrO 2 present. Data are listed for comparison of the CTE of several other polycrystalline oxides investigated by Holcombe at Oak Ridge
Effect of rolling motion on the expansion and contraction loss coefficients
International Nuclear Information System (INIS)
Yan, B.H.; Gu, H.Y.
2013-01-01
Highlights: ► The expansion and contraction loss coefficients in rolling motion are analyzed. ► Effects of rolling motion on the expansion and contraction loss coefficients are different. ► The spanwise and transverse additional forces contribute slightly to the local loss. ► The oscillations of loss coefficients increase as the strengthening of rolling motion. - Abstract: The sudden expansion and sudden contraction loss coefficients in rolling motion are investigated with CFD code FLUENT. The calculation results are validated with experimental and theoretical results in steady state. The effects of rolling motion on the expansion and contraction loss coefficients are different. The effects of spanwise and transverse additional forces on the expansion and contraction loss coefficients are weak. The effect of velocity oscillation on the contraction loss coefficient is more significant than that on the expansion loss coefficient. The oscillation of local loss coefficient also becomes more and more irregular as the strengthening of rolling motion
Molecular dynamics study of the thermal expansion coefficient of silicon
Energy Technology Data Exchange (ETDEWEB)
Nejat Pishkenari, Hossein, E-mail: nejat@sharif.edu; Mohagheghian, Erfan; Rasouli, Ali
2016-12-16
Due to the growing applications of silicon in nano-scale systems, a molecular dynamics approach is employed to investigate thermal properties of silicon. Since simulation results rely upon interatomic potentials, thermal expansion coefficient (TEC) and lattice constant of bulk silicon have been obtained using different potentials (SW, Tersoff, MEAM, and EDIP) and results indicate that SW has a better agreement with the experimental observations. To investigate effect of size on TEC of silicon nanowires, further simulations are performed using SW potential. To this end, silicon nanowires of different sizes are examined and their TEC is calculated by averaging in different directions ([100], [110], [111], and [112]) and various temperatures. Results show that as the size increases, due to the decrease of the surface effects, TEC approaches its bulk value. - Highlights: • MD simulations of TEC and lattice constant of bulk silicon. • Effects of four potentials on the results. • Comparison to experimental data. • Investigating size effect on TEC of silicon nanowires.
Growth And Export Expansion In Mauritius - A Time Series Analysis ...
African Journals Online (AJOL)
Growth And Export Expansion In Mauritius - A Time Series Analysis. ... RV Sannassee, R Pearce ... Using Granger Causality tests, the short-run analysis results revealed that there is significant reciprocal causality between real export earnings ...
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
Off-diagonal series expansion for quantum partition functions
Hen, Itay
2018-05-01
We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.
Modulated Hermite series expansions and the time-bandwidth product
Brinker, den A.C.; Sarroukh, B.E.
2000-01-01
The harmonically modulated Hermite series constitute an orthonormal basis in the Hilbert space of square-integrable functions. This basis comprises three free parameters, namely a translation, a modulation, and a scale factor. In practical situations, we are interested in series expansions that are
Student understanding of Taylor series expansions in statistical mechanics
Directory of Open Access Journals (Sweden)
Trevor I. Smith
2013-08-01
Full Text Available One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.
Student understanding of Taylor series expansions in statistical mechanics
Smith, Trevor I.; Thompson, John R.; Mountcastle, Donald B.
2013-12-01
One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.
International Nuclear Information System (INIS)
Su, Guozhen; Chen, Liwei; Chen, Jincan
2014-01-01
Due to quantum size effects (QSEs), the isobaric thermal expansion coefficient and isothermal compressibility well defined for macroscopic systems are invalid for finite-size systems. The two parameters are redefined and calculated for a finite-size ideal Fermi gas confined in a rectangular container. It is found that the isobaric thermal expansion coefficient and isothermal compressibility are generally anisotropic, i.e., they are generally different in different directions. Moreover, it is found the thermal expansion coefficient may be negative in some directions under the condition that the pressures in all directions are kept constant. - Highlights: • Isobaric thermal expansion coefficient and isothermal compressibility are redefined. • The two parameters are calculated for a finite-size ideal Fermi gas. • The two parameters are generally anisotropic for a finite-size system. • Isobaric thermal expansion coefficient may be negative in some directions
International Nuclear Information System (INIS)
Kato, H.; Chen, H.-S.; Inoue, A.
2008-01-01
The thermal expansion coefficients of 13 metallic glasses were measured using a thermo-mechanical analyser. A unique correlation was found between the linear thermal expansion coefficient and the glass transition temperature-their product is nearly constant ∼8.24 x 10 -3 . If one assumes the Debye expression for thermal activation, the total linear thermal expansion up to glass transition temperature (T g ) is reduced to 6 x 10 -3 , nearly 25% of that at the fusion of pure metals
Lorig, Matthew; Sircar, Ronnie
2015-01-01
We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series approximation for this quantity. The zeroth-order approximation of the value function and optimal investment strategy correspond to those obtained by Merton (1969) when the risky...
Scheibler, Robin; Hurley, Paul
2012-03-01
We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.
High-temperature series expansions for random Potts models
Directory of Open Access Journals (Sweden)
M.Hellmund
2005-01-01
Full Text Available We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique, quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2 and 4-state Potts model in three dimensions up to the order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.
Laboratory measurements of the coefficient of thermal expansion of Olkiluoto drill core samples
International Nuclear Information System (INIS)
Aakesson, U.
2012-04-01
The coefficient of thermal expansion and the wet density has been determined on 22 specimens from the ONKALO drillholes ONK-PP167, ONK-PP199, ONK-PP224, ONK-PP225 and ONK-PP226, Olkiluoto, Finland. The coefficient of thermal expansion has been determined in the temperature interval 20-60 deg C. The results indicated that the thermal expansion was almost linear, and the coefficient of thermal expansion for the investigated specimens range between 3.2 and 14.4 x 10 -6 mm/mm deg C, and the wet density between 2,610 and 2,820 kg/m 3 . The granite pegmatite has slightly lower coefficient of thermal expansion and wet density than gneissic rocks. (orig.)
Series expansion in fractional calculus and fractional differential equations
Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao
2009-01-01
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...
Corsetti, James A; Green, William E; Ellis, Jonathan D; Schmidt, Greg R; Moore, Duncan T
2016-10-10
Characterizing the thermal properties of optical materials is necessary for understanding how to design an optical system for changing environmental conditions. A method is presented for simultaneously measuring both the linear coefficient of thermal expansion and the temperature-dependent refractive index coefficient of a sample interferometrically in air. Both the design and fabrication of the interferometer is presented as well as a discussion of the results of measuring both a steel and a CaF2 sample.
Corsetti, James A.; Green, William E.; Ellis, Jonathan D.; Schmidt, Greg R.; Moore, Duncan T.
2017-01-01
A system combining an interferometer with an environmental chamber for measuring both coefficient of thermal expansion (CTE) and temperature-dependent refractive index (dn/dT) simultaneously is presented. The operation and measurement results of this instrument are discussed.
Determination of coefficient of thermal expansion effects on Louisiana's PCC pavement design.
2011-12-01
With the development of the Mechanistic Empirical Pavement Design Guide (MEPDG) as a new pavement design tool, the : coefficient of thermal expansion (CTE) is now considered a more important design parameter in estimating pavement : performance inclu...
2009-01-01
PROBLEM: The coefficient of thermal expansion (CTE) is a fundamental property of construction : materials such as steel and concrete. Although the CTE of steel is a well-defined : constant, the CTE of concrete varies substantially with aggregate type...
2012-10-01
The Coefficient of Thermal Expansion (CTE) is an important parameter in Portland Cement Concrete (PCC) pavement analysis and design as it is directly proportional to the magnitude of temperature-related pavement deformations throughout the pavement s...
2011-12-01
The coefficient of thermal expansion (CTE) has been widely considered as a fundamental property of : Portland cement concrete (PCC) pavement but has never played an important role in the thickness design : procedure for PCC pavement until recently. I...
International Nuclear Information System (INIS)
Boyarskij, S.V.
1986-01-01
Experimental results are presented for internal friction and linear expansion coefficient at zirconium and cobalt in the temperature range from 440 K to the point of the phase transition of the first kind (1138 K for Zr and 706 for Co). Anomalous changes of the internal friction and linear expansion coefficient in the phase transition region are found. Theoretical considerations are given to explain the sharp decrease of the internal friction as temperature approaches the phase transition point
Defining chemical expansion: the choice of units for the stoichiometric expansion coefficient
DEFF Research Database (Denmark)
Marrocchelli, Dario; Chatzichristodoulou, Christodoulos; Bishop, Sean R.
2014-01-01
Chemical expansion refers to the spatial dilation of a material that occurs upon changes in its composition. When this dilation is caused by a gradual, iso-structural increase in the lattice parameter with composition, it is related to the composition change by the stoichiometric expansion coeffi...... are provided for changes in oxygen content in fluorite, perovskite, and Ruddlesden-Popper (K2NiF4) phase materials used in solid oxide fuel cells....
Mahler Measure Variations, Eisenstein Series and Instanton Expansions
Stienstra, J.
2007-01-01
This paper points at an intriguing inverse function relation with on the one hand the coefficients of the Eisenstein series in Rodriguez Villegas’ paper on “Modular Mahler Measures” and on the other hand the instanton numbers in papers on “Non-Critical Strings” by Klemm- Mayr-Vafa and
Recurrence formulas for evaluating expansion series of depletion functions
International Nuclear Information System (INIS)
Vukadin, Z.
1991-01-01
A high-accuracy analytical method for solving the depletion equations for chains of radioactive nuclides is based on the formulation of depletion functions. When all the arguments of the depletion function are too close to each other, series expansions of the depletion function have to be used. However, the high-accuracy series expressions for the depletion functions of high index become too complicated. Recursion relations are derived which enable an efficient high-accuracy evaluation of the depletion functions with high indices. (orig.) [de
Synchronization of complex chaotic systems in series expansion form
International Nuclear Information System (INIS)
Ge Zhengming; Yang Chenghsiung
2007-01-01
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy
Invar hardening under keeping of low values of temperature coefficient of linear expansion
International Nuclear Information System (INIS)
Bashnin, Yu.A.; Shiryaeva, A.N.; Omel'chenko, A.V.
1982-01-01
Complex invar alloying with chromium, zirconium and nitrogen is conducted for increasing hardness and assuring low values of the temperature coefficient of linear expansion. It is shown that alloying with nitride-forming elements-chromium, zirconium and the following high-temperature saturation under high pressure with nitrogen provides the invar hardening at assuring a low temperature coefficient of linear expansion. Saturation with nitrogen under 100 MPa pressure at 1050 deg C during 3 hours permits to prepare an invar containing up to 0.2% N 2 uniformly distributed over the whole cross section of samples with 4 mm diameter. Nitrogen in invar alloys alloyed with chromium and zirconium affects the Curie point similarly to carbon and nickel shifting it towards higher temperatures, it slightly changes the value of the temperature coefficient of linear expansion and provides linear character of thermal expansion dependence on temperature in the +100 deg C - -180 deg C range
International Nuclear Information System (INIS)
Volkov, A.G.; Kortov, S.V.; Povzner, A.A.
1996-01-01
The low temperature measurements of thermal coefficient of linear expansion of strong paramagnet FeSi are carried out. The results obtained are discussed with in the framework of spin-fluctuation theory. It is shown that electronic part of the thermal coefficient of linear expansion is negative in the range of temperatures lower that of the semiconductor-metal phase transition. In metal phase it becomes positive. This specific features of the thermal coefficient is explained by the spin-fluctuation renormalization of d-electronic states density
Thermal expansion coefficient measurement from electron diffraction of amorphous films in a TEM.
Hayashida, Misa; Cui, Kai; Malac, Marek; Egerton, Ray
2018-05-01
We measured the linear thermal expansion coefficients of amorphous 5-30 nm thick SiN and 17 nm thick Formvar/Carbon (F/C) films using electron diffraction in a transmission electron microscope. Positive thermal expansion coefficient (TEC) was observed in SiN but negative coefficients in the F/C films. In case of amorphous carbon (aC) films, we could not measure TEC because the diffraction radii required several hours to stabilize at a fixed temperature. Crown Copyright © 2018. Published by Elsevier B.V. All rights reserved.
Kompan, T. A.; Korenev, A. S.; Lukin, A. Ya.
2008-10-01
The artificial material sitall CO-115M was developed purposely as a material with an extra-low thermal expansion. The controlled crystallization of an aluminosilicate glass melt leads to the formation of a mixture of β-spodumen, β-eucryptite, and β-silica anisotropic microcrystals in a matrix of residual glass. Due to the small size of the microcrystals, the material is homogeneous and transparent. Specific lattice anharmonism of these microcrystal materials results in close to zero average thermal linear expansion coefficient (TLEC) of the sitall material. The thermal expansion coefficient of this material was measured using an interferometric method in line with the classical approach of Fizeau. To obtain the highest accuracy, the registration of light intensity of the total interference field was used. Then, the parameters of the interference pattern were calculated. Due to the large amount of information in the interference pattern, the error of the calculated fringe position was less than the size of a pixel of the optical registration system. The thermal expansion coefficient of the sitall CO-115M and its temperature dependence were measured. The TLEC value of about 3 × 10-8 K-1 to 5 × 10-8 K-1 in the temperature interval from -20 °C to +60 °C was obtained. A special investigation was carried out to show the homogeneity of the material.
Prediction and control of the coefficient of thermal expansion of concrete
International Nuclear Information System (INIS)
Ziegeldorf, S.; Kleiser, K.; Hilsdorf, H.K.
1979-01-01
Prediction and control of the coefficient of thermal expansion of concrete. In this report various procedures for the prediction of the coefficient of thermal expansion of concrete are summarized. The values predicted with these procedures are compared to experimental data. In the experimental investigation the coefficient of thermal expansion of various types of aggregates and types of concrete both in a dry and a moist state in the temperature range RT/180 0 C have been measured. The most significant result obtained is that for equal volume fractions the thermal properties of coarse aggregates have a more pronounced effect upon thermal expansion of concrete than those of fine aggregates. In the analysis an attempt has been made to estimate the thermal expansion of concrete from the properties of the concrete components by means of a finite element procedure. On the basis of the experimental data and of the analysis of internal temperature stresses in the concrete a simple relationship for the determination of the coefficient of thermal expansion of concrete has been deduced. In this relationship different thermal properties of coarse and fine aggregates may be taken into account. Compared to other methods this relationship yields, both for dry and for moist concrete, values which are in good agreement with the experimental data. (orig.) [de
Effect of graphene nanoplatelets on coefficient of thermal expansion of polyetherimide composite
International Nuclear Information System (INIS)
Wu, Huang; Drzal, Lawrence T.
2014-01-01
Thermal expansion is one of the major concerns for polymer composites. In this research, graphene nanoplatelets (GNPs) were added to polyetherimide (PEId) thermoplastic polymer in order to reduce the coefficient of thermal expansion (CTE) of the injection molded composite. First, the coefficient of linear thermal expansion (LTE) was measured in three directions in the anisotropic coupon: 0°, 90° and the out of plane Z direction. It is found that the GNP particles are very effective in terms of reducing the LTE in 0° direction due to high degree of alignment. After annealing above glass transition temperature, significant increase of 0° LTE and decrease of Z° LTE were observed. The bulk CTE was calculated by adding up the LTEs in all three directions and is found to be independent of annealing. Second, several models were applied to predict both CTE and LTE. It is found that Schapery's lower limit model fits the experimental CTE very well. Chow's model was applied for LTEs in three directions. The behavior of GNP-5/PEId composites is explained by the combination of Chow's model and morphology obtained by scanning electron microscope (SEM). - Highlights: • Coefficient of thermal expansion (CTE) of polymer composite is characterized. • Reduction of linear thermal expansion depends on filler orientation. • Filler orientation is characterized based on the location of the specimen. • Filler orientation is changed by annealing, causing subsequent change in CTE. • CTE and linear thermal expansion coefficient are modeled
International Nuclear Information System (INIS)
Deev, V.I.; Sobolev, V.P.; Kruglov, A.B.; Pridantsev, A.I.
1984-01-01
Results of experimental investigation of heat conduction coefficient and coefficient of linear thermal expansion and thermal shrinkages of the STEF-1 textolite-glass widely used in superconducting magnetic systems as electric insulating and structural material are presented. Samples of two types have been died: sample axisa is perpendicular to a plae of fiberglass layers ad sample axis is parallel to a plane of fiberglass layers. Heat conduction coefficient was decreased almost a five times with temperature decrease from 300 up to 5K and was slightly dependent on a sample type. Temperature variation of linear dimensions in a sample of the first type occurs in twice as fast as compared to the sample of the second type
Thermal expansion coefficients of obliquely deposited MgF2 thin films and their intrinsic stress.
Jaing, Cheng-Chung
2011-03-20
This study elucidates the effects of columnar angles and deposition angles on the thermal expansion coefficients and intrinsic stress behaviors of MgF2 films with columnar microstructures. The behaviors associated with temperature-dependent stresses in the MgF2 films are measured using a phase-shifting Twyman-Green interferometer with a heating stage and the application of a phase reduction algorithm. The thermal expansion coefficients of MgF2 films at various columnar angles were larger than those of glass substrates. The intrinsic stress in the MgF2 films with columnar microstructures was compressive, while the thermal stress was tensile. The thermal expansion coefficients of MgF2 films with columnar microstructures and their intrinsic stress evidently depended on the deposition angle and the columnar angle.
International Nuclear Information System (INIS)
Blagonravov, L A; Karchevskiy, O O; Ivannikov, P V; Soboleva, A V
2008-01-01
The first results of the thermal expansion coefficient measurement obtained for liquid conductors using a new modulation method are presented. The method is based on a superposition of two periodical influences on a liquid metal. The thermal expansion coefficient α P is determined by means of measuring the amplitudes of oscillations of electric current power w ∼ and pressure p ∼ . In the present work the K-Na alloy of the eutectic composition was used as a sample. Distinction of the experimental data obtained by authors from the literature data is 30 to 40%. Such a difference is in the range of error of determination of α P from the density data of K-Na alloy. The method allows direct determination of the thermal expansion coefficient of liquid conductors in absolute units
International Nuclear Information System (INIS)
Alexander, J.E.
1978-06-01
The report describes a test which was conducted to determine the variation in thermal expansion coefficients of specimens from several material heats of Type 304 stainless steel. The purpose of this document is to identify the procedures, equipment, and analysis used in performing this test. From a review of the data which were used in establishing the values given for mean coefficient of thermal expansion in the 1968 ASME Boiler and Pressure Vessel Code, Section III, a +-3.3-percent maximum variation was determined for Type 304 CRES in the temperature range of interest. The results of the test reduced this variation to +-0.53 percent based on a 95/99-percent tolerance interval for the material tested. The testing equipment, procedure, and analysis are not complicated and this type of test is recommended for applications in which the variation in thermal expansion coefficients is desired for a limited number of material heats
Directory of Open Access Journals (Sweden)
Boping Li
2015-01-01
Full Text Available At present, studies on the surface tension of air tunnel terrazzo under wind load and how regularly it is affected by temperature are relatively less, and the measured results of the thermal expansion coefficient of terrazzo have not yet been given. In this paper, based on the top terrazzo surface structure of the inner wall of the wind tunnel, the tensile performance tests of terrazzo surface layer are conducted, while the thermal expansion coefficient of the six terrazzo test blocks were tested. The tests and analysis show that the construction of terrazzo surface, based on the proposed construction process, can effectively guarantee the reliable cement performance for the binding layer between mortar and concrete base layer, terrazzo surface layer and the cement mortar layer. And the thermal expansion coefficient of terrazzo can be valued at 1.06e-5/ºC.
Stochastic series expansion simulation of the t -V model
Wang, Lei; Liu, Ye-Hua; Troyer, Matthias
2016-04-01
We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.
The JPL Cryogenic Dilatometer: Measuring the Thermal Expansion Coefficient of Aerospace Materials
Halverson, Peter G.; Dudick, Matthew J.; Karlmann, Paul; Klein, Kerry J.; Levine, Marie; Marcin, Martin; Parker, Tyler J.; Peters, Robert D.; Shaklan, Stuart; VanBuren, David
2007-01-01
This slide presentation details the cryogenic dilatometer, which is used by JPL to measure the thermal expansion coefficient of materials used in Aerospace. Included is a system diagram, a picture of the dilatometer chamber and the laser source, a description of the laser source, pictures of the interferometer, block diagrams of the electronics and software and a picture of the electronics, and software. Also there is a brief review of the accurace.error budget. The materials tested are also described, and the results are shown in strain curves, JPL measured strain fits are described, and the coefficient of thermal expansion (CTE) is also shown for the materials tested.
Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions
International Nuclear Information System (INIS)
Ohtani, Nobuo
1976-01-01
A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)
Thermal expansion coefficient determination of polylactic acid using digital image correlation
Botean, Adrian-Ioan
2018-02-01
This paper aims determining the linear thermal expansion coefficient (CTE) of polylactic acid (PLA) using an optical method for measuring deformations called digital image correlation method (DIC). Because PLA is often used in making many pieces with 3D printing technology, it is opportune to know this coefficient to obtain a higher degree of precision in the construction of parts and to monitor deformations when these parts are subjected to a thermal gradient. Are used two PLA discs with 20 and 40% degree of filling. In parallel with this approach was determined the linear thermal expansion coefficient (CTE) for the copper cylinder on the surface of which are placed the two discs of PLA.
Thermal expansion coefficient determination of polylactic acid using digital image correlation
Directory of Open Access Journals (Sweden)
Botean Adrian - Ioan
2018-01-01
Full Text Available This paper aims determining the linear thermal expansion coefficient (CTE of polylactic acid (PLA using an optical method for measuring deformations called digital image correlation method (DIC. Because PLA is often used in making many pieces with 3D printing technology, it is opportune to know this coefficient to obtain a higher degree of precision in the construction of parts and to monitor deformations when these parts are subjected to a thermal gradient. Are used two PLA discs with 20 and 40% degree of filling. In parallel with this approach was determined the linear thermal expansion coefficient (CTE for the copper cylinder on the surface of which are placed the two discs of PLA.
Ground state energies from converging and diverging power series expansions
International Nuclear Information System (INIS)
Lisowski, C.; Norris, S.; Pelphrey, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-01-01
It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh–Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state’s spatial extension is comparable to L. Once the binding strength is so strong that the ground state’s extension is less than L, the power expansion becomes divergent, consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.
Ground state energies from converging and diverging power series expansions
Energy Technology Data Exchange (ETDEWEB)
Lisowski, C.; Norris, S.; Pelphrey, R.; Stefanovich, E., E-mail: eugene-stefanovich@usa.net; Su, Q.; Grobe, R.
2016-10-15
It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh–Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state’s spatial extension is comparable to L. Once the binding strength is so strong that the ground state’s extension is less than L, the power expansion becomes divergent, consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.
Linear thermal expansion coefficient of MgAl2O4(s)
International Nuclear Information System (INIS)
Dash, A.; Samui, P.; Naik, Y.P.; Chaudhary, Z.S.
2011-01-01
The coefficient of linear thermal expansion (α av ) of MgAl 2 O 4 (s) has been determined using a Netzsch 402 PC dilatometer with Al 2 O 3 (s) as the push-rod. The change in length per unit length was recorded as a function of temperature between room temperature to 1273 K at a heating rate of 8 K.min /1 , in argon flowing atmosphere. The average of three measurements was quoted as the α av for MgAl 2 O 4 (s). The linear thermal expansion was measured to an accuracy of ±3%. (author)
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
Wavelet Correlation Coefficient of 'strongly correlated' financial time series
Razdan, Ashok
2003-01-01
In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two variables. In econophysics correlation coefficient forms important input to evolve hierarchial tree and minimum spanning tree of financial data.
Analytic structure and power series expansion of the Jost function for the two-dimensional problem
International Nuclear Information System (INIS)
Rakityansky, S A; Elander, N
2012-01-01
For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. (paper)
Zhang, Richard X; Fisher, Timothy; Raman, Arvind; Sands, Timothy D
2009-01-01
In this article, a precise and convenient technique based on the atomic force microscope (AFM) is developed to measure the linear coefficient of thermal expansion of a porous anodic alumina thin film. A stage was used to heat the sample from room temperature up to 450 K. Thermal effects on AFM probes and different operation modes at elevated temperatures were also studied, and a silicon AFM probe in the tapping mode was chosen for the subsequent measurements due to its temperature insensitivi...
International Nuclear Information System (INIS)
Zhou, X; Zhang, Z Y; Zhang, Q M; Liu, Q; Ding, Y Y; Zhou, L; Cao, J
2015-01-01
We report the measurements of the densities of linear alkylbenzene at three temperatures over 4 to 23 °C with pressures up to 10 MPa. The measurements have been analysed to yield the isobaric thermal expansion coefficients and, so far for the first time, isothermal compressibilities of linear alkylbenzene. Relevance of results for current generation (i.e., Daya Bay) and next generation (i.e. JUNO) large liquid scintillator neutrino detectors are discussed. (paper)
Nickel-base alloys having a low coefficient of thermal expansion
International Nuclear Information System (INIS)
Baldwin, J.F.; Maxwell, D.H.
1975-01-01
Alloy compositions consisting predominantly of nickel, chromium, molybdenum, carbon, and boron are disclosed. The alloys possess a duplex structure consisting of a nickel--chromium--molybdenum matrix and a semi-continuous network of refractory carbides and borides. A combination of desirable properties is provided by these alloys, including elevated temperature strength, resistance to oxidation and hot corrosion, and a very low coefficient of thermal expansion
Mapping Thermal Expansion Coefficients in Freestanding 2D Materials at the Nanometer Scale
Hu, Xuan; Yasaei, Poya; Jokisaari, Jacob; Öǧüt, Serdar; Salehi-Khojin, Amin; Klie, Robert F.
2018-02-01
Two-dimensional materials, including graphene, transition metal dichalcogenides and their heterostructures, exhibit great potential for a variety of applications, such as transistors, spintronics, and photovoltaics. While the miniaturization offers remarkable improvements in electrical performance, heat dissipation and thermal mismatch can be a problem in designing electronic devices based on two-dimensional materials. Quantifying the thermal expansion coefficient of 2D materials requires temperature measurements at nanometer scale. Here, we introduce a novel nanometer-scale thermometry approach to measure temperature and quantify the thermal expansion coefficients in 2D materials based on scanning transmission electron microscopy combined with electron energy-loss spectroscopy to determine the energy shift of the plasmon resonance peak of 2D materials as a function of sample temperature. By combining these measurements with first-principles modeling, the thermal expansion coefficients (TECs) of single-layer and freestanding graphene and bulk, as well as monolayer MoS2 , MoSe2 , WS2 , or WSe2 , are directly determined and mapped.
Directory of Open Access Journals (Sweden)
V. S. Zarubin
2015-01-01
Full Text Available The rational use of composites as structural materials, while perceiving the thermal and mechanical loads, to a large extent determined by their thermoelastic properties. From the presented review of works devoted to the analysis of thermoelastic characteristics of composites, it follows that the problem of estimating these characteristics is important. Among the thermoelastic properties of composites occupies an important place its temperature coefficient of linear expansion.Along with fiber composites are widely used in the technique of dispersion hardening composites, in which the role of inclusions carry particles of high-strength and high-modulus materials, including nanostructured elements. Typically, the dispersed particles have similar dimensions in all directions, which allows the shape of the particles in the first approximation the ball.In an article for the composite with isotropic spherical inclusions of a plurality of different materials by the self-produced design formulas relating the temperature coefficient of linear expansion with volume concentration of inclusions and their thermoelastic characteristics, as well as the thermoelastic properties of the matrix of the composite. Feature of the method is the self-accountability thermomechanical interaction of a single inclusion or matrix particles with a homogeneous isotropic medium having the desired temperature coefficient of linear expansion. Averaging over the volume of the composite arising from such interaction perturbation strain and stress in the inclusions and the matrix particles and makes it possible to obtain such calculation formulas.For the validation of the results of calculations of the temperature coefficient of linear expansion of the composite of this type used two-sided estimates that are based on the dual variational formulation of linear thermoelasticity problem in an inhomogeneous solid containing two alternative functional (such as Lagrange and Castigliano
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
Chung, Sang K.; Thiessen, David B.; Rhim, Won-Kyu
1996-01-01
A noncontact measurement technique for the density and the thermal expansion refractory materials in their molten as well as solid phases is presented. This technique is based on the video image processing of a levitated sample. Experiments were performed using the high-temperature electrostatic levitator (HTESL) at the Jet Propulsion Laboratory in which 2-3 mm diameter samples can be levitated, melted, and radiatively cooled in a vacuum. Due to the axisymmetric nature of the molten samples when levitated in the HTESL, a rather simple digital image analysis can be employed to accurately measure the volumetric change as a function of temperature. Density and the thermal expansion coefficient measurements were made on a pure nickel sample to test the accuracy of the technique in the temperature range of 1045-1565 C. The result for the liquid phase density can be expressed by p = 8.848 + (6.730 x 10(exp -4)) x T (degC) g/cu cm within 0.8% accuracy, and the corresponding thermal expansion coefficient can be expressed by Beta=(9.419 x 10(exp -5)) - (7.165 x 10(exp -9) x T (degC)/K within 0.2% accuracy.
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.
Chernyshov, A. D.; Goryainov, V. V.; Danshin, A. A.
2018-03-01
The stress problem for the elastic wedge-shaped cutter of finite dimensions with mixed boundary conditions is considered. The differential problem is reduced to the system of linear algebraic equations by applying twice the fast expansions with respect to the angular and radial coordinate. In order to determine the unknown coefficients of fast expansions, the pointwise method is utilized. The problem solution derived has explicit analytical form and it’s valid for the entire domain including its boundary. The computed profiles of the displacements and stresses in a cross-section of the cutter are provided. The stress field is investigated for various values of opening angle and cusp’s radius.
International Nuclear Information System (INIS)
Yarmukhamedov, R.; Baye, D.
2011-01-01
Explicit relations between the effective-range expansion and the nuclear vertex constant or asymptotic normalization coefficient (ANC) for the virtual decay B→A+a are derived for an arbitrary orbital momentum together with the corresponding location condition for the (A+a) bound-state energy. They are valid both for the charged case and for the neutral case. Combining these relations with the standard effective-range function up to order six makes it possible to reduce to two the number of free effective-range parameters if an ANC value is known from experiment. Values for the scattering length, effective range, and form parameter are determined in this way for the 16 O+p, α+t, and α+ 3 He collisions in partial waves where a bound state exists by using available ANCs deduced from experiments. The resulting effective-range expansions for these collisions are valid up to energies larger than 5 MeV.
Hirai, Akiko; Bitou, Youichi; Oike, Yoshiyuki
2018-06-01
The long-term stability of NEXCERA™ ceramics having a low coefficient of thermal expansion was evaluated over a period of eight years. Several gauge blocks of differing lengths were prepared, using two types of NEXCERA. Each gauge block was kept wrung to a platen and its absolute length was periodically measured by gauge block interferometer during the eight years. Relative uncertainties of measurement of changes in gauge block length were estimated as 4.1 × 10‑8 and 2.9 × 10‑8 for 200 mm and 800 mm gauge blocks, respectively. The experimental results show the trend of expansion and a relative change of less than 0.1 × 10‑6/year for every gauge block.
Tian, Xiao-mei; Zeng, Li; Wei, Bin; Huang, Yi-feng
2015-12-01
To investigate the thermal expansion coefficient of different processing parameters upon the Co-Cr alloy prepared by selective laser melting (SLM) technique, in order to provide technical support for clinical application of SLM technology. The heating curve of self-made Co-Cr alloy was protracted from room temperature to 980°C centigrade with DIL402PC thermal analysis instrument, keeping temperature rise rate and cooling rate at 5 K/min, and then the thermal expansion coefficient of 9 groups of Co-Cr alloy was measured from 20°C centigrade to 500°C centigrade and 600°C centigrade. The 9 groups thermal expansion coefficient values of Co-Cr alloy heated from 20°C centigrade to 500°C centigrade were 13.9×10(-6)/K,13.6×10(-6)/K,13.9×10(-6)/K,13.7×10(-6)/K,13.5×10(-6)/K,13.8×10(-6)/K,13.7×10(-6)/K,13.7×10(-6)/K,and 13.9×10(-6)/K, respectively; when heated from 20°C centigrade to 600°C centigrade, they were 14.2×10(-6)/K,13.9×10(-6)/K,13.8×10(-6)/K,14.0×10(-6)/K,14.1×10(-6)/K,14.1×10(-6)/K,13.9×10(-6)/K,14.2×10(-6)/K, and 13.7×10(-6)/K, respectively. The results showed that the Co-Cr alloy has good matching with the VITA VMK 95 porcelain powder and can meet the requirement of clinic use.
Domenegueti, Jose Francisco Miras; Andrade, Acacio A; Pilla, Viviane; Zilio, Sergio Carlos
2017-01-09
A low-cost single arm double interferometer was developed for the concurrent measurement of linear thermal expansion (α) and thermo-optic (dn/dT) coefficients of transparent samples with plane and parallel surfaces. Owing to its common-path optical arrangement, the device is compact and stable, and allows the simultaneous measurement of interferences arising from a low-finesse Fabry-Perot etalon and from a Mach-Zehnder-type interferometer. The method was demonstrated with measurements of solid (silica, BK7, SF6) and liquid (water, ethanol and acetone) samples.
Measurement of the Thermal Expansion Coefficient for Ultra-High Temperatures up to 3000 K
Kompan, T. A.; Kondratiev, S. V.; Korenev, A. S.; Puhov, N. F.; Inochkin, F. M.; Kruglov, S. K.; Bronshtein, I. G.
2018-03-01
The paper is devoted to a new high-temperature dilatometer, a part of the State Primary Standard of the thermal expansion coefficient (TEC) unit. The dilatometer is designed for investigation and certification of materials for TEC standards in the range of extremely high temperatures. The critical review of existing methods of TEC measurements is given. Also, the design, principles of operation and metrological parameters of the new device are described. The main attention is paid to the system of machine vision that allows accurate measurement of elongation at high temperatures. The results of TEC measurements for graphite GIP-4, single crystal Al2O3, and some other materials are also presented.
Nakanishi, Koichi; Kogure, Akinori; Fujii, Takenao; Kokawa, Ryohei; Deuchi, Keiji; Kuwana, Ritsuko; Takamatsu, Hiromu
2013-10-09
If a fixed stress is applied to the three-dimensional z-axis of a solid material, followed by heating, the amount of thermal expansion increases according to a fixed coefficient of thermal expansion. When expansion is plotted against temperature, the transition temperature at which the physical properties of the material change is at the apex of the curve. The composition of a microbial cell depends on the species and condition of the cell; consequently, the rate of thermal expansion and the transition temperature also depend on the species and condition of the cell. We have developed a method for measuring the coefficient of thermal expansion and the transition temperature of cells using a nano thermal analysis system in order to study the physical nature of the cells. The tendency was seen that among vegetative cells, the Gram-negative Escherichia coli and Pseudomonas aeruginosa have higher coefficients of linear expansion and lower transition temperatures than the Gram-positive Staphylococcus aureus and Bacillus subtilis. On the other hand, spores, which have low water content, overall showed lower coefficients of linear expansion and higher transition temperatures than vegetative cells. Comparing these trends to non-microbial materials, vegetative cells showed phenomenon similar to plastics and spores showed behaviour similar to metals with regards to the coefficient of liner thermal expansion. We show that vegetative cells occur phenomenon of similar to plastics and spores to metals with regard to the coefficient of liner thermal expansion. Cells may be characterized by the coefficient of linear expansion as a physical index; the coefficient of linear expansion may also characterize cells structurally since it relates to volumetric changes, surface area changes, the degree of expansion of water contained within the cell, and the intensity of the internal stress on the cellular membrane. The coefficient of linear expansion holds promise as a new index for
Modeling of thermal expansion coefficient of perovskite oxide for solid oxide fuel cell cathode
Heydari, F.; Maghsoudipour, A.; Alizadeh, M.; Khakpour, Z.; Javaheri, M.
2015-09-01
Artificial intelligence models have the capacity to eliminate the need for expensive experimental investigation in various areas of manufacturing processes, including the material science. This study investigates the applicability of adaptive neuro-fuzzy inference system (ANFIS) approach for modeling the performance parameters of thermal expansion coefficient (TEC) of perovskite oxide for solid oxide fuel cell cathode. Oxides (Ln = La, Nd, Sm and M = Fe, Ni, Mn) have been prepared and characterized to study the influence of the different cations on TEC. Experimental results have shown TEC decreases favorably with substitution of Nd3+ and Mn3+ ions in the lattice. Structural parameters of compounds have been determined by X-ray diffraction, and field emission scanning electron microscopy has been used for the morphological study. Comparison results indicated that the ANFIS technique could be employed successfully in modeling thermal expansion coefficient of perovskite oxide for solid oxide fuel cell cathode, and considerable savings in terms of cost and time could be obtained by using ANFIS technique.
Virtual thermal expansion coefficient of Cu precipitated in the Fe95Cu5 alloy
International Nuclear Information System (INIS)
Koeszegi, L.; Somogyvari, Z.
1999-01-01
Complete text of publication follows. Precipitations on grain boundaries play very important role in the formation of material's characteristics like embrittlement, durability etc. It was already shown [1] that Cu precipitations are under different stress conditions than the bulk material. The situation is more complicated in the case when a construction is exposed to temperature changes as well. In that case not only the residual stresses during the fabrication but the different thermal expansion coefficients can produce additional problems. This situation was modelled using Fe 95 Cu 5 alloy where Cu precipitates on the grain boundaries. The alloy was produced by high-frequency melting and an extra heat treatment was used to produce a quasi-equilibrium state. Pure Cu was also measured to compare the behaviours. Cu(111) Bragg peak was measured at different temperatures by high resolution neutron diffraction. The measurements were carried out on the G5-2 spectrometer at LLB in Saclay. Measurements show that not only residual stress can be recognised on the Cu precipitates but the thermal expansion coefficient of these precipitates definitly differ from the ones of pure Cu. (author)
International Nuclear Information System (INIS)
Li, Cheng; Liu, Qianwen; Peng, Xiaobin; Fan, Shangchun
2016-01-01
Application of the Fabry–Perot (FP) interference method for determining the coefficient of thermal expansion (CTE) of a graphene diaphragm is investigated in this paper. A miniature extrinsic FP interferometric (EFPI) sensor was fabricated by using an approximate 8-layer graphene diaphragm. The extremely thin diaphragm was transferred onto the endface of a ferrule with an inner diameter of 125 μ m, and van der Waals interactions between the graphene diaphragm and its substrate created a low finesse FP interferometer with a cavity length of 36.13 μ m. Double reference FP cavities using two cleaved optical fibers as reflectors were also constructed to differentially cancel the thermal expansion effects of the trapped gas and adhesive material. A temperature test demonstrated an approximate cavity length change of 166.1 nm °C −1 caused by film thermal expansion in the range of 20–60 °C. Then along with the established thermal deformation model of the suspended circular diaphragm, the calculated CTE ranging from −9.98 × 10 −6 K −1 to −2.09 × 10 −6 K −1 conformed well to the previously measured results. The proposed method would be applicable in other types of elastic materials as the sensitive diaphragm of an EFPI sensor over a wide temperature range. (paper)
International Nuclear Information System (INIS)
Sabry, R.; Zahran, M.A.; Fan Engui
2004-01-01
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found
Symmetries of some hypergeometric series: Implications for 3j- and 6j-coefficients
International Nuclear Information System (INIS)
Louck, J.D.; Beyer, W.A.; Biedenharn, L.C.; Stein, P.R.
1986-10-01
The occurrence of generalized hypergeometric series as factors, in the Wigner-Clebsch-Gordan (3j) and Racah (6j) coefficients is well known. The recently discovered S 5 symmetry of the Saalscheutzian 4 F 3 series may be used to extend the symmetries of the 6j-coefficients to the much larger group generated by S 5 and the group of Regge symmetries. (A similar extension may be carried out for the 3j-coefficients). The required extension of the domain of definition of the 6j-coefficients and the properties of its symmetry group is developed here. 7 refs
Stochastic Simulation and Forecast of Hydrologic Time Series Based on Probabilistic Chaos Expansion
Li, Z.; Ghaith, M.
2017-12-01
Hydrological processes are characterized by many complex features, such as nonlinearity, dynamics and uncertainty. How to quantify and address such complexities and uncertainties has been a challenging task for water engineers and managers for decades. To support robust uncertainty analysis, an innovative approach for the stochastic simulation and forecast of hydrologic time series is developed is this study. Probabilistic Chaos Expansions (PCEs) are established through probabilistic collocation to tackle uncertainties associated with the parameters of traditional hydrological models. The uncertainties are quantified in model outputs as Hermite polynomials with regard to standard normal random variables. Sequentially, multivariate analysis techniques are used to analyze the complex nonlinear relationships between meteorological inputs (e.g., temperature, precipitation, evapotranspiration, etc.) and the coefficients of the Hermite polynomials. With the established relationships between model inputs and PCE coefficients, forecasts of hydrologic time series can be generated and the uncertainties in the future time series can be further tackled. The proposed approach is demonstrated using a case study in China and is compared to a traditional stochastic simulation technique, the Markov-Chain Monte-Carlo (MCMC) method. Results show that the proposed approach can serve as a reliable proxy to complicated hydrological models. It can provide probabilistic forecasting in a more computationally efficient manner, compared to the traditional MCMC method. This work provides technical support for addressing uncertainties associated with hydrological modeling and for enhancing the reliability of hydrological modeling results. Applications of the developed approach can be extended to many other complicated geophysical and environmental modeling systems to support the associated uncertainty quantification and risk analysis.
International Nuclear Information System (INIS)
Bae, Youngmin; Kim, Young In
2014-01-01
Highlights: • Turbulent flow in axisymmetric sudden expansion with a chamfer is studied numerically. • Reynolds number dependency of the local loss coefficient is investigated. • Extended correlation is proposed for estimation of the local loss coefficient. - Abstract: This paper reports the pressure losses in turbulent flows through axisymmetric sudden expansions having a slight chamfer on the edge. A parametric study is performed for dimensionless chamfer lengths of 0–0.5, expansion ratios of 2–6, and chamfer angles of 0–45° in a Reynolds number range of 1 × 10 5 –8 × 10 5 . The chamfer effect on the expansion losses and its dependence on the Reynolds number are analyzed in detail along with a discussion of the relevant flow features. On the basis of numerical results, an existing correlation of the local loss coefficient is also extended to take into account the effect of the Reynolds number additionally
Series expansion of two-dimensional fields produced by iron-core magnets
International Nuclear Information System (INIS)
Satoh, Kotaro.
1997-02-01
This paper discusses the validity of a series expansion of two-dimensional magnetic fields with harmonic functions, and suggests that the series may not converge outside of the pole gap. It also points out that this difficulty may appear due to a slow convergence of the series near to the pole edge, even within the convergent area. (author)
Thermal Coefficient of Linear Expansion Modified by Dendritic Segregation in Nickel-Iron Alloys
Ogorodnikova, O. M.; Maksimova, E. V.
2018-05-01
The paper presents investigations of thermal properties of Fe-Ni and Fe-Ni-Co casting alloys affected by the heterogeneous distribution of their chemical elements. It is shown that nickel dendritic segregation has a negative effect on properties of studied invars. A mathematical model is proposed to explore the influence of nickel dendritic segregation on the thermal coefficient of linear expansion (TCLE) of the alloy. A computer simulation of TCLE of Fe-Ni-Co superinvars is performed with regard to a heterogeneous distribution of their chemical elements over the whole volume. The ProLigSol computer software application is developed for processing the data array and results of computer simulation.
Elasticity moduli, thermal expansion coefficients and Debye temperature of titanium alloys
International Nuclear Information System (INIS)
Beletskij, V.M.; Glej, V.A.; Maksimyuk, P.A.; Tabachnik, V.I.; Opanasenko, V.F.
1979-01-01
Studied are the characteristics of titanium alloys which reflect best the bonding forces for atoms in a crystal lattice: elastic modules, their temperature dependences, thermal expansion coefficient and Debye temperatures. For the increase of the accuracy of measuring modules and especially their changes with temperature an ultrasonic echo-impulse method of superposition has been used. The temperature dependences of Young modulus of the VT1-0, VT16 and VT22 titanium alloys are plotted. The Young module and its change with temperature depend on the content of alloying elements. The Young module decrease with temperature may be explained within the framework of the inharmonic effect theory. The analysis of the results obtained permits to suppose that alloying of titanium alloys with aluminium results in an interatomic interaction increase that may be one of the reasons of their strength increase
Ceramic materials with low thermal conductivity and low coefficients of thermal expansion
Brown, Jesse; Hirschfeld, Deidre; Liu, Dean-Mo; Yang, Yaping; Li, Tingkai; Swanson, Robert E.; Van Aken, Steven; Kim, Jin-Min
1992-01-01
Compositions having the general formula (Ca.sub.x Mg.sub.1-x)Zr.sub.4 (PO.sub.4).sub.6 where x is between 0.5 and 0.99 are produced by solid state and sol-gel processes. In a preferred embodiment, when x is between 0.5 and 0.8, the MgCZP materials have near-zero coefficients of thermal expansion. The MgCZPs of the present invention also show unusually low thermal conductivities, and are stable at high temperatures. Macrostructures formed from MgCZP are useful in a wide variety of high-temperature applications. In a preferred process, calcium, magnesium, and zirconium nitrate solutions have their pH adjusted to between 7 and 9 either before or after the addition of ammonium dihydrogen phosphate. After dehydration to a gel, and calcination at temperatures in excess of 850.degree. C. for approximately 16 hours, single phase crystalline MgCZP powders with particle sizes ranging from approximately 20 nm to 50 nm result. The MgCZP powders are then sintered at temperatures ranging from 1200.degree. C. to 1350.degree. C. to form solid macrostructures with near-zero bulk coefficients of thermal expansion and low thermal conductivities. Porous macrostructures of the MgCZP powders of the present invention are also formed by combination with a polymeric powder and a binding agent, and sintering at high temperatures. The porosity of the resulting macrostructures can be adjusted by varying the particle size of the polymeric powder used.
Bruggeman, R.W.; Diamantis, N.
2016-01-01
The Fourier coefficient of a second order Eisenstein series is described as a shifted convolution sum. This description is used to obtain the spectral decomposition of and estimates for the shifted convolution sum.
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.
Constantin, Lucian A; Fabiano, Eduardo; Della Sala, Fabio
2017-09-12
Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.
Directory of Open Access Journals (Sweden)
Guo Zheng-Hong
2016-01-01
Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.
Narea, J. Freddy; Muñoz, Aarón A.; Castro, Jorge; Muñoz, Rafael A.; Villalba, Caroleny E.; Martinez, María. F.; Bravo, Kelly D.
2013-11-01
Human skin has been studied in numerous investigations, given the interest in knowing information about physiology, morphology and chemical composition. These parameters can be determined using non invasively optical techniques in vivo, such as the diffuse reflectance spectroscopy. The human skin color is determined by many factors, but primarily by the amount and distribution of the pigment melanin. The melanin is produced by the melanocytes in the basal layer of the epidermis. This research characterize the spectral response of the human skin using the coefficients of Fourier series expansion. Simulating the radiative transfer equation for the Monte Carlo method to vary the concentration of the melanocytes (fme) in a simplified model of human skin. It fits relating the Fourier series coefficient a0 with fme. Therefore it is possible to recover the skin biophysical parameter.
Sinev, Leonid S.; Petrov, Ivan D.
2017-01-01
Processing results of measurements of linear thermal expansion coefficients and linear thermal expansion of two brands of borosilicate glasses --- LK5 and Borofloat 33 --- are presented. The linear thermal expansion of glass samples have been determined in the temperature range 130 to 800 K (minus 143 to 526 $\\deg$C) using thermomechanical analyzer TMA7100. Relative imprecision of indirectly measured linear thermal expansion coefficients and linear thermal expansion of both glass brands is le...
Non-vanishing of Taylor coefficients and Poincaré series
DEFF Research Database (Denmark)
O'Sullivan, C.; Risager, Morten S.
2013-01-01
We prove recursive formulas for the Taylor coefficients of cusp forms, such as Ramanujan's Delta function, at points in the upper half-plane. This allows us to show the non-vanishing of all Taylor coefficients of Delta at CM points of small discriminant as well as the non-vanishing of certain...... Poincaré series. At a "generic" point, all Taylor coefficients are shown to be non-zero. Some conjectures on the Taylor coefficients of Delta at CM points are stated....
A study of the coefficient of thermal expansion of nuclear graphites
International Nuclear Information System (INIS)
Hacker, P.J.
2001-02-01
This thesis presents the results of a study of the Coefficient of Thermal Expansion (CTE) of two grades of nuclear graphite that are used as the moderator in the Magnox and Advanced Gas-Cooled reactors operated in the UK. This work has two main aims, the first is to characterise those elements of the graphite microstructure that control CTE within these materials and to relate these to the effects induced within the reactor. The second is to develop a microstructural model, of general applicability, that can initially be applied to model the CTE changes within the graphites under reactor conditions (neutron irradiation and radiolytic oxidation). These aims have been met by study in three interlinked areas, theoretical, experimental and modelling. Previous to this study, a loose assembly of single crystals together with changes in small scale nanometric porosity (Mrozowski cracks) were used to describe CTE behaviour of nuclear graphite both as-received and under reactor conditions. Within the experimental part of this thesis the graphite nanostructure was studied using, primarily, Transmission Electron Microscopy (TEM). This work concluded that structure on this scale was complex and that the loose assembly of single crystals was a poor microstructural approximation for modelling the CTE of these materials. Other experimental programmes measured the CTE of highly oxidised samples and simulated the effects of irradiation. The former discovered that CTE remained largely unaffected to high weight losses. This insensitivity was explained by ''The Continuous Network Hypothesis'' that was also related to classical percolation theory. The final part of the thesis modelled an abstraction of the key microstructural features identified in the previous parts of the thesis. This approach has been applied to AGR moderator graphite where it has successfully modelled the thermal expansion behaviour of the as-received, irradiated and oxidised material. (author)
Directory of Open Access Journals (Sweden)
Z. EZZOUINE
2015-07-01
Full Text Available In this study, we present a newly designed electromagnetic dilatometer with micrometer accuracy for the measurement of the coefficient of thermal expansion of a solid in the 30 °C – 96 °C temperature range .The device has a graphical user interface to view real time data measurement. Iron and copper were subjected to temperature change in the thermal expansion experiment causing them to expand linearly. The voltage delivered in the electromagnetic dilatometer system, which includes the information about linear expansion and temperature change were transferred to a computer via a data acquisition card, presented by a program created in the LabVIEW environment, and the amount of linear expansion was detected in real time. The minimal change in length of the sample that can be resolved is 5µm, which yields the sensitivity comprised between 10-4 µm and 10-5 µm. In order to calibrate the electromagnetic dilatometer, thermal expansion coefficients of copper and Iron have been measured. By this technique, the thermal expansion coefficient can be determined with an acceptable accuracy. The present results appear also to agree well with those reported previously in the literature.
Teaching Graphical Simulations of Fourier Series Expansion of Some Periodic Waves Using Spreadsheets
Singh, Iqbal; Kaur, Bikramjeet
2018-01-01
The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…
International Nuclear Information System (INIS)
Hall, G.; Marsden, B.J.; Fok, A.; Smart, J.
2002-01-01
In the 1960s, J.H.W. Simmons derived a theoretical relationship between the coefficient of thermal expansion (CTE) and dimensional changes in irradiated graphite. At low irradiation dose, the theory was shown to be consistent with experimental observations. However, at higher doses the results diverge. Despite this, modified versions of this theory have been used as the basis of the design and life prediction calculations for graphite-moderated reactors. This paper revisits Simmons's theory, summarising the assumptions made in its derivation. The paper then modifies and applies the theory to the dimensional change and CTE change behaviour in isotropic nuclear graphite, making use of trends in irradiated behaviour recently derived using finite element analyses. The importance of these issues to present HTR technology is that the life of HTR graphite components is related to their irradiated dimensional change behaviour. A more in depth understanding of this behaviour will allow suitable graphite material to be selected or new graphite types to be developed. (author)
Cho, M; Jang, J; Suhr, J
2011-02-01
This study involves the investigation of the geometry effect of nano-fillers on thermally induced dimensional stability of epoxy composites by experimentally evaluating the linear coefficient of thermal expansion (CTE). Carbon nanofibers (CNF) were chosen as the filler in epoxy matrix to investigate the effect of an aspect ratio on the CTE of the nanocomposites at three different volume fractions of 0.5, 1, and 2% of the nano-filler. The composites were fabricated using a mechanical mixing method. The CTE values were evaluated by measuring thermal strains of the composites and also compared with a micromechanics model. It was observed that the composites with short CNF (average L/d = 10) show better thermal stability than one of the composites with long CNF (average L/d = 70), and the thermal stability of the composites was proportional to the volume fraction of the filler in each composite. In addition, the CTE of mutliwalled carbon nanotubes (MWNT) reinforced epoxy composites was evaluated and compared with the CTE of the CNF reinforced composites. Interestingly, the MWNT reinforced composites show the greatest thermal stability with an 11.5% reduction in the CTE over the pure epoxy. The experimental data was compared with micromechanics model.
International Nuclear Information System (INIS)
Cheng, Chao-Lin; Fang, Weileun; Tsai, Ming-Han
2015-01-01
Many standard CMOS processes, provided by existing foundries, are available. These standard CMOS processes, with stacking of various metal and dielectric layers, have been extensively applied in integrated circuits as well as micro-electromechanical systems (MEMS). It is of importance to determine the material properties of the metal and dielectric films to predict the performance and reliability of micro devices. This study employs an existing approach to determine the coefficients of thermal expansion (CTEs) of metal and dielectric films for standard CMOS processes. Test cantilevers with different stacking of metal and dielectric layers for standard CMOS processes have been designed and implemented. The CTEs of standard CMOS films can be determined from measurements of the out-of-plane thermal deformations of the test cantilevers. To demonstrate the feasibility of the present approach, thin films prepared by the Taiwan Semiconductor Manufacture Company 0.35 μm 2P4M CMOS process are characterized. Eight test cantilevers with different stacking of CMOS layers and an auxiliary Si cantilever on a SOI wafer are fabricated. The equivalent elastic moduli and CTEs of the CMOS thin films including the metal and dielectric layers are determined, respectively, from the resonant frequency and static thermal deformation of the test cantilevers. Moreover, thermal deformations of cantilevers with stacked layers different to those of the test beams have been employed to verify the measured CTEs and elastic moduli. (paper)
Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method
Li, Xiaowang; Deng, Zhongmin
2016-01-01
A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white no...
International Nuclear Information System (INIS)
Devine, R.T.; Hsu, Hsiao-Hua
1994-01-01
The current basis for conversion coefficients for calibrating individual photon dosimeters in terms of dose equivalents is found in the series of papers by Grosswent. In his calculation the collision kerma inside the phantom is determined by calculation of the energy fluence at the point of interest and the use of the mass energy absorption coefficient. This approximates the local absorbed dose. Other Monte Carlo methods can be sued to provide calculations of the conversion coefficients. Rogers has calculated fluence-to-dose equivalent conversion factors with the Electron-Gamma Shower Version 3, EGS3, Monte Carlo program and produced results similar to Grosswent's calculations. This paper will report on calculations using the Integrated TIGER Series Version 3, ITS3, code to calculate the conversion coefficients in ICRU Tissue and in PMMA. A complete description of the input parameters to the program is given and comparison to previous results is included
Energy Technology Data Exchange (ETDEWEB)
Jo, Hyu Sang; Kang, Hee Yong; Lee, Gyo Woo [Chonbuk National University, Jeonju (Korea, Republic of)
2015-02-15
In this experimental study, the thermal stability values of micrometer-sized silica particle-reinforced epoxy composite specimens were evaluated by measuring their thermal expansion coefficients and Young's moduli. For all specimens used in this study (from the baseline specimen to that containing 70 wt% silica filler), the thermal expansion coefficients and Young's moduli were gradually reduced down to 25% and increased up to 51%, respectively. The results of the experiment were compared with those of certain empirical models. The experimental results of the measurement of thermal expansion coefficients corresponded well with those of Kerner's model, which considers the bulk and shear moduli of the matrix and silica filler. However, the results of the measurement of Young's moduli using the empirical Mori-Tanaka model were observed to match better with those of the experiment. The comparison of the results of the experiment with those of the empirical models demonstrated that a reliable model for measuring the thermal expansion coefficients and Young's moduli of composite specimens needs to consider certain property variations in the composites in addition to volume fraction changes in the filler and matrix.
International Nuclear Information System (INIS)
Jo, Hyu Sang; Kang, Hee Yong; Lee, Gyo Woo
2015-01-01
In this experimental study, the thermal stability values of micrometer-sized silica particle-reinforced epoxy composite specimens were evaluated by measuring their thermal expansion coefficients and Young's moduli. For all specimens used in this study (from the baseline specimen to that containing 70 wt% silica filler), the thermal expansion coefficients and Young's moduli were gradually reduced down to 25% and increased up to 51%, respectively. The results of the experiment were compared with those of certain empirical models. The experimental results of the measurement of thermal expansion coefficients corresponded well with those of Kerner's model, which considers the bulk and shear moduli of the matrix and silica filler. However, the results of the measurement of Young's moduli using the empirical Mori-Tanaka model were observed to match better with those of the experiment. The comparison of the results of the experiment with those of the empirical models demonstrated that a reliable model for measuring the thermal expansion coefficients and Young's moduli of composite specimens needs to consider certain property variations in the composites in addition to volume fraction changes in the filler and matrix
Muñoz Morales, Aarón A; Vázquez Y Montiel, Sergio
2012-10-01
The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.
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)
Directory of Open Access Journals (Sweden)
Stella Crosara Lopes
2009-04-01
Full Text Available The purpose of this study was to evaluate the metal-ceramic bond strength (MCBS of 6 metal-ceramic pairs (2 Ni-Cr alloys and 1 Pd-Ag alloy with 2 dental ceramics and correlate the MCBS values with the differences between the coefficients of linear thermal expansion (CTEs of the metals and ceramics. Verabond (VB Ni-Cr-Be alloy, Verabond II (VB2, Ni-Cr alloy, Pors-on 4 (P, Pd-Ag alloy, and IPS (I and Duceram (D ceramics were used for the MCBS test and dilatometric test. Forty-eight ceramic rings were built around metallic rods (3.0 mm in diameter and 70.0 mm in length made from the evaluated alloys. The rods were subsequently embedded in gypsum cast in order to perform a tensile load test, which enabled calculating the CMBS. Five specimens (2.0 mm in diameter and 12.0 mm in length of each material were made for the dilatometric test. The chromel-alumel thermocouple required for the test was welded into the metal test specimens and inserted into the ceramics. ANOVA and Tukey's test revealed significant differences (p=0.01 for the MCBS test results (MPa, with PI showing higher MCBS (67.72 than the other pairs, which did not present any significant differences. The CTE (10-6 oC-1 differences were: VBI (0.54, VBD (1.33, VB2I (-0.14, VB2D (0.63, PI (1.84 and PD (2.62. Pearson's correlation test (r=0.17 was performed to evaluate of correlation between MCBS and CTE differences. Within the limitations of this study and based on the obtained results, there was no correlation between MCBS and CTE differences for the evaluated metal-ceramic pairs.
Lopes, Stella Crosara; Pagnano, Valéria Oliveira; Rollo, João Manuel Domingos de Almeida; Leal, Mônica Barbosa; Bezzon, Osvaldo Luiz
2009-01-01
The purpose of this study was to evaluate the metal-ceramic bond strength (MCBS) of 6 metal-ceramic pairs (2 Ni-Cr alloys and 1 Pd-Ag alloy with 2 dental ceramics) and correlate the MCBS values with the differences between the coefficients of linear thermal expansion (CTEs) of the metals and ceramics. Verabond (VB) Ni-Cr-Be alloy, Verabond II (VB2), Ni-Cr alloy, Pors-on 4 (P), Pd-Ag alloy, and IPS (I) and Duceram (D) ceramics were used for the MCBS test and dilatometric test. Forty-eight ceramic rings were built around metallic rods (3.0 mm in diameter and 70.0 mm in length) made from the evaluated alloys. The rods were subsequently embedded in gypsum cast in order to perform a tensile load test, which enabled calculating the CMBS. Five specimens (2.0 mm in diameter and 12.0 mm in length) of each material were made for the dilatometric test. The chromel-alumel thermocouple required for the test was welded into the metal test specimens and inserted into the ceramics. ANOVA and Tukey's test revealed significant differences (p=0.01) for the MCBS test results (MPa), with PI showing higher MCBS (67.72) than the other pairs, which did not present any significant differences. The CTE (10(-6) oC(-1)) differences were: VBI (0.54), VBD (1.33), VB2I (-0.14), VB2D (0.63), PI (1.84) and PD (2.62). Pearson's correlation test (r=0.17) was performed to evaluate of correlation between MCBS and CTE differences. Within the limitations of this study and based on the obtained results, there was no correlation between MCBS and CTE differences for the evaluated metal-ceramic pairs.
Chee Siang, GO
2017-07-01
Experimental test was carried out to determine the coefficient of thermal expansion (CTE) value of 20MPa mass concrete using granite aggregate. The CTE value was established using procedure proposed by Kada et al. 2002 in determining the magnitude of early-ages CTE through laboratory test which is a rather accurate way by eliminating any possible superimposed effect of others early-age thermal deformation shrinkages such as autogenous, carbonation, plastic and drying shrinkage. This was done by submitting granite concrete block samples instrumented with ST4 vibrating wire extensometers to thermal shocks. The response of the concrete samples to this shock results in a nearly instantaneous deformation, which are measured by the sensor. These deformations, as well as the temperature signal, are used to calculate the CTE. By repeating heat cycles, the variation in the early-ages of concrete CTE over time was monitored and assessed for a period of upto 7 days. The developed CTE value facilitating the verification and validation of actual maximum permissible critical temperature differential limit (rather than arbitrarily follow published value) of cracking potential. For thick sections, internal restraint is dominant and this is governed by differentials mainly. Of the required physical properties for thermal modelling, CTE is of paramount importance that with given appropriate internal restraint factor the condition of cracking due to internal restraint is governs by equation, ΔTmax= 3.663ɛctu / αc. Thus, it can be appreciated that an increase in CTE will lower the maximum allowable differential for cracking avoidance in mass concrete while an increase of tensile strain capacity will increase the maximum allowable temperature differential.
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)
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.
Lu, Yi; Haverkort, Maurits W.
2017-12-01
We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.
Using a Michelson Interferometer to Measure Coefficient of Thermal Expansion of Copper
Scholl, Ryan; Liby, Bruce W.
2009-01-01
When most materials are heated they expand. This concept is usually demonstrated using some type of mechanical measurement of the linear expansion of a metal rod. We have developed an alternative laboratory method for measuring thermal expansion by using a Michelson interferometer. Using the method presented, interference, interferometry, and the…
Regularization and asymptotic expansion of certain distributions defined by divergent series
Directory of Open Access Journals (Sweden)
Ricardo Estrada
1995-01-01
Full Text Available The regularization of the distribution ∑n=−∞∞δ(x−pn. which gives a regularized value to the divergent series ∑n=−∞∞φ(pn is obtained in several spaces of test functions. The asymptotic expansion as ϵ→0+of series of the type ∑n=0∞φ(ϵ pn is also obtained.
Teaching graphical simulations of Fourier series expansion of some periodic waves using spreadsheets
Singh, Iqbal; Kaur, Bikramjeet
2018-05-01
The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave, half wave rectifier and full wave rectifier signals.
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2014-01-01
Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.
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.
Series expansion solution of the Wegner-Houghton renormalisation group equation
International Nuclear Information System (INIS)
Margaritis, A.; Odor, G.; Patkos, A.
1987-11-01
The momentum independent projection of the Wegner-Houghton renormalisation group equation is solved with power series expansion. Convergence rate is analyzed for the n-vector model. Further evidence is presented for the first order nature of the chiral symmetry restoration at finite temperature in QCD with 3 light flavors. (author) 16 refs
A Series Expansion Approach to Risk Analysis of an Inventory System with Sourcing
Berkhout, J.; Heidergott, B.F.
2014-01-01
In this paper we extend the series expansion approach for uni-chain Markov processes to a special case of finite multi-chains with possible transient states. We will show that multi-chain Markov models arise naturally in simple models such as a single item inventory system with sourcing, i.e., with
Directory of Open Access Journals (Sweden)
SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Energy Technology Data Exchange (ETDEWEB)
Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
International Nuclear Information System (INIS)
Ku, Min Ye; Kim, Jung Hyun; Kang, Hee Yong; Lee, Gyo Woo
2013-01-01
By using shear mixing and ultrasonication, we fabricated specimens of well-dispersed multi-walled carbon nano tube composites. To confirm the proper dispersion of the filler, we used scanning electron microscopy images for quantitative evaluation and a tensile test for qualitative assessment. Furthermore, the coefficients of thermal expansion of several specimens having different filler contents were calculated from the measured thermal strains and temperatures of the specimens. Based on the microscopy images of the well-dispersed fillers and the small deviations in the measurements of the tensile strength and stiffness, we confirmed the proper dispersion of absentee in the epoxy. As the filler contents were increased, the values of tensile strength increased from 58.33 to 68.81 MPa, and those of stiffness increased from 2.93 to 3.27 GPa. At the same time, the coefficients of thermal expansion decreased. This implies better thermal stability of the specimen
International Nuclear Information System (INIS)
Paris, R.B.; Wood, A.D.
1984-11-01
The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper
Fréour , Sylvain; Gloaguen , David; François , Marc; Guillén , Ronald
2006-01-01
International audience; The scope of this work is the determination of the coefficients of thermal expansion of the Ti-17 beta-phase. A rigorous inverse thermo-elastic self-consistent scale transition inicro-mechanical model extended to multi-phase materials was used. The experimental data required for the application of the inverse method were obtained from both the available literature and especially dedicated X-ray diffraction lattice strain measurements performed on the studied (alpha + b...
Energy Technology Data Exchange (ETDEWEB)
Freour, S. [GeM, Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Universite de Nantes, Ecole Centrale de Nantes, 37 Boulevard de l' Universite, BP 406, 44 602 Saint-Nazaire cedex (France)]. E-mail: freour@crttsn.univ-nantes.fr; Gloaguen, D. [GeM, Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Universite de Nantes, Ecole Centrale de Nantes, 37 Boulevard de l' Universite, BP 406, 44 602 Saint-Nazaire cedex (France); Francois, M. [Laboratoire des Systemes Mecaniques et d' Ingenierie Simultanee (LASMIS FRE CNRS 2719), Universite de Technologie de Troyes, 12 Rue Marie Curie, BP 2060, 10010 Troyes (France); Guillen, R. [GeM, Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Universite de Nantes, Ecole Centrale de Nantes, 37 Boulevard de l' Universite, BP 406, 44 602 Saint-Nazaire cedex (France)
2006-04-15
scope of this work is the determination of the coefficients of thermal expansion of the Ti-17 {beta}-phase. A rigorous inverse thermo-elastic self-consistent scale transition micro-mechanical model extended to multi-phase materials was used. The experimental data required for the application of the inverse method were obtained from both the available literature and especially dedicated X-ray diffraction lattice strain measurements performed on the studied ({alpha} + {beta}) two-phase titanium alloy.
Wavelet based correlation coefficient of time series of Saudi Meteorological Data
International Nuclear Information System (INIS)
Rehman, S.; Siddiqi, A.H.
2009-01-01
In this paper, wavelet concepts are used to study a correlation between pairs of time series of meteorological parameters such as pressure, temperature, rainfall, relative humidity and wind speed. The study utilized the daily average values of meteorological parameters of nine meteorological stations of Saudi Arabia located at different strategic locations. The data used in this study cover a period of 16 years between 1990 and 2005. Besides obtaining wavelet spectra, we also computed the wavelet correlation coefficients between two same parameters from two different locations and show that strong correlation or strong anti-correlation depends on scale. The cross-correlation coefficients of meteorological parameters between two stations were also calculated using statistical function. For coastal to costal pair of stations, pressure time series was found to be strongly correlated. In general, the temperature data were found to be strongly correlated for all pairs of stations and the rainfall data the least.
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.
Power Series Expansion of Propagator for Path Integral and Its Applications
International Nuclear Information System (INIS)
Ou Yuanjin; Liang Xianting
2007-01-01
In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.
Directory of Open Access Journals (Sweden)
Sobczyk Tadeusz J.
2015-09-01
Full Text Available Energy based approach was used in the study to formulate a set of functions approximating the magnetic flux linkages versus independent currents. The simplest power series that approximates field co-energy and linked fluxes for a two winding core of an induction machine are described by a set of common unknown coefficients. The authors tested three algorithms for the coefficient estimation using Weighted Least-Squared Method for two different positions of the coils. The comparison of the approximation accuracy was accomplished in the specified area of the currents. All proposed algorithms of the coefficient estimation have been found to be effective. The algorithm based solely on the magnetic field co-energy values is significantly simpler than the method based on the magnetic flux linkages estimation concept. The algorithm based on the field co-energy and linked fluxes seems to be the most suitable for determining simultaneously the coefficients of power series approximating linked fluxes and field co-energy.
Evaluating the coefficients of autocorrelation in a series of annual run-off of the Far East rivers
Energy Technology Data Exchange (ETDEWEB)
Sakharyuk, A V
1981-01-01
An evaluation is made of the coefficients of autocorrelation in series of annual river run-off based on group analysis using data on the distribution law of sampling correlation coefficients of temporal series subordinate to the III type Pearson's distribution.
Energy of the amplitude mode in the bicubic antiferromagnet: Series expansion results
Oitmaa, J.
2018-05-01
Series expansion methods are used to study the quantum critical behavior of the bicubic spin-1/2 antiferromagnet. Excitation energies are computed throughout the Brillouin zone, for both the Néel and dimer phases. We compute the energy of the amplitude/Higgs mode and show that it becomes degenerate with the magnon modes at the quantum critical point, as expected on general symmetry grounds.
A Formula for the Coefficient of Thermal Expansion of Crude Oils ...
African Journals Online (AJOL)
A new formula for the calculation of the coefficient of world crude oils has been developed. The formula is semi theoretical. The empirical part was obtained by regression calculation of the Formation Volume Factor of the gas free crude oil at reservoir temperature. Comparison of the calculated values of the Formation ...
International Nuclear Information System (INIS)
Calais, Daniel; Saada, Georges; Simenel, Nicole
1959-01-01
The anisotropy of the expansion coefficients of uranium, zirconium and zinc provoke internal tensions in the course of cooling these metals. These tensions are eliminated in the case of zinc by restoration to room temperature, but persist in uranium and zirconium and are responsible for the absence of an elastic limit in these two metals. Reprint of a paper published in Comptes rendus des seances de l'Academie des Sciences, t. 249, p. 1225-1227, sitting of 5 October 1959 [fr
Linear thermal expansion coefficient of cast Fe-Ni invar and Fe-Ni-Co superinvar alloys
International Nuclear Information System (INIS)
Ogorodnikova, O.M.; Chermenskaya, E.V.; Rabinovich, S.V.; Grachev, S.V.
1999-01-01
Cast invar alloys Fe-Ni (28-35 wt. % Ni) are investigated using metallography, dilatometry and X-ray methods as soon as the crystallization is completed and again after low-temperature treatment resulting in martensitic transformation in low nickel alloys. Nickel distribution in a cast superinvar Fe-32% Ni-4% Co is studied by means of X-ray spectrum microanalysis. The results obtained permit the correction of model concepts about cast invars and the estimate of a coefficient of linear expansion depending on phase composition and nickel microsegregation [ru
Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method
Directory of Open Access Journals (Sweden)
Xiaowang Li
2016-01-01
Full Text Available A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.
Directory of Open Access Journals (Sweden)
Naoki Yamamoto
2011-01-01
Full Text Available A new technique for measuring Young's modulus of an ultra-thin film, with a thickness in the range of about 10 nm, was developed by combining an optical lever technique for measuring the residual stress and X-ray diffraction for measuring the strain in the film. The new technique was applied to analyze the mechanical properties of Ga-doped ZnO (GZO films, that have become the focus of significant attention as a substitute material for indium-tin-oxide transparent electrodes. Young's modulus of the as-deposited GZO films decreased with thickness; the values for 30 nm and 500 nm thick films were 205 GPa and 117 GPa, respectively. The coefficient of linear thermal expansion of the GZO films was measured using the new technique in combination with in-situ residual stress measurement during heat-cycle testing. GZO films with 30–100 nm thickness had a coefficient of linear thermal expansion in the range of 4.3 × 10−6 – 5.6 × 10−6 °C−1.
Directory of Open Access Journals (Sweden)
Monzavi A
2002-07-01
Full Text Available Waxes have a lot of applications in dentistry. Such materials are of thermoplastic type that undergoes deformation in different temperatures. Two important properties of base plate waxes are flow and their coefficient of linear thermal expansion. Recently, different institutions, inside the country, produce dentistry waxes, while they have not been standardized. Consequently, consumers' dissatisfaction are observed. In this research, the two above- mentioned factors were compared between three kinds of Iranian waxes with Cavex that is foreign production, based on test number 24 of ADA. To measure the flow rate in the temperatures of 23, 37 and 45°c, Wilcoxon statistical analysis was used. The results showed that in 23°c, the flow rate of Cavex and Azardent waxes met ADA standards; however, it was not true for two others types. In 37°c, the flow of none of the waxes was standardized and in 45°c their flow was acceptable, moreover, thermal expansion coefficient, for Cavex and Azardent types, was based on ADA standard.
Directory of Open Access Journals (Sweden)
Abdollah Saboori
2017-12-01
Full Text Available In this research, copper nanocomposites reinforced by graphene nanoplatelets (GNPs were fabricated using a wet mixing method followed by a classical powder metallurgy route. In order to find the best dispersion technique, ball milling and wet mixing were chosen. Qualitative evaluation of the structure of the graphene after mixing indicated that the wet mixing is an appropriate technique to disperse the GNPs. Thereafter, the influence of graphene content on microstructure, density, hardness, elastic modulus, and thermal expansion coefficient of composites was investigated. It was shown that by increasing the graphene content the aggregation of graphene is more obvious and, thus, these agglomerates affect the final properties adversely. In comparison with the unreinforced Cu, Cu–GNP composites were lighter, and their hardness and Young’s modulus were higher as a consequence of graphene addition. According to the microstructural observation of pure copper and its composites after sintering, it was concluded that grain refinement is the main mechanism of strengthening in this research. Apart from the mechanical characteristics, the coefficient of thermal expansion of composites decreased remarkably and the combination of this feature with appropriate mechanical properties can make them a promising candidate for use in electronic packaging applications.
Energy Technology Data Exchange (ETDEWEB)
Zheng, Fasong [The State Key Lab of Precision Measurement Technology and Instrument, Department of Precision Instruments, Tsinghua University, Beijing 100084 (China); Departments of Physics, College of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Tan, Yidong; Zhang, Shulian, E-mail: zsl-dpi@mail.tsinghua.edu.cn [The State Key Lab of Precision Measurement Technology and Instrument, Department of Precision Instruments, Tsinghua University, Beijing 100084 (China); Lin, Jing; Ding, Yingchun [Departments of Physics, College of Science, Beijing University of Chemical Technology, Beijing 100029 (China)
2015-04-15
The noncooperative and ultrahigh sensitive length measurement approach is of great significance to the study of a high-precision thermal expansion coefficient (TEC) determination of materials at a wide temperature range. The novel approach is presented in this paper based on the Nd:YAG microchip laser feedback interferometry with 1064 nm wavelength, the beam frequency of which is shifted by a pair of acousto-optic modulators and then the heterodyne phase measurement technique is used. The sample is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams are perpendicular and coaxial on each surface of the sample, the configuration which can not only achieve the length measurement of sample but also eliminate the influence of the distortion of the sample supporter. The reference beams inject on the reference mirrors which are put as possible as near the holes, respectively, to eliminate the air disturbances and the influence of thermal lens effect out of the furnace chamber. For validation, the thermal expansion coefficients of aluminum and steel 45 samples are measured from room temperature to 748 K, which proved measurement repeatability of TECs is better than 0.6 × 10{sup −6}(K{sup −1}) at the range of 298 K–598 K and the high-sensitive non-contact measurement of the low reflectivity surface induced by the oxidization of the samples at the range of 598 K–748 K.
International Nuclear Information System (INIS)
Kim, Jae Kwan; Cho, Hye Sung; Jung, Ho-Sup; Suh, Kahp-Yang; Lim, Kipil; Kim, Ki-Bum; Choi, Dae-Geun; Jeong, Jun-Ho
2012-01-01
We report on nanoimprinting of polymer thin films at 30 nm scale resolution using two types of ultraviolet (UV)-curable, flexible polymer molds: perfluoropolyether (PFPE) and polyurethane acrylate (PUA). It was found that the quality of nanopatterning at the 30 nm scale is largely determined by the combined effects of surface tension and the coefficient of thermal expansion of the polymer mold. In particular, the polar component of surface tension may play a critical role in clean release of the mold, as evidenced by much reduced delamination or broken structures for the less polarized PFPE mold when patterning a relatively hydrophilic PMMA film. In contrast, such problems were not notably observed with a relatively hydrophobic PS film for both polymer molds. In addition, the demolding characteristic was also influenced by the coefficient of thermal expansion so that no delamination or uniformity problems were observed when patterning a UV-curable polymer film at room temperature. These results suggest that a proper polymeric mold material needs to be chosen for patterning polymer films under different surface properties and processing conditions, providing insights into how a clean demolding characteristic can be obtained at 30 nm scale nanopatterning. (paper)
Laurent series expansion of sunrise-type diagrams using configuration space techniques
International Nuclear Information System (INIS)
Groote, S.; Koerner, J.G.; Pivovarov, A.A.
2004-01-01
We show that configuration space techniques can be used to efficiently calculate the complete Laurent series ε-expansion of sunrise-type diagrams to any loop order in D-dimensional space-time for any external momentum and for arbitrary mass configurations. For negative powers of ε the results are obtained in analytical form. For positive powers of ε including the finite ε 0 contribution the result is obtained numerically in terms of low-dimensional integrals. We present general features of the calculation and provide exemplary results up to five-loop order which are compared to available results in the literature. (orig.)
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.
Conformal expansions and renormalons
Energy Technology Data Exchange (ETDEWEB)
Rathsman, J.
2000-02-07
The coefficients in perturbative expansions in gauge theories are factorially increasing, predominantly due to renormalons. This type of factorial increase is not expected in conformal theories. In QCD conformal relations between observables can be defined in the presence of a perturbative infrared fixed-point. Using the Banks-Zaks expansion the authors study the effect of the large-order behavior of the perturbative series on the conformal coefficients. The authors find that in general these coefficients become factorially increasing. However, when the factorial behavior genuinely originates in a renormalon integral, as implied by a postulated skeleton expansion, it does not affect the conformal coefficients. As a consequence, the conformal coefficients will indeed be free of renormalon divergence, in accordance with previous observations concerning the smallness of these coefficients for specific observables. The authors further show that the correspondence of the BLM method with the skeleton expansion implies a unique scale-setting procedure. The BLM coefficients can be interpreted as the conformal coefficients in the series relating the fixed-point value of the observable with that of the skeleton effective charge. Through the skeleton expansion the relevance of renormalon-free conformal coefficients extends to real-world QCD.
Directory of Open Access Journals (Sweden)
Shiqi Zhou
2013-10-01
Full Text Available Monte Carlo simulations in the canonical ensemble are performed for fluid with potential consisting of a square-well plus a square-barrier to obtain thermodynamic properties such as pressure, excess energy, constant volume excess heat capacity, and excess chemical potential, and structural property such as radial distribution function. The simulations cover a wide density range for the fluid phase, several temperatures, and different combinations of the parameters defining the potential. These simulation data have been used to test performances of a coupling parameter series expansion (CPSE recently proposed by one of the authors [S. Zhou, Phys. Rev. E 74, 031119 (2006], and a traditional 2nd-order high temperature series expansion (HTSE based on a macroscopic compressibility approximation (MAC used with confidence since its introduction in 1967. It is found that (i the MCA-based 2nd-order HTSE unexpectedly and depressingly fails for most situations investigated, and the present simulation results can serve well as strict criteria for testing liquid state theories. (ii The CPSE perturbation scheme is shown to be capable of predicting very accurately most of the thermodynamic properties simulated, but the most appropriate level of truncating the CPSE differs and depends on the range of the potential to be calculated; in particular, the shorter the potential range is, the higher the most appropriate truncating level can be, and along with rising of the potential range the performance of the CPSE perturbation scheme will decrease at higher truncating level. (iii The CPSE perturbation scheme can calculate satisfactorily bulk fluid rdf, and such calculations can be done for all fluid states of the whole phase diagram. (iv The CPSE is a convergent series at higher temperatures, but show attribute of asymptotic series at lower temperatures, and as a result, the surest asymptotic value occurs at lower-order truncation.
On the group of substitutions of formal power series with integer coefficients
International Nuclear Information System (INIS)
Babenko, I K; Bogatyi, S A
2008-01-01
We study certain properties of the group J(Z) of substitutions of formal power series in one variable with integer coefficients. We show that J(Z), regarded as a topological group, has four generators and cannot be generated by fewer elements. In particular, we show that the one-dimensional continuous homology of J(Z) is isomorphic to Z oplus Z oplus Z 2 oplus Z 2 . We study various topological and geometric properties of the coset space J(R)/J(Z). We compute the real cohomology H-tilde*(J(Z);R) with uniformly locally constant supports and show that it is naturally isomorphic to the cohomology of the nilpotent part of the Lie algebra of formal vector fields on the line
On power series expansions of the S-resolvent operator and the Taylor formula
Colombo, Fabrizio; Gantner, Jonathan
2016-12-01
The S-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of n-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of S-spectrum and of S-resolvent operator. Since most of the properties that hold for the Riesz-Dunford functional calculus extend to the S-functional calculus, it can be considered its non commutative version. In this paper we show that the Taylor formula of the Riesz-Dunford functional calculus can be generalized to the S-functional calculus. The proof is not a trivial extension of the classical case because there are several obstructions due to the non commutativity of the setting in which we work that have to be overcome. To prove the Taylor formula we need to introduce a new series expansion of the S-resolvent operators associated to the sum of two n-tuples of operators. This result is a crucial step in the proof of our main results, but it is also of independent interest because it gives a new series expansion for the S-resolvent operators. This paper is addressed to researchers working in operator theory and in hypercomplex analysis.
International Nuclear Information System (INIS)
Lesnaya, M.I.; Volokitin, G.G.; Kashchuk, V.A.
1976-01-01
Results are reported of an experimental research into the influence of small additions of α-transition metals on the temperature coefficient of linear expansion of titanium and vanadium. Using the configuration model of substance as the basis, expeained are the lowering of the critical liquefaction temperature or the melting point of vanadium and the raising of it, as caused by the addition of metals of the 6 group of the periodic chart and by the addition of metals of the 8 group, respectively, and also a shift in the temperature of the polymorphic α-β-transformation of titanium. Suggested as the best alloying metal for vanadium are tungsten and tantalum; for titaniums is vanadium whose admixtures lower the melting point and shift the polymorphic transformation temperature by as much as 100 to 120 degrees
Jedamzik, Ralf; Westerhoff, Thomas
2017-09-01
The coefficient of thermal expansion (CTE) and its spatial homogeneity from small to large formats is the most important property of ZERODUR. Since more than a decade SCHOTT has documented the excellent CTE homogeneity. It started with reviews of past astronomical telescope projects like the VLT, Keck and GTC mirror blanks and continued with dedicated evaluations of the production. In recent years, extensive CTE measurements on samples cut from randomly selected single ZERODUR parts in meter size and formats of arbitrary shape, large production boules and even 4 m sized blanks have demonstrated the excellent CTE homogeneity in production. The published homogeneity data shows single ppb/K peak to valley CTE variations on medium spatial scale of several cm down to small spatial scale of only a few mm mostly at the limit of the measurement reproducibility. This review paper summarizes the results also in respect to the increased CTE measurement accuracy over the last decade of ZERODUR production.
Monitoring rubber plantation expansion using Landsat data time series and a Shapelet-based approach
Ye, Su; Rogan, John; Sangermano, Florencia
2018-02-01
The expansion of tree plantations in tropical forests for commercial rubber cultivation threatens biodiversity which may affect ecosystem services, and hinders ecosystem productivity, causing net carbon emission. Numerous studies refer to the challenge of reliably distinguishing rubber plantations from natural forest, using satellite data, due to their similar spectral signatures, even when phenology is incorporated into an analysis. This study presents a novel approach for monitoring the establishment and expansion of rubber plantations in Seima Protection Forest (SPF), Cambodia (1995-2015), by detecting and analyzing the 'shapelet' structure in a Landsat-NDVI time series. This paper introduces a new classification procedure consisting of two steps: (1) an exhaustive-searching algorithm to detect shapelets that represent a period for relatively low NDVI values within an image time series; and (2) a t-test used to determine if NDVI values of detected shapelets are significantly different than their non-shapelet trend, thereby indicating the presence of rubber plantations. Using this approach, historical rubber plantation events were mapped over the twenty-year timespan. The shapelet algorithm produced two types of information: (1) year of rubber plantation establishment; and (2) pre-conversion land-cover type (i.e., agriculture, or natural forest). The overall accuracy of the rubber plantation map for the year of 2015 was 89%. The multi-temporal map products reveal that more than half of the rubber planting activity (57%) took place in 2010 and 2011, following the granting of numerous rubber concessions two years prior. Seventy-three percent of the rubber plantations were converted from natural forest and twenty-three percent were established on non-forest land-cover. The shapelet approach developed here can be used reliably to improve our understanding of the expansion of rubber production beyond Seima Protection Forest of Cambodia, and likely elsewhere in the
Reilly, J.; Abdel-Jaber, H.; Yarnold, M.; Glisic, B.
2017-04-01
Structural Health Monitoring aims to characterize the performance of a structure from a combination of recorded sensor data and analytic techniques. Many methods are concerned with quantifying the elastic response of the structure, treating temperature changes as noise in the analysis. While these elastic profiles do demonstrate a portion of structural behavior, thermal loads on a structure can induce comparable strains to elastic loads. Understanding this relationship between the temperature of the structure and the resultant strain and displacement can provide in depth knowledge of the structural condition. A necessary parameter for this form of analysis is the Coefficient of Thermal Expansion (CTE). The CTE of a material relates the amount of expansion or contraction a material undergoes per degree change in temperature, and can be determined from temperature-strain relationship given that the thermal strain can be isolated. Many times with concrete, the actual amount of expansion with temperature in situ varies from the given values for the CTE due to thermally generated elastic strain, which complicates evaluation of the CTE. To accurately characterize the relationship between temperature and strain on a structure, the actual thermal behavior of the structure needs to be analyzed. This rate can vary for different parts of a structure, depending on boundary conditions. In a case of unrestrained structures, the strain in the structure should be linearly related to the temperature change. Thermal gradients in a structure can affect this relationship, as they induce curvature and deplanations in the cross section. This paper proposes a method that addresses these challenges in evaluating the CTE.
International Nuclear Information System (INIS)
Roger, M.; Suaudeau, E.; Bernier, M.E.R.
1987-08-01
High temperature series expansions with a multiple-exchange Hamiltonian are performed to fourth order in arbitrary magnetic field for both phases of solid 3 He. The susceptibility series are analysed with Pade approximants and compared with recent experimental results. For the hcp phase we estimate the ferromagnetic ordering temperature from susceptibility series and discuss the influence of four-particle exchange in lowering the transition
International Nuclear Information System (INIS)
Li Yan-Chao; Wang Chun-Hui; Qu Yang; Gao Long; Cong Hai-Fang; Yang Yan-Ling; Gao Jie; Wang Ao-You
2011-01-01
This paper proposes a novel method of multi-beam laser heterodyne measurement for metal linear expansion coefficient. Based on the Doppler effect and heterodyne technology, the information is loaded of length variation to the frequency difference of the multi-beam laser heterodyne signal by the frequency modulation of the oscillating mirror, this method can obtain many values of length variation caused by temperature variation after the multi-beam laser heterodyne signal demodulation simultaneously. Processing these values by weighted-average, it can obtain length variation accurately, and eventually obtain the value of linear expansion coefficient of metal by the calculation. This novel method is used to simulate measurement for linear expansion coefficient of metal rod under different temperatures by MATLAB, the obtained result shows that the relative measurement error of this method is just 0.4%. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Li, Yan-Chao; Wang, Chun-Hui; Qu, Yang; Gao, Long; Cong, Hai-Fang; Yang, Yan-Ling; Gao, Jie; Wang, Ao-You
2011-01-01
This paper proposes a novel method of multi-beam laser heterodyne measurement for metal linear expansion coefficient. Based on the Doppler effect and heterodyne technology, the information is loaded of length variation to the frequency difference of the multi-beam laser heterodyne signal by the frequency modulation of the oscillating mirror, this method can obtain many values of length variation caused by temperature variation after the multi-beam laser heterodyne signal demodulation simultaneously. Processing these values by weighted-average, it can obtain length variation accurately, and eventually obtain the value of linear expansion coefficient of metal by the calculation. This novel method is used to simulate measurement for linear expansion coefficient of metal rod under different temperatures by MATLAB, the obtained result shows that the relative measurement error of this method is just 0.4%.
Energy Technology Data Exchange (ETDEWEB)
Svetlov, I L; Sukhanov, N N; Krivko, A I; Roshchina, I N; Khatsinskaia, I M
1987-01-01
Experimental data are presented on the temperature dependence of the short- term strength characteristics, Young's modulus, and linear expansion coefficients of single crystals of a nickel alloy, ZhS6F, with crystallographic orientations along the 001, 111, 011, and 112 lines. It is found that the mechanical properties and Young's modulus of the alloy crystals exibit anisotropy in the temperature range 20-900 C. The linear thermal expansion coefficient is isotropic up to 900 C and equal to that of the equiaxed alloy. 10 references.
Dolgov, Sergey
2015-11-03
We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some quantities of interest (mean, variance, and exceedance probabilities). We assume that the random diffusion coefficient is given as a smooth transformation of a Gaussian random field. In this case, the PCE is delivered by a complicated formula, which lacks an analytic TT representation. To construct its TT approximation numerically, we develop the new block TT cross algorithm, a method that computes the whole TT decomposition from a few evaluations of the PCE formula. The new method is conceptually similar to the adaptive cross approximation in the TT format but is more efficient when several tensors must be stored in the same TT representation, which is the case for the PCE. In addition, we demonstrate how to assemble the stochastic Galerkin matrix and to compute the solution of the elliptic equation and its postprocessing, staying in the TT format. We compare our technique with the traditional sparse polynomial chaos and the Monte Carlo approaches. In the tensor product polynomial chaos, the polynomial degree is bounded for each random variable independently. This provides higher accuracy than the sparse polynomial set or the Monte Carlo method, but the cardinality of the tensor product set grows exponentially with the number of random variables. However, when the PCE coefficients are implicitly approximated in the TT format, the computations with the full tensor product polynomial set become possible. In the numerical experiments, we confirm that the new methodology is competitive in a wide range of parameters, especially where high accuracy and high polynomial degrees are required.
Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr
2016-01-01
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435
Jiao, S.; Yu, J.; Wang, Y.; Zhu, L.; Zhou, Q.
2018-04-01
In recent decades, urbanization has resulted a massive increase in the amount of infrastructure especially large buildings in large cities worldwide. There has been a noticeable expansion of entire cities both horizontally and vertically. One of the common consequences of urban expansion is the increase of ground loads, which may trigger land subsidence and can be a potential threat of public safety. Monitoring trends of urban expansion and land subsidence using remote sensing technology is needed to ensure safety along with urban planning and development. The Defense Meteorological Satellite Program Operational Line scan System (DMSP/OLS) Night-Time Light (NTL) images have been used to study urbanization at a regional scale, proving the capability of recognizing urban expansion patterns. In the current study, a normalized illuminated urban area dome volume (IUADV) based on inter-calibrated DMSP/OLS NTL images is shown as a practical approach for estimating urban expansion of Beijing at a single period in time and over subsequent years. To estimate the impact of urban expansion on land subsidence, IUADV was correlated with land subsidence rates obtained using the Stanford Method for Persistent Scatterers (StaMPS) approach within the Persistent Scatterers InSAR (PSInSAR) methodology. Moderate correlations are observed between the urban expansion based on the DMSP/OLS NTL images and land subsidence. The correlation coefficients between the urban expansion of each year and land subsidence tends to gradually decrease over time (Coefficient of determination R = 0.80 - 0.64 from year 2005 to year 2010), while the urban expansion of two sequential years exhibit an opposite trend (R = 0.29 - 0.57 from year 2005 to year 2010) except for the two sequential years between 2007 and 2008 (R = 0.14).
International Nuclear Information System (INIS)
Hall, G.; Marsden, B.J.; Fok, S.L.; Smart, J.
2003-01-01
In the 1960s, a theoretical relationship between the dimensional changes and the coefficient of thermal expansion of irradiated graphite was derived by J.H.W. Simmons. The theory was shown to be comparable with experimental observations at low irradiation doses, but shown to diverge at higher irradiation doses. However, various modified versions of this theory have been used as the foundation of design and life prediction calculations for graphite-moderated reactors. This paper re-examines the Simmons relationship, summarising its derivation and assumptions. The relationship was then modified to incorporate the high dose, high strain changes that were assumed to be represented in the changes in Young's modulus with irradiation dose. By scrutinising the behaviour of finite element analyses, it was possible to use a modified Simmons relationship to predict the dimensional changes of an isotropic and anisotropic graphite to high irradiation doses. These issues are important to present high-temperature reactors (HTRs) as the life of HTR graphite components is dependent upon their dimensional change behaviour. A greater understanding of this behaviour will help in the selection and development of graphite materials
International Nuclear Information System (INIS)
Arregui-Mena, José David; Margetts, Lee; Griffiths, D.V.; Lever, Louise; Hall, Graham; Mummery, Paul M.
2015-01-01
In this paper, the authors test the hypothesis that tiny spatial variations in material properties may lead to significant pre-service stresses in virgin graphite bricks. To do this, they have customised ParaFEM, an open source parallel finite element package, adding support for stochastic thermo-mechanical analysis using the Monte Carlo Simulation method. For an Advanced Gas-cooled Reactor brick, three heating cases have been examined: a uniform temperature change; a uniform temperature gradient applied through the thickness of the brick and a simulated temperature profile from an operating reactor. Results are compared for mean and stochastic properties. These show that, for the proof-of-concept analyses carried out, the pre-service von Mises stress is around twenty times higher when spatial variability of material properties is introduced. The paper demonstrates that thermal gradients coupled with material incompatibilities may be important in the generation of stress in nuclear graphite reactor bricks. Tiny spatial variations in coefficient of thermal expansion (CTE) and Young's modulus can lead to the presence of thermal stresses in bricks that are free to expand. - Highlights: • Open source software has been modified to include random variability in CTE and Young's modulus. • The new software closely agrees with analytical solutions and commercial software. • Spatial variations in CTE and Young's modulus produce stresses that do not occur with mean values. • Material variability may induce pre-service stress in virgin graphite.
Energy Technology Data Exchange (ETDEWEB)
Arregui-Mena, José David, E-mail: jose.arreguimena@postgrad.manchester.ac.uk [School of Mechanical, Aerospace, and Civil Engineering, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Margetts, Lee, E-mail: lee.margetts@manchester.ac.uk [School of Mechanical, Aerospace, and Civil Engineering, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Griffiths, D.V., E-mail: d.v.griffiths@mines.edu [Colorado School of Mines, 1500 Illinois St, Golden, CO 80401 (United States); Lever, Louise, E-mail: louise.lever@manchester.ac.uk [Research Computing, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Hall, Graham, E-mail: graham.n.hall@manchester.ac.uk [School of Mechanical, Aerospace, and Civil Engineering, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom); Mummery, Paul M., E-mail: paul.m.mummery@manchester.ac.uk [School of Mechanical, Aerospace, and Civil Engineering, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom)
2015-10-15
In this paper, the authors test the hypothesis that tiny spatial variations in material properties may lead to significant pre-service stresses in virgin graphite bricks. To do this, they have customised ParaFEM, an open source parallel finite element package, adding support for stochastic thermo-mechanical analysis using the Monte Carlo Simulation method. For an Advanced Gas-cooled Reactor brick, three heating cases have been examined: a uniform temperature change; a uniform temperature gradient applied through the thickness of the brick and a simulated temperature profile from an operating reactor. Results are compared for mean and stochastic properties. These show that, for the proof-of-concept analyses carried out, the pre-service von Mises stress is around twenty times higher when spatial variability of material properties is introduced. The paper demonstrates that thermal gradients coupled with material incompatibilities may be important in the generation of stress in nuclear graphite reactor bricks. Tiny spatial variations in coefficient of thermal expansion (CTE) and Young's modulus can lead to the presence of thermal stresses in bricks that are free to expand. - Highlights: • Open source software has been modified to include random variability in CTE and Young's modulus. • The new software closely agrees with analytical solutions and commercial software. • Spatial variations in CTE and Young's modulus produce stresses that do not occur with mean values. • Material variability may induce pre-service stress in virgin graphite.
Wu, Zi Yi; Xie, Ping; Sang, Yan Fang; Gu, Hai Ting
2018-04-01
The phenomenon of jump is one of the importantly external forms of hydrological variabi-lity under environmental changes, representing the adaption of hydrological nonlinear systems to the influence of external disturbances. Presently, the related studies mainly focus on the methods for identifying the jump positions and jump times in hydrological time series. In contrast, few studies have focused on the quantitative description and classification of jump degree in hydrological time series, which make it difficult to understand the environmental changes and evaluate its potential impacts. Here, we proposed a theatrically reliable and easy-to-apply method for the classification of jump degree in hydrological time series, using the correlation coefficient as a basic index. The statistical tests verified the accuracy, reasonability, and applicability of this method. The relationship between the correlation coefficient and the jump degree of series were described using mathematical equation by derivation. After that, several thresholds of correlation coefficients under different statistical significance levels were chosen, based on which the jump degree could be classified into five levels: no, weak, moderate, strong and very strong. Finally, our method was applied to five diffe-rent observed hydrological time series, with diverse geographic and hydrological conditions in China. The results of the classification of jump degrees in those series were closely accorded with their physically hydrological mechanisms, indicating the practicability of our method.
International Nuclear Information System (INIS)
Sakamoto, Yoshiaki; Takebe, Shinichi; Ogawa, Hiromichi; Inagawa, Satoshi; Sasaki, Tomozou
2001-01-01
In order to study sorption behavior of U series radionuclides (Pb, Ra, Th, Ac, Pa and U) under aerated zone environment (loam-rain water system) and aquifer environment (sand-groundwater system) for safety assessment of U bearing waste, pH dependence of distribution coefficients of each element has been obtained. The pH dependence of distribution coefficients of Pb, Ra, Th, Ac and U was analyzed by model calculation based on aqueous speciation of each element and soil surface charge characteristics, which is composed of a cation exchange capacity and surface hydroxyl groups. From the model calculation, the sorption behavior of Pb, Ra, Th, Ac and U could be described by a combination of cation exchange reaction and surface-complexation model. (author)
Nakanishi, Koichi; Kogure, Akinori; Deuchi, Keiji; Kuwana, Ritsuko; Takamatsu, Hiromu; Ito, Kiyoshi
2015-01-01
We previously developed a method for evaluating the heat resistance of microorganisms by measuring the transition temperature at which the coefficient of linear expansion of a cell changes. Here, we performed heat resistance measurements using a scanning probe microscope with a nano thermal analysis system. The microorganisms studied included six strains of the genus Bacillus or related genera, one strain each of the thermophilic obligate anaerobic bacterial genera Thermoanaerobacter and Moorella, two strains of heat-resistant mold, two strains of non-sporulating bacteria, and one strain of yeast. Both vegetative cells and spores were evaluated. The transition temperature at which the coefficient of linear expansion due to heating changed from a positive value to a negative value correlated strongly with the heat resistance of the microorganism as estimated from the D value. The microorganisms with greater heat resistance exhibited higher transition temperatures. There was also a strong negative correlation between the coefficient of linear expansion and heat resistance in bacteria and yeast, such that microorganisms with greater heat resistance showed lower coefficients of linear expansion. These findings suggest that our method could be useful for evaluating the heat resistance of microorganisms.
International Nuclear Information System (INIS)
Bernal, P.J.; Van Hook, W.A.
1986-01-01
The molar volumes, isobaric expansion coefficients, and isentropic compressibilities of solutions of a number of carbohydrates and their deuterated isomers were determined in H 2 O and D 2 O between 288.15 and 328.15 K and over a wide range of solute-to-solvent mole ratios. The results are discussed in terms of the specific hydration model. (author)
International Nuclear Information System (INIS)
Petrov, K.; Will, G.
1981-01-01
High-temperature treatment of tungsten carbide-cobalt hard alloys in TiB 2 media leads to the formation of a surface diffusion coating which contains orthorhombic WCoB. The function of this compound in enhancing wear resistance of cutting tools, is discussed. The thermal expansion of WCoB is of primary interest, since the wear resistance of the coating reflects the degree of matching of the thermal expansion coefficients of the different phases. Preparation of the samples is described and experimental details of the X-ray diffraction measurements are given. The temperature dependence of the lattice parameters for the range 300 to 973 K, and the corresponding linear thermal expansion coefficients along the three principal crystallographic directions, are given. The results are discussed in terms of the bonding features of the solid. (U.K.)
Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach
Directory of Open Access Journals (Sweden)
Weiping Li
2016-03-01
Full Text Available In this paper, we derive a pricing formula for arithmetic Asian options by using the Edgeworth series expansion. Our pricing formula consists of a Black-Scholes-Merton type formula and a finite sum with the estimation of the remainder term. Moreover, we present explicitly a method to compute each term in our pricing formula. The hedging formulas (greek letters for the arithmetic Asian options are obtained as well. Our formulas for the long lasting question on pricing and hedging arithmetic Asian options are easy to implement with enough accuracy. Our numerical illustration shows that the arithmetic Asian options worths less than the European options under the standard Black-Scholes assumptions, verifies theoretically that the volatility of the arithmetic average is less than the one of the underlying assets, and also discovers an interesting phenomena that the arithmetic Asian option for large fixed strikes such as stocks has higher volatility (elasticity than the plain European option. However, the elasticity of the arithmetic Asian options for small fixed strikes as trading in currencies and commodity products is much less than the elasticity of the plain European option. These findings are consistent with the ones from the hedgings with respect to the time to expiration, the strike, the present underlying asset price, the interest rate and the volatility.
The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics
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
CSIR Research Space (South Africa)
Shatalov, MY
2006-01-01
Full Text Available -scale structure to guarantee the numerical accuracy of solution. In the present paper the authors propose to use a novel method of solution of the Helmholtz integral equation, which is based on expansion of the integrands in double Fourier series. The main...
Naji, Ghassan Abdul-Hamid; Omar, Ros Anita; Yahya, Rosiyah
2017-03-01
In all-ceramic systems, a high incidence of veneer chip-off has been reported in clinical studies. Coefficient of thermal expansion (CTE) behaviour is one of the factors that may increase residual stress in the interface and influence the veneer/core bond strength. Therefore, this study aimed to evaluate the effect of sodalite zeolite-infiltration on the CTE behaviour and bond strength of different all-ceramic prostheses. The case-study groups were synthesized sodalite zeolite-infiltrated alumina (IA-SOD) and synthesized sodalite zeolite-infiltrated zirconia-toughened alumina (ZTA) (IZ-SOD), while the control groups were glass-infiltrated alumina (IA-glass) and glass-infiltrated ZTA (IZ-glass). Forty cylindrical-shaped samples measuring 5 mm in diameter and 10 mm in height were tested for CTE using a thermo-mechanical analyser machine, and forty disc-shaped ceramic samples measuring 12 mm in diameter and 1.2 ± 0.2 mm in thickness were prepared using specially designed stainless steel split mould and veneered by cylinder-shaped (2 mm high × 2 mm diameter) low-fusing porcelain (Vita VM7). The veneer/core samples were sintered and tested for shear bond strength using a high precision universal testing machine. Scanning electron microscope, stereo microscope, atomic force microscope, and energy-dispersive X-ray spectroscopy were used to investigate the structural characteristics of samples at the fracture surface. The collected data were analyzed with a one-way ANOVA and Tukey HSD test (α=.05). IZ-SOD revealed highest CTE and shear bond strength values, while the IA-glass revealed the lowest values than the other groups. There was no significant difference in CTE and bond strength among IZ-SOD, IA-SOD and IZ-glass samples (p>0.05). The experimental SOD zeolite-infiltrated samples revealed higher CTE mismatch and bond strength along with a more favourable mode of failure than did the commercial glass-infiltrated samples. Sandblast technique is considered as effective
Wang, Kaihua; Chen, Hua; Jiang, Weiping; Li, Zhao; Ma, Yifang; Deng, Liansheng
2018-04-01
There are apparent seasonal variations in GPS height time series, and thermal expansion is considered to be one of the potential geophysical contributors. The displacements introduced by thermal expansion are usually derived without considering the annex height and underground part of the monument (e.g. located on roof or top of the buildings), which may bias the geophysical explanation of the seasonal oscillation. In this paper, the improved vertical displacements are derived by a refined thermal expansion model where the annex height and underground depth of the monument are taken into account, and then 560 IGS stations are adopted to validate the modeled thermal expansion (MTE) displacements. In order to evaluate the impact of thermal expansion on GPS heights, the MTE displacements of 80 IGS stations with less data discontinuities are selected to compare with their observed GPS vertical (OGV) displacements with the modeled surface loading (MSL) displacements removed in advance. Quantitative analysis results show the maximum annual and semiannual amplitudes of the MTE are 6.65 mm (NOVJ) and 0.51 mm (IISC), respectively, and the maximum peak-to-peak oscillation of the MTE displacements can be 19.4 mm. The average annual amplitude reductions are 0.75 mm and 1.05 mm respectively after removing the MTE and MSL displacements from the OGV, indicating the seasonal oscillation induced by thermal expansion is equivalent to >75% of the impact of surface loadings. However, there are rarely significant reductions for the semiannual amplitude. Given the result in this study that thermal expansion can explain 17.3% of the annual amplitude in GPS heights on average, it must be precisely modeled both in GPS precise data processing and GPS time series analysis, especially for those stations located in the middle and high latitudes with larger annual temperature oscillation, or stations with higher monument.
Evaluation of random errors in Williams’ series coefficients obtained with digital image correlation
International Nuclear Information System (INIS)
Lychak, Oleh V; Holyns’kiy, Ivan S
2016-01-01
The use of the Williams’ series parameters for fracture analysis requires valid information about their error values. The aim of this investigation is the development of the method for estimation of the standard deviation of random errors of the Williams’ series parameters, obtained from the measured components of the stress field. Also, the criteria for choosing the optimal number of terms in the truncated Williams’ series for derivation of their parameters with minimal errors is proposed. The method was used for the evaluation of the Williams’ parameters, obtained from the data, and measured by the digital image correlation technique for testing a three-point bending specimen. (paper)
Modified Chapman–Enskog expansion: A new way to treat divergent series
International Nuclear Information System (INIS)
She Zhen-Su
2017-01-01
The resolution by Chen and Sun of divergent Chapman–Enskog expansion problem will not only build a unified foundation for non-equilibrium dynamics modeling at all Mach number and Knudsen number, but also shed light to a large class of difficult theoretical problems involving divergent expansion on strong nonlinearity. (paper)
Luceri, V.; Sciarretta, C.; Bianco, G.
2012-12-01
The redistribution of the mass within the earth system induces changes in the Earth's gravity field. In particular, the second-degree geopotential coefficients reflect the behaviour of the Earth's inertia tensor of order 2, describing the main mass variations of our planet impacting the EOPs. Thanks to the long record of accurate and continuous laser ranging observations to Lageos and other geodetic satellites, SLR is the only current space technique capable to monitor the long time variability of the Earth's gravity field with adequate accuracy. Time series of low-degree geopotential coefficients are estimated with our analysis of SLR data (spanning more than 25 years) from several geodetic satellites in order to detect trends and periodic variations related to tidal effects and atmospheric/oceanic mass variations. This study is focused on the variations of the second-degree Stokes coefficients related to the Earth's principal figure axis and oblateness: C21, S21 and C20. On the other hand, surface mass load variations induce excitations in the EOPs that are proportional to the same second-degree coefficients. The time series of direct estimates of low degree geopotential and those derived from the EOP excitation functions are compared and presented together with their time and frequency analysis.
Li, Litong; Lv, Dajuan; Yang, Minghong; Xiong, Liangming; Luo, Jie
2018-01-26
In this paper, a hybrid sensor was fabricated using a IR-femtosecond laser to measure the thermal expansion and thermo-optical coefficient of silica-based fiber Bragg gratings (FBGs). The hybrid sensor was composed of an inline fiber Fabry-Perot interferometer (FFPI) cavity and a type-II FBG. Experiment results showed that the type-II FBG had three high reflectivity resonances in the wavelength ranging from 1100 to 1600 nm, showing the peaks in 1.1, 1.3 and 1.5 μm, respectively. The thermal expansion and thermo-optical coefficient (1.3 μm, 1.5 μm) of silica-based FBG, under temperatures ranging from 30 to 1100 °C, had been simultaneously calculated by measuring the wavelength of the type-II FBG and FFPI cavity length.
Woodruff, David; Wu, Yi-Fang
2012-01-01
The purpose of this paper is to illustrate alpha's robustness and usefulness, using actual and simulated educational test data. The sampling properties of alpha are compared with the sampling properties of several other reliability coefficients: Guttman's lambda[subscript 2], lambda[subscript 4], and lambda[subscript 6]; test-retest reliability;…
International Nuclear Information System (INIS)
Sato, Kaoru; Endo, Akira; Saito, Kimiaki
2008-10-01
This report presents a complete set of conversion coefficients of organ doses and effective doses calculated for external photon exposure using five Japanese adult voxel phantoms developed at the Japan Atomic Energy Agency (JAEA). At the JAEA, high-resolution Japanese voxel phantoms have been developed to clarify the variation of organ doses due to the anatomical characteristics of Japanese, and three male phantoms (JM, JM2 and Otoko) and two female phantoms (JF and Onago) have been constructed up to now. The conversion coefficients of organ doses and effective doses for the five voxel phantoms have been calculated for six kinds of idealized irradiation geometries from monoenergetic photons ranging from 0.01 to 10 MeV using EGS4, a Monte Carlo code for the simulation of coupled electron-photon transport. The dose conversion coefficients are given as absorbed dose and effective dose per unit air-kerma free-in-air, and are presented in tables and figures. The calculated dose conversion coefficients are compared with those of voxel phantoms based on the Caucasian and the recommended values in ICRP74 in order to discuss (1) variation of organ dose due to the body size and individual anatomy, such as position and shape of organs, and (2) effect of posture on organ doses. The present report provides valuable data to study the influence of the body characteristics of Japanese upon the organ doses and to discuss developing reference Japanese and Asian phantoms. (author)
Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.
2015-01-01
We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some
Tien, Chuen-Lin; Lin, Tsai-Wei
2012-10-20
We present a new method based on fast Fourier transform (FFT) for evaluating the thermal expansion coefficient and thermomechanical properties of thin films. The silicon nitride thin films deposited on Corning glass and Si wafers were prepared by plasma-enhanced chemical vapor deposition in this study. The anisotropic residual stress and thermomechanical properties of silicon nitride thin films were studied. Residual stresses in thin films were measured by a modified Michelson interferometer associated with the FFT method under different heating temperatures. We found that the average residual-stress value increases when the temperature increases from room temperature to 100°C. Increased substrate temperature causes the residual stress in SiN(x) film deposited on Si wafers to be more compressive, but the residual stress in SiN(x) film on Corning glass becomes more tensile. The residual-stress versus substrate-temperature relation is a linear correlation after heating. A double substrate technique is used to determine the thermal expansion coefficients of the thin films. The experimental results show that the thermal expansion coefficient of the silicon nitride thin films is 3.27×10(-6)°C(-1). The biaxial modulus is 1125 GPa for SiN(x) film.
Series expansions of the density of states in SU(2) lattice gauge theory
International Nuclear Information System (INIS)
Denbleyker, A.; Du, Daping; Liu, Yuzhi; Meurice, Y.; Velytsky, A.
2008-01-01
We calculate numerically the density of states n(S) for SU(2) lattice gauge theory on L 4 lattices [S is the Wilson's action and n(S) measures the relative number of ways S can be obtained]. Small volume dependences are resolved for small values of S. We compare ln(n(S)) with weak and strong coupling expansions. Intermediate order expansions show a good overlap for values of S corresponding to the crossover. We relate the convergence of these expansions to those of the average plaquette. We show that, when known logarithmic singularities are subtracted from ln(n(S)), expansions in Legendre polynomials appear to converge and could be suitable to determine the Fisher's zeros of the partition function.
Scoggins, John F; Weinberg, Daniel A
2017-06-01
Published estimates of the healthcare coinsurance elasticity coefficient have typically relied on annual observations of individual healthcare expenditures even though health plan membership and expenditures are traditionally reported in monthly units and several studies have stressed the need for demand models to recognize the episodic nature of healthcare. Summing individual healthcare expenditures into annual observations complicates two common challenges of statistical inference, heteroscedasticity, and regressor endogeneity. This paper estimates the elasticity coefficient using a monthly panel data model that addresses the heteroscedasticity and endogeneity problems with relative ease. Healthcare claims data from employees of King County, Washington, during 2005 to 2011 were used to estimate the mean point elasticity coefficient: -0.314 (0.015 standard error) to -0.145 (0.015 standard error) depending on model specification. These estimates bracket the -0.2 point estimate (range: -0.22 to -0.17) derived from the famous Rand Health Insurance Experiment. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Optimizing the coefficients of the leading terms of the Born Series: FWI+MVA+more
Alkhalifah, Tariq Ali
2017-05-26
The scattering series theoretically utilizes a model perturbation framework to explain the difference between the seismic modeled data corresponding to a background model and those measured in the field corresponding to the real Earth. These perturbations include short wavelength features like those predicted by full waveform inversion (FWI) gradients, and long wavelength features often constrained by migration velocity analysis (MVA) objectives. The Born series, however, is not a convergent series. If the perturbations are large, we probably will not be able to explain the data difference. Thus, using the leading terms of the Born in an iterative process, in which they are scaled properly, allows us to avoid such limitations and update the short and long wavelength components of the velocity model. In fact, the FWI update is manifested in the first term of the Born series, and the MVA update is represented by the transmission (first Fresnel zone) part of the second term. In this case, FWI and MVA are code names for dividing the optimized update to reflectivity based portions and those adequate for the background, respectively. Examples on synthetic and real data demonstrate this logic.
Boehm, K; Rösgen, J; Hinz, H-J
2006-02-15
A new method is described that permits the continuous and synchronous determination of heat capacity and expansibility data. We refer to it as pressure-modulated differential scanning calorimetry (PMDSC), as it involves a standard DSC temperature scan and superimposes on it a pressure modulation of preselected format. The power of the method is demonstrated using salt solutions for which the most accurate heat capacity and expansibility data exist in the literature. As the PMDSC measurements could reproduce the parameters with high accuracy and precision, we applied the method also to an aqueous suspension of multilamellar DSPC vesicles for which no expansibility data had been reported previously for the transition region. Excellent agreement was obtained between data from PMDSC and values from independent direct differential scanning densimetry measurements. The basic theoretical background of the method when using sawtooth-like pressure ramps is given under Supporting Information, and a complete statistical thermodynamic derivation of the general equations is presented in the accompanying paper.
Directory of Open Access Journals (Sweden)
Masatoshi Hasegawa
2017-10-01
Full Text Available This paper reviews the development of new high-temperature polymeric materials applicable to plastic substrates in image display devices with a focus on our previous results. Novel solution-processable colorless polyimides (PIs with ultra-low linear coefficients of thermal expansion (CTE are proposed in this paper. First, the principles of the coloration of PI films are briefly discussed, including the influence of the processing conditions on the film coloration, as well as the chemical and physical factors dominating the low CTE characteristics of the resultant PI films to clarify the challenges in simultaneously achieving excellent optical transparency, a very high Tg, a very low CTE, and excellent film toughness. A possible approach of achieving these target properties is to use semi-cycloaliphatic PI systems consisting of linear chain structures. However, semi-cycloaliphatic PIs obtained using cycloaliphatic diamines suffer various problems during precursor polymerization, cyclodehydration (imidization, and film preparation. In particular, when using trans-1,4-cyclohexanediamine (t-CHDA as the cycloaliphatic diamine, a serious problem emerges: salt formation in the initial stages of the precursor polymerization, which terminates the polymerization in some cases or significantly extends the reaction period. The system derived from 3,3′,4,4′-biphenyltetracarboxylic dianhydride (s-BPDA and t-CHDA can be polymerized by a controlled heating method and leads to a PI film with relatively good properties, i.e., excellent light transmittance at 400 nm (T400 = ~80%, a high Tg (>300 °C, and a very low CTE (10 ppm·K−1. However, this PI film is somewhat brittle (the maximum elongation at break, εb max is about 10%. On the other hand, the combination of cycloaliphatic tetracarboxylic dianhydrides and aromatic diamines does not result in salt formation. The steric structures of cycloaliphatic tetracarboxylic dianhydrides significantly influence
Li, Huaiyong; Zhang, Siyuan; Zhou, Shihong; Cao, Xueqiang
2009-09-01
Theoretical researches are performed on the alpha-R2MoO6 (R = Y, Gd, Tb Dy, Ho, Er, Tm and Yb) and pyrochlore-type R2Mo2O7 (R = Y, Nd, Sm, Gd, Tb and Dy) rare earth molybdates by using chemical bond theory of dielectric description. The chemical bonding characteristics and their relationship with thermal expansion property and compressibility are explored. The calculated values of linear thermal expansion coefficient (LTEC) and bulk modulus agree well with the available experimental values. The calculations reveal that the LTECs and the bulk moduli do have linear relationship with the ionic radii of the lanthanides: the LTEC decreases from 6.80 to 6.62 10(-6)/K and the bulk modulus increases from 141 to 154 GPa when R goes in the order Gd, Tb Dy, Ho, Er, Tm, and Yb in the alpha-R2MoO6 series; while in the R2Mo2O7 series, the LTEC ranges from 6.80 to 6.61 10(-6)/K and the bulk modulus ranges from 147 to 163 GPa when R varies in the order Nd, Sm, Gd, Tb and Dy. Copyright 2008 Wiley Periodicals, Inc.
Modeling urban expansion in Yangon, Myanmar using Landsat time-series and stereo GeoEye Images
Sritarapipat, Tanakorn; Takeuchi, Wataru
2016-06-01
This research proposed a methodology to model the urban expansion based dynamic statistical model using Landsat and GeoEye Images. Landsat Time-Series from 1978 to 2010 have been applied to extract land covers from the past to the present. Stereo GeoEye Images have been employed to obtain the height of the building. The class translation was obtained by observing land cover from the past to the present. The height of the building can be used to detect the center of the urban area (mainly commercial area). It was assumed that the class translation and the distance of multi-centers of the urban area also the distance of the roads affect the urban growth. The urban expansion model based on the dynamic statistical model was defined to refer to three factors; (1) the class translation, (2) the distance of the multicenters of the urban areas, and (3) the distance from the roads. Estimation and prediction of urban expansion by using our model were formulated and expressed in this research. The experimental area was set up in Yangon, Myanmar. Since it is the major of country's economic with more than five million population and the urban areas have rapidly increased. The experimental results indicated that our model of urban expansion estimated urban growth in both estimation and prediction steps in efficiency.
González-Benito, J; Castillo, E; Cruz-Caldito, J F
2015-07-28
Nanothermal-expansion of poly(ethylene-co-vinylacetate), EVA, and poly(methyl methacrylate), PMMA, in the form of films was measured to finally obtain linear coefficients of thermal expansion, CTEs. The simple deflection of a cantilever in an atomic force microscope, AFM, was used to monitor thermal expansions at the nanoscale. The influences of: (a) the structure of EVA in terms of its composition (vinylacetate content) and (b) the size of PMMA chains in terms of the molecular weight were studied. To carry out this, several polymer samples were used, EVA copolymers with different weight percents of the vinylacetate comonomer (12, 18, 25 and 40%) and PMMA polymers with different weight average molecular weights (33.9, 64.8, 75.600 and 360.0 kg mol(-1)). The dependencies of the vinyl acetate weight fraction of EVA and the molecular weight of PMMA on their corresponding CTEs were analyzed to finally explain them using new, intuitive and very simple models based on the rule of mixtures. In the case of EVA copolymers a simple equation considering the weighted contributions of each comonomer was enough to estimate the final CTE above the glass transition temperature. On the other hand, when the molecular weight dependence is considered the free volume concept was used as novelty. The expansion of PMMA, at least at the nanoscale, was well and easily described by the sum of the weighted contributions of the occupied and free volumes, respectively.
International Nuclear Information System (INIS)
Wisniak, Jaime; Cortez, Gladis; Peralta, Rene D.; Infante, Ramiro; Elizalde, Luis E.; Amaro, Tlaloc A.; Garcia, Omar; Soto, Homero
2008-01-01
Densities of the binary systems of dimethyl carbonate with butyl methacrylate, allyl methacrylate, styrene, and vinyl acetate have been measured as a function of the composition at (293.15, 303.15, and 313.15) K at atmospheric pressure, using an Anton Paar DMA 5000 oscillating U-tube densimeter. The excess molar volumes are negative for the (dimethyl carbonate + vinyl acetate) system and positive for the three other binaries, and become more so as the temperature increases from (293.15 to 313.15) K. The apparent volumes were used to calculate the values of the partial excess molar volumes at infinite dilution. The excess coefficient of thermal expansion is positive for the four binary systems. The calculated excess molar volumes were correlated with the Redlich-Kister equation and with a series of Legendre polynomials. An explanation of the results is offered based on the FT-IR (ATR) spectra of several mixtures of the different systems
Energy Technology Data Exchange (ETDEWEB)
Wisniak, Jaime [Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)], E-mail: wisniak@bgumail.bgu.ac.il; Cortez, Gladis; Peralta, Rene D.; Infante, Ramiro; Elizalde, Luis E. [Centro de Investigacion en Quimica Aplicada, Saltillo 25253, Coahuila (Mexico); Amaro, Tlaloc A.; Garcia, Omar; Soto, Homero [Facultad de Ciencias Quimicas, Universidad Autonoma de Coahuila, Saltillo 25280, Coahuila (Mexico)
2008-12-15
Densities of the binary systems of dimethyl carbonate with butyl methacrylate, allyl methacrylate, styrene, and vinyl acetate have been measured as a function of the composition at (293.15, 303.15, and 313.15) K at atmospheric pressure, using an Anton Paar DMA 5000 oscillating U-tube densimeter. The excess molar volumes are negative for the (dimethyl carbonate + vinyl acetate) system and positive for the three other binaries, and become more so as the temperature increases from (293.15 to 313.15) K. The apparent volumes were used to calculate the values of the partial excess molar volumes at infinite dilution. The excess coefficient of thermal expansion is positive for the four binary systems. The calculated excess molar volumes were correlated with the Redlich-Kister equation and with a series of Legendre polynomials. An explanation of the results is offered based on the FT-IR (ATR) spectra of several mixtures of the different systems.
International Nuclear Information System (INIS)
Dalle Donne, M.; Dorner, S.
1980-12-01
Measurements have been performed of the density and volumetric thermal expansion coefficient of liquid sodium tetraborate (borax) and of sodium metaborate both pure and with two different amounts of UO 2 dissolved in each. These data are required for the design of core-catchers based on sodium borates. The measurements have been performed with the buoyancy method in the temperature range from 850 0 C to 1325 0 C. The data for the pure borax and for the sodium metaborate agree reasonably well with the data from the literature, giving confidence that the measurements are correct and the new data for the salts with UO 2 are reliable. (orig.) [de
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
1977-01-01
topography of the state of knowledge on the thermal expansion of nonmetallic solids. We believe there is also much food for reflec- West Lafayette...34 Lithium Silicates ......... 713 209 Magnesium Metasilicate MgSiO. .. ......... 715 210 Magnesium Orthosilicate Mg2 SiO . . . . . . . . . . . . 718 211...Antiferromagnetism of Praseodymium," Phys. Rev. Letters, 12(20), 553-5, 1964. 66. Goode, J.M., "Phase Transition Temperature of Polonium ,"J. Chem. Phys., 26(5), 1269
1975-01-01
the thermal expansion of metallic elements, alloys, and intermetallic compounds. We believe there is also much food for reflection by the specialist...24 39 Plutonium Pu ........ ............... 260 40’ t Polonium Po ..... ............... 270 41* Potassium K ..... ............... 271 42...923 209 NIckel-Palladium NI-Pd..................926 210 * Nickel-Pitaum Ni-Pt.................90 211 Nickel-Silicon NI-SI.................932 212
Nong, Duong H; Lepczyk, Christopher A; Miura, Tomoaki; Fox, Jefferson M
2018-01-01
Urbanization has been driven by various social, economic, and political factors around the world for centuries. Because urbanization continues unabated in many places, it is crucial to understand patterns of urbanization and their potential ecological and environmental impacts. Given this need, the objectives of our study were to quantify urban growth rates, growth modes, and resultant changes in the landscape pattern of urbanization in Hanoi, Vietnam from 1993 to 2010 and to evaluate the extent to which the process of urban growth in Hanoi conformed to the diffusion-coalescence theory. We analyzed the spatiotemporal patterns and dynamics of the built-up land in Hanoi using landscape expansion modes, spatial metrics, and a gradient approach. Urbanization was most pronounced in the periods of 2001-2006 and 2006-2010 at a distance of 10 to 35 km around the urban center. Over the 17 year period urban expansion in Hanoi was dominated by infilling and edge expansion growth modes. Our findings support the diffusion-coalescence theory of urbanization. The shift of the urban growth areas over time and the dynamic nature of the spatial metrics revealed important information about our understanding of the urban growth process and cycle. Furthermore, our findings can be used to evaluate urban planning policies and aid in urbanization issues in rapidly urbanizing countries.
Lepczyk, Christopher A.; Miura, Tomoaki; Fox, Jefferson M.
2018-01-01
Urbanization has been driven by various social, economic, and political factors around the world for centuries. Because urbanization continues unabated in many places, it is crucial to understand patterns of urbanization and their potential ecological and environmental impacts. Given this need, the objectives of our study were to quantify urban growth rates, growth modes, and resultant changes in the landscape pattern of urbanization in Hanoi, Vietnam from 1993 to 2010 and to evaluate the extent to which the process of urban growth in Hanoi conformed to the diffusion-coalescence theory. We analyzed the spatiotemporal patterns and dynamics of the built-up land in Hanoi using landscape expansion modes, spatial metrics, and a gradient approach. Urbanization was most pronounced in the periods of 2001–2006 and 2006–2010 at a distance of 10 to 35 km around the urban center. Over the 17 year period urban expansion in Hanoi was dominated by infilling and edge expansion growth modes. Our findings support the diffusion-coalescence theory of urbanization. The shift of the urban growth areas over time and the dynamic nature of the spatial metrics revealed important information about our understanding of the urban growth process and cycle. Furthermore, our findings can be used to evaluate urban planning policies and aid in urbanization issues in rapidly urbanizing countries. PMID:29734346
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Bajo, F. [Universidad de Extremadura, Badajoz (Spain). Dept. de Electronica e Ingenieria Electromecanica; Ortiz, A.L.; Cumbrera, F.L. [Universidad de Extremadura, Badajoz (Spain). Dept. de Fisica
2001-07-01
Deconvolution of X-ray diffraction profiles is a fundamental step in obtaining reliable results in the microstructural characterization (crystallite size, lattice microstrain, etc) of polycrystalline materials. In this work we have analyzed a powder sample of 9-YSZ using a technique based on the Fourier series expansion of the pure profile. This procedure, which can be combined with regularization methods, is specially powerful to minimize the effects of the ill-posed nature of the linear integral equation involved in the kinematical theory of X-ray diffraction. Finally, the deconvoluted profiles have been used to obtain microstructural parameters by means of the integral-breadth method. (orig.)
International Nuclear Information System (INIS)
Brakman, C.M.
1985-01-01
Diffraction intensity pole figures are often used for the determination of orientation distribution function (o.d.f.) expansion coefficients. The intensity can be seen as a convolution of the o.d.f. times unity with respect to one rotation angle (about the direction of measurement). The 'normal' polycrystalline diffraction experiment only yields the even-order o.d.f. coefficients. The experiment itself imposes a centre of inversion even upon non-centrosymmetric crystals. Crystals may exhibit a centre of inversion themselves. The hkl and anti hanti kanti l contributions to the intensity are indistinguishable then owing to the centre of inversion. As a consequence, the odd-order coefficients cannot be determined. The mean value of a general physical property determined by means of diffraction can be taken as a convolution of the o.d.f. times the single-crystal value of the physical property with respect to the rotation angle mentioned before. The dependency of the physical property on the rotation angle leads to more information being extracted from the o.d.f. in the property's mean-value pole figure. Then, all o.d.f. coefficients may be present in the mean value, i.e. the measurement. Consequently, diffraction-line-shift strain pole figures exhibit even- and odd-order o.d.f. coefficients, present or induced centres of inversion notwithstanding. If the dependency of the single-crystal strain on the rotation angle is known no model of elastic polycrystal coupling is needed. However, this does not occur in practice. The present state of the art does not allow the Kroener model to be used for textured materials. In this paper the Reuss model is used. If the (applied) macrostresses are known, the o.d.f. coefficients can be obtained from the formulae presented. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco)
2014-04-01
Self-consistent ab initio calculations, based on Density Functional Theory (DFT) approach and using Full Potential Linear Augmented Plane Wave (FLAPW) method within GGA+U approximation, are performed to investigate both electronic and magnetic properties of the GdS layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Gd layers. Magnetic moment considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the High Temperature Series Expansions (HTSEs) calculations to compute other magnetic parameters. Using the Heisenberg model, the exchange interactions between the magnetic atoms Gd–Gd in the same layer and between the magnetic atoms in the adjacent bilayers are estimated. This estimate is obtained using the antiferromagnetic and ferromagnetic energies computed by abinitio calculations for GdS layers. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility of GdS with antiferromagnetic moment (m{sub Gd}) is given up to sixth order series versus of (J{sub 11}(Gd–Gd)/k{sub B}T). The Néel temperature T{sub N} is obtained by mean field theory and by HTSEs of the magnetic susceptibility series using the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is calculated for GdS layers. - Highlights: • Electronic and magnetic properties of GdS are investigated using the ab initio calculations. • Obtained data from abinitio calculations are used as input for HTSEs to compute other magnetic parameters. • Néel temperature and critical exponent are deduced using HTSE method.
International Nuclear Information System (INIS)
Masrour, R.; Hlil, E.K.; Hamedoun, M.; Benyoussef, A.
2014-01-01
Self-consistent ab initio calculations, based on Density Functional Theory (DFT) approach and using Full Potential Linear Augmented Plane Wave (FLAPW) method within GGA+U approximation, are performed to investigate both electronic and magnetic properties of the GdS layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Gd layers. Magnetic moment considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the High Temperature Series Expansions (HTSEs) calculations to compute other magnetic parameters. Using the Heisenberg model, the exchange interactions between the magnetic atoms Gd–Gd in the same layer and between the magnetic atoms in the adjacent bilayers are estimated. This estimate is obtained using the antiferromagnetic and ferromagnetic energies computed by abinitio calculations for GdS layers. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility of GdS with antiferromagnetic moment (m Gd ) is given up to sixth order series versus of (J 11 (Gd–Gd)/k B T). The Néel temperature T N is obtained by mean field theory and by HTSEs of the magnetic susceptibility series using the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is calculated for GdS layers. - Highlights: • Electronic and magnetic properties of GdS are investigated using the ab initio calculations. • Obtained data from abinitio calculations are used as input for HTSEs to compute other magnetic parameters. • Néel temperature and critical exponent are deduced using HTSE method
Núñez-Rojas, Edgar; Aguilar-Pineda, Jorge Alberto; Pérez de la Luz, Alexander; de Jesús González, Edith Nadir; Alejandre, José
2018-02-08
The transferable potential for a phase equilibria force field in its united-atom version, TraPPE_UA, is evaluated for 41 polar liquids that include alcohols, thiols, ethers, sulfides, aldehydes, ketones, and esters to determine its ability to reproduce experimental properties that were not included in the parametrization procedure. The intermolecular force field parameters for pure components were fit to reproduce experimental boiling temperature, vapor-liquid coexisting densities, and critical point (temperature, density, and pressure) using Monte Carlo simulations in different ensembles. The properties calculated in this work are liquid density, heat of vaporization, dielectric constant, surface tension, volumetric expansion coefficient, and isothermal compressibility. Molecular dynamics simulations were performed in the gas and liquid phases, and also at the liquid-vapor interface. We found that relative error between calculated and experimental data is 1.2% for density, 6% for heat of vaporization, and 6.2% for surface tension, in good agreement with the experimental data. The dielectric constant is systematically underestimated, and the relative error is 37%. Evaluating the performance of the force field to reproduce the volumetric expansion coefficient and isothermal compressibility requires more experimental data.
Energy Technology Data Exchange (ETDEWEB)
Melaina, M. W.; Heath, G.; Sandor, D.; Steward, D.; Vimmerstedt, L.; Warner, E.; Webster, K. W.
2013-04-01
Achieving the Department of Energy target of an 80% reduction in greenhouse gas emissions by 2050 depends on transportation-related strategies combining technology innovation, market adoption, and changes in consumer behavior. This study examines expanding low-carbon transportation fuel infrastructure to achieve deep GHG emissions reductions, with an emphasis on fuel production facilities and retail components serving light-duty vehicles. Three distinct low-carbon fuel supply scenarios are examined: Portfolio: Successful deployment of a range of advanced vehicle and fuel technologies; Combustion: Market dominance by hybridized internal combustion engine vehicles fueled by advanced biofuels and natural gas; Electrification: Market dominance by electric drive vehicles in the LDV sector, including battery electric, plug-in hybrid, and fuel cell vehicles, that are fueled by low-carbon electricity and hydrogen. A range of possible low-carbon fuel demand outcomes are explored in terms of the scale and scope of infrastructure expansion requirements and evaluated based on fuel costs, energy resource utilization, fuel production infrastructure expansion, and retail infrastructure expansion for LDVs. This is one of a series of reports produced as a result of the Transportation Energy Futures (TEF) project, a Department of Energy-sponsored multi-agency project initiated to pinpoint underexplored transportation-related strategies for abating GHGs and reducing petroleum dependence.
Detecting settlement expansion using hyper-temporal SAR time-series
CSIR Research Space (South Africa)
Kleynhans, W
2014-07-01
Full Text Available The detection of new informal settlements in South Africa using time-series data derived from coarse resolution satellite imagery has recently been an active area of research. Most of the previous methods presented using hyper-temporal satellite...
International Nuclear Information System (INIS)
Rudaz, S.
1990-01-01
Asymptotic series for the Hurwitz zeta function, its derivative, and related functions (including the Riemann zeta function of odd integer argument) are derived as an illustration of a simple, direct method of broad applicability, inspired by the calculus of finite differences
Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion
Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi
2011-01-01
An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…
Singh, R. R. P.; Young, A. P.
2017-12-01
We discuss generation of series expansions for Ising spin glasses with a symmetric ±J (i.e., bimodal) distribution on d -dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us to go to higher order than for a general distribution. We discuss two types of problems, one classical and one quantum. The classical problem is that of the Ising spin glass in a longitudinal magnetic field h , for which we obtain high temperature series expansions in variables tanh(J /T ) and tanh(h /T ) . The quantum problem is a T =0 study of the Ising spin glass in a transverse magnetic field hT for which we obtain a perturbation theory in powers of J /hT . These methods require (i) enumeration and counting of all connected clusters that can be embedded in the lattice up to some order n , and (ii) an evaluation of the contribution of each cluster for the quantity being calculated, known as the weight. We discuss a general method that takes the much smaller list (and count) of all no free-end (NFE) clusters on a lattice up to some order n and automatically generates all other clusters and their counts up to the same order. The weights for finite clusters in both cases have a simple graphical interpretation that allows us to proceed efficiently for a general configuration of the ±J bonds and at the end perform suitable disorder averaging. The order of our computations is limited by the weight calculations for the high-temperature expansions of the classical model, while they are limited by graph counting for the T =0 quantum system. Details of the calculational methods are presented.
Monitoring agricultural expansion in Burkina Faso over 14 years with 30 m resolution time series
DEFF Research Database (Denmark)
Knauer, Kim; Gessner, Ursula; Fensholt, Rasmus
2017-01-01
Burkina Faso ranges amongst the fastest growing countries in the world with an annual population growth rate of more than three percent. This trend has consequences for food security since agricultural productivity is still on a comparatively low level in Burkina Faso. In order to compensate...... for the low productivity, the agricultural areas are expanding quickly. The mapping and monitoring of this expansion is difficult, even on the basis of remote sensing imagery, since the extensive farming practices and frequent cloud coverage in the area make the delineation of cultivated land from other land...... cover and land use types a challenging task. However, as the rapidly increasing population could have considerable effects on the natural resources and on the regional development of the country, methods for improved mapping of LULCC (land use and land cover change) are needed. For this study, we...
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000, Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Boutahar, A.; Lassri, H. [LPMMAT, Université Hassan II-Casablanca, Faculté des Sciences, BP 5366 Maârif (Morocco)
2015-11-01
The self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the Mn{sub 2}Au. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn plans. Magnetic moment considered to lie along (110) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Mn–Mn in Mn{sub 2}Au are given by using the experiment results and the mean field theory. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility with the magnetic moments in Mn{sub 2}Au (m{sub Mn}) is given up to tenth order series in, 1/k{sub B}T. The Néel temperature T{sub N} is obtained by HTSEs combined with the Padé approximant method. The critical exponent associated with the magnetic susceptibility is deduced as well. - Highlights: • The both electronic and magnetic properties of the Mn{sub 2}Au are studied. • The exchange interactions between the magnetic atoms Mn–Mn in Mn{sub 2}Au are given. • The Néel temperature T{sub N} of Mn{sub 2}Au is obtained by HTSEs method. • The critical exponent associated with the magnetic susceptibility is deduced.
International Nuclear Information System (INIS)
Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng
2014-01-01
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process
Energy Technology Data Exchange (ETDEWEB)
Calais, Daniel; Saada, Georges; Simenel, Nicole [Commissariat a l' energie atomique et aux energies alternatives - CEA (France)
1959-07-01
The anisotropy of the expansion coefficients of uranium, zirconium and zinc provoke internal tensions in the course of cooling these metals. These tensions are eliminated in the case of zinc by restoration to room temperature, but persist in uranium and zirconium and are responsible for the absence of an elastic limit in these two metals. Reprint of a paper published in Comptes rendus des seances de l'Academie des Sciences, t. 249, p. 1225-1227, sitting of 5 October 1959 [French] L'anisotropie des coefficients de dilatation de l'uranium, du zirconium et du zinc provoque au cours du refroidissement de ces metaux des tensions internes. Eliminees par restauration a la temperature ambiante dans le cas du zinc, ces tensions persistent pour l'uranium et le zirconium et sont responsable de l'absence de limite elastique dans ces deux metaux. Reproduction d'un article publie dans les Comptes rendus des seances de l'Academie des Sciences, t. 249, p. 1225-1227, seance du 5 octobre 1959.
International Nuclear Information System (INIS)
Kanazu, Tsutomu
1998-01-01
When a reinforced concrete member is exposed to high temperature conditions over 100degC, tensile strain occurs in the concrete and compressive strain occurs in reinforcements due to a difference of thermal expansion coefficients between concrete and reinforcement. Its mechanism is the same as that of restrained stress caused by drying shrinkage of concrete; tensile stress occurs in the concrete because drying shrinkage strain is restrained by reinforcements, but there is a different point that the phenomenon at a high temperature condition includes the change of mechanical properties of concrete and reinforcement. In the study, the phenomenon is measured in the experiments and is clarified quantitatively. Moreover, the estimation method, which is derived from expanding the equation of average strain of reinforcement in the CEB Design Manual, is suggested and is verified by the comparison with the experimental results. (author)
International Nuclear Information System (INIS)
Dalle Donne, M.; Dorner, S.; Roth, A.
1983-01-01
Measurements have been performed of the density, of the volumetric thermal expansion coefficient and of the viscosity of liquid sodium tetraborate (borax) and of sodium metaborate both pure and with two different amounts of UO 2 dissolved in each. The viscosity measurements have been performed for the solution of sodium tetraborate with UO 2 and CeO 2 , and with CeO 2 only as well. These data are required for the design of core-catchers based on sodium borates. The density measurements have been performed with the buoyancy method in the temperature range from 825 0 C to 1300 0 C, the viscosity measurements in the temperature range 700-1250 0 C with a modified Haake viscosity balance. The balance was previously calibrated at ambient temperature with a standard calibration liquid and at high temperatures, with data for pure borax available from the literature. (orig.)
A Novel SOFC/SOEC Sealing Glass with a Low SiO2 Content and a High Thermal Expansion Coefficient
DEFF Research Database (Denmark)
Kiebach, Wolff-Ragnar; Agersted, Karsten; Zielke, Philipp
2017-01-01
phase boundaries. To reduce the amount of Si emission, a low Si containing sealing glass (chemical composition: 48 mol% CaO, 19 mol% ZnO, 21 mol% B2O3 and 12 mol% SiO2) was developed at DTU. In this presentation, the results from thermal characterization, like thermal expansion coefficient, glass......Solid oxide cells require seals that can function in harsh, elevated temperature environments. In the case of solid oxide electrolysis (SOEC), also a low Si content is desired, since Si impurities from the glass sealing can be transported to the active fuel electrode and poison the Ni-YSZ triple...... transition temperature, crystallization temperature, etc., of the glass will be presented. Additionally, the crystallization behavior of the glass was analyzed by in-situ X-ray diffraction, recording temperature resolved XRD spectra from 30 °C up to 900 °C. Furthermore, the long-term stability...
Lee, Ya-Ju; Chou, Chun-Yang; Huang, Chun-Ying; Yao, Yung-Chi; Haung, Yi-Kai; Tsai, Meng-Tsan
2017-10-31
The coefficient of thermal expansion (CTE) is a physical quantity that indicates the thermal expansion value of a material upon heating. For advanced thermal management, the accurate and immediate determination of the CTE of packaging materials is gaining importance because the demand for high-power lighting-emitting diodes (LEDs) is currently increasing. In this study, we used optical coherence tomography (OCT) to measure the CTE of an InGaN-based (λ = 450 nm) high-power LED encapsulated in polystyrene resin. The distances between individual interfaces of the OCT images were observed and recorded to derive the instantaneous CTE of the packaged LED under different injected currents. The LED junction temperature at different injected currents was established with the forward voltage method. Accordingly, the measured instantaneous CTE of polystyrene resin varied from 5.86 × 10 -5 °C -1 to 14.10 × 10 -5 °C -1 in the junction temperature range 25-225 °C and exhibited a uniform distribution in an OCT scanning area of 200 × 200 μm. Most importantly, this work validates the hypothesis that OCT can provide an alternative way to directly and nondestructively determine the spatially resolved CTE of the packaged LED device, which offers significant advantages over traditional CTE measurement techniques.
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.
Directory of Open Access Journals (Sweden)
Youngsun Kim
2017-05-01
Full Text Available The most common structure used for current transformers (CTs consists of secondary windings around a ferromagnetic core past the primary current being measured. A CT used as a surge protection device (SPD may experience large inrushes of current, like surges. However, when a large current flows into the primary winding, measuring the magnitude of the current is difficult because the ferromagnetic core becomes magnetically saturated. Several approaches to reduce the saturation effect are described in the literature. A Rogowski coil is representative of several devices that measure large currents. It is an electrical device that measures alternating current (AC or high-frequency current. However, such devices are very expensive in application. In addition, the volume of a CT must be increased to measure sufficiently large currents, but for installation spaces that are too small, other methods must be used. To solve this problem, it is necessary to analyze the magnetic field and electromotive force (EMF characteristics when designing a CT. Thus, we proposed an analysis method for the CT under an inrush current using the time-domain finite element method (TDFEM. The input source current of a surge waveform is expanded by a Fourier series to obtain an instantaneous value. An FEM model of the device is derived in a two-dimensional system and coupled with EMF circuits. The time-derivative term in the differential equation is solved in each time step by the finite difference method. It is concluded that the proposed algorithm is useful for analyzing CT characteristics, including the field distribution. Consequently, the proposed algorithm yields a reference for obtaining the effects of design parameters and magnetic materials for special shapes and sizes before the CT is designed and manufactured.
Kim, Youngsun
2017-05-01
The most common structure used for current transformers (CTs) consists of secondary windings around a ferromagnetic core past the primary current being measured. A CT used as a surge protection device (SPD) may experience large inrushes of current, like surges. However, when a large current flows into the primary winding, measuring the magnitude of the current is difficult because the ferromagnetic core becomes magnetically saturated. Several approaches to reduce the saturation effect are described in the literature. A Rogowski coil is representative of several devices that measure large currents. It is an electrical device that measures alternating current (AC) or high-frequency current. However, such devices are very expensive in application. In addition, the volume of a CT must be increased to measure sufficiently large currents, but for installation spaces that are too small, other methods must be used. To solve this problem, it is necessary to analyze the magnetic field and electromotive force (EMF) characteristics when designing a CT. Thus, we proposed an analysis method for the CT under an inrush current using the time-domain finite element method (TDFEM). The input source current of a surge waveform is expanded by a Fourier series to obtain an instantaneous value. An FEM model of the device is derived in a two-dimensional system and coupled with EMF circuits. The time-derivative term in the differential equation is solved in each time step by the finite difference method. It is concluded that the proposed algorithm is useful for analyzing CT characteristics, including the field distribution. Consequently, the proposed algorithm yields a reference for obtaining the effects of design parameters and magnetic materials for special shapes and sizes before the CT is designed and manufactured.
International Nuclear Information System (INIS)
Ohki, Naohisa; Harayama, Yasuo; Takeda, Tsuneo; Izumi, Fumio.
1977-12-01
In safety evaluation of a fuel rod, estimation of the stored energy in the fuel rod is indispensable. For this estimation, the temperature distribution in the fuel rod is calculated. Most important in determination of the temperature distribution is the gap heat transfer coefficient (gap conductance) between pellet surface and cladding inner surface. Under fuel rod operating condition, the mixed gas in the gap is composed of He, Xe and Kr. He is initial seald gas. Xe and Kr are fission-product gases, of which the quantities depend on the fuel burn-up. In program GAPCON series (GAPCON and GAPCON-THERMAL-1 and -2) and FREG-3, these quantities are given as a function of the irradiation time, power rating and neutron flux in estimation of the thermal conductivity of the mixed gas. The methods of calculating the quantities of Xe and Kr in the programs have been examined. Input of the neutron flux which influences F.P. gas production rates is better than the determination from the fuel-rod power rating. (auth.)
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
Directory of Open Access Journals (Sweden)
Shiqi Zhou
2011-12-01
Full Text Available Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426 1st-order high temperature series expansion (HTSE TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861, have some serious shortcomings: (i the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE and a non hard sphere (HS perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii We give a quantitative analysis on why
International Nuclear Information System (INIS)
Ishikawa, Nobuyuki; Suzuki, Katsuo
1999-01-01
Having advantages of setting independently feedback characteristics such as disturbance rejection specification and reference response characteristics, two-degree-of-freedom (2DOF) control is widely utilized to improve the control performance. The ordinary design method such as model matching usually derives high-ordered feedforward element of 2DOF controller. In this paper, we propose a new design method for low order feedforward element which is based on Pade approximation of the denominator series expansion. The features of the proposed method are as follows: (1) it is suited to realize reference response characteristics in low frequency region, (2) the order of the feedforward element can be selected apart from the feedback element. These are essential to the 2DOF controller design. With this method, 2DOF reactor power controller is designed and its control performance is evaluated by numerical simulation with reactor dynamics model. For this evaluation, it is confirmed that the controller designed by the proposed method possesses equivalent control characteristics to the controller by the ordinary model matching method. (author)
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
Calculation of generalized secant integral using binomial coefficients
International Nuclear Information System (INIS)
Guseinov, I.I.; Mamedov, B.A.
2004-01-01
A single series expansion relation is derived for the generalized secant (GS) integral in terms of binomial coefficients, exponential integrals and incomplete gamma functions. The convergence of the series is tested by the concrete cases of parameters. The formulas given in this study for the evaluation of GS integral show good rate of convergence and numerical stability
Fu, Shichen; Li, Yiming; Zhang, Minjun; Zong, Kai; Cheng, Long; Wu, Miao
2018-01-01
To realize unmanned pose detection of a coalmine boom-type roadheader, an ultra-wideband (UWB) pose detection system (UPDS) for a roadheader is designed, which consists of four UWB positioning base stations and three roadheader positioning nodes. The positioning base stations are used in turn to locate the positioning nodes of the roadheader fuselage. Using 12 sets of distance measurement information, a time-of-arrival (TOA) positioning model is established to calculate the 3D coordinates of three positioning nodes of the roadheader fuselage, and the three attitude angles (heading, pitch, and roll angles) of the roadheader fuselage are solved. A range accuracy experiment of a UWB P440 module was carried out in a narrow and closed tunnel, and the experiment data show that the mean error and standard deviation of the module can reach below 2 cm. Based on the TOA positioning model of the UPDS, we propose a fusion-positioning algorithm based on a Caffery transform and Taylor series expansion (CTFPA). We derived the complete calculation process, designed a flowchart, and carried out a simulation of CTFPA in MATLAB, comparing 1000 simulated positioning nodes of CTFPA and the Caffery positioning algorithm (CPA) for a 95 m long tunnel. The positioning error field of the tunnel was established, and the influence of the spatial variation on the positioning accuracy of CPA and CTFPA was analysed. The simulation results show that, compared with CPA, the positioning accuracy of CTFPA is clearly improved, and the accuracy of each axis can reach more than 5 mm. The accuracy of the X-axis is higher than that of the Y- and Z-axes. In section X-Y of the tunnel, the root mean square error (RMSE) contours of CTFPA are clear and orderly, and with an increase in the measuring distance, RMSE increases linearly. In section X-Z, the RMSE contours are concentric circles, and the variation ratio is nonlinear.
2003-01-01
Many critical gas turbine engine components are currently made from Ni-base superalloys that are coated with a thermal barrier coating (TBC). The TBC consists of a ZrO2-based top coat and a bond coat that is used to enhance the bonding between the superalloy substrate and the top coat. MCrAlY alloys (CoCrAlY and NiCrAlY) are currently used as bond coats and are chosen for their very good oxidation resistance. TBC life is frequently limited by the oxidation resistance of the bond coat, along with a thermal expansion mismatch between the metallic bond coat and the ceramic top coat. The aim of this investigation at the NASA Glenn Research Center was to develop a new longer life, higher temperature bond coat by improving both the oxidation resistance and the thermal expansion characteristics of the bond coat. Nickel aluminide (NiAl) has excellent high-temperature oxidation resistance and can sustain a protective Al2O3 scale to longer times and higher temperatures in comparison to MCrAlY alloys. Cryomilling of NiAl results in aluminum nitride (AlN) formation that reduces the coefficient of thermal expansion (CTE) of the alloy and enhances creep strength. Thus, additions of cryomilled NiAl-AlN to CoCrAlY were examined as a potential bond coat. In this work, the composite alloy was investigated as a stand-alone substrate to demonstrate its feasibility prior to actual use as a coating. About 85 percent of prealloyed NiAl and 15 percent of standard commercial CoCrAlY alloys were mixed and cryomilled in an attritor with stainless steel balls used as grinding media. The milling was carried out in the presence of liquid nitrogen. The milled powder was consolidated by hot extrusion or by hot isostatic pressing. From the consolidated material, oxidation coupons, four-point bend, CTE, and tensile specimens were machined. The CTE measurements were made between room temperature and 1000 C in an argon atmosphere. It is shown that the CTE of the NiAl-AlN-CoCrAlY composite bond coat
The Exponential Model for the Spectrum of a Time Series: Extensions and Applications
DEFF Research Database (Denmark)
Proietti, Tommaso; Luati, Alessandra
The exponential model for the spectrum of a time series and its fractional extensions are based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion form the cepstrum of the time series. After deriving the cepstrum of important classes of time...
International Nuclear Information System (INIS)
Yun, Y.
2015-01-01
Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)
Energy Technology Data Exchange (ETDEWEB)
Canciam, Cesar Augusto [Universidade Tecnologica Federal do Parana (UTFPR), Campus Ponta Grossa, PR (Brazil)], e-mail: canciam@utfpr.edu.br
2012-07-01
When evaluating the consumption of bio fuels, the knowledge of the density is of great importance for rectify the effect of temperature. The thermal expansion coefficient is a thermodynamic property that provides a measure of the density variation in response to temperature variation, keeping the pressure constant. This study aimed to predict the thermal expansion coefficients of ethyl bio diesels from castor beans, soybeans, sunflower seeds and Mabea fistulifera Mart. oils and of methyl bio diesels from soybeans, sunflower seeds, souari nut, cotton, coconut, castor beans and palm oils, from beef tallow, chicken fat and hydrogenated vegetable fat residual. For this purpose, there was a linear regression analysis of the density of each bio diesel a function of temperature. These data were obtained from other works. The thermal expansion coefficients for bio diesels are between 6.3729x{sup 10-4} and 1.0410x10{sup -3} degree C-1. In all the cases, the correlation coefficients were over 0.99. (author)
Energy Technology Data Exchange (ETDEWEB)
Melaina, W. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Heath, Garvin [National Renewable Energy Lab. (NREL), Golden, CO (United States); Sandor, Debra [National Renewable Energy Lab. (NREL), Golden, CO (United States); Steward, Darlene [National Renewable Energy Lab. (NREL), Golden, CO (United States); Vimmerstedt, Laura [National Renewable Energy Lab. (NREL), Golden, CO (United States); Warner, Ethan [National Renewable Energy Lab. (NREL), Golden, CO (United States); Webster, Karen W. [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2013-04-01
The petroleum-based transportation fuel system is complex and highly developed, in contrast to the nascent low-petroleum, low-carbon alternative fuel system. This report examines how expansion of the low-carbon transportation fuel infrastructure could contribute to deep reductions in petroleum use and greenhouse gas (GHG) emissions across the U.S. transportation sector. Three low-carbon scenarios, each using a different combination of low-carbon fuels, were developed to explore infrastructure expansion trends consistent with a study goal of reducing transportation sector GHG emissions to 80% less than 2005 levels by 2050.These scenarios were compared to a business-as-usual (BAU) scenario and were evaluated with respect to four criteria: fuel cost estimates, resource availability, fuel production capacity expansion, and retail infrastructure expansion.
Caleman, Carl; van Maaren, Paul J; Hong, Minyan; Hub, Jochen S; Costa, Luciano T; van der Spoel, David
2012-01-10
The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats
International Nuclear Information System (INIS)
Trukhanov, G.Ya.
2005-01-01
Time-dependent neutron transport theory of G.Ya. Trukhanov and S.A. Podosenov is developed. Errors of calculating of power series expansion coefficients, γ k , in this theory were estimated. It has been found that power series convergence radius R=|χ 1,2 |= 0.9595. Power series convergence speed were estimated [ru
Gao, Feng; DeColstoun, Eric Brown; Ma, Ronghua; Weng, Qihao; Masek, Jeffrey G.; Chen, Jin; Pan, Yaozhong; Song, Conghe
2012-01-01
Cities have been expanding rapidly worldwide, especially over the past few decades. Mapping the dynamic expansion of impervious surface in both space and time is essential for an improved understanding of the urbanization process, land-cover and land-use change, and their impacts on the environment. Landsat and other medium-resolution satellites provide the necessary spatial details and temporal frequency for mapping impervious surface expansion over the past four decades. Since the US Geological Survey opened the historical record of the Landsat image archive for free access in 2008, the decades-old bottleneck of data limitation has gone. Remote-sensing scientists are now rich with data, and the challenge is how to make best use of this precious resource. In this article, we develop an efficient algorithm to map the continuous expansion of impervious surface using a time series of four decades of medium-resolution satellite images. The algorithm is based on a supervised classification of the time-series image stack using a decision tree. Each imerpervious class represents urbanization starting in a different image. The algorithm also allows us to remove inconsistent training samples because impervious expansion is not reversible during the study period. The objective is to extract a time series of complete and consistent impervious surface maps from a corresponding times series of images collected from multiple sensors, and with a minimal amount of image preprocessing effort. The approach was tested in the lower Yangtze River Delta region, one of the fastest urban growth areas in China. Results from nearly four decades of medium-resolution satellite data from the Landsat Multispectral Scanner (MSS), Thematic Mapper (TM), Enhanced Thematic Mapper plus (ETM+) and China-Brazil Earth Resources Satellite (CBERS) show a consistent urbanization process that is consistent with economic development plans and policies. The time-series impervious spatial extent maps derived
Li, Peng; Jin, Feng
2018-01-01
The dynamic model about the anti-plane vibration of a contoured quartz plate with thickness changing continuously is established by ignoring the effect of small elastic constant c 56. The governing equation is solved using the power series expansion technique, and the trapped thickness shear modes caused by bulge thickness are revealed. Theoretically, the proposed method is more general, which can be capable of handling various thickness profiles defined mathematically. After the convergence of the series is demonstrated and the correctness is numerically validated with the aid of finite element method results, systematic parametric studies are subsequently carried out to quantify the effects of the geometry parameter upon the trapped modes, including resonant frequency and mode shape. After that, the band structures of thickness shear waves propagation in a periodically contoured quartz plate, as well as the power transmission spectra, are obtained based on the power series expansion technique. It is revealed that broad stop bands below cut-off frequency exist owing to the trapped modes excited by the geometry inhomogeneity, which has little relationship with the structural periodicity, and its physical mechanism is different from the Bragg scattering effect. The outcome is widely applicable, and can be utilized to provide theoretical and practical guidance for the design and manufacturing of quartz resonators and wave filters.
International Nuclear Information System (INIS)
Jensen, Iwan
2012-01-01
Earlier this year Chan extended the low-density series for the hard-squares partition function κ(z) to 92 terms. Here we analyse this extended series focusing on the behaviour at the dominant singularity z d which lies on the negative fugacity axis. We find that the series has a confluent singularity of order at least 2 at z d with exponents θ = 0.833 33(2) and θ′ = 1.6676(3). We thus confirm that the exponent θ has the exact value 5/6 as observed by Dhar. (comment)
Jairo A. Diaz; Robert J. Moon; Jeffrey P. Youngblood
2014-01-01
Thermal expansion represents a vital indicator of the processing history and dimensional stability of materials. Solvent-sensitive, thin, and compliant samples are particularly challenging to test. Here we describe how textures highlighted by contrast enhanced optical microscopy modes (i.e., polarized light (PL), phase contrast (PC)) and bright field (BF) can be used...
Jaszczuk, Phillip; Rogers, Gary F; Guzman, Raphael; Proctor, Mark R
2016-05-01
A defect in a phosphate-regulating gene leads to the most common form of rickets: X-linked hypophosphatemic rickets (XLH) or vitamin D-resistant rickets (VDDR). XLH has been associated with craniosynostosis, the sagittal suture being the most commonly involved. We present three patients with rickets and symptomatic sagittal suture craniosynostosis all of whom presented late (>2 years of age). Two had a severe phenotype and papilledema, while the third presented with an osseous bulging near the anterior fontanel and experienced chronic headaches. All underwent successful cranial vault expansion. Rachitic patients with scaphocephaly should be screened for craniosynostosis.
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000, Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O.; El Moussaoui, H. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)
2015-03-15
Self-consistent ab initio calculations, based on density functional theory (DFT) approach and using a full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the Fe{sub 3}O{sub 4}. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Fe plans. Magnetic moment considered to lie along (010) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Fe–Fe in Fe{sub 3}O{sub 4} are given using the mean field theory. The high temperature series expansions (HTSEs) of the magnetic susceptibility of with the magnetic moments, m{sub Fe} in Fe{sub 3}O{sub 4} is given up to seventh order series in (1/k{sub B}T). The Néel temperature T{sub N} is obtained by HTSEs of the magnetic susceptibility series combined with the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is deduced as well. - Highlights: • Ab initio calculations, based on DFT approach and FLAPW are used to study the electronic properties of Fe{sub 3}O{sub 4}. • Magnetic moments of Fe{sub 1} and Fe{sub 2} are estimated to −/+3.44 µ{sub B}. • HTSE method is used to calculate the Néel temperature of Fe{sub 3}O{sub 4}.
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
Second- and Higher-Order Virial Coefficients Derived from Equations of State for Real Gases
Parkinson, William A.
2009-01-01
Derivation of the second- and higher-order virial coefficients for models of the gaseous state is demonstrated by employing a direct differential method and subsequent term-by-term comparison to power series expansions. This communication demonstrates the application of this technique to van der Waals representations of virial coefficients.…
International Nuclear Information System (INIS)
Pietsch, U.; Marlow, D.
1986-01-01
The amount of the measured room temperature thermal expansion coefficient of tetragonal strained layers grown lattice matched on the InP substrate used is about 30% greater the expected one for a cubic 'relaxed' material. This issue has to be taken into account for the determination of the composition of the quarternary Ga/sub x/In/sub 1-x/As/sub y/P/sub 1-y/ layers from both X-ray and photoluminescence data as well as for the estimation of the thermally created stress field of optoelectronic devices. (author)
International Nuclear Information System (INIS)
Sadeghi, Y.
2006-01-01
Computer Programs are important tools in physics. Analysis of the experimental data and the control of complex handle physical phenomenon and the solution of numerical problem in physics help scientist to the behavior and simulate the process. In this paper, calculation of several Fourier series gives us a visual and analytic impression of data analyses from Fourier series. One of important aspect in data analyses is to find optimum method for de-noising. Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution corresponding to its scale. They have advantages over usual traditional methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Transformed data by wavelets in frequency space has time information and can clearly show the exact location in time of the discontinuity. This aspect makes wavelets an excellent tool in the field of data analysis. In this paper, we show how Fourier series and wavelets can analyses data in Damavand tokamak. ?
Multipole expansion of acoustical Bessel beams with arbitrary order and location.
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.
Eslami, Taban; Saeed, Fahad
2018-04-20
Functional magnetic resonance imaging (fMRI) is a non-invasive brain imaging technique, which has been regularly used for studying brain’s functional activities in the past few years. A very well-used measure for capturing functional associations in brain is Pearson’s correlation coefficient. Pearson’s correlation is widely used for constructing functional network and studying dynamic functional connectivity of the brain. These are useful measures for understanding the effects of brain disorders on connectivities among brain regions. The fMRI scanners produce huge number of voxels and using traditional central processing unit (CPU)-based techniques for computing pairwise correlations is very time consuming especially when large number of subjects are being studied. In this paper, we propose a graphics processing unit (GPU)-based algorithm called Fast-GPU-PCC for computing pairwise Pearson’s correlation coefficient. Based on the symmetric property of Pearson’s correlation, this approach returns N ( N − 1 ) / 2 correlation coefficients located at strictly upper triangle part of the correlation matrix. Storing correlations in a one-dimensional array with the order as proposed in this paper is useful for further usage. Our experiments on real and synthetic fMRI data for different number of voxels and varying length of time series show that the proposed approach outperformed state of the art GPU-based techniques as well as the sequential CPU-based versions. We show that Fast-GPU-PCC runs 62 times faster than CPU-based version and about 2 to 3 times faster than two other state of the art GPU-based methods.
Directory of Open Access Journals (Sweden)
Kim Knauer
2017-02-01
Full Text Available Burkina Faso ranges amongst the fastest growing countries in the world with an annual population growth rate of more than three percent. This trend has consequences for food security since agricultural productivity is still on a comparatively low level in Burkina Faso. In order to compensate for the low productivity, the agricultural areas are expanding quickly. The mapping and monitoring of this expansion is difficult, even on the basis of remote sensing imagery, since the extensive farming practices and frequent cloud coverage in the area make the delineation of cultivated land from other land cover and land use types a challenging task. However, as the rapidly increasing population could have considerable effects on the natural resources and on the regional development of the country, methods for improved mapping of LULCC (land use and land cover change are needed. For this study, we applied the newly developed ESTARFM (Enhanced Spatial and Temporal Adaptive Reflectance Fusion Model framework to generate high temporal (8-day and high spatial (30 m resolution NDVI time series for all of Burkina Faso for the years 2001, 2007, and 2014. For this purpose, more than 500 Landsat scenes and 3000 MODIS scenes were processed with this automated framework. The generated ESTARFM NDVI time series enabled extraction of per-pixel phenological features that all together served as input for the delineation of agricultural areas via random forest classification at 30 m spatial resolution for entire Burkina Faso and the three years. For training and validation, a randomly sampled reference dataset was generated from Google Earth images and based on expert knowledge. The overall accuracies of 92% (2001, 91% (2007, and 91% (2014 indicate the well-functioning of the applied methodology. The results show an expansion of agricultural area of 91% between 2001 and 2014 to a total of 116,900 km². While rainfed agricultural areas account for the major part of this
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, BP. 63, 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O.; El Moussaoui, H. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)
2014-06-01
Self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the MnSe lattice. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn lattices. Magnetic moments considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The zero-field high temperature static susceptibility series of the spin −4.28 nearest-neighbor Ising model on face centered cubic (fcc) and lattices is thoroughly analyzed by means of a power series coherent anomaly method (CAM). The exchange interaction between the magnetic atoms and the Néel temperature are deduced using the mean filed and HTSEs theories. - Highlights: • Ab initio calculations are used to investigate both electronic and magnetic properties of the MnSe alloys. • Obtained data from ab initio calculations are used as input for the HTSEs. • The Néel temperature is obtained for MnSe alloys.
Sastre, Francisco; Moreno-Hilario, Elizabeth; Sotelo-Serna, Maria Guadalupe; Gil-Villegas, Alejandro
2018-02-01
The microcanonical-ensemble computer simulation method (MCE) is used to evaluate the perturbation terms Ai of the Helmholtz free energy of a square-well (SW) fluid. The MCE method offers a very efficient and accurate procedure for the determination of perturbation terms of discrete-potential systems such as the SW fluid and surpass the standard NVT canonical ensemble Monte Carlo method, allowing the calculation of the first six expansion terms. Results are presented for the case of a SW potential with attractive ranges 1.1 ≤ λ ≤ 1.8. Using semi-empirical representation of the MCE values for Ai, we also discuss the accuracy in the determination of the phase diagram of this system.
Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.
2013-09-01
Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.
El Grini, A.; Salmi, S.; Masrour, R.; Hamedoun, M.; Bouslykhane, K.; Marzouk, A.; Hourmatallah, A.; Benzakour, N.
2018-06-01
The Green's function theory and high-temperature series expansions technical have been developed for magnetic systems GeNi2-xCoxO4. We have applied the Green's function theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, considering all components of the magnetization when an external magnetic field is applied in (x,z)-plane. The second theory combined with the Padé approximants method for a randomly diluted Heisenberg magnet is used to deduce the magnetic phase diagram of GeNi2 - xCoxO4 systems. The critical exponents ? and ? and associated with the magnetic susceptibility ? and the correlation length ξ, respectively, have been deduced. The theoretical results are compared with those given by magnetic measurements.
Radial expansion for spinning conformal blocks
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.
A REDUCE program for symbolic computation of Puiseux expansions
International Nuclear Information System (INIS)
Gerdt, V.P.; Tiller, P.
1991-01-01
The program is described for computation of Puiseux expansions of algebraic functions. The Newton diagram method is used for construction of initial coefficients of all the Puiseux series at the given point. The program is written in computer algebra language Reduce. Some illustrative examples are given. 20 refs
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
Estimation of pure autoregressive vector models for revenue series ...
African Journals Online (AJOL)
This paper aims at applying multivariate approach to Box and Jenkins univariate time series modeling to three vector series. General Autoregressive Vector Models with time varying coefficients are estimated. The first vector is a response vector, while others are predictor vectors. By matrix expansion each vector, whether ...
Vert, Vicente B.; Serra, José M.
The influence of different application-oriented factors on the electrochemical activity and stability of TbBaCo 3ZnO 7+ δ when used as a solid oxide fuel cell cathode has been studied. Calcination at temperatures above 900 °C (e.g. 1000 °C) leads to a significant increase in the electrode polarization resistance. The effect of the sintering temperature of the TbBaCo 3ZnO 7+ δ cathode seems to be more important than the effect produced by the Tb substitution as observed when compared with 900 °C-sintered YBaCo 3ZnO 7+ δ; and ErBaCo 3ZnO 7+ δ electrode performances. The presence of CO 2 in the air flow leads to an increase of roughly 10% in the polarization resistance for the whole studied temperature range (500-850 °C) while this effect is reversible. Analysis of the impedance spectroscopy measurements shows that the exchange rate constant (k G from Gerischer element) is significantly affected by CO 2 at temperatures below 700 °C, while the diffusion coefficient related parameter is slightly influenced at low temperatures. Electrode degrades with a low constant rate of 1 mΩ cm 2 h -1 after 60 h. This cathode material exhibits high CO 2 tolerance, as shown by temperature programmed treatment under a continuous gas flow of air with 5% CO 2, and a relatively low thermal expansion coefficient.
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
Negative thermal expansion materials
International Nuclear Information System (INIS)
Evans, J.S.O.
1997-01-01
The recent discovery of negative thermal expansion over an unprecedented temperature range in ZrW 2 O 8 (which contracts continuously on warming from below 2 K to above 1000 K) has stimulated considerable interest in this unusual phenomenon. Negative and low thermal expansion materials have a number of important potential uses in ceramic, optical and electronic applications. We have now found negative thermal expansion in a large new family of materials with the general formula A 2 (MO 4 ) 3 . Chemical substitution dramatically influences the thermal expansion properties of these materials allowing the production of ceramics with negative, positive or zero coefficients of thermal expansion, with the potential to control other important materials properties such as refractive index and dielectric constant. The mechanism of negative thermal expansion and the phase transitions exhibited by this important new class of low-expansion materials will be discussed. (orig.)
Singh, R. R. P.; Young, A. P.
2017-08-01
We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.
Low-temperature thermal expansion
International Nuclear Information System (INIS)
Collings, E.W.
1986-01-01
This chapter discusses the thermal expansion of insulators and metals. Harmonicity and anharmonicity in thermal expansion are examined. The electronic, magnetic, an other contributions to low temperature thermal expansion are analyzed. The thermodynamics of the Debye isotropic continuum, the lattice-dynamical approach, and the thermal expansion of metals are discussed. Relative linear expansion at low temperatures is reviewed and further calculations of the electronic thermal expansion coefficient are given. Thermal expansions are given for Cu, Al and Ti. Phenomenologic thermodynamic relationships are also discussed
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Thermal expansion of beryllium oxide
International Nuclear Information System (INIS)
Solodukhin, A.V.; Kruzhalov, A.V.; Mazurenko, V.G.; Maslov, V.A.; Medvedev, V.A.; Polupanova, T.I.
1987-01-01
Precise measurements of temperature dependence of the coefficient of linear expansion in the 22-320 K temperature range on beryllium oxide monocrystals are conducted. A model of thermal expansion is suggested; the range of temperature dependence minimum of the coefficient of thermal expansion is well described within the frames of this model. The results of the experiment may be used for investigation of thermal stresses in crystals
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.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node
New results for virial coefficients of hard spheres in D dimensions
Indian Academy of Sciences (India)
We present new results for the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D ... for the hard sphere gas of particles of diameter σ in D dimensions defined by the two-body potential. U(r) = ..... [22] A J Guttmann, Asymptotic analysis of power-series expansions, in Phase transitions and critical phenomena ...
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.
Tallentire, Sarah E; Child, Felicity; Fall, Ian; Vella-Zarb, Liana; Evans, Ivana Radosavljević; Tucker, Matthew G; Keen, David A; Wilson, Claire; Evans, John S O
2013-08-28
We describe the synthesis and characterization of a family of materials, Zr1-xSnxMo2O8 (0 thermal expansion coefficient can be systematically varied from negative to zero to positive values. These materials allow tunable expansion in a single phase as opposed to using a composite system. Linear thermal expansion coefficients, αl, ranging from -7.9(2) × 10(-6) to +5.9(2) × 10(-6) K(-1) (12-500 K) can be achieved across the series; contraction and expansion limits are of the same order of magnitude as the expansion of typical ceramics. We also report the various structures and thermal expansion of "cubic" SnMo2O8, and we use time- and temperature-dependent diffraction studies to describe a series of phase transitions between different ordered and disordered states of this material.
The U.S. EPA Sustainable and Healthy Communities Seminar Series presents the Tribal Science Webinar Series that will look to develop a forum for discussion of the complex environmental issues facing many tribal and indigenous communities.
The Thermal Expansion Of Feldspars
Hovis, G. L.; Medford, A.; Conlon, M.
2009-12-01
Hovis and others (1) investigated the thermal expansion of natural and synthetic AlSi3 feldspars and demonstrated that the coefficient of thermal expansion (α) decreases significantly, and linearly, with increasing room-temperature volume (VRT). In all such feldspars, therefore, chemical expansion limits thermal expansion. The scope of this work now has been broadened to include plagioclase and Ba-K feldspar crystalline solutions. X-ray powder diffraction data have been collected between room temperature and 925 °C on six plagioclase specimens ranging in composition from anorthite to oligoclase. When combined with thermal expansion data for albite (2,3,4) a steep linear trend of α as a function of VRT emerges, reflecting how small changes in composition dramatically affect expansion behavior. The thermal expansion data for five synthetic Ba-K feldspars ranging in composition from 20 to 100 mole percent celsian, combined with data for pure K-feldspar (3,4), show α-VRT relationships similar in nature to the plagioclase series, but with a slope and intercept different from the latter. Taken as a group all Al2Si2 feldspars, including anorthite and celsian from the present study along with Sr- (5) and Pb-feldspar (6) from other workers, show very limited thermal expansion that, unlike AlSi3 feldspars, has little dependence on the divalent-ion (or M-) site occupant. This apparently is due to the necessitated alternation of Al and Si in the tetrahedral sites of these minerals (7), which in turn locks the tetrahedral framework and makes the M-site occupant nearly irrelevant to expansion behavior. Indeed, in feldspar series with coupled chemical substitution it is the change away from a 1:1 Al:Si ratio that gives feldspars greater freedom to expand. Overall, the relationships among α, chemical composition, and room-temperature volume provide useful predictive tools for estimating feldspar thermal expansion and give insight into the controls of expansion behavior in
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Mahlab, M.S.
1975-01-01
All the presently available techniques for solving Schroedinger's differential equation for helium-like atoms display poor convergence of the wave function in the neighborhood of the singularities of the Hamiltonian operator. In general most of the methods of solving this equation will converge in the appropriate limit to the exact wave function; however, convergence is slow, especially near the singularities of this differential equation. These difficulties become readily apparent from local energy studies. A technique is presented that avoids these difficulties. The wave function it produces is specifically most accurate at the singularities of the Hamiltonian. The novel aspect of this treatment is the subdivision of the space spanned by the wave function. Different expansions are picked such that they converge rapidly in each of the different subdivisions. These expansions may be constructed in such a way that they obey the boundary conditions in their respective subdivision. Most importantly, all the information available from the recursion relations associated with the differential equation may be incorporated into these expansions. A systematic procedure is presented such that these expansions may be brought together to form a wave function that satisfies all the continuity requirements. An S-state helium wave function was constructed to demonstrate that this method of treatment is feasible, and capable of indefinite systematic improvement. A discussion of several new asymptotic expansions that were constructed for the helium wave function, as well as an improved functional form for the small electron-nucleus wave function, is included in this presentation
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2017-01-01
We study a vectorial asymptotically free gauge theory, with gauge group $G$ and $N_f$ massless fermions in a representation $R$ of this group, that exhibits an infrared (IR) zero in its beta function, $\\beta$, at the coupling $\\alpha=\\alpha_{IR}$ in the non-Abelian Coulomb phase. For general $G......_f$-dependent expansion variable. These are the highest orders to which these expansions have been calculated. We apply these general results to theories with $G={\\rm SU}(N_c)$ and $R$ equal to the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. It is shown that for all...
International Nuclear Information System (INIS)
Egorov, Gennadiy I.; Makarov, Dmitriy M.; Kolker, Arkadiy M.
2013-01-01
Highlights: ► Molar isothermal compressions and molar isobaric expansions were evaluated. ► Coefficients of thermal pressure and internal pressure were obtained. ► Concentration dependences of coefficients under study display extremes. ► Temperature and pressure dependences of internal pressure of the mixture were linear. -- Abstract: Molar isothermal compressions, molar isobaric expansions, molar coefficients of thermal pressure, and internal pressure were calculated over the whole concentration range of {water (1) + tert-butanol (2)} mixture at pressures from 0.1 to 100 MPa and temperatures from 278.15 to 323.15 K. It was revealed that the extremes, observed on concentration dependences of molar isothermal compression K T,m and molar isobaric expansion E P,m of the mixture, became more pronounced with pressure growth and temperature lowering. Values of molar thermal pressure coefficients of the mixture sharply rose at compositions with small TBA mole fraction and then decreased practically linearly with the alcohol content increasing. Temperature and pressure dependences of the mixture internal pressure were almost linear, and at low TBA concentrations changed significantly from the dependences of water, tert-butanol and their mixtures at large alcohol content
On summation of perturbation expansions
International Nuclear Information System (INIS)
Horzela, A.
1985-04-01
The problem of the restoration of physical quantities defined by divergent perturbation expansions is analysed. The Pad'e and Borel summability is proved for alternating perturbation expansions with factorially growing coefficients. The proof is based on the methods of the classical moments theory. 17 refs. (author)
Electrical Resistance Alloys and Low-Expansion Alloys
DEFF Research Database (Denmark)
Kjer, Torben
1996-01-01
The article gives an overview of electrical resistance alloys and alloys with low thermal expansion. The electrical resistance alloys comprise resistance alloys, heating alloys and thermostat alloys. The low expansion alloys comprise alloys with very low expansion coefficients, alloys with very low...... thermoelastic coefficients and age hardenable low expansion alloys....
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.
Jolley, LB W
2004-01-01
Over 1,100 common series, all grouped for easy reference. Arranged by category, these series include arithmetical and geometrical progressions, powers and products of natural numbers, figurate and polygonal numbers, inverse natural numbers, exponential and logarithmic series, binomials, simple inverse products, factorials, trigonometrical and hyperbolic expansions, and additional series. 1961 edition.
Principles of Thermal Expansion in Feldspars
Hovis, Guy; Medford, Aaron; Conlon, Maricate; Tether, Allison; Romanoski, Anthony
2010-05-01
Following the recent thermal expansion work of Hovis et al. (1) on AlSi3 feldspars, we have investigated the thermal expansion of plagioclase, Ba-K, and Ca-K feldspar crystalline solutions. X-ray powder diffraction data were collected between room temperature and 925 °C on six natural plagioclase specimens ranging in composition from anorthite to oligoclase, the K-exchanged equivalents of these plagioclase specimens, and five synthetic Ba-K feldspars with compositions ranging from 25 to 99 mol % BaAl2Si2O8. The resulting thermal expansion coefficients (α) for volume have been combined with earlier results for end-member Na- and K-feldspars (2,3). Unlike AlSi3 feldspars, Al2Si2 feldspars, including anorthite and celsian from the present study plus Sr- and Pb-feldspar from other workers (4,5), show essentially constant and very limited thermal expansion, regardless of divalent cation size. In the context of structures where the Lowenstein rule (6) requires Al and Si to alternate among tetrahedra, the proximity of bridging Al-O-Si oxygen ions to divalent neighbors (ranging from 0 to 2) produces short Ca-O (or Ba-O) bonds (7,8) that apparently are the result of local charge-balance requirements (9). Gibbs et al. (10) suggest that short bonds such as these have a partially covalent character. This in turn stiffens the structure. Thus, for feldspar series with coupled substitution the change away from a purely divalent M-site occupant gives the substituting (less strongly bonded) monovalent cations increasingly greater influence on thermal expansion. Overall, then, thermal expansion in the feldspar system is well represented on a plot of α against room-temperature volume, where one sees a quadrilateral bounded by data for (A) AlSi3 feldspars whose expansion behavior is controlled largely by the size of the monovalent alkali-site occupant, (B) Al2Si2 feldspars whose expansion is uniformly limited by partially-covalent bonds between divalent M-site occupants and
Accelerating the loop expansion
International Nuclear Information System (INIS)
Ingermanson, R.
1986-01-01
This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi 4 theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs
Thermal expansion in small metallic particles
International Nuclear Information System (INIS)
Ivanov, A.S.
1985-01-01
An anomalously low thermal expansion observable in small particles is attributed to extending effect of the shell. It is shown that the coefficient of thermal expansion of the oxide-film-coated aluminium particles calculated using elastic constants and coefficients of thermal expansion of massive materials agres well with those measured experimentally. The linear dilatation of the shell, its stress to rupture and the values of the structural tension are estimated vs the temperature
A double expansion method for the frequency response of finite-length beams with periodic parameters
Ying, Z. G.; Ni, Y. Q.
2017-03-01
A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response
Integer Solutions of Binomial Coefficients
Gilbertson, Nicholas J.
2016-01-01
A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…
Simulating the market coefficient of relative risk aversion
Directory of Open Access Journals (Sweden)
Samih Antoine Azar
2014-12-01
Full Text Available In this paper, expected utility, defined by a Taylor series expansion around expected wealth, is maximized. The coefficient of relative risk aversion (CRRA that is commensurate with a 100% investment in the risky asset is simulated. The following parameters are varied: the riskless return, the market standard deviation, the market stock premium, and the skewness and the kurtosis of the risky return. Both the high extremes and the low extremes are considered. With these figures, the upper bound of the market CRRA is 3.021 and the lower bound is 0.466. Log utility, which corresponds to a CRRA of 1, is not excluded.
Crisanto-Neto, J. C.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.
2016-09-01
In practice, the Lévy α-stable distribution is usually expressed in terms of the Fourier integral of its characteristic function. Indeed, known closed form expressions are relatively scarce given the huge parameters space: 0\\lt α ≤slant 2 ({{L\\'{e}vy}} {{index}}), -1≤slant β ≤slant 1 ({{skewness}}),σ \\gt 0 ({{scale}}), and -∞ \\lt μ \\lt ∞ ({{shift}}). Hence, systematic efforts have been made towards the development of proper methods for analytically solving the mentioned integral. As a further contribution in this direction, here we propose a new way to tackle the problem. We consider an approach in which one first solves the Fourier integral through a formal (thus not necessarily convergent) series representation. Then, one uses (if necessary) a pertinent sum-regularization procedure to the resulting divergent series, so as to obtain an exact formula for the distribution, which is amenable to direct numerical calculations. As a concrete study, we address the centered, symmetric, unshifted and unscaled distribution (β =0, μ =0, σ =1), with α ={α }M=2/M, M=1,2,3\\ldots . Conceivably, the present protocol could be applied to other sets of parameter values.
Thermal and Hygric Expansion of High Performance Concrete
J. Toman; R. Černý
2001-01-01
The linear thermal expansion coefficient of two types of high performance concrete was measured in the temperature range from 20 °C to 1000 °C, and the linear hygric expansion coefficient was determined in the moisture range from dry material to saturation water content. Comparative methods were applied for measurements of both coefficients. The experimental results show that both the effect of temperature on the values of linear thermal expansion coefficients and the effect of moisture on th...
Directory of Open Access Journals (Sweden)
Ahmet Demir
2016-01-01
Full Text Available The transmission of sound in a duct with sudden area expansion and extended inlet is investigated in the case where the walls of the duct lie in the finite overlapping region lined with acoustically absorbent materials. By using the series expansion in the overlap region and using the Fourier transform technique elsewhere we obtain a Wiener-Hopf equation whose solution involves a set of infinitely many unknown expansion coefficients satisfying a system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound transmission are studied.
International Nuclear Information System (INIS)
Taylor, D.
1984-01-01
This paper gives regression data for a modified second order polynomial fitted to the expansion data of, and percentage expansions for dioxides with (a) the fluorite and antifluorite structure: AmO 2 , BkO 2 , CeO 2 , CmO 2 , HfO 2 , Li 2 O, NpO 2 , PrO 2 , PuO 2 , ThO 2 , UO 2 , ZrO 2 , and (b) the rutile structure: CrO 2 , GeO 2 , IrO 2 , MnO 2 , NbO 2 , PbO 2 , SiO 2 , SnO 2 , TeO 2 , TiO 2 and VO 2 . Reduced expansion curves for the dioxides showed only partial grouping into iso-electronic series for the fluorite structures and showed that the 'law of corresponding states' did not apply to the rutile structures. (author)
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Thermal and Hygric Expansion of High Performance Concrete
Directory of Open Access Journals (Sweden)
J. Toman
2001-01-01
Full Text Available The linear thermal expansion coefficient of two types of high performance concrete was measured in the temperature range from 20 °C to 1000 °C, and the linear hygric expansion coefficient was determined in the moisture range from dry material to saturation water content. Comparative methods were applied for measurements of both coefficients. The experimental results show that both the effect of temperature on the values of linear thermal expansion coefficients and the effect of moisture on the values of linear hygric expansion coefficients are very significant and cannot be neglected in practical applications.
International Nuclear Information System (INIS)
Knoll, J.
1985-10-01
A quantum dynamical model is suggested which describes the expansion and disassembly phase of highly excited compounds formed in energetic heavy-ion collisions. First applications in two space and one time dimensional model world are discussed and qualitatively compared to standard freeze-out concepts. (orig.)
Indian Academy of Sciences (India)
of a system under investigation is to model the system in terms of some ... The organization of the paper is as follows: In §2, a brief account of the (G /G)- expansion ...... It is interesting to note that from the general results, one can easily recover.
Extraction of Dunham coefficients from Murrell-Sorbie parameters
International Nuclear Information System (INIS)
Lim Teikcheng
2008-01-01
A set of relationships between parameters of the Dunham and Murrell-Sorbie potential energy function is developed. By employing Taylor series expansion and comparison of terms arranged in increasing order of bond length, a set of Dunham coefficients is obtained as functions of Murrell- Sorbie parameters. The conversion functions reveal the importance of factorials in extracting Dunham coefficients from Murrell-Sorbie parameters. Plots of both functions, based on parameters of the latter, reveal good correlation near the equilibrium bond length for a group of diatomic molecules. Potential function relations, such as that shown in this paper, are useful when the preferred/reliable data is based on a potential function different from that adopted in available computational software. (orig.)
Transverse thermal expansion of carbon fiber/epoxy matrix composites
Helmer, J. F.; Diefendorf, R. J.
1983-01-01
Thermal expansion coefficients and moduli of elasticity have been determined experimentally for a series of epoxy-matrix composites reinforced with carbon and Kevlar fibers. It is found that in the transverse direction the difference between the properties of the fiber and the matrix is not as pronounced as in the longitudinal direction, where the composite properties are fiber-dominated. Therefore, the pattern of fiber packing tends to affect transverse composite properties. The transverse properties of the composites tested are examined from the standpoint of the concept of homogeneity defined as the variation of packing (or lack thereof) throughout a sample.
Glass ceramics for sealing to high-thermal-expansion metals
International Nuclear Information System (INIS)
Wilder, J.A. Jr.
1980-10-01
Glass ceramics were studied, formulated in the Na 2 O CaO.P 2 O 5 , Na 2 O.BaOP 2 O 5 , Na 2 O.Al 2 O 3 .P 2 O 5 , and Li 2 O.BaO.P 2 O 5 systems to establish their suitability for sealing to high thermal expansion metals, e.g. aluminum, copper, and 300 series stainless steels. Glass ceramics in Na 2 O.CaO.P 2 O 5 and Na 2 O.BaO.P 2 O 5 systems have coefficients of thermal expansion in the range 140 x 10 -1 per 0 C less than or equal to α less than or equal to 225 x 10 -7 per 0 C and fracture toughness values generally greater than those of phosphate glasses; they are suitable for fabricating seals to high thermal expansion metals. Crystal phases include NaPo 3 , (NaPO 3 ) 3 , NaBa(PO 3 ) 3 , and NaCa(PO 3 ) 3 . Glass ceramics formed in the Na 2 O.Al 2 O 3 .P 2 O 5 systems have coefficients of thermal expansion greater than 240 x 10 -7 per 0 C, but they have extensive microcracking. Due to their low thermal expansion values (α less than or equal to 120 x 10 -7 per 0 C), glass ceramics in the Li 2 O.BaO.P 2 O 5 system are unsuitable for sealing to high thermal expansion metals
Eisenstein series for infinite-dimensional U-duality groups
Fleig, Philipp; Kleinschmidt, Axel
2012-06-01
We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.
Negative thermal expansion materials: technological key for control of thermal expansion
Koshi Takenaka
2012-01-01
Most materials expand upon heating. However, although rare, some materials contract upon heating. Such negative thermal expansion (NTE) materials have enormous industrial merit because they can control the thermal expansion of materials. Recent progress in materials research enables us to obtain materials exhibiting negative coefficients of linear thermal expansion over −30 ppm K−1. Such giant NTE is opening a new phase of control of thermal expansion in composites. Specifically examining pra...
LPV system identification using series expansion models
Toth, R.; Heuberger, P.S.C.; Hof, Van den P.M.J.; Santos, dos P.L.; Perdicoúlis, T.P.A.; Novara, C.; Ramos, J.A.; Rivera, D.E.
2011-01-01
This review volume reports the state-of-the-art in Linear Parameter Varying (LPV) system identification. Written by world renowned researchers, the book contains twelve chapters, focusing on the most recent LPV identification methods for both discrete-time and continuous-time models, using different
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)
Design of materials with extreme thermal expansion using a three-phase topology optimization method
DEFF Research Database (Denmark)
Sigmund, Ole; Torquato, S.
1997-01-01
Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases...... materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion...
From greedy to lazy expansions and their driving dynamics
Dajani, K.; Kraaikamp, C.
2001-01-01
In this paper we study the ergodic properties of non-greedy series expansions to non-integer bases β > 1. It is shown that the so-called 'lazy' expansion is isomorphic to the 'greedy' expansion. Furthermore, a class of expansions to base β > 1, β =2 Z, 'in between' the lazy and the greedy
Convergent WKB Series--How Can It be ?
International Nuclear Information System (INIS)
Ezawa, Hiroshi; Nakamura, Toru; Watanabe, Keiji
2008-01-01
Schroedinger equation for a polynomial potential with the highest order term having an even power and a positive coefficient is solved for high eigenvalues E n in two different ways after Liouville transformation, (a) converting the differential equation into integral equation and solving it iteratively and (b) by the WKB method. While the series solution in powers of 1/√(E n ) from (b) is known to diverge, we show that the one from (a) converges. We show then that asymptotic re-expansion of the convergent series from (a) agrees with the divergent series from (b). Actually, we have been able to show the agreement only up to order (1/√(E n )) 5 , but we believe that it holds to all orders. If this is true, the divergent WKB series can be reorganized into a convergent series, which is in fact obtained by the method of iteration (a)
Low Thermal Expansion Glass Ceramics
Bach, Hans
2005-01-01
This book appears in the authoritative series reporting the international research and development activities conducted by the Schott group of companies. This series provides an overview of Schott's activities for scientists, engineers, and managers from all branches of industry worldwide in which glasses and glass ceramics are of interest. Each volume begins with a chapter providing a general idea of the current problems, results, and trends relating to the subjects treated. This new extended edition describes the fundamental principles, the manufacturing process, and applications of low thermal expansion glass ceramics. The composition, structure, and stability of polycrystalline materials having a low thermal expansion are described, and it is shown how low thermal expansion glass ceramics can be manufactured from appropriately chosen glass compositions. Examples illustrate the formation of this type of glass ceramic by utilizing normal production processes together with controlled crystallization. Thus g...
Low thermal expansion glass ceramics
1995-01-01
This book is one of a series reporting on international research and development activities conducted by the Schott group of companies With the series, Schott aims to provide an overview of its activities for scientists, engineers, and managers from all branches of industry worldwide where glasses and glass ceramics are of interest Each volume begins with a chapter providing a general idea of the current problems, results, and trends relating to the subjects treated This volume describes the fundamental principles, the manufacturing process, and applications of low thermal expansion glass ceramics The composition, structure, and stability of polycrystalline materials having a low thermal expansion are described, and it is shown how low thermal expansion glass ceramics can be manufactured from appropriately chosen glass compositions Examples illustrate the formation of this type of glass ceramic by utilizing normal production processes together with controlled crystallization Thus glass ceramics with thermal c...
A summation procedure for expansions in orthogonal polynomials
International Nuclear Information System (INIS)
Garibotti, C.R.; Grinstein, F.F.
1977-01-01
Approximants to functions defined by formal series expansions in orthogonal polynomials are introduced. They are shown to be convergent even out of the elliptical domain where the original expansion converges
International Nuclear Information System (INIS)
Decanini, Yves; Folacci, Antoine
2006-01-01
Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients--i.e., the DeWitt and Hadamard coefficients--that define them
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
Chromatic Derivatives, Chromatic Expansions and Associated Spaces
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 ...
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan
2015-01-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
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.
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.
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.
Validation of correction factors for concrete coefficient of thermal expansion.
2010-07-01
To complete the objectives, AASHTO T 366-09 results will be compared to ASHTO TP 60-00 results. The results will then be used as input values for the MEPDG and the results evaluated. : Major changes between AASHTO TP 60-00 and AASHTO T 336-09 will be...
The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators
Ahmedov, Anvarjon
2018-03-01
In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral
Regulation of gas infrastructure expansion
International Nuclear Information System (INIS)
De Joode, J.
2012-01-01
The topic of this dissertation is the regulation of gas infrastructure expansion in the European Union (EU). While the gas market has been liberalised, the gas infrastructure has largely remained in the regulated domain. However, not necessarily all gas infrastructure facilities - such as gas storage facilities, LNG import terminals and certain gas transmission pipelines - need to be regulated, as there may be scope for competition. In practice, the choice of regulation of gas infrastructure expansion varies among different types of gas infrastructure facilities and across EU Member States. Based on a review of economic literature and on a series of in-depth case studies, this study explains these differences in choices of regulation from differences in policy objectives, differences in local circumstances and differences in the intrinsic characteristics of the infrastructure projects. An important conclusion is that there is potential for a larger role for competition in gas infrastructure expansion.
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.,
Extended moment series and the parameters of the negative binomial distribution
International Nuclear Information System (INIS)
Bowman, K.O.
1984-01-01
Recent studies indicate that, for finite sample sizes, moment estimators may be superior to maximum likelihood estimators in some regions of parameter space. In this paper a statistic based on the central moment of the sample is expanded in a Taylor series using 24 derivatives and many more terms than previous expansions. A summary algorithm is required to find meaningful approximants using the higher-order coefficients. A example is presented and a comparison between theoretical assessment and simulation results is made
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.
Negative thermal expansion materials: technological key for control of thermal expansion.
Takenaka, Koshi
2012-02-01
Most materials expand upon heating. However, although rare, some materials contract upon heating. Such negative thermal expansion (NTE) materials have enormous industrial merit because they can control the thermal expansion of materials. Recent progress in materials research enables us to obtain materials exhibiting negative coefficients of linear thermal expansion over -30 ppm K -1 . Such giant NTE is opening a new phase of control of thermal expansion in composites. Specifically examining practical aspects, this review briefly summarizes materials and mechanisms of NTE as well as composites containing NTE materials, based mainly on activities of the last decade.
Negative thermal expansion materials: technological key for control of thermal expansion
Directory of Open Access Journals (Sweden)
Koshi Takenaka
2012-01-01
Full Text Available Most materials expand upon heating. However, although rare, some materials contract upon heating. Such negative thermal expansion (NTE materials have enormous industrial merit because they can control the thermal expansion of materials. Recent progress in materials research enables us to obtain materials exhibiting negative coefficients of linear thermal expansion over −30 ppm K−1. Such giant NTE is opening a new phase of control of thermal expansion in composites. Specifically examining practical aspects, this review briefly summarizes materials and mechanisms of NTE as well as composites containing NTE materials, based mainly on activities of the last decade.
Negative thermal expansion materials: technological key for control of thermal expansion
International Nuclear Information System (INIS)
Takenaka, Koshi
2012-01-01
Most materials expand upon heating. However, although rare, some materials contract upon heating. Such negative thermal expansion (NTE) materials have enormous industrial merit because they can control the thermal expansion of materials. Recent progress in materials research enables us to obtain materials exhibiting negative coefficients of linear thermal expansion over −30 ppm K −1 . Such giant NTE is opening a new phase of control of thermal expansion in composites. Specifically examining practical aspects, this review briefly summarizes materials and mechanisms of NTE as well as composites containing NTE materials, based mainly on activities of the last decade. (topical review)
Operator product expansion in QCD at short distance. Part 2
Energy Technology Data Exchange (ETDEWEB)
Mallik, S
1984-03-19
We describe a simple momentum-space method of evaluating Wilson coefficients of gluon operators in an operator product expansion (OPE). This extends an earlier configuration-space method suitable for calculating the coefficients for light quarks. The method is illustrated by calculating the coefficients of the Lorentz scalar gluon operator of dimension four appearing in different two-point functions.
Clustering Coefficients for Correlation Networks.
Masuda, Naoki; Sakaki, Michiko; Ezaki, Takahiro; Watanabe, Takamitsu
2018-01-01
Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly
Clustering Coefficients for Correlation Networks
Directory of Open Access Journals (Sweden)
Naoki Masuda
2018-03-01
Full Text Available Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients
Clustering Coefficients for Correlation Networks
Masuda, Naoki; Sakaki, Michiko; Ezaki, Takahiro; Watanabe, Takamitsu
2018-01-01
Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly
Structure of large spin expansion of anomalous dimensions at strong coupling
Energy Technology Data Exchange (ETDEWEB)
Beccaria, M. [Physics Department, Salento University and INFN, 73100 Lecce (Italy)], E-mail: matteo.beccaria@le.infn.it; Forini, V. [Humboldt-Universitaet zu Berlin, Institut fuer Physik, D-12489 Berlin (Germany)], E-mail: forini@aei.mpg.de; Tirziu, A. [Department of Physics, Purdue University, W. Lafayette, IN 47907-2036 (United States)], E-mail: atirziu@purdue.edu; Tseytlin, A.A. [Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)], E-mail: tseytlin@imperial.ac.uk
2009-05-01
The anomalous dimensions of planar N=4 SYM theory operators like tr({phi}D{sub +}{sup S}{phi}) expanded in large spin S have the asymptotics {gamma}=flnS+f{sub c}+1/S (f{sub 11}lnS+f{sub 10})+..., where f (the universal scaling function or cusp anomaly), f{sub c} and f{sub mn} are given by power series in the 't Hooft coupling {lambda}. The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing {gamma} in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS{sub 5}. The large spin expansion of the classical string energy happens to have exactly the same structure as that of {gamma} in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f{sub c}, f{sub 11}, f{sub 10} and verify the functional/reciprocity relations at subleading 1/({radical}({lambda})) order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions.
Structure of large spin expansion of anomalous dimensions at strong coupling
International Nuclear Information System (INIS)
Beccaria, M.; Forini, V.; Tirziu, A.; Tseytlin, A.A.
2009-01-01
The anomalous dimensions of planar N=4 SYM theory operators like tr(ΦD + S Φ) expanded in large spin S have the asymptotics γ=flnS+f c +1/S (f 11 lnS+f 10 )+..., where f (the universal scaling function or cusp anomaly), f c and f mn are given by power series in the 't Hooft coupling λ. The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing γ in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS 5 . The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f c , f 11 , f 10 and verify the functional/reciprocity relations at subleading 1/(√(λ)) order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions
Thermal expansion of diamond at low temperatures.
Stoupin, Stanislav; Shvyd'ko, Yuri V
2010-02-26
Temperature variation of a lattice parameter of a synthetic diamond crystal (type IIa) was measured using high-energy-resolution x-ray Bragg diffraction in backscattering. A 2 order of magnitude improvement in the measurement accuracy allowed us to directly probe the linear thermal expansion coefficient at temperatures below 100 K. The lowest value measured was 2x10{-9} K-1. It was found that the coefficient deviates from the expected Debye law (T3) while no negative thermal expansion was observed. The anomalous behavior might be attributed to tunneling states due to low concentration impurities.
Correlation expansion: a powerful alternative multiple scattering calculation method
International Nuclear Information System (INIS)
Zhao Haifeng; Wu Ziyu; Sebilleau, Didier
2008-01-01
We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion
Effective potential of the three-dimensional Ising model: The pseudo-ɛ expansion study
Sokolov, A. I.; Kudlis, A.; Nikitina, M. A.
2017-08-01
The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for the critical values of g6, g8, g10, R6 =g6 / g42, R8 =g8 / g43 and R10 =g10 / g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ɛ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6* = 1.6488 and R6* = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ɛ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8* = 0.868, the number being close to the lattice estimate R8* = 0.871 and compatible with the result of 3D RG analysis R8* = 0.857. Pseudo-ɛ expansions for R10* and g10* are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.
Interbasis expansions for isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)
2012-03-12
The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.
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.)
Regular approach for generating van der Waals C{sub s} coefficients to arbitrary orders
Energy Technology Data Exchange (ETDEWEB)
Ovsiannikov, Vitali D [Department of Physics, Voronezh State University, 394006 Voronezh (Russian Federation); Mitroy, J [Faculty of Technology, Charles Darwin University, Darwin, NT 0909 (Australia)
2006-01-14
A completely general formalism is developed to describe the energy E{sup disp} = {sigma}{sub s}C{sub s}/R{sup s} of dispersion interaction between two atoms in spherically symmetric states. Explicit expressions are given up to the tenth order of perturbation theory for the dispersion energy E{sup disp} and dispersion coefficients C{sub s}. The method could, in principle, be used to derive the expressions for any s while including all contributing orders of perturbation theory for asymptotic interaction between two atoms. The theory is applied to the calculation of the complete series up to s = 30 for two hydrogen atoms in their ground state. A pseudo-state series expansion of the two-atom Green function gives rapid convergence of the series for radial matrix elements. The numerical values of C{sub s} are computed up to C{sub 30} to a relative accuracy of 10{sup -7} or better. The dispersion coefficients for the hydrogen-antihydrogen interaction are obtained from the H-H coefficients by simply taking the absolute magnitude of C{sub s}.
Regular approach for generating van der Waals Cs coefficients to arbitrary orders
International Nuclear Information System (INIS)
Ovsiannikov, Vitali D; Mitroy, J
2006-01-01
A completely general formalism is developed to describe the energy E disp = Σ s C s /R s of dispersion interaction between two atoms in spherically symmetric states. Explicit expressions are given up to the tenth order of perturbation theory for the dispersion energy E disp and dispersion coefficients C s . The method could, in principle, be used to derive the expressions for any s while including all contributing orders of perturbation theory for asymptotic interaction between two atoms. The theory is applied to the calculation of the complete series up to s = 30 for two hydrogen atoms in their ground state. A pseudo-state series expansion of the two-atom Green function gives rapid convergence of the series for radial matrix elements. The numerical values of C s are computed up to C 30 to a relative accuracy of 10 -7 or better. The dispersion coefficients for the hydrogen-antihydrogen interaction are obtained from the H-H coefficients by simply taking the absolute magnitude of C s
Virial expansion for almost diagonal random matrices
International Nuclear Information System (INIS)
Yevtushenko, Oleg; Kravtsov, Vladimir E
2003-01-01
Energy level statistics of Hermitian random matrices H-circumflex with Gaussian independent random entries H i≥j is studied for a generic ensemble of almost diagonal random matrices with (vertical bar H ii vertical bar 2 ) ∼ 1 and (vertical bar H i≠j vertical bar 2 ) bF(vertical bar i - j vertical bar) parallel 1. We perform a regular expansion of the spectral form-factor K(τ) = 1 + bK 1 (τ) + b 2 K 2 (τ) + c in powers of b parallel 1 with the coefficients K m (τ) that take into account interaction of (m + 1) energy levels. To calculate K m (τ), we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges colouring with (m + 1) colours. Expressions for K 1 (τ) and K 2 (τ) in terms of infinite series are found for a generic function F(vertical bar i - j vertical bar ) in the Gaussian orthogonal ensemble (GOE), the Gaussian unitary ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and power-law banded matrix ensembles are considered as examples
Advanced computer algebra algorithms for the expansion of Feynman integrals
International Nuclear Information System (INIS)
Ablinger, Jakob; Round, Mark; Schneider, Carsten
2012-10-01
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+ε-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.
Advanced computer algebra algorithms for the expansion of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2012-10-15
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+{epsilon}-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.
Taylor-series method for four-nucleon wave functions
International Nuclear Information System (INIS)
Sandulescu, A.; Tarnoveanu, I.; Rizea, M.
1977-09-01
Taylor-series method for transforming the infinite or finite well two-nucleon wave functions from individual coordinates to relative and c.m. coordinates, by expanding the single particle shell model wave functions around c.m. of the system, is generalized to four-nucleon wave functions. Also the connections with the Talmi-Moshinsky method for two and four harmonic oscillator wave functions are deduced. For both methods Fortran IV programs for the expansion coefficients have been written and the equivalence of corresponding expressions numerically proved. (author)
1 / n Expansion for the Number of Matchings on Regular Graphs and Monomer-Dimer Entropy
Pernici, Mario
2017-08-01
Using a 1 / n expansion, that is an expansion in descending powers of n, for the number of matchings in regular graphs with 2 n vertices, we study the monomer-dimer entropy for two classes of graphs. We study the difference between the extensive monomer-dimer entropy of a random r-regular graph G (bipartite or not) with 2 n vertices and the average extensive entropy of r-regular graphs with 2 n vertices, in the limit n → ∞. We find a series expansion for it in the numbers of cycles; with probability 1 it converges for dimer density p diverges as |ln(1-p)| for p → 1. In the case of regular lattices, we similarly expand the difference between the specific monomer-dimer entropy on a lattice and the one on the Bethe lattice; we write down its Taylor expansion in powers of p through the order 10, expressed in terms of the number of totally reducible walks which are not tree-like. We prove through order 6 that its expansion coefficients in powers of p are non-negative.
ANL results for LMFR reactivity coefficients benchmark
International Nuclear Information System (INIS)
Hill, Robert
2000-01-01
The fast reactor analysis methods developed at ANL were extensively tested in ZPR and ZPPR experiments, applied to EBR-2 and FFTF test reactors. The basic nuclear data library used was ENDF/B-V.2 with the ETOE-2 data processing code and the ENDF/B-VI. Multigroup constants were generated by Monte Carlo code MCNP 2 -2. Neutron flux calculation were done by DIF3D code applying neutron diffusion theory and finite difference method. The results obtained include basic parameters; fuel and structure regional Doppler coefficients; geometry expansion fuel coefficients; kinetics parameters. In general, agreement between phase 1 and 2 results were excellent
The second virial coefficient of bounded Mie potentials
Heyes, D. M.; Pereira de Vasconcelos, T.
2017-12-01
The second virial coefficient (SVC) of bounded generalizations of the Mie m:n potential ϕ (r ) =λ [1 /(aq+rq ) m /q-1 /(aq+rq ) n /q ] , where λ, a, q, m, and n are constants (a ≥ 0), is explored. The particle separation distance is r. This potential could be used as an effective interaction between polymeric dispersed colloidal particles of various degrees of interpenetrability. The SVC is negative for all temperatures for a, greater than a critical value, ac, which coincides with the range of a, where the system is thermodynamically unstable. The Boyle temperature and the temperature at which the SVC is a maximum diverge to +∞ as a → ac from below. Various series expansion expressions for the SVC are derived following on from those derived for the Mie potential itself (i.e., a = 0) in the study of Heyes et al. [J. Chem. Phys. 145, 084505 (2016)]. Formulas based on an expansion of the exponential in the Mayer function definition of the SVC are formally convergent, but pose numerical problems for the useful range of a < 1. High temperature expansion (HTE) formulas extending those in the previous publication are derived, which in contrast converge rapidly for the full a range. The HTE formulas derived in this work could be useful in guiding the choice of nucleation and growth experimental conditions for dispersed soft polymeric particles. Inter alia, the SVC of the inverse power special case of the Bounded Mie potential, i .e ., ϕ (r ) =1 /(aq+rq ) m /q, are also derived.
Origami structures for tunable thermal expansion
Boatti, Elisa; Bertoldi, Katia
Materials with engineered thermal expansion, capable of achieving targeted and extreme area/volume changes in response to variations in temperature, are important for a number of aerospace, optical, energy, and microelectronic applications. While most of the proposed structures with tunable coefficient of thermal expansion consist of bi-material 2D or 3D lattices, here we propose a periodic metastructure based on a bilayer Miura-Ori origami fold. We combine experiments and simulations to demonstrate that by tuning the geometrical and mechanical parameters an extremely broad range of thermal expansion coefficients can be obtained, spanning both negative and positive values. Additionally, the thermal properties along different directions can be adjusted independently. Differently from all previously reported systems, the proposed structure is non-porous.
Thermal expansion of quaternary nitride coatings
Tasnádi, Ferenc; Wang, Fei; Odén, Magnus; Abrikosov, Igor A.
2018-04-01
The thermal expansion coefficient of technologically relevant multicomponent cubic nitride alloys are predicted using the Debye model with ab initio elastic constants calculated at 0 K and an isotropic approximation for the Grüneisen parameter. Our method is benchmarked against measured thermal expansion of TiN and Ti(1-x)Al x N as well as against results of molecular dynamics simulations. We show that the thermal expansion coefficients of Ti(1-x-y)X y Al x N (X = Zr, Hf, Nb, V, Ta) solid solutions monotonously increase with the amount of alloying element X at all temperatures except for Zr and Hf, for which they instead decrease for y≳ 0.5 .
Renormalization and operator product expansion in theories with massless particles
International Nuclear Information System (INIS)
Anikin, S.A.; Smirnov, V.A.
1985-01-01
Renormalization procedure in theories including massless particles is presented. With the help of counterterm formalism the operator product expansion for arbitrary composite fields is derived. The coefficient functions are explicitly expressed in terms of certain Green's functions. (author)
Asymptotic series and functional integrals in quantum field theory
International Nuclear Information System (INIS)
Shirkov, D.V.
1979-01-01
Investigations of the methods for analyzing ultra-violet and infrared asymptotics in the quantum field theory (QFT) have been reviewed. A powerful method of the QFT analysis connected with the group property of renormalized transformations has been created at the first stage. The result of the studies of the second period is the constructive solution of the problem of outgoing the framework of weak coupling. At the third stage of studies essential are the asymptotic series and functional integrals in the QFT, which are used for obtaining the asymptotic type of the power expansion coefficients in the coupling constant at high values of the exponents for a number of simple models. Further advance to higher values of the coupling constant requires surmounting the difficulties resulting from the asymptotic character of expansions and a constructive application in the region of strong coupling (g >> 1)
Thermal expansion of spinel-type Si3N4
DEFF Research Database (Denmark)
Paszkowics, W.; Minkikayev, R.; Piszora, P.
2004-01-01
The lattice parameter and thermal expansion coefficient (TEC) for the spinel-type Si3N4 phase prepared under high-pressure and high-temperature conditions are determined for 14 K......The lattice parameter and thermal expansion coefficient (TEC) for the spinel-type Si3N4 phase prepared under high-pressure and high-temperature conditions are determined for 14 K...
Spherical-wave expansions of piston-radiator fields.
Wittmann, R C; Yaghjian, A D
1991-09-01
Simple spherical-wave expansions of the continuous-wave fields of a circular piston radiator in a rigid baffle are derived. These expansions are valid throughout the illuminated half-space and are useful for efficient numerical computation in the near-field region. Multipole coefficients are given by closed-form expressions which can be evaluated recursively.
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)
Negative thermal expansion of lithium aluminosilicate ceramics at cryogenic temperatures
International Nuclear Information System (INIS)
Garcia-Moreno, Olga; Fernandez, Adolfo; Khainakov, Sergei; Torrecillas, Ramon
2010-01-01
Five lithium aluminosilicate compositions of the LAS system have been synthesized and sintered. The coefficient of thermal expansion of the sintered samples has been studied down to cryogenic conditions. The data presented here under cryogenic conditions will be of value in the future design of new composite materials with very low thermal expansion values. The variation in thermal expansion properties with composition and sintering temperature was studied and is discussed in relation to composition and crystal structure.
Transport Coefficients of Fluids
Eu, Byung Chan
2006-01-01
Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium.
Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method
Chu, Chunlei
2012-07-01
Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.
δ expansion applied to quantum electrodynamics
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Milton, K.A.
1992-01-01
A recently proposed technique known as the δ expansion provides a nonperturbative treatment of a quantum field theory. The δ-expansion approach can be applied to electrodynamics in such a way that local gauge invariance is preserved. In this paper it is shown that for electrodynamic processes involving only external photon lines and no external electron lines the δ expansion is equivalent to a fermion loop expansion. That is, the coefficient of δ n in the δ expansion is precisely the sum of all n-electron-loop Feynman diagrams in a conventional weak-coupling approximation. This equivalence does not extend to processes having external electron lines. When external electron lines are present, the δ expansion is truly nonperturbative and does not have a simple interpretation as a resummation of conventional Feynman diagrams. To illustrate the nonperturbative character of the δ expansion we perform a speculative calculation of the fermion condensate in the massive Schwinger model in the limit of large coupling constant
International Nuclear Information System (INIS)
Boyd, John P.; Rangan, C.; Bucksbaum, P.H.
2003-01-01
The Fourier-sine-with-mapping pseudospectral algorithm of Fattal et al. [Phys. Rev. E 53 (1996) 1217] has been applied in several quantum physics problems. Here, we compare it with pseudospectral methods using Laguerre functions and rational Chebyshev functions. We show that Laguerre and Chebyshev expansions are better suited for solving problems in the interval r in R set of [0,∞] (for example, the Coulomb-Schroedinger equation), than the Fourier-sine-mapping scheme. All three methods give similar accuracy for the hydrogen atom when the scaling parameter L is optimum, but the Laguerre and Chebyshev methods are less sensitive to variations in L. We introduce a new variant of rational Chebyshev functions which has a more uniform spacing of grid points for large r, and gives somewhat better results than the rational Chebyshev functions of Boyd [J. Comp. Phys. 70 (1987) 63
Adjustment of activity coefficients as a function of changes in temperature, using the SIT
International Nuclear Information System (INIS)
Giffaut, E.; Vitorge, P.; Capdevila, H.
1993-11-01
The aim of this work is to propose and to check approximations to calculate from only a few experimental measurements, ionic strength, I, and temperature, T, influences on Gibbs energy, G, redox formal potential, E, and standard equilibrium constant, K. Series expansions versus T are first used: S and Cp/2T a are typically the -G first and second order terms. In the same way, -ΔH and T 2 ΔCp/2 are the first and second order terms of R in K expansions versus 1/T. This type of approximation is discussed for the E of the M 4+ /M 3+ , MO 2 2+ /MO 2 + and MO 2 (CO 3 ) 3 4- /MO 2 (CO 3 ) 3 5- couples (M = U or Pu) measured from 5 to 70 deg C, for the standard ΔG of some solid U compounds, calculated from 17 to 117 deg C, and for ΔCp, ΔG and Ig K of the CO 2 (aq)/HCO 3 - equilibrium from 0 to 150 deg C. Excess functions, X ex , are then calculated from activity coefficients, γ: enthalpy, H, or heat capacity, Cp, adjustment as a function of I changes is needed only when the γ adjustment as a function of T changes is needed. The SIT coefficient, ε, variations with T, are small and roughly linear for the above redox equilibria and for chloride electrolytes mean γ: first order expansion seems enough to deduce ε, and then the excess functions G ex , S ex and H ex , in this T range; but second order expansion is more consistent to estimate Cp ex . (authors). 25 refs., 3 tabs., 1 fig
Energy Technology Data Exchange (ETDEWEB)
Dzenus, M.; Hundhausen, W.; Jansing, W.
1979-10-15
This discourse recounts efforts put into the SNR-2 project; specifically the development of compensation devices. The various prototypes of these compensation devices are described and the state of development reviewed. The expansion joints were developed on the basis of specific design criteria whereby differentiation is made between expansion joints of small and large nominal diameter. Expansion joints for installation in the sodium-filled primary piping are equipped with safety bellows in addition to the actual working bellows.
Instanton expansions for mass deformed N=4 super Yang-Mills theories
International Nuclear Information System (INIS)
Minahan, J.A.; Nemeschansky, D.; Warner, N.P.
1998-01-01
We derive modular anomaly equations from the Seiberg-Witten-Donagi curves for softly broken N=4 SU(n) gauge theories. From these equations we can derive recursion relations for the pre-potential in powers of m 2 , where m is the mass of the adjoint hypermultiplet. Given the perturbative contribution of the pre-potential and the presence of ''gaps'', we can easily generate the m 2 expansion in terms of polynomials of Eisenstein series, at least for relatively low rank groups. This enables us to determine efficiently the instanton expansion up to fairly high order for these gauge groups, e.g. eighth order for SU(3). We find that after taking a derivative, the instanton expansion of the pre-potential has integer coefficients. We also postulate the form of the modular anomaly equations, the recursion relations and the form of the instanton expansions for the SO(2n) and E n gauge groups, even though the corresponding Seiberg-Witten-Donagi curves are unknown at this time. (orig.)
Thermal expansion of NZP-family alkali-metal (Na, K) zirconium phosphates
International Nuclear Information System (INIS)
Orlova, A.I.; Kemenov, D.V.; Pet'kov, V.I.; Samojlov, S.G.; Kazantsev, G.N.
2000-01-01
By means of high-temperature X-ray diffraction one investigated into thermal expansion of alkali-zirconium phosphates crystallizing in NaZr 2 (PO 4 ) 3 structure type within 20-700 deg C temperature range. One synthesized phosphates of A x Zr 2.25-0.25x (PO 4 ) 3 type two series where A-Na (x = 0.5; 1.0; 2.0; 3.0; 4.0; 5.0) and K (x = 1.0; 3.0; 5.0). One calculated for them a and c parameters of the elementary cells and α a and α c linear expansion temperature coefficients. Anisotropy of thermal expansion the maximum one for AZr 2 (PO 4 ) 3 and Na 5 Zr(PO 4 ) 3 phosphates was determined. K 5 Zr(PO 4 ) 3 compound was characterized by the minimum thermal expansion at the near-zero anisotropy of Na 5 Zr(PO 4 ) 3 [ru
Treatment of divergent expansions in scattering theory
International Nuclear Information System (INIS)
Gersten, A.; Malin, S.
1978-01-01
One of the biggest obstacles in applying quantum field theory to realistic scattering problems are the divergencies of pertubation expansions for large coupling constants and the divergencies of partial wave expansions for massless particles exchanges. There exist, however, methods of summation of the divergent expansions which can lead to significant application in physics. In this paper we treat the problem of summing such expansions using three methods: (i) a generalization of the Pade approximation to the multivariable case. The suggested definition is unique and preserves unitarity. (ii) The summation of divergent partial waves for arbitrary spins. (iii) A successful application of a series inversion to the 3 P 1 nucleon-nucleon phase shift up to 200 MeV. (orig./WL) [de
Towards finite density QCD with Taylor expansions
International Nuclear Information System (INIS)
Karsch, F.; Schaefer, B.-J.; Wagner, M.; Wambach, J.
2011-01-01
Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective N f =2+1 flavor Polyakov quark-meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective N f =2+1 flavor Polyakov quark-meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.
Shen, Fei-Ran; Kuang, Hao; Hu, Feng-Xia; Wu, Hui; Huang, Qing-Zhen; Liang, Fei-Xiang; Qiao, Kai-Ming; Li, Jia; Wang, Jing; Liu, Yao; Zhang, Lei; He, Min; Zhang, Ying; Zuo, Wen-Liang; Sun, Ji-Rong; Shen, Bao-Gen
2017-10-01
Materials with zero thermal expansion (ZTE) or precisely tailored thermal expansion are in urgent demand of modern industries. However, the overwhelming majority of materials show positive thermal expansion. To develop ZTE or negative thermal expansion (NTE) materials as compensators has become an important challenge. Here, we present the evidence for the realization of ultra-low thermal expansion in Mn-Co-Ge-In particles. The bulk with the Ni2In-type hexagonal structure undergoes giant NTE owing to a martensitic magnetostructural transition. The major finding is that the thermal expansion behavior can be totally controlled by modulating the crystallinity degree and phase transition from atomic scale. Self-compensation effect leads to ultra-low thermal expansion with a linear expansion coefficient as small as +0.68 × 10-6/K over a wide temperature range around room temperature. The present study opens an avenue to reach ZTE particularly from the large class of giant NTE materials based on phase transition.
Directory of Open Access Journals (Sweden)
Fei-Ran Shen
2017-10-01
Full Text Available Materials with zero thermal expansion (ZTE or precisely tailored thermal expansion are in urgent demand of modern industries. However, the overwhelming majority of materials show positive thermal expansion. To develop ZTE or negative thermal expansion (NTE materials as compensators has become an important challenge. Here, we present the evidence for the realization of ultra-low thermal expansion in Mn–Co–Ge–In particles. The bulk with the Ni2In-type hexagonal structure undergoes giant NTE owing to a martensitic magnetostructural transition. The major finding is that the thermal expansion behavior can be totally controlled by modulating the crystallinity degree and phase transition from atomic scale. Self-compensation effect leads to ultra-low thermal expansion with a linear expansion coefficient as small as +0.68 × 10−6/K over a wide temperature range around room temperature. The present study opens an avenue to reach ZTE particularly from the large class of giant NTE materials based on phase transition.
Park, Hee-Jung; Lee, Jun Hyup; Park, Sujin; Kim, Tae-Il
2018-02-01
This study utilized a strong quasi-experimental design to test the hypothesis that the implementation of a policy to expand dental care services resulted in an increase in the usage of dental outpatient services. A total of 45,650,000 subjects with diagnoses of gingivitis or advanced periodontitis who received dental scaling were selected and examined, utilizing National Health Insurance claims data from July 2010 through November 2015. We performed a segmented regression analysis of the interrupted time-series to analyze the time-series trend in dental costs before and after the policy implementation, and assessed immediate changes in dental costs. After the policy change was implemented, a statistically significant 18% increase occurred in the observed total dental cost per patient, after adjustment for age, sex, and residence area. In addition, the dental costs of outpatient gingivitis treatment increased immediately by almost 47%, compared with a 15% increase in treatment costs for advanced periodontitis outpatients. This policy effect appears to be sustainable. The introduction of the new policy positively impacted the immediate and long-term outpatient utilization of dental scaling treatment in South Korea. While the policy was intended to entice patients to prevent periodontal disease, thus benefiting the insurance system, our results showed that the policy also increased treatment accessibility for potential periodontal disease patients and may improve long-term periodontal health in the South Korean population.
2018-01-01
Purpose This study utilized a strong quasi-experimental design to test the hypothesis that the implementation of a policy to expand dental care services resulted in an increase in the usage of dental outpatient services. Methods A total of 45,650,000 subjects with diagnoses of gingivitis or advanced periodontitis who received dental scaling were selected and examined, utilizing National Health Insurance claims data from July 2010 through November 2015. We performed a segmented regression analysis of the interrupted time-series to analyze the time-series trend in dental costs before and after the policy implementation, and assessed immediate changes in dental costs. Results After the policy change was implemented, a statistically significant 18% increase occurred in the observed total dental cost per patient, after adjustment for age, sex, and residence area. In addition, the dental costs of outpatient gingivitis treatment increased immediately by almost 47%, compared with a 15% increase in treatment costs for advanced periodontitis outpatients. This policy effect appears to be sustainable. Conclusions The introduction of the new policy positively impacted the immediate and long-term outpatient utilization of dental scaling treatment in South Korea. While the policy was intended to entice patients to prevent periodontal disease, thus benefiting the insurance system, our results showed that the policy also increased treatment accessibility for potential periodontal disease patients and may improve long-term periodontal health in the South Korean population. PMID:29535886
Numerical studies of QCD renormalons in high-order perturbative expansions
International Nuclear Information System (INIS)
Bauer, Clemens
2013-01-01
Perturbative expansions in four-dimensional non-Abelian gauge theories such as Quantum Chromodynamics (QCD) are expected to be divergent, at best asymptotic. One reason is that it is impossible to strictly exclude from the relevant Feynman diagrams those energy regions in which a perturbative treatment is inapplicable. The divergent nature of the series is then signaled by a rapid (factorial) growth of the perturbative expansion coefficients, commonly referred to as a renormalon. In QCD, the most severe divergences occur in the infrared (IR) limit and therefore they are classified as IR renormalons. Their appearance can be understood within the well-accepted Operator Product Expansion (OPE) framework. According to the OPE, the perturbative calculation of a physical observable must be amended by non-perturbative power corrections that come in the form of condensates, universal characteristics of the rich QCD vacuum structure. Adding up perturbative and non-perturbative contributions, the ambiguity due to the renormalon cancels and the physical observable is well-defined. Although the field has made considerable progress in the last twenty years, a proof of renormalon existence is still pending. It has only been tested assuming strong simplifications or in toy models. The aim of this thesis is to provide the first numerical evidence for renormalon existence in the gauge sector of QCD. We use Numerical Stochastic Perturbation Theory (NSPT) to directly obtain perturbative coefficients within lattice regularization, a means to replace continuum spacetime by a four-dimensional hypercubic lattice. A peculiar feature of NSPT are comparatively low simulation costs when reaching high expansion orders. We examine two distinct observables: the static self-energy of an isolated quark and the elementary plaquette. Following the OPE classification, the static quark self-energy is ideally suited for a renormalon study. Taking into account peculiarities of the lattice approach such
Convergence of mayer expansions
International Nuclear Information System (INIS)
Brydges, D.C.
1986-01-01
The tree graph bound of Battle and Federbush is extended and used to provide a simple criterion for the convergence of (iterated) Mayer expansions. As an application estimates on the radius of convergence of the Mayer expansion for the two-dimensional Yukawa gas (nonstable interaction) are obtained
An operator expansion technique for path integral analysis
International Nuclear Information System (INIS)
Tsvetkov, I.V.
1995-01-01
A new method of path integral analysis in the framework of a power series technique is presented. The method is based on the operator expansion of an exponential. A regular procedure to calculate the correction terms is found. (orig.)
The hard ellipsoid-of-revolution fluid II. The y-expansion equation of state
Mulder, B.M.; Frenkel, D.
1985-01-01
The γ-expansion as introduced by Barboy and Gelbart is applied to a system of hard ellipsoids-of-revolution. The expansion is truncated after the third order term yielding an approximate theory requiring the second- and third-virial coefficients as inputs. As the third virial coefficient is not
A convergence theorem for asymptotic expansions of Feynman amplitudes
International Nuclear Information System (INIS)
Mabouisson, A.P.C.
1999-06-01
The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to ∞, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)
Analytic continuation of tgensor fields along geodesics by covariant Taylor series
International Nuclear Information System (INIS)
Tsirulev, A.N.
1995-01-01
It is shown that in a certain normal neighborhood of a submanifold-the analog of a normal neighborhood of a point-the covariant derivatives of all orders of an arbitrary tensor field and of the curvature and torsion along geodesics normal to the submanifold, taken at points of the submanifold, determine under conditions of analyticity the given tensor field by Taylor series with tensor coefficients. Explicit expressions are obtained that provide a recursive procedure for calculating the coefficients of the series in any order. Special cases of the expansion of the components of a pseudo-Riemannian metric with respect to a metric connection without torsion for a point and hypersurface are considered
High thermal expansion, sealing glass
Brow, R.K.; Kovacic, L.
1993-11-16
A glass composition is described for hermetically sealing to high thermal expansion materials such as aluminum alloys, stainless steels, copper, and copper/beryllium alloys, which includes between about 10 and about 25 mole percent Na[sub 2]O, between about 10 and about 25 mole percent K[sub 2]O, between about 5 and about 15 mole percent Al[sub 2]O[sub 3], between about 35 and about 50 mole percent P[sub 2]O[sub 5] and between about 5 and about 15 mole percent of one of PbO, BaO, and mixtures thereof. The composition, which may also include between 0 and about 5 mole percent Fe[sub 2]O[sub 3] and between 0 and about 10 mole percent B[sub 2]O[sub 3], has a thermal expansion coefficient in a range of between about 160 and 210[times]10[sup [minus]7]/C and a dissolution rate in a range of between about 2[times]10[sup [minus]7] and 2[times]10[sup [minus]9]g/cm[sup 2]-min. This composition is suitable to hermetically seal to metallic electrical components which will be subjected to humid environments over an extended period of time.
Measuring correlations between non-stationary series with DCCA coefficient
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2014-01-01
Roč. 402, č. 1 (2014), s. 291-298 ISSN 0378-4371 R&D Projects: GA ČR(CZ) GP14-11402P Grant - others:GA ČR(CZ) GAP402/11/0948 Program:GA Institutional support: RVO:67985556 Keywords : power-law cross-correlations * long - term memory * econophysics Subject RIV: AH - Economics Impact factor: 1.732, year: 2014 http://library.utia.cas.cz/separaty/2014/E/kristoufek-0433533.pdf
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)
Leptodermous expansion of finite-nucleus incompressibility
International Nuclear Information System (INIS)
Nayak, R.C.
1990-01-01
We consider the influence of higher-order terms in the leptodermous expansion used to extract the incompressibility K v of infinite nuclear matter from data on the breathing mode of finite nuclei. The terms we calculate are the curvature term K cv A -2/3 , the surface-symmetry term K ss I 2 A -1/3 , the quartic volume-symmetry term K 4 I 4 , and a Coulomb-exchange term. Working within the framework of the scaling model we derive expressions for their coefficients in terms of quantities that are defined for infinite and semi-infinite nuclear matter. We calculate these coefficients for four different Skyrme-type forces, using the extended Thomas-Fermi (ETF) approximation. With the same forces we also calculate the incompressibility K (A, I) for a number of finite nuclei, fit the results to the leptodermous expansion, and thereby extract new results for the same coefficients. The comparison of the two calculations shows that the leptodermous expansion is converging rapidly. Of the new terms, the term K 4 I 4 is quite negligible, the curvature term should be included, and we discuss to what extent the other higher-order terms are significant. (orig.)
Large J expansion in ABJM theory revisited.
Dimov, H; Mladenov, S; Rashkov, R C
Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of the AdS/CFT correspondence. On the string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of a large-charge expansion of the dispersion relations for simple semiclassical strings in an [Formula: see text] background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three methods look different, power series expansions show their consistency.
Attenuation coefficients of soils
International Nuclear Information System (INIS)
Martini, E.; Naziry, M.J.
1989-01-01
As a prerequisite to the interpretation of gamma-spectrometric in situ measurements of activity concentrations of soil radionuclides the attenuation of 60 to 1332 keV gamma radiation by soil samples varying in water content and density has been investigated. A useful empirical equation could be set up to describe the dependence of the mass attenuation coefficient upon photon energy for soil with a mean water content of 10%, with the results comparing well with data in the literature. The mean density of soil in the GDR was estimated at 1.6 g/cm 3 . This value was used to derive the linear attenuation coefficients, their range of variation being 10%. 7 figs., 5 tabs. (author)
Controlled Thermal Expansion Alloys
National Aeronautics and Space Administration — There has always been a need for controlled thermal expansion alloys suitable for mounting optics and detectors in spacecraft applications. These alloys help...
Thermal expansion in 3d-metal Prussian Blue Analogs-A survey study
International Nuclear Information System (INIS)
Adak, Sourav; Daemen, Luke L.; Hartl, Monika; Williams, Darrick; Summerhill, Jennifer; Nakotte, Heinz
2011-01-01
We present a comprehensive study of the structural properties and the thermal expansion behavior of 17 different Prussian Blue Analogs (PBAs) with compositions M II 3 [(M') III (CN) 6 ] 2 .nH 2 O and M II 2 [Fe II (CN) 6 ].nH 2 O, where M II =Mn, Fe, Co, Ni, Cu and Zn, (M') III =Co, Fe and n is the number of water molecules, which range from 5 to 18 for these compounds. The PBAs were synthesized via standard chemical precipitation methods, and temperature-dependent X-ray diffraction studies were performed in the temperature range between -150 deg. C (123 K) and room-temperature. The vast majority of the studied PBAs were found to crystallize in cubic structures of space groups Fm3-bar m, F4-bar 3m and Pm3-bar m. The temperature dependence of the lattice parameters was taken to compute an average coefficient of linear thermal expansion in the studied temperature range. Of the 17 compounds, 9 display negative values for the average coefficient of linear thermal expansion, which can be as large as 39.7x 1 0 -6 K -1 for Co 3 [Co(CN) 6 ] 2 .12H 2 O. All of the M II 3 [Co III (CN) 6 ] 2 .nH 2 O compounds show negative thermal expansion behavior, which correlates with the Irving-Williams series for metal complex stability. The thermal expansion behavior for the PBAs of the M II 3 [Fe III (CN) 6 ] 2 .nH 2 O family are found to switch between positive (for M=Mn, Co, Ni) and negative (M=Cu, Zn) behavior, depending on the choice of the metal cation (M). On the other hand, all of the M II 2 [Fe II (CN) 6 ].nH 2 O compounds show positive thermal expansion behavior. - Graphical Abstract: The structure of Prussian Blue analogs (PBAs) consists of two types of metal centered octahedral units connected by cyanide ligand. Lattice and interstitial water molecules are present in these framework structures. All the PBAs of the M 3 [Co(CN) 6 ] 2 .nH 2 O family show negative thermal expansion (NTE) behavior. The lattice parameters and magnitude of NTE correlates inversely with the Irving
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
Cumulants in perturbation expansions for non-equilibrium field theory
International Nuclear Information System (INIS)
Fauser, R.
1995-11-01
The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)
Diffusion coefficient calculations for cylindrical cells
International Nuclear Information System (INIS)
Lam-Hime, M.
1983-03-01
An accurate and general diffusion coefficient calculation for cylindrical cells is described using isotropic scattering integral transport theory. This method has been particularly applied to large regular lattices of graphite-moderated reactors with annular coolant channels. The cells are divided into homogeneous zones, and a zone-wise flux expansion is used to formulate a collision probability problem. The reflection of neutrons at the cell boundary is accounted for by the conservation of the neutron momentum. The uncorrected diffusion coefficient Benoist's definition is used, and the described formulation does not neglect any effect. Angular correlation terms, energy coupling non-uniformity and anisotropy of the classical flux are exactly taken into account. Results for gas-graphite typical cells are given showing the importance of these approximations
Doppler coefficient measurements in Zebra Core 5
International Nuclear Information System (INIS)
Baker, A.R.; Wheeler, R.C.
1965-11-01
Measurements using a central hot loop in Zebra Core 5 are described. Results are given for the Doppler coefficients found in a number of assemblies with PuO 2 and 16% PuO 2 /84% depleted UO 2 pins, loaded with different combinations of steel, sodium or void pins. The mixed oxide results are in general about 20% more negative than was calculated using the FD2 data set, but agreement is good if the plutonium contributions in the calculations are omitted. The small positive Doppler coefficient calculated for Pu239 was not observed, and two measurements indicated instead a small negative effect. The Doppler effect in the mixed oxide systems was found to vary approximately as 1/T. The results from the empty loop and non-fissile assemblies indicate either a small negative Doppler effect in steel or alternatively the presence of an unexplained expansion effect. (author)
Mayer coefficients in two-dimensional Coulomb systems
International Nuclear Information System (INIS)
Speer, E.R.
1986-01-01
It is shown that, for neutral systems of particles of arbitrary charges in two dimensions, with hard cores, coefficients of the Mayer series for the pressure exist in the thermodynamic limit below certain thresholds in the temperature. The methods used here apply also to correlation functions and yield bounds on the asymptotic behavior of their Mayer coefficients
Thermal expansion of fibre-reinforced composites
International Nuclear Information System (INIS)
Schneider, B.
1991-07-01
The integral thermal expansion and the coefficient of thermal expansion (CTE) of carbon and Kevlar fibre-reinforced composites were measured with high accuracy from 5 K to room temperature. For this, a laser dilatometer and a sophisticated measuring procedure were used. CTE dependence on the orientation angle ω of angle-ply laminates was determined for samples with 5 different fibre alignments (UD 0deg, +/-30deg, +/-45deg, +/-60deg and UD 90deg). A high variability of the CTE with the orientation angle was shown. At angles of approximately +/-30deg even negative CTEs were found. With suitable reinforcing fibres being selected, their absolute values rose up to 30-100% of the positive CTEs of metals. Hence, composites of this type would be suitable as compensating materials in metal constructions where little thermal expansion is desired. To check the lamination theory, theoretical computations of the CTE- ω -dependence were compared with the measured values. An excellent agreement was found. Using the lamination theory, predictions about the expansion behaviour of angle-ply laminates can be made now, if the thermal and mechanical properties of the unidirectional (UD) laminate are known. Furthermore, it is possible to carry out simulation computations aimed at investigating the influence of a single parameter of the UD-laminate (e.g. shear modulus) on the expansion of the angle-ply laminate. (orig.) [de
The Truth About Ballistic Coefficients
Courtney, Michael; Courtney, Amy
2007-01-01
The ballistic coefficient of a bullet describes how it slows in flight due to air resistance. This article presents experimental determinations of ballistic coefficients showing that the majority of bullets tested have their previously published ballistic coefficients exaggerated from 5-25% by the bullet manufacturers. These exaggerated ballistic coefficients lead to inaccurate predictions of long range bullet drop, retained energy and wind drift.
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.)
Power coefficient anomaly in Joyo, (2)
International Nuclear Information System (INIS)
Ishikawa, Makoto; Yamashita, Yoshioki; Sasaki, Makoto; Nara, Yoshihiko.
1981-12-01
In this report, the presumption about the mechanism having caused the power coefficient anomaly in Joyo during the 75 MW power-raising test in 1979 is described. After the previous report, the new information about the results of the post-irradiation examination and the analysis of the power coefficient of Joyo were able to be obtained. From these information, the mechanism of causing the anomaly was presumed as follows. In 50 MW operation, the fuel burnup reached about 10,000 MWD/ton at the end of second cycle, and produced fission gas was almost retained in fuel pellets. When the power was raised from 50 MW to 75 MW for the first time, the fission gas began to be released when 50 MW was somewhat exceeded. The fission gas release caused the temperature rise and cracking of fuel pellets, and elongated fuel stack length abruptly. These phenomena induced to enlarge the fuel expansion reactivity effect and Doppler reactivity effect, and caused the anomalous behavior of power coefficient. After reaching 75 MW, the fuel stack length did not respond normally to reactor power change, and the magnitude of power coefficient became smaller. The reactivity was lost considerably from the core after the anomaly. (Kako, I.)
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.)
Nonperturbative path integral expansion II
International Nuclear Information System (INIS)
Kaiser, H.J.
1976-05-01
The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)
Extracting OPE coefficient of Konishi at four loops
Energy Technology Data Exchange (ETDEWEB)
Goncalves, Vasco [ICTP South American Institute for Fundamental Research Instituto de Fisica Teorica,UNESP, Universidad Estadual Paulista, Rua Dr. Bento T. Ferraz 271, 01140-070, Sao Paulo, SP (Brazil)
2017-03-15
In this short note we compute the OPE coefficient of two 20{sup ′} operators and the Konishi operator. To this end, we use the OPE decomposition of a four point function of four 20{sup ′} operators and the method of asymptotic expansions to compute the leading term, in the OPE limit, of all integrals contributing to the four point function.
on some properties of the alternating sylvester series and alternating
African Journals Online (AJOL)
DJFLEX
. (iii) above is known in literature as the alternating Sylvester series while (iv) is known as the alternating Engel expansion (Kalpazidou and Ganatsiou (1991)). We are interested in studying the properties of these alternating series. Theorem 2: ...
A non-perturbative operator product expansion
International Nuclear Information System (INIS)
Bietenholz, W.; Cundy, N.; Goeckeler, M.
2009-10-01
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photonmomenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition. (orig.)
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Determination of rolling resistance coefficient based on normal tyre stiffness
Rykov, S. P.; Tarasuyk, V. N.; Koval, V. S.; Ovchinnikova, N. I.; Fedotov, A. I.; Fedotov, K. V.
2018-03-01
The purpose of the article is to develop analytical dependence of wheel rolling resistance coefficient based on the mathematical description of normal tyre stiffness. The article uses the methods of non-holonomic mechanics and plane section methods. The article shows that the abscissa of gravity center of tyre stiffness expansion by the length of the contact area is the shift of normal road response. It can be used for determining rolling resistance coefficient. When determining rolling resistance coefficient using ellipsis and power function equations, one can reduce labor costs for testing and increase assessment accuracy.
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander; Matthies, Hermann G.; Pojonk, Oliver; Rosic, Bojana V.; Zander, Elmar
2014-01-01
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Hirschman, Isidore Isaac
2014-01-01
This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the app
On a generalized oscillator: invariance algebra and interbasis expansions
International Nuclear Information System (INIS)
Hakopyan, E.M.; Pogosyan, G.S.; Sisakyan, A.N.; Kibler, M.
1998-01-01
This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the super integrable character for the generalized oscillator system is investigated from the point of view of a quadratic invariance algebra
International Nuclear Information System (INIS)
Dzenus, M.; Hundhausen, W.; Jansing, W.
1980-01-01
This discourse recounts efforts put into the SNR-2 project; specifically the development of compensation devices. The various prototypes of these compensation devices are described and the state of the development reviewed. Large Na (sodium)-heat transfer systems require a lot of valuable space if the component lay-out does not include compensation devices. So, in order to condense the spatial requirement as much as possible, expansion joints must be integrated into the pipe system. There are two basic types to suit the purpose: axial expansion joints and angular expansion joints. The expansion joints were developed on the basis of specific design criteria whereby differentiation is made between expansion joints of small and large nominal diameter. Expansion joints for installation in the sodium-filled primary piping are equipped with safety bellows in addition to the actual working bellows. Expansion joints must be designed and mounted in a manner to completely withstand seismic forces. The design must exclude any damage to the bellows during intermittent operations, that is, when sodium is drained the bellows' folds must be completely empty; otherwise residual solidified sodium could destroy the bellows when restarting. The expansion joints must be engineered on the basis of the following design data for the secondary system of the SNR project: working pressure: 16 bar; failure mode pressure: 5 events; failure mode: 5 sec., 28.5 bar, 520 deg. C; working temperature: 520 deg. C; temperature transients: 30 deg. C/sec.; service life: 200,000 h; number of load cycles: 10 4 ; material: 1.4948 or 1.4919; layer thickness of folds: 0.5 mm; angular deflection (DN 800): +3 deg. C or; axial expansion absorption (DN 600): ±80 mm; calculation: ASME class. The bellows' development work is not handled within this scope. The bellows are supplied by leading manufacturers, and warrant highest quality. Multiple bellows were selected on the basis of maximum elasticity - a property
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
International Nuclear Information System (INIS)
Rosa, S.; Pinho, F.T.
2006-01-01
The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section
Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers
Energy Technology Data Exchange (ETDEWEB)
Rosa, S. [Escola Superior de Tecnologia e Gestao, Instituto Politecnico, Campus de Santa Apolonia, 5301-857 Braganca (Portugal)]. E-mail: srosa@ipb.pt; Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, DEM, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes (Portugal)]. E-mail: fpinho@fe.up.pt
2006-04-15
The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finite-volume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 deg. to 90 deg. and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section.
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.
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
Off-diagonal expansion quantum Monte Carlo.
Albash, Tameem; Wagenbreth, Gene; Hen, Itay
2017-12-01
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.
International Nuclear Information System (INIS)
Loussaief, Abdelkader
2007-01-01
In this work we extend the use of multipole moments expansion to the case of inner radiation fields. A series expansion of the photon flux was established. The main advantage of this approach is that it offers the opportunity to treat both inner and external radiation field cases. We determined the expression of the inner multipole moments in both spherical harmonics and in cartesian coordinates. As an application we applied the analytical model to a radiation facility used for small target irradiation. Theoretical, experimental and simulation studies were performed, in air and in a product, and good agreement was reached.Conventional dose distribution study for gamma irradiation facility involves the use of isodose maps. The establishment of these maps requires the measurement of the absorbed dose in many points, which makes the task expensive experimentally and very long by simulation. However, a lack of points of measurement can distort the dose distribution cartography. To overcome these problems, we present in this paper a mathematical method to describe the dose distribution in air. This method is based on the multipole expansion in spherical harmonics of the photon flux emitted by the gamma source. The determination of the multipole coefficients of this development allows the modeling of the radiation field around the gamma source. (Author)
Hay, Tanya; Jones, Rhys; Beaumont, Kevin; Kemp, Mark
2009-09-01
The relationship between rat pharmacokinetics and physicochemical parameters [the partition coefficient between octanol and buffer at pH 7.4 (log D((7.4))) and pK(a)] was studied for a series of tetrahydropyran compounds. Sixteen compounds ranging in log D((7.4)) 0.1 to 1.8 were administered intravenously to rats, and the pharmacokinetic parameters were determined from blood concentration time curves. Across the series, a weak correlation was observed between log D((7.4)) and blood clearance, suggesting that log D((7.4)) values less than 0.5 were required to prevent clearance at hepatic blood flow. In terms of the volume of distribution (V(d)), the compounds fell into three distinct subseries characterized by the number of basic centers and differences in ionization of each basic center at physiological pH. These were referred to as the monobasic, weak second base, and strong second base subseries. All the compounds exhibited V(d) greater than body water, as would be expected from their lipophilic and basic nature. For a given clog P, the strong second base subseries showed higher V(d) than the weak second base subseries, which in turn exhibited higher values than the monobasic subseries. In addition, for the weak second base subseries, V(d) could be tuned by modulating the pK(a) of the second basic center. This relationship was rationalized in respect to the interactions of the ionizable centers with phospholipid heads in the cell membrane and/or lysosomal trapping. Compounds in the weak second base subseries showed optimal V(d), and when combined with a log D((7.4)) of 0.1, driving to moderate blood clearance, one compound showed the optimal pharmacokinetic profile.
Conformal Dimensions via Large Charge Expansion.
Banerjee, Debasish; Chandrasekharan, Shailesh; Orlando, Domenico
2018-02-09
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series.
Giovannini, Massimo
2015-01-01
Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
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.
Setting time and thermal expansion of two endodontic cements.
Santos, Alailson D; Araújo, Eudes B; Yukimitu, Keizo; Barbosa, José C; Moraes, João C S
2008-09-01
The purpose of this study was to evaluate the setting time and the thermal expansion coefficient of 2 endodontic cements, MTA-Angelus and a novel cement called CER. The setting time was determined in accordance to ANSI/ADA specifications no. 57. Three samples of 10 mm diameter and 2 mm thickness were prepared for each cement. The thermal expansion measurements were performed by strain gauge technique. Four samples of each cement were prepared using silicone rings of 5 mm diameter and 2 mm thickness. The data were analyzed statistically using the Student t test. The setting time obtained for the MTA-Angelus and CER cements was 15 (SD 1) min and 7 (SD 1) min, respectively. The linear coefficient of thermal expansion was 8.86 (SD 0.28) microstrain/ degrees C for MTA-Angelus and 11.76 (SD 1.20) microstrain/ degrees C for CER. The statistical analysis showed significant difference (P linear coefficient of thermal expansion between the 2 cements. The CER cement has a coefficient of expansion similar to dentin, which could contribute to a decrease of microleakage degree.
Directory of Open Access Journals (Sweden)
J. Li
2017-09-01
Full Text Available Since twentieth Century, the process of economic globalization has made great progress, and Southeast Asia has developed rapidly under the background of international industrial transferring. In this paper, the 6 important nodes cities in China - Indochina Peninsula along the economic corridor are took as study area. The main data is time series Landsat data. The method of object-oriented random forest classification was used to extract the classification results of study area from 2000 to 2015. The urban expansion of the node cities was evaluated by calculating the expansion speed of the impervious surface and the landscape pattern metrics. The results indicated that the method of object oriented random forest classification can effectively extract the urban impervious surface. the overall accuracy is over 81 %, and the Kappa coefficient is over 0.82. In the past 15 years, the expansion speed of Vientiane city was fastest in 6 countries. The area of urban impervious surface expanded 8 times than that of 2000.The pattern of expansion is summarized as “gather first-diffuse then”, “diffuse first-gather then” and “gather”. Overall, the process of urbanization of these cities are still in the rising period.
African Journals Online (AJOL)
raoul
2011-03-22
Mar 22, 2011 ... The thoracic x-ray found a left basal site; hence the patient was initially treated ... assessment found a hyperleukocytosis at 13000 elements/mm³. ... homogeneous or heterogeneous mass, the attenuation coefficient is not.
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)
Thermal expansion behavior of fluor-chlorapatite crystalline solutions
Hovis, G.; Harlov, D.; Gottschalk, M.; Hudacek, W.; Wildermuth, S.
2009-04-01
Apatite Ca5(PO4)3(F,Cl,OH,CO3) occurs widely as an accessory mineral in many igneous and metamorphic rocks and in nature displays a wide range of F-Cl-OH-CO3 mixtures (e.g., O'Reilly and Griffin, 2000) that have been used to interpret the role of fluids, e.g. Cl, F, and OH activities, during metamorphic and igneous processes (e.g., Harlov and Förster, 2002). It is important, therefore, to understand the thermodynamic behavior of these solid solutions, including their thermal expansion properties. Fluorapatite - chlorapatite samples were synthesized at the GFZ-Potsdam (Hovis, Harlov, Hahn and Steigert, 2007) using an adaptation of the molten flux method of Cherniak (2000). Dry CaF2 and CaCl2 (0.1 mole total) were mixed with Ca3(PO4)2 (0.03 moles), placed in a Pt crucible, equilibrated for 15 hours at 1375 °C, cooled to 1220 °C at 3 °C/hour, removed from the oven and cooled in air. Crystals were separated from the flux by boiling the quenched product in water. F:Cl fractions for each sample were determined via Rietveld refinement of X-ray powder diffraction data. Chemical homogeneity was confirmed by Rietveld refinement and high-contrast back-scattered electron imaging. Room-temperature unit-cell volumes were determined at the GFZ-Potsdam through Rietveld analysis of X-ray powder diffraction data and also at Lafayette College by standard unit-cell refinement techniques (Holland and Redfern, 1997) using NBS/NIST 640a Si as an internal standard. High-temperature unit-cell dimensions were calculated from X-ray powder diffraction data collected at Cambridge University from room temperature to 1000 °C on a Bruker D8 X-ray diffractometer. NBS Si again was utilized as an internal standard; high-temperature Si peak positions were taken from Parrish (1953). Results indicate that despite the considerable size difference between fluorine and chlorine ions, reflected by substantially different unit-cell sizes at room temperature, the coefficient of thermal expansion across
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
OPEC future capacity expansions
International Nuclear Information System (INIS)
Sandrea, I.
2005-01-01
This conference presentation examined OPEC future capacity expansions including highlights from 2000-2004 from the supply perspective and actions by OPEC; OPEC spare capacity in 2005/2006; medium-term capacity expansion and investments; long-term scenarios, challenges and opportunities; and upstream policies in member countries. Highlights from the supply perspective included worst than expected non-OPEC supply response; non-OPEC supply affected by a number of accidents and strikes; geopolitical tensions; and higher than expected demand for OPEC crude. OPEC's actions included closer relationship with other producers and consumers; capacity expansions in 2004 and 2005/2006; and OPEC kept the market well supplied with crude in 2004. The presentation also provided data using graphical charts on OPEC net capacity additions until 2005/2006; OPEC production versus spare capacity from 2003 to 2005; OPEC production and capacity to 2010; and change in required OPEC production from 2005-2020. Medium term expansion to 2010 includes over 60 projects. Medium-term risks such as project execution, financing, costs, demand, reserves, depletion, integration of Iraq, and geopolitical tensions were also discussed. The presentation concluded that in the long term, large uncertainties remain; the peak of world supply is not imminent; and continued and enhanced cooperation is essential to market stability. tabs., figs
Physics suggests that the interplay of momentum, continuity, and geometry in outward radial flow must produce density and concomitant pressure reductions. In other words, this flow is intrinsically auto-expansive. It has been proposed that this process is the key to understanding...
Thermal expansion of UO2 and simulated DUPIC fuel
International Nuclear Information System (INIS)
Ho Kang, Kweon; Jin Ryu, Ho; Chan Song, Kee; Seung Yang, Myung
2002-01-01
The lattice parameters of simulated DUPIC fuel and UO 2 were measured from room temperature to 1273 K using neutron diffraction to investigate the thermal expansion and density variation with temperature. The lattice parameter of simulated DUPIC fuel is lower than that of UO 2 , and the linear thermal expansion of simulated DUPIC fuel is higher than that of UO 2 . For the temperature range from 298 to 1273 K, the average linear thermal expansion coefficients for UO 2 and simulated DUPIC fuel are 10.471x10 -6 and 10.751x10 -6 K -1 , respectively
Negative thermal expansion induced by intermetallic charge transfer.
Azuma, Masaki; Oka, Kengo; Nabetani, Koichiro
2015-06-01
Suppression of thermal expansion is of great importance for industry. Negative thermal expansion (NTE) materials which shrink on heating and expand on cooling are therefore attracting keen attention. Here we provide a brief overview of NTE induced by intermetallic charge transfer in A-site ordered double perovskites SaCu 3 Fe 4 O 12 and LaCu 3 Fe 4- x Mn x O 12 , as well as in Bi or Ni substituted BiNiO 3 . The last compound shows a colossal dilatometric linear thermal expansion coefficient exceeding -70 × 10 -6 K -1 near room temperature, in the temperature range which can be controlled by substitution.
Residual stress of particulate polymer composites with reduced thermal expansion
International Nuclear Information System (INIS)
Nishino, T; Kotera, M; Sugiura, Y
2009-01-01
Thermal expansion behavior was investigated for tangusten zirconium phosphate (Zr 2 (WO 4 )(PO 4 ) 2 (ZWP)) particulate filled poly(ether ether ketone) (PEEK) composite. ZWP is known as ceramic filler with a negative thermal expansion. By incorporating ZWP with 40 volume %, the linear thermal expansion coefficient of the PEEK composite was reduced to almost same value (2.53 X 10 -5 K -1 ) with that of aluminum. This decrease was found to be quite effective for the decrease of the residual stress at the interface between aluminum plate and the composite.
Thermal expansion study of simulated DUPIC fuel using neutron diffraction
International Nuclear Information System (INIS)
Kang, Kweon Ho; Ryu, H. J.; Bae, J. H.; Kim, H. S.; Song, K. C.; Yang, M. S.; Choi, Y. N.; Han, Y. S.; Oh, H. S.
2001-07-01
The lattice parameters of simulated DUPIC fuel and UO2 were measured from room temperature to 1273 K using neutron diffraction to investigate the thermal expansion and density variation with temperature. The lattice parameter of simulated DUPIC fuel is lower than that of UO2 and the linear thermal expansion of simulated DUPIC fuel is higher than that of UO2. For the temperature range from 298 to 1273 K, the average linear thermal expansion coefficients for UO2 and simulated DUPIC fuel are 10.471 ''10-6 and 10.751 ''10-6 K-1, respectively
Expansion of Tubular with Elastomers in Multilateral Wells
Directory of Open Access Journals (Sweden)
Md Velden
2013-06-01
Full Text Available The use of solid expandable tubular technology during the last decade has focused on solving many challenges in well drilling and delivery including zonal isolation, deep drilling, conservation of hole sizes, etc. not only as pioneered solution but also providing cost effective and long lasting solutions. Concurrently, the technology was extended for construction of multilateral in typical wells. The process of horizontal tubular expansion is similar to the vertical expansion of expandable tubular in down-hole environment with the addition of uniformly distributed force due to its weight. The expansion is targeted to increase its diameter such that post expansion characteristics remain within allowable limits. In this study a typical expandable tubular of 57.15 mm outer diameter and 6.35 mm wall thickness was used with two different elastomer seals of 5 and 7 mm thickness placed at equal spacing of 200 mm. The developed stress contours during expansion process clearly showed the high stress areas in the vicinity of expansion region which lies around the mandrel. These high stresses may result in excessive wear of the mandrel. It was also found out that the drawing force increases as the mandrel angle, expansion ratio, and friction coefficient increases. A mandrel angle of 20o requires minimum expansion force and can be considered as an optimum geometrical parameter to lower the power required for expansion.
On the Kendall Correlation Coefficient
Stepanov, Alexei
2015-01-01
In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendall rank correlation coefficient and show that the later is free of n. We also prove that in continuous case the Kendall correlation coefficient converges in probability to its expected value. We then propose to consider the expected value of the Kendall rank ...
Wigner-Kirkwood expansion of the phase-space density for half infinite nuclear matter
International Nuclear Information System (INIS)
Durand, M.; Schuck, P.
1987-01-01
The phase space distribution of half infinite nuclear matter is expanded in a ℎ-series analogous to the low temperature expansion of the Fermi function. Besides the usual Wigner-Kirkwood expansion, oscillatory terms are derived. In the case of a Woods-Saxon potential, a smallness parameter is defined, which determines the convergence of the series and explains the very rapid convergence of the Wigner-Kirkwood expansion for average (nuclear) binding energies
Student Understanding of Taylor Series Expansions in Statistical Mechanics
Smith, Trevor I.; Thompson, John R.; Mountcastle, Donald B.
2013-01-01
One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann…
Energy Technology Data Exchange (ETDEWEB)
Fain, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1963-05-15
A completely ionised medium is considered in which the variations of the distribution functions for each species of particles is governed by the Fokker-Planck equation. The interaction operator is of a form given by Rosenbluth - Macdonald - Judd. The distribution functions are expanded into orthogonal polynomial series in the velocity space. In a first stage these functions are first split up into spherical harmonic series (or, in an equivalent form, into series of scalar products of irreducible cartesian tensors), with coefficients which are a function of the velocity modulus as well as space and time coordinates. In the second stage these coefficients are expanded into series of orthogonal functions of the velocity modulus; the 1 order harmonic is represented by the product of a Maxwell distribution and of a SONINE polynomial series, having an index of 1 + 1 / 2, which have as variable the reduced energy of the particles (in terms of a basic temperature), with coefficients which then only depend on the space and time coordinates. In the first part the relationship is established between the expansion coefficients and the moments of the distribution function, as well as the hydrodynamic values. In the second part the expansion using spherical harmonics is applied to the Fokker-Planck equation. The general expression for the second member is given as well as the particular expressions corresponding to the cases where the operator is linearized. In the third part the complete expansion in orthogonal polynomial series is applied to the Fokker-Planck equation. The expression of the generating functions is given for all the harmonics in the case of the linearized operator, as well as the transport equations for the first four harmonics. (author) [French] On considere un milieu completement ionise ou l'evolution des fonctions de distribution pour chaque espece de particules est regie par l'equation de FOKKER-PLANCK. L'operateur d'interaction se met sous la forme
One loop integration with hypergeometric series by using recursion relations
International Nuclear Information System (INIS)
Watanabe, Norihisa; Kaneko, Toshiaki
2014-01-01
General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with ''LoopTools'' for the case of two- and three-point functions as examples
Ultimate load capacities of expansion anchor bolts
International Nuclear Information System (INIS)
Czarnecki, R.M.; Manrique, M.A.; Samaddar, S.K.
1993-01-01
A summary of available experimental expansion anchor bolt test data is presented. These data were collected as part of programs by the nuclear industry to address generic issues related to verification of seismic adequacy of equipment in nuclear power plants. Some of the data presented are suitable for use in seismic probabilistic risk assessments. For example, mean values of ultimate strength, along with their standard deviation and coefficients of variation, for a range of most typical expansion anchor bolt sizes are presented. Effects of interaction between shear and tension, edge distance, spacing, and cracking of the concrete are presented in a manner that is more suitable for use in deterministic evaluations. Related industry programs to derive anchor bolt capacities are briefly discussed. Recommendations for areas of further investigation are also presented
Intrinsic thermal expansion of crystal defects
International Nuclear Information System (INIS)
Ganne, J.-P.
1981-02-01
Although the phenomenon of thermal expansion has long been known, the intrinsic thermal expansion coefficient (ITEC) βsub(d) of a point defect, derived from its formation volume vsub(d), has never been measured directly. The differential dilatometer by interferometry built by ASTY and GILDER is described. It has allowed βsub(d) to be measured for several defects. Vacancies and small interstitial loops were produced in aluminium by low temperature (20 K) fast neutron irradiation followed by an anneal up to the beginning of stage III (160 K). The very high value of the measured ratio βsub(d)/β 0 (12+-4) is comparable with a lattice statics calculated (42) value (11.5 0 [fr
International Nuclear Information System (INIS)
Lewis, C.
1997-01-01
The Olympic Dam orebody is the 6th largest copper and the single largest uranium orebody in the world. Mine production commenced in June 1988, at an annual production rate of around 45,000 tonnes of copper and 1,000 tonnes of uranium. Western Mining Corporation announced in 1996 a proposed $1.25 billion expansion of the Olympic Dam operation to raise the annual production capacity of the mine to 200,000 tonnes of copper, approximately 3,700 tonnes of uranium, 75,000 ounces of gold and 950,000 ounces of silver by 2001. Further optimisation work has identified a faster track expansion route, with an increase in the capital cost to $1.487 billion but improved investment outcome, a new target completion date of end 1999, and a new uranium output of 4,600 tonnes per annum from that date
Financing electricity expansion
International Nuclear Information System (INIS)
Hyman, L.S.
1994-01-01
Expansion of electricity supply is associated with economic development. The installation and enlargement of power systems in developing countries entails a huge financial burden, however. Energy consumers in such countries must pay not only for supplies but for the cost of raising the capital for expansion on the international markets. Estimates are presented for the capital expenditure for electricity supply over the period 1990 to 2020 for the major world regions, using approximations for the cost of plant and capital and for the returns earned. These data lead to the conclusion that the five regions with the lowest per capita incomes are those which will need the major part of the capital expenditure and the highest percentage of external finance. (6 tables) (UK)
Bigravity from gradient expansion
International Nuclear Information System (INIS)
Yamashita, Yasuho; Tanaka, Takahiro
2016-01-01
We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.
International Nuclear Information System (INIS)
Suess, S.T.
1987-01-01
Magnetic clouds are a carefully defined subclass of all interplanetary signatures of coronal mass ejections whose geometry is thought to be that of a cylinder embedded in a plane. It has been found that the total magnetic pressure inside the clouds is higher than the ion pressure outside, and that the clouds are expanding at 1 AU at about half the local Alfven speed. The geometry of the clouds is such that even though the magnetic pressure inside is larger than the total pressure outside, expansion will not occur because the pressure is balanced by magnetic tension - the pinch effect. The evidence for expansion of clouds at 1 AU is nevertheless quite strong so another reason for its existence must be found. It is demonstrated that the observations can be reproduced by taking into account the effects of geometrical distortion of the low plasma beta clouds as they move away from the Sun
Spatial correlation in 3D MIMO channels using fourier coefficients of power spectrums
Nadeem, Qurrat-Ul-Ain
2015-03-01
In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for the standardized three-dimensional (3D) multiple-input multiple-output (MIMO) channel. This novel SCF is developed for a uniform linear array of antennas with non-isotropic antenna patterns. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials to obtain a closed-form expression for the SCF for arbitrary angular distributions and antenna patterns. The resulting expression depends on the underlying angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. Numerical results validate the proposed analytical expression and study the impact of angular spreads on the correlation. The derived SCF will help evaluate the performance of correlated 3D MIMO channels in the future. © 2015 IEEE.
IKEA's International Expansion
Harapiak, Clayton
2013-01-01
This case concerns a global retailing firm that is dealing with strategic management and marketing issues. Applying a scenario of international expansion, this case provides a thorough analysis of the current business environment for IKEA. Utilizing a variety of methods (e.g. SWOT, PESTLE, McKinsey Matrix) the overall objective is to provide students with the opportunity to apply their research skills and knowledge regarding a highly competitive industry to develop strategic marketing strateg...
International Nuclear Information System (INIS)
Matsuki, Takayuki
1976-01-01
Symmetric eikonal expansion for the scattering amplitude is formulated for nonrelativistic and relativistic potential scatterings and also for the quantum field theory. The first approximations coincide with those of Levy and Sucher. The obtained scattering amplitudes are time reversal invariant for all cases and are crossing symmetric for the quantum field theory in each order of approximation. The improved eikonal phase introduced by Levy and Sucher is also derived from the different approximation scheme from the above. (auth.)
Electric Grid Expansion Planning with High Levels of Variable Generation
Energy Technology Data Exchange (ETDEWEB)
Hadley, Stanton W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); You, Shutang [Univ. of Tennessee, Knoxville, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Liu, Yilu [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-02-01
Renewables are taking a large proportion of generation capacity in U.S. power grids. As their randomness has increasing influence on power system operation, it is necessary to consider their impact on system expansion planning. To this end, this project studies the generation and transmission expansion co-optimization problem of the US Eastern Interconnection (EI) power grid with a high wind power penetration rate. In this project, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. This study analyzed a time series creation method to capture the diversity of load and wind power across balancing regions in the EI system. The obtained time series can be easily introduced into the MIP co-optimization problem and then solved robustly through available MIP solvers. Simulation results show that the proposed time series generation method and the expansion co-optimization model and can improve the expansion result significantly after considering the diversity of wind and load across EI regions. The improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare. This study shows that modelling load and wind variations and diversities across balancing regions will produce significantly different expansion result compared with former studies. For example, if wind is modeled in more details (by increasing the number of wind output levels) so that more wind blocks are considered in expansion planning, transmission expansion will be larger and the expansion timing will be earlier. Regarding generation expansion, more wind scenarios will slightly reduce wind generation expansion in the EI system and increase the expansion of other generation such as gas. Also, adopting detailed wind scenarios will reveal that it may be uneconomic to expand transmission networks for transmitting a large amount of wind power through a long distance
Exchange splitting of the interaction energy and the multipole expansion of the wave function
Energy Technology Data Exchange (ETDEWEB)
Gniewek, Piotr, E-mail: pgniewek@tiger.chem.uw.edu.pl; Jeziorski, Bogumił, E-mail: jeziorsk@chem.uw.edu.pl [Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw (Poland)
2015-10-21
The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.
Operator product expansion and its thermal average
Energy Technology Data Exchange (ETDEWEB)
Mallik, S [Saha Inst. of Nuclear Physics, Calcutta (India)
1998-05-01
QCD sum rules at finite temperature, like the ones at zero temperature, require the coefficients of local operators, which arise in the short distance expansion of the thermal average of two-point functions of currents. We extend the configuration space method, applied earlier at zero temperature, to the case at finite temperature. We find that, upto dimension four, two new operators arise, in addition to the two appearing already in the vacuum correlation functions. It is argued that the new operators would contribute substantially to the sum rules, when the temperature is not too low. (orig.) 7 refs.
Expansions of general stationary stochastic optical fields: general formalism
International Nuclear Information System (INIS)
Martinez-Herrero, R.; Mejias, P.M.
1985-01-01
A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed
U.S. Department of Health & Human Services — The Centers for Medicare and Medicaid Services (CMS) offers several different Chart Series with data on beneficiary health status, spending, operations, and quality...
Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal
International Nuclear Information System (INIS)
Konno, R; Hatayama, N; Takahashi, Y; Nakano, H
2009-01-01
Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal is investigated according to the recent theoretical development of magneto-volume effect for the three-dimensional weak ferromagnets. We particularly focus on the T 2 -linear thermal expansion of magnetic origin at low temperatures, so far disregarded by conventional theories. As the effect of thermal spin fluctuations we have found that the T-linear thermal expansion coefficient shows strong enhancement by assuming the double Lorentzian form of the non-interacting dynamical susceptibility justified in the small wave-number and low frequency region. It grows faster in proportional to y -1/2 as we approach the magnetic instability point than two-dimensional nearly antiferromagnetic metals with ln(1/y s ) dependence, where y and y s are the inverses of the reduced uniform and staggered magnetic susceptibilities, respectively. Our result is consistent with the Grueneisen's relation between the thermal expansion coefficient and the specific heat at low temperatures. In 2-dimensional electron gas we find that the thermal expansion coefficient is divergent with a finite y when the higher order term of non-interacting dynamical susceptibility is taken into account.
Amide temperature coefficients in the protein G B1 domain
International Nuclear Information System (INIS)
Tomlinson, Jennifer H.; Williamson, Mike P.
2012-01-01
Temperature coefficients have been measured for backbone amide 1 H and 15 N nuclei in the B1 domain of protein G (GB1), using temperatures in the range 283–313 K, and pH values from 2.0 to 9.0. Many nuclei display pH-dependent coefficients, which were fitted to one or two pK a values. 1 H coefficients showed the expected behaviour, in that hydrogen-bonded amides have less negative values, but for those amides involved in strong hydrogen bonds in regular secondary structure there is a negative correlation between strength of hydrogen bond and size of temperature coefficient. The best correlation to temperature coefficient is with secondary shift, indicative of a very approximately uniform thermal expansion. The largest pH-dependent changes in coefficient are for amides in loops adjacent to sidechain hydrogen bonds rather than the amides involved directly in hydrogen bonds, indicating that the biggest determinant of the temperature coefficient is temperature-dependent loss of structure, not hydrogen bonding. Amide 15 N coefficients have no clear relationship with structure.
International Nuclear Information System (INIS)
Martin, P.; Zamudio-Cristi, J.
1982-01-01
A method is described to obtain fractional approximations for linear first order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the highest and lowest power of the variable after the sustitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Pade method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which give three exact digits for most of the real values of the variable. Approximations of higher accuracy and of the same degree than other authors are also obtained. (Author) [pt
The 1/ N Expansion of Tensor Models Beyond Perturbation Theory
Gurau, Razvan
2014-09-01
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.
Translation of Bernstein Coefficients Under an Affine Mapping of the Unit Interval
Alford, John A., II
2012-01-01
We derive an expression connecting the coefficients of a polynomial expanded in the Bernstein basis to the coefficients of an equivalent expansion of the polynomial under an affine mapping of the domain. The expression may be useful in the calculation of bounds for multi-variate polynomials.
Low expansion and high gain Nd laser glasses
International Nuclear Information System (INIS)
Izumitani, Tetsuro; Peng, B.
1995-01-01
Due to the relationship between Judd-Ofelt intensity parameter and covalency, new laser glasses have been developed which have low expansion coefficients (85--91 x 10 -7 /cm C, 0--70 C) and high emission cross sections. They have good chemical properties, high Young's modulus and high thermal conductivities. These glasses are suitable for the National Ignition Facility
Thermal expansion of the superconducting ferromagnet UCoGe
Gasparini, A.; Huang, Y.K.; Hartbaum, J.; v. Löhneysen, H.; de Visser, A.
2010-01-01
We report measurements of the coefficient of linear thermal expansion, α(T), of the superconducting ferromagnet UCoGe. The data taken on a single-crystalline sample along the orthorhombic crystal axes reveal a pronounced anisotropy with the largest length changes along the b axis. The large values
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
From Free Expansion to Abrupt Compression of an Ideal Gas
Anacleto, Joaquim; Pereira, Mario G.
2009-01-01
Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 [less than or equal] r [less than or equal] 1 for expansions and r [greater than or equal] 1 for compressions.…
Expansions for Coulomb wave functions
Boersma, J.
1969-01-01
In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are
Magnetic susceptibilities and thermal expansion of artificial graphites
International Nuclear Information System (INIS)
Cornuault, P.; Herpin, A.; Hering, H.; Seguin, M.; Commissariat a l'Energie Atomique, Saclay
1960-01-01
Starting from measurements of the magnetic susceptibility made in the two principal directions of a graphite bar, the distribution function of the normals to the carbon planes in the crystallites has been evaluated. The effect of different variation in the manufacturing process on this crystalline anisotropy has been studied. From this crystalline anisotropy we have calculated the thermal expansion coefficient possessed by a compact mass of crystallites having exactly the same orientational anisotropy as the porous body consideration. The difference between this and the observed expansion coefficient leads to the determination of the expansion of the non-graphitic part of the mass which turns out to have a negative value and is also anisotropic. We have attempted to draw some conclusions from this result. (author) [fr
A non-uniform expansion mechanical safety model of the stent.
Yang, J; Huang, N; Du, Q
2009-01-01
Stents have a serial unstable structure that readily leads to non-uniform expansion. Non-uniform expansion in turn creates a stent safety problem. We explain how a stent may be simplified to a serial unstable structure, and present a method to calculate the non-uniform expansion of the stent on the basis of the serial unstable structure. We propose a safety criterion based on the expansion displacement instead of the strain, and explain that the parameter Rd, the ratio of the maximum displacement of the elements to normal displacement, is meaningful to assess the safety level of the stent. We also examine how laser cutting influences non-uniform expansion. The examples illustrate how to calculate the parameter Rd to assess non-uniform expansion of the stent, and demonstrate how the laser cutting offset and strengthening coefficient of the material influence the stent expansion behaviour. The methods are valuable for assessing stent safety due to non-uniform expansion.
Thermal expansion data of (Th,U)O2 fuels
International Nuclear Information System (INIS)
Sengupta, A.K.; Banerjee, J.; Bhagat, R.K.; Ramachandran, R.; Majumdar, S.; Purushotham, D.S.C.
2000-04-01
Thermal expansion data for sintered ThO 2 and ThO 2 containing 2, 4, 6, 10 and 20% UO 2 pellets were measured using a high temperature dilatometer in the temperature range from ambient to 1773 K. The dilatometer was first calibrated using a standard graphite sample as reference material. The reproducibility of the dilatometer was tested by measuring the coefficient of expansion of tungsten (NBS SRM 737) and comparing the data with that recommended by National Bureau of Standard. It was observed that there is close agreement between the experimental and reported data. The coefficient of expansion data of (Th,U)O 2 fuel indicate that out of all the six compositions, ThO 2 +2%UO 2 showed the maximum expansion of around 1.75% at 1773 K. However, the expansion data for all the compositions were very close to each other. Empirical equation correlating thermal expansion and temperature for all six compositions have been generated and reported. (author)
In2Mo3O12: A low negative thermal expansion compound
International Nuclear Information System (INIS)
Marinkovic, Bojan A.; Ari, Monica; Jardim, Paula Mendes; Avillez, Roberto R. de; Rizzo, Fernando; Ferreira, Fabio Furlan
2010-01-01
Orthorhombic In 2 Mo 3 O 12 has low negative linear coefficient of thermal expansion (α l = -1.85 x 10 -6 o C -1 ) as evaluated by X-ray powder diffraction using a synchrotron facility. The linear coefficient of thermal expansion for orthorhombic In 2 Mo 3 O 12 is directly dependent on the inherent volume distortion parameter (υ) of InO 6 . This finding strongly corroborates the recently proposed relationship between the linear coefficient of thermal expansion in A 2 M 3 O 12 compounds (α l ) and the distortion level of AO 6 polyhedra. With the increase of inherent distortion parameter (υ) of AO 6 polyhedra, the linear coefficient of thermal expansion becomes more negative. Another important feature of AO 6 polyhedra, including InO 6 , is that their distortion increases as a function of temperature. Orthorhombic In 2 Mo 3 O 12 is stable in the studied temperature range, 370-760 o C.
Isotropic oscillator in the space of constant positive curvature. Interbasis expansions
International Nuclear Information System (INIS)
Akopyan, E.M.; Pogosyan, G.S.; Sisakyan, A.N.; Vinitskij, S.I.
1997-01-01
The Schroedinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the spherical and cylindrical bases of the oscillator are calculated. It is shown that the relevant coefficients are expressed through the generalised hypergeometric functions 4 F 3 of the unit argument or 6j Racah symbols extended over their indices to the region of real values. Limiting transitions to a free motion and flat space are considered in detail. Elliptic bases of the oscillator are constructed in the form of expansion over the spherical and cylindrical bases. The corresponding expansion coefficients are shown to obey the three-term recurrence relations expansion coefficients are shown to obey the three-term recurrence relations
Coefficient Alpha: A Reliability Coefficient for the 21st Century?
Yang, Yanyun; Green, Samuel B.
2011-01-01
Coefficient alpha is almost universally applied to assess reliability of scales in psychology. We argue that researchers should consider alternatives to coefficient alpha. Our preference is for structural equation modeling (SEM) estimates of reliability because they are informative and allow for an empirical evaluation of the assumptions…
Coefficient estimates of negative powers and inverse coefficients for ...
Indian Academy of Sciences (India)
and the inequality is sharp for the inverse of the Koebe function k(z) = z/(1 − z)2. An alternative approach to the inverse coefficient problem for functions in the class S has been investigated by Schaeffer and Spencer [27] and FitzGerald [6]. Although, the inverse coefficient problem for the class S has been completely solved ...
Measuring of heat transfer coefficient
DEFF Research Database (Denmark)
Henningsen, Poul; Lindegren, Maria
Subtask 3.4 Measuring of heat transfer coefficient Subtask 3.4.1 Design and setting up of tests to measure heat transfer coefficient Objective: Complementary testing methods together with the relevant experimental equipment are to be designed by the two partners involved in order to measure...... the heat transfer coefficient for a wide range of interface conditions in hot and warm forging processes. Subtask 3.4.2 Measurement of heat transfer coefficient The objective of subtask 3.4.2 is to determine heat transfer values for different interface conditions reflecting those typically operating in hot...
Seeley-Gilkey coefficients for the fourth-order operators on a Riemannian manifold
International Nuclear Information System (INIS)
Gusynin, V.P.
1989-01-01
A new covariant method for computing the coefficients in the heat kernel expansion is suggested. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a Riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimension of the space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method suggested allows one to calculate coefficients by computer using the analytical calculation system. 19 refs.; 1 fig
Radial expansion and multifragmentation
International Nuclear Information System (INIS)
Angelique, J.C.; Bizard, G.; Bougault, R.; Brou, R.; Buta, A.; Colin, J.; Cussol, D.; Durand, D.; Kerambrun, A.; Le Brun, C.; Lecolley, J.F.; Lopez, O.; Louvel, M.; Meslin, C.; Nakagawa, T.; Patry, J.P.; Peter, J.; Popescu, R.; Regimbart, R.; Steckmeyer, J.C.; Tamain, B.; Vient, E.; Yuasa-Nakagawa, K.; Wieloch, A.
1998-01-01
The light systems 36 Ar + 27 Al and 64 Zn + nat Ti were measured at several bombarding energies between ∼ 35 and 95 MeV/nucleon. It was found that the predominant part of the cross section is due to binary collisions. In this paper the focus is placed on the properties of the quasi-projectile nuclei. In the central collisions the excitation energies of the quasi-projectile reach values exceeding largely 10 MeV/nucleon. The slope of the high energy part of the distribution can give only an upper limit of the apparent temperature (the average temperature along the decay chain). The highly excited quasi-projectile may get rapidly fragmented rather than sequentially. The heavy fragments are excited and can emit light particles (n, p, d, t, 3 He, α,...) what perturbs additionally the spectrum of these particles. Concerning the expansion energy, one can determine the average kinetic energies of the product (in the quasi-projectile-framework) and compare with simulation values. To fit the experimental data an additional radial expansion energy is to be considered. The average expansion energy depends slightly on the impact parameter but it increases with E * / A, ranging from 0.4 to 1,2 MeV/nucleon for an excitation energy increasing from 7 to 10.5 MeV/nucleon. This collective radial energy seems to be independent of the fragment mass, what is possibly valid for the case of larger quasi-projectile masses. The origin of the expansion is to be determined. It may be due to a compression in the interaction zone at the initial stage of the collision, which propagates in the quasi-projectile and quasi-target, or else, may be due, simply, to the increase of thermal energy leading to a rapid fragment emission. The sequential de-excitation calculation overestimates light particle emission and consequently heavy residues, particularly, at higher excitation energies. This disagreement indicates that a sequential process can not account for the di-excitation of very hot nuclei
DEFF Research Database (Denmark)
Kolbæk, Ditte; Lundh Snis, Ulrika
Abstract: This paper analyses an online community of master’s students taking a course in ICT and organisational learning. The students initiated and facilitated an educational design for organisational learning called Proactive Review in the organisation where they are employed. By using an online...... discussion forum on Google groups, they created new ways of reflecting and learning. We used netnography to select qualitative postings from the online community and expansive learning concepts for data analysis. The findings show how students changed practices of organisational learning...
Load regulating expansion fixture
International Nuclear Information System (INIS)
Wagner, L.M.; Strum, M.J.
1998-01-01
A free standing self contained device for bonding ultra thin metallic films, such as 0.001 inch beryllium foils is disclosed. The device will regulate to a predetermined load for solid state bonding when heated to a bonding temperature. The device includes a load regulating feature, whereby the expansion stresses generated for bonding are regulated and self adjusting. The load regulator comprises a pair of friction isolators with a plurality of annealed copper members located there between. The device, with the load regulator, will adjust to and maintain a stress level needed to successfully and economically complete a leak tight bond without damaging thin foils or other delicate components. 1 fig
Partially linear varying coefficient models stratified by a functional covariate
Maity, Arnab
2012-10-01
We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.
Calculation of self-diffusion coefficients in iron
Directory of Open Access Journals (Sweden)
Baohua Zhang
2014-01-01
Full Text Available On the basis of available P-V-T equation of state of iron, the temperature and pressure dependence of self-diffusion coefficients in iron polymorphs (α, δ, γ and ɛ phases have been successfully reproduced in terms of the bulk elastic and expansivity data by means of a thermodynamical model that interconnects point defects parameters with bulk properties. The calculated diffusion parameters, such as self-diffusion coefficient, activation energy and activation volume over a broad temperature range (500-2500 K and pressure range (0-100 GPa, compare favorably well with experimental or theoretical ones when the uncertainties are considered.
Bell numbers, determinants and series
Indian Academy of Sciences (India)
In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients. Keywords. p-adic series; Bell numbers. 1. Introduction. Bell numbers, Bn [2] ...
A complete basis for a perturbation expansion of the general N-body problem
International Nuclear Information System (INIS)
Laing, W Blake; Kelle, David W; Dunn, Martin; Watson, Deborah K
2009-01-01
We discuss a basis set developed to calculate perturbation coefficients in an expansion of the general N-body problem. This basis has two advantages. First, the basis is complete order-by-order for the perturbation series. Second, the number of independent basis tensors spanning the space for a given order does not scale with N, the number of particles, despite the generality of the problem. At first order, the number of basis tensors is 25 for all N, i.e. the problem scales as N 0 , although one would initially expect an N 6 scaling at first order. The perturbation series is expanded in inverse powers of the spatial dimension. This results in a maximally symmetric configuration at lowest order which has a point group isomorphic with the symmetric group, S N . The resulting perturbation series is order-by-order invariant under the N! operations of the S N point group which is responsible for the slower than exponential growth of the basis. In this paper, we demonstrate the completeness of the basis and perform the first test of this formalism through first order by comparing to an exactly solvable fully interacting problem of N particles with a two-body harmonic interaction potential
Improvements to the Chebyshev expansion of attenuation correction factors for cylindrical samples
International Nuclear Information System (INIS)
Mildner, D.F.R.; Carpenter, J.M.
1990-01-01
The accuracy of the Chebyshev expansion coefficients used for the calculation of attenuation correction factors for cylinderical samples has been improved. An increased order of expansion allows the method to be useful over a greater range of attenuation. It is shown that many of these coefficients are exactly zero, others are rational numbers, and others are rational frations of π -1 . The assumptions of Sears in his asymptotic expression of the attenuation correction factor are also examined. (orig.)
Diamond Thermal Expansion Measurement Using Transmitted X-ray Back-diffraction.
Giles, Carlos; Adriano, Cris; Lubambo, Adriana Freire; Cusatis, Cesar; Mazzaro, Irineu; Hönnicke, Marcelo Goncalves
2015-01-01
The linear thermal expansion coefficient of diamond has been measured using forward-diffracted profiles in X-ray backscattering. This experimental technique is presented as an alternative way of measuring thermal expansion coefficients of solids in the high-resolution Bragg backscattering geometry without the intrinsic difficulty of detecting the reflected beam. The temperature dependence of the lattice parameter is obtained from the high sensitivity of the transmitted profiles to the Bragg a...
Stiffness and thermal expansion of ZrB2: an ab initio study
International Nuclear Information System (INIS)
Milman, V; Winkler, B; Probert, M I J
2005-01-01
The stiffness and thermal expansion coefficient of ZrB 2 are calculated within the density functional theory formalism. The stiffness tensor obtained here using the static finite strain technique is in good agreement with the results of resonant ultrasonic measurements and points to a possible misinterpretation of the experimentally obtained compression data. The methodology of evaluating thermal expansion coefficients from molecular dynamics simulations for small unit cells is validated for a number of systems: metals, semiconductors and insulators
Structure and thermal expansion of NbC complex carbides
International Nuclear Information System (INIS)
Khatsinskaya, I.M.; Chaporova, I.N.; Cheburaeva, R.F.; Samojlov, A.I.; Logunov, A.V.; Ignatova, I.A.; Dodonova, L.P.
1983-01-01
Alloying dependences of the crystal lattice parameters at indoor temperature and coefficient of thermal linear exspansion within a 373-1273 K range are determined for complex NbC-base carbides by the method of mathematical expemental design. It is shown that temperature changes in the linear expansion coefficient of certain complex carbides as distinct from NbC have an anomaly (minimum) within 773-973 K caused by occurring reversible phase transformations. An increase in the coefficient of thermal linear expansion and a decrease in hardness of NbC-base tungsten-, molybdenum-, vanadium- and hafnium-alloyed carbides show a weakening of a total chemical bond in the complex carbides during alloying
Løken, Andreas; Haugsrud, Reidar; Bjørheim, Tor S
2016-11-16
Differentiating chemical and thermal expansion is virtually impossible to achieve experimentally. While thermal expansion stems from a softening of the phonon spectra, chemical expansion depends on the chemical composition of the material. In the present contribution, we, for the first time, completely decouple thermal and chemical expansion through first principles phonon calculations on BaCeO 3 , providing new fundamental insights to lattice expansion. We assess the influence of defects on thermal expansion, and how this in turn affects the interpretation of chemical expansion and defect thermodynamics. The calculations reveal that the linear thermal expansion coefficient is lowered by the introduction of oxygen vacancies being 10.6 × 10 -6 K -1 at 300 K relative to 12.2 × 10 -6 K -1 for both the protonated and defect-free bulk lattice. We further demonstrate that the chemical expansion coefficient upon hydration varies with temperature, ranging from 0.070 to 0.115 per mole oxygen vacancy. Ultimately, we find that, due to differences in the thermal expansion coefficients under dry and wet conditions, the chemical expansion coefficients determined experimentally are grossly underestimated - around 55% lower in the case of 10 mol% acceptor doped BaCeO 3 . Lastly, we evaluate the effect of these volume changes on the vibrational thermodynamics.
Thermal expansion of granite rocks
International Nuclear Information System (INIS)
Stephansson, O.
1978-04-01
The thermal expansion of rocks is strongly controlled by the thermal expansion of the minerals. The theoretical thermal expansion of the Stripa Granite is gound to be 21 . 10 -6 [deg C] -1 at 25 deg C and 38 . 10 -6 [deg C] -1 at 400 deg C. The difference in expansion for the rock forming minerals causes micro cracking at heating. The expansion due to micro cracks is found to be of the same order as the mineral expansion. Most of the micro cracks will close at pressures of the order of 10 - 20 MPa. The thermal expansion of a rock mass including the effect of joints is determined in the pilot heater test in the Stripa Mine
Energy Technology Data Exchange (ETDEWEB)
Froschauer, K J
1993-01-01
A study of the development of five provincial hydroelectric utilities in Canada indicates that power companies and the state invited manufacturers to use hydroelectricity and natural resources in order to diversify provincial economies. These hydro expansions also show that utilities and government designed hydro projects to serve continental requirements; serving both objectives became problematic. It is argued that when the Canadian state and firms such as utilities use hydro expansions to serve both continentalism and industrialization, then at best they foster dependent industrialization and staple processing. At worst, they overbuild the infrastructure to generate provincial surplus energy for continental, rather than national, integration. Hydro developments became subject to state intervention in Canada mainly through the failures of private utilities to provide power for the less-lucrative industrial markets within provincial subregions. Although the state and utilities invited foreign firms to manufacture hydro equipment within the provinces and others to use electricity to diversify production beyond resource processing, such a diversification did not occur. Since 1962, ca 80% of industrial energy was used to semi-process wood-derived products, chemicals, and metals. The idea for a national power network became undermined by interprovincial political-economic factors and since 1963, the federal national/continential power policy prevailed. 187 refs., 6 figs., 52 tabs.
International Nuclear Information System (INIS)
Vogeleer, J. P.
1985-01-01
The expansion of the primary tubes or sleeves of the steam generator of a nuclear reactor plant are measured while the tubes or sleeves are being expanded. A primary tube or sleeve is expanded by high pressure of water which flows through a channel in an expander body. The water is supplied through an elongated conductor and is introduced through a connector on the shank connected to the conductor at its outer end. A wire extends through the mandrel and through the conductor to the end of the connector. At its inner end the wire is connected to a tapered pin which is subject to counteracting forces produced by the pressure of the water. The force on the side where the wire is connected to the conductor is smaller than on the opposite side. The tapered pin is moved in the direction of the higher force and extrudes the wire outwardly of the conductor. The tapered surface of the tapered pin engages transverse captive plungers which are maintained in engagement with the expanding tube or sleeve as they are moved outwardly by the tapered pin. The wire and the connector extend out of the generator and, at its outer end, the wire is connected to an indicator which measures the extent to which the wire is moved by the tapered pin, thus measuring the expansion of the tube or sleeve as it progresses
Mao, Shi-Chun; Wu, Zhen-Sen
2008-12-01
An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.
Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions
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
The effect of gamma irradiation on the thermal expansion behaviour of oriented polypropylene
International Nuclear Information System (INIS)
Godjevargov, L.; Novakovic, L.J.; Kostoski, D.
1991-01-01
Quenched and air-cooled samples of oriented polypropylene have been irradiated to 300 kGy adsorbed dose in the presence of air. The parallel thermal expansion coefficient decreases and becomes negative with increasing orientation. The effect of adsorbed dose on the thermal expansion behaviour is practically negligible. (author) 4 refs.; 4 figs
Gabor's signal expansion on a quincunx lattice and the modified Zak transform
Leest, van A.J.; Bastiaans, M.J.
1999-01-01
Gabor's expansion of a signal on a quincunx lattice with oversampling by a rational factor is presented for continuous-time signals. It is shown how a modified Zak transform instead of the ordinary Zak transform can be helpful in determining Gabor's signal expansion coefficients and how it can be
Gabor's signal expansion and the Zak transform with non-critical sampling
Bastiaans, M.J.; Geilen, M.C.W.; Boashash, B.; HHrle, N.; Zoubir, A.M.
1996-01-01
Gabor's expansion of a signal into a set of shifted and modulated versions of a synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window with the help of which Gabor's expansion coefficients can be determined. The Zak transform is
Shape memory effects, thermal expansion and B19' martensite texture in titanium nickelide
International Nuclear Information System (INIS)
Zel'dovich, V.I.; Sobyanina, G.A.; Rinkevich, O.S.; Gundyrev, V.M.
1996-01-01
The influence of plastic deformation by tension and cold rolling on shape memory effect, reverse shape memory effect, thermal expansion and texture state of martensite in titanium nickelide is under study. The relationship of thermal expansion coefficient to the value of strain during direct and reverse shape memory effect is established
Colossal negative thermal expansion in reduced layered ruthenate.
Takenaka, Koshi; Okamoto, Yoshihiko; Shinoda, Tsubasa; Katayama, Naoyuki; Sakai, Yuki
2017-01-10
Large negative thermal expansion (NTE) has been discovered during the last decade in materials of various kinds, particularly materials associated with a magnetic, ferroelectric or charge-transfer phase transition. Such NTE materials have attracted considerable attention for use as thermal-expansion compensators. Here, we report the discovery of giant NTE for reduced layered ruthenate. The total volume change related to NTE reaches 6.7% in dilatometry, a value twice as large as the largest volume change reported to date. We observed a giant negative coefficient of linear thermal expansion α=-115 × 10 -6 K -1 over 200 K interval below 345 K. This dilatometric NTE is too large to be attributable to the crystallographic unit-cell volume variation with temperature. The highly anisotropic thermal expansion of the crystal grains might underlie giant bulk NTE via microstructural effects consuming open spaces in the sintered body on heating.
Expansion of all multitrace tree level EYM amplitudes
Du, Yi-Jian; Feng, Bo; Teng, Fei
2017-12-01
In this paper, we investigate the expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive expansions of tree level EYM amplitudes with an arbitrary number of gluons, gravitons and traces by those amplitudes with fewer traces or/and gravitons. Then we give many support evidence, including proofs using the Cachazo-He-Yuan (CHY) formula and Britto-Cachazo-Feng-Witten (BCFW) recursive relation. As a byproduct, two types of generalized BCJ relations for multitrace EYM are further proposed, which will be useful in the BCFW proof. After one applies the recursive expansions repeatedly, any multitrace EYM amplitudes can be given in the Kleiss-Kuijf (KK) basis of tree level color ordered Yang-Mills (YM) amplitudes. Thus the Bern-Carrasco-Johansson (BCJ) numerators, as the expansion coefficients, for all multitrace EYM amplitudes are naturally constructed.
Pressure-induced reversal between thermal contraction and expansion in ferroelectric PbTiO3
Jinlong Zhu; Jianzhong Zhang; Hongwu Xu; Sven C. Vogel; Changqing Jin; Johannes Frantti; Yusheng Zhao
2014-01-01
Materials with zero/near zero thermal expansion coefficients are technologically important for applications in thermal management and engineering. To date, this class of materials can only be produced by chemical routes, either by changing chemical compositions or by composting materials with positive and negative thermal expansion. Here, we report for the first time a physical route to achieve near zero thermal expansion through application of pressure. In the stability field of tetragonal P...
Some results from a Mellin transform expansion for the heat Kernel
International Nuclear Information System (INIS)
Malbouisson, A.P.C.; Simao, F.R.A.; Camargo Filho, A.F. de.
1988-01-01
The coefficients of a new Heat Kernel expansion, in the case of a differential operator containing a gauge field. The meromorphic structure of the generalized zeta-function obtained by that expansion is compared with the one obtained in a proceeding paper. The expansion is applied to anomalies, obtaining a general formula for arbitrary dimension D. The special cases D=2 and D=3 are investigated. (author) [pt
Effective elasticity coefficients of native rocks and consolidated granular matter
International Nuclear Information System (INIS)
Schulz, Beatrix M.; Schulz, Michael
2008-01-01
The elastic coefficients of binary heterogeneous materials, such as several native rock materials or consolidated granular matter will be determined in terms of a perturbation expansion. Furthermore, in order to check the validity of the obtained results, these are compared with numerical investigations using Boole's model of randomly distributed spheres. Finally, we apply the results on several classes of native rocks and consolidated granular materials
Directory of Open Access Journals (Sweden)
Gilberto Herrera-Ruíz
2013-03-01
Full Text Available A New Adaptive Self-Tuning Fourier Coefficients Algorithm for Periodic Torque Ripple Minimization in Permanent Magnet Synchronous Motors (PMSM Torque ripple occurs in Permanent Magnet Synchronous Motors (PMSMs due to the non-sinusoidal flux density distribution around the air-gap and variable magnetic reluctance of the air-gap due to the stator slots distribution. These torque ripples change periodically with rotor position and are apparent as speed variations, which degrade the PMSM drive performance, particularly at low speeds, because of low inertial filtering. In this paper, a new self-tuning algorithm is developed for determining the Fourier Series Controller coefficients with the aim of reducing the torque ripple in a PMSM, thus allowing for a smoother operation. This algorithm adjusts the controller parameters based on the component’s harmonic distortion in time domain of the compensation signal. Experimental evaluation is performed on a DSP-controlled PMSM evaluation platform. Test results obtained validate the effectiveness of the proposed self-tuning algorithm, with the Fourier series expansion scheme, in reducing the torque ripple.
Gómez-Espinosa, Alfonso; Hernández-Guzmán, Víctor M; Bandala-Sánchez, Manuel; Jiménez-Hernández, Hugo; Rivas-Araiza, Edgar A; Rodríguez-Reséndiz, Juvenal; Herrera-Ruíz, Gilberto
2013-03-19
A New Adaptive Self-Tuning Fourier Coefficients Algorithm for Periodic Torque Ripple Minimization in Permanent Magnet Synchronous Motors (PMSM) Torque ripple occurs in Permanent Magnet Synchronous Motors (PMSMs) due to the non-sinusoidal flux density distribution around the air-gap and variable magnetic reluctance of the air-gap due to the stator slots distribution. These torque ripples change periodically with rotor position and are apparent as speed variations, which degrade the PMSM drive performance, particularly at low speeds, because of low inertial filtering. In this paper, a new self-tuning algorithm is developed for determining the Fourier Series Controller coefficients with the aim of reducing the torque ripple in a PMSM, thus allowing for a smoother operation. This algorithm adjusts the controller parameters based on the component's harmonic distortion in time domain of the compensation signal. Experimental evaluation is performed on a DSP-controlled PMSM evaluation platform. Test results obtained validate the effectiveness of the proposed self-tuning algorithm, with the Fourier series expansion scheme, in reducing the torque ripple.
Volterra Series Based Distortion Effect
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2010-01-01
A large part of the characteristic sound of the electric guitar comes from nonlinearities in the signal path. Such nonlinearities may come from the input- or output-stage of the amplier, which is often equipped with vacuum tubes or a dedicated distortion pedal. In this paper the Volterra series...... expansion for non linear systems is investigated with respect to generating good distortion. The Volterra series allows for unlimited adjustment of the level and frequency dependency of each distortion component. Subjectively relevant ways of linking the dierent orders are discussed....
A feasibility study on wavelet transform for reactivity coefficient estimation
International Nuclear Information System (INIS)
Shimazu, Yoichiro
2000-01-01
Recently, a new method using Fourier transform has been introduced in place of the conventional method in order to reduce the time required for the measurement of moderator temperature coefficient in domestic PWRs. The basic concept of these methods is to eliminate noise in the reactivity signal. From this point of view, wavelet analysis is also known as an effective method. In this paper, we tried to apply this method to estimate reactivity coefficients of a nuclear reactor. The basic idea of the reactivity coefficient estimation is to analyze the ratios themselves of the corresponding expansion coefficients of the wavelet transform of the signals of reactivity and the relevant parameter. The concept requires no inverse wavelet transform. Based on numerical simulations, it is found that the method can reasonably estimate reactivity coefficient, for example moderator temperature coefficient, with less length of time sequence data than those required for Fourier transform method. We will continue this study to examine the validity of the estimation procedure for the actual reactor data and further to estimate the other reactivity coefficients. (author)
African Journals Online (AJOL)
calciphylaxis is prevention through rigorous control of phosphate and calcium balance. We here present two ... The authors declared no conflict of interest. Introduction. Calciphylaxis is a rare but serious disorder .... were reported to resolve the calciphylaxis lesions in a chronic renal failure patient [20]. In a series of five.
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
African Journals Online (AJOL)
abp
13 oct. 2017 ... This is an Open Access article distributed under the terms of the Creative Commons Attribution ... Bifocal leg fractures pose many challenges for the surgeon due to .... Dans notre serie, le taux d'infection est reste dans un.
Indian Academy of Sciences (India)
The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...
African Journals Online (AJOL)
Administrator
Key words: Case report, case series, concept analysis, research design. African Health Sciences 2012; (4): 557 - 562 http://dx.doi.org/10.4314/ahs.v12i4.25. PO Box 17666 .... According to the latest version of the Dictionary of. Epidemiology ...
216-B-3 expansion ponds closure plan
Energy Technology Data Exchange (ETDEWEB)
1994-10-01
This document describes the activities for clean closure under the Resource Conservation and Recovery Act of 1976 (RCRA) of the 216-B-3 Expansion Ponds. The 216-B-3 Expansion Ponds are operated by the US Department of Energy, Richland Operations Office (DOE-RL) and co-operated by Westinghouse Hanford Company (Westinghouse Hanford). The 216-B-3 Expansion Ponds consists of a series of three earthen, unlined, interconnected ponds that receive waste water from various 200 East Area operating facilities. The 3A, 3B, and 3C ponds are referred to as Expansion Ponds because they expanded the capability of the B Pond System. Waste water (primarily cooling water, steam condensate, and sanitary water) from various 200 East Area facilities is discharged to the Bypass pipe (Project X-009). Water discharged to the Bypass pipe flows directly into the 216-B-3C Pond. The ponds were operated in a cascade mode, where the Main Pond overflowed into the 3A Pond and the 3A Pond overflowed into the 3C Pond. The 3B Pond has not received waste water since May 1985; however, when in operation, the 3B Pond received overflow from the 3A Pond. In the past, waste water discharges to the Expansion Ponds had the potential to have contained mixed waste (radioactive waste and dangerous waste). The radioactive portion of mixed waste has been interpreted by the US Department of Energy (DOE) to be regulated under the Atomic Energy Act of 1954; the dangerous waste portion of mixed waste is regulated under RCRA.
216-B-3 expansion ponds closure plan
International Nuclear Information System (INIS)
1994-10-01
This document describes the activities for clean closure under the Resource Conservation and Recovery Act of 1976 (RCRA) of the 216-B-3 Expansion Ponds. The 216-B-3 Expansion Ponds are operated by the US Department of Energy, Richland Operations Office (DOE-RL) and co-operated by Westinghouse Hanford Company (Westinghouse Hanford). The 216-B-3 Expansion Ponds consists of a series of three earthen, unlined, interconnected ponds that receive waste water from various 200 East Area operating facilities. The 3A, 3B, and 3C ponds are referred to as Expansion Ponds because they expanded the capability of the B Pond System. Waste water (primarily cooling water, steam condensate, and sanitary water) from various 200 East Area facilities is discharged to the Bypass pipe (Project X-009). Water discharged to the Bypass pipe flows directly into the 216-B-3C Pond. The ponds were operated in a cascade mode, where the Main Pond overflowed into the 3A Pond and the 3A Pond overflowed into the 3C Pond. The 3B Pond has not received waste water since May 1985; however, when in operation, the 3B Pond received overflow from the 3A Pond. In the past, waste water discharges to the Expansion Ponds had the potential to have contained mixed waste (radioactive waste and dangerous waste). The radioactive portion of mixed waste has been interpreted by the US Department of Energy (DOE) to be regulated under the Atomic Energy Act of 1954; the dangerous waste portion of mixed waste is regulated under RCRA
Kato expansion in quantum canonical perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)
2016-06-15
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.