WorldWideScience

Sample records for phase approximation results

  1. Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

    Science.gov (United States)

    Kulkarni, Rishikesh; Rastogi, Pramod

    2018-02-01

    A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

  2. Warm ''pasta'' phase in the Thomas-Fermi approximation

    International Nuclear Information System (INIS)

    Avancini, Sidney S.; Menezes, Debora P.; Chiacchiera, Silvia; Providencia, Constanca

    2010-01-01

    In the present article, the 'pasta' phase is studied at finite temperatures within a Thomas-Fermi (TF) approach. Relativistic mean-field models, both with constant and density-dependent couplings, are used to describe this frustrated system. We compare the present results with previous ones obtained within a phase-coexistence description and conclude that the TF approximation gives rise to a richer inner ''pasta'' phase structure and the homogeneous matter appears at higher densities. Finally, the transition density calculated within TF is compared with the results for this quantity obtained with other methods.

  3. Quasilinear theory without the random phase approximation

    International Nuclear Information System (INIS)

    Weibel, E.S.; Vaclavik, J.

    1980-08-01

    The system of quasilinear equations is derived without making use of the random phase approximation. The fluctuating quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations posses the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations

  4. Multijet final states: exact results and the leading pole approximation

    International Nuclear Information System (INIS)

    Ellis, R.K.; Owens, J.F.

    1984-09-01

    Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest

  5. A note on the geometric phase in adiabatic approximation

    International Nuclear Information System (INIS)

    Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.

    2005-01-01

    The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough

  6. Semi-classical approximation to path integrals - phases and catastrophes

    International Nuclear Information System (INIS)

    Levit, S.

    1977-01-01

    Problems of phases and catastrophes were encountered when trying to apply the classical S-matrix theory to the scattering phenomena in nuclear physics. The path integral formulation provided a suitable basis for the treatment of these and related problems. Within conventional mathematical language it was possible to give practical prescriptions and discuss their limitations. Since the semi-classical (stationary phase) approximation is commonly used in any application of the path integral method, the results are not restricted to the scattering problems and may be of general interest. The derivation of the uniform approximations in the energy representation should use the exact path integral expression as the starting point, rather than performing Fourier transforms on the expressions derived in the present lecture. (B.G.)

  7. Toward a consistent random phase approximation based on the relativistic Hartree approximation

    International Nuclear Information System (INIS)

    Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.

    1992-01-01

    We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data

  8. Number-conserving random phase approximation with analytically integrated matrix elements

    International Nuclear Information System (INIS)

    Kyotoku, M.; Schmid, K.W.; Gruemmer, F.; Faessler, A.

    1990-01-01

    In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem

  9. Analysis of expansion phase experiments with improved approximation schemes

    International Nuclear Information System (INIS)

    Foit, J.J.

    1987-05-01

    A steady-state flow of a single-phase and incompressible fluid across a singularity is studied. Based on these theoretical considerations new approximation methods for the pressure gradient term in the SIMMER-II momentum equations are proposed which give a satisfactory pressure change in flows across singularities. The expansion phase experiments with a dipplate performed by SRI-International are evaluated to examine the quality of the proposed approximation schemes. (orig.) [de

  10. Photoabsorption for helium, lithium, and beryllium atoms in the random-phase approximation with exchange

    International Nuclear Information System (INIS)

    Amusia, M.Y.; Cherepkov, N.A.; Zivanovic, D.; Radojevic, V.

    1976-01-01

    The photoionization cross sections and the oscillator strengths for helium, lithium, and beryllium atoms are calculated in the framework of the random-phase approximation with exchange. The energy-level shift for discrete transitions is taken into account consistently in this approximation. The results are compared with other many-body calculations and with experimental data. The comparison shows that the random-phase approximation with exchange can even be used for systems with a small number of particles

  11. Static correlation beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian Sommer

    2014-01-01

    derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, second order screened exchange gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived...

  12. Beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

    We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...

  13. Random-phase approximation and broken symmetry

    International Nuclear Information System (INIS)

    Davis, E.D.; Heiss, W.D.

    1986-01-01

    The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)

  14. RCS estimation of linear and planar dipole phased arrays approximate model

    CERN Document Server

    Singh, Hema; Jha, Rakesh Mohan

    2016-01-01

    In this book, the RCS of a parallel-fed linear and planar dipole array is derived using an approximate method. The signal propagation within the phased array system determines the radar cross section (RCS) of phased array. The reflection and transmission coefficients for a signal at different levels of the phased-in scattering array system depend on the impedance mismatch and the design parameters. Moreover the mutual coupling effect in between the antenna elements is an important factor. A phased array system comprises of radiating elements followed by phase shifters, couplers, and terminating load impedance. These components lead to respective impedances towards the incoming signal that travels through them before reaching receive port of the array system. In this book, the RCS is approximated in terms of array factor, neglecting the phase terms. The mutual coupling effect is taken into account. The dependence of the RCS pattern on the design parameters is analyzed. The approximate model is established as a...

  15. Localization and stationary phase approximation on supermanifolds

    Science.gov (United States)

    Zakharevich, Valentin

    2017-08-01

    Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds.

  16. The Kubo-Greenwood formula as a result of the random phase approximation for the electrons of the metal

    Science.gov (United States)

    Ivliev, S. V.

    2017-12-01

    For calculation of short laser pulse absorption in metal the imaginary part of permittivity, which is simply related to the conductivity, is required. Currently to find the static and dynamic conductivity the Kubo-Greenwood formula is most commonly used. It describes the electromagnetic energy absorption in the one-electron approach. In the present study, this formula is derived directly from the expression for the permittivity expression in the random phase approximation, which in fact is equivalent to the method of the mean field. The detailed analysis of the role of electron-electron interaction in the calculation of the matrix elements of the velocity operator is given. It is shown that in the one-electron random phase approximation the single-particle conductive electron wave functions in the field of fixed ions should be used. The possibility of considering the exchange and correlation effects by means of an amendment to a local function field is discussed.

  17. Does the Berry phase in a quantum optical system originate from the rotating wave approximation?

    International Nuclear Information System (INIS)

    Wang, Minghao; Wei, L.F.; Liang, J.Q.

    2015-01-01

    The Berry phase (BP) in a quantized light field demonstrated more than a decade ago (Fuentes-Guridi et al., 2002 [9]) has attracted considerable attention, since it plays an important role in the cavity quantum electrodynamics. However, it is argued in Larson (2012) [15] that such a BP is just due to the rotating wave approximation (RWA) and the relevant BP should vanish beyond this approximation. Based on a consistent analysis we conclude in this letter that the BP in a generic Rabi model actually exists, no matter whether the RWA is applied. The existence of BP is also generalized to a three-level atom in the quantized cavity field. - Highlights: • Non-zero Berry phases for the Rabi model (without rotating wave approximation) are verified. • A general formulation of Berry phases for both the JC model and the Rabi model is presented. • The claim of vanishing Berry phase in the Rabi model is a result of improper semiclassical approximation. • Analytic solutions for the Rabi model is presented in the semiclassical approximation

  18. Analytic approximations for the elastic moduli of two-phase materials

    DEFF Research Database (Denmark)

    Zhang, Z. J.; Zhu, Y. K.; Zhang, P.

    2017-01-01

    Based on the models of series and parallel connections of the two phases in a composite, analytic approximations are derived for the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of elastically isotropic two-phase composites containing second phases of various volume...

  19. Analytical approximations to seawater optical phase functions of scattering

    Science.gov (United States)

    Haltrin, Vladimir I.

    2004-11-01

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

  20. Self-consistent GW0 results for the electron gas: Fixed screened potential W0 within the random-phase approximation

    International Nuclear Information System (INIS)

    von Barth, U.; Holm, B.

    1996-01-01

    With the aim of properly understanding the basis for and the utility of many-body perturbation theory as applied to extended metallic systems, we have calculated the electronic self-energy of the homogeneous electron gas within the GW approximation. The calculation has been carried out in a self-consistent way; i.e., the one-electron Green function obtained from Dyson close-quote s equation is the same as that used to calculate the self-energy. The self-consistency is restricted in the sense that the screened interaction W is kept fixed and equal to that of the random-phase approximation for the gas. We have found that the final results are marginally affected by the broadening of the quasiparticles, and that their self-consistent energies are still close to their free-electron counterparts as they are in non-self-consistent calculations. The reduction in strength of the quasiparticles and the development of satellite structure (plasmons) gives, however, a markedly smaller dynamical self-energy leading to, e.g., a smaller reduction in the quasiparticle strength as compared to non-self-consistent results. The relatively bad description of plasmon structure within the non-self-consistent GW approximation is marginally improved. A first attempt at including W in the self-consistency cycle leads to an even broader and structureless satellite spectrum in disagreement with experiment. copyright 1996 The American Physical Society

  1. Coded diffraction system in X-ray crystallography using a boolean phase coded aperture approximation

    Science.gov (United States)

    Pinilla, Samuel; Poveda, Juan; Arguello, Henry

    2018-03-01

    Phase retrieval is a problem present in many applications such as optics, astronomical imaging, computational biology and X-ray crystallography. Recent work has shown that the phase can be better recovered when the acquisition architecture includes a coded aperture, which modulates the signal before diffraction, such that the underlying signal is recovered from coded diffraction patterns. Moreover, this type of modulation effect, before the diffraction operation, can be obtained using a phase coded aperture, just after the sample under study. However, a practical implementation of a phase coded aperture in an X-ray application is not feasible, because it is computationally modeled as a matrix with complex entries which requires changing the phase of the diffracted beams. In fact, changing the phase implies finding a material that allows to deviate the direction of an X-ray beam, which can considerably increase the implementation costs. Hence, this paper describes a low cost coded X-ray diffraction system based on block-unblock coded apertures that enables phase reconstruction. The proposed system approximates the phase coded aperture with a block-unblock coded aperture by using the detour-phase method. Moreover, the SAXS/WAXS X-ray crystallography software was used to simulate the diffraction patterns of a real crystal structure called Rhombic Dodecahedron. Additionally, several simulations were carried out to analyze the performance of block-unblock approximations in recovering the phase, using the simulated diffraction patterns. Furthermore, the quality of the reconstructions was measured in terms of the Peak Signal to Noise Ratio (PSNR). Results show that the performance of the block-unblock phase coded apertures approximation decreases at most 12.5% compared with the phase coded apertures. Moreover, the quality of the reconstructions using the boolean approximations is up to 2.5 dB of PSNR less with respect to the phase coded aperture reconstructions.

  2. Relativistic quasiparticle random phase approximation in deformed nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Pena Arteaga, D.

    2007-06-25

    Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)

  3. Photons in dense nuclear matter: Random-phase approximation

    Science.gov (United States)

    Stetina, Stephan; Rrapaj, Ermal; Reddy, Sanjay

    2018-04-01

    We present a comprehensive and pedagogic discussion of the properties of photons in cold and dense nuclear matter based on the resummed one-loop photon self-energy. Correlations among electrons, muons, protons, and neutrons in β equilibrium that arise as a result of electromagnetic and strong interactions are consistently taken into account within the random phase approximation. Screening effects, damping, and collective excitations are systematically studied in a fully relativistic setup. Our study is relevant to the linear response theory of dense nuclear matter, calculations of transport properties of cold dense matter, and investigations of the production and propagation of hypothetical vector bosons such as the dark photons.

  4. Variational random phase approximation for the anharmonic oscillator

    International Nuclear Information System (INIS)

    Dukelsky, J.; Schuck, P.

    1990-04-01

    The recently derived Variational Random Phase Approximation is examined using the anharmonic oscillator model. Special attention is paid to the ground state RPA wave function and the convergence of the proposed truncation scheme to obtain the diagonal density matrix. Comparison with the standard Coupled Cluster method is made

  5. Approximated transport-of-intensity equation for coded-aperture x-ray phase-contrast imaging.

    Science.gov (United States)

    Das, Mini; Liang, Zhihua

    2014-09-15

    Transport-of-intensity equations (TIEs) allow better understanding of image formation and assist in simplifying the "phase problem" associated with phase-sensitive x-ray measurements. In this Letter, we present for the first time to our knowledge a simplified form of TIE that models x-ray differential phase-contrast (DPC) imaging with coded-aperture (CA) geometry. The validity of our approximation is demonstrated through comparison with an exact TIE in numerical simulations. The relative contributions of absorption, phase, and differential phase to the acquired phase-sensitive intensity images are made readily apparent with the approximate TIE, which may prove useful for solving the inverse phase-retrieval problem associated with these CA geometry based DPC.

  6. Random phase approximation: from Giant to Intra-doublet resonances

    International Nuclear Information System (INIS)

    Amusia, M.Ya.

    2004-01-01

    We discuss here the history and current achievements of one of the most powerful approaches of 20th century physics--the random phase approximation (RPA) that permits us to study collective or multiparticle effects in atoms, nuclei, molecules and clusters, as well as in quantum liquids. We concentrate on RPA application to studies of isolated atoms where it permits one to disclose the collective multielectron nature of so-called Giant resonances and predict a number of others, like Interference and Intra-doublet resonances. We present general theory as well as results of concrete calculations for a number of atoms

  7. Random phase approximation: from Giant to Intra-doublet resonances

    Energy Technology Data Exchange (ETDEWEB)

    Amusia, M.Ya. E-mail: amusia@vms.huji.ac.il

    2004-06-01

    We discuss here the history and current achievements of one of the most powerful approaches of 20th century physics--the random phase approximation (RPA) that permits us to study collective or multiparticle effects in atoms, nuclei, molecules and clusters, as well as in quantum liquids. We concentrate on RPA application to studies of isolated atoms where it permits one to disclose the collective multielectron nature of so-called Giant resonances and predict a number of others, like Interference and Intra-doublet resonances. We present general theory as well as results of concrete calculations for a number of atoms.

  8. Approximate characteristics for one-dimensional two-phase flows

    International Nuclear Information System (INIS)

    Sarayloo, A.; Peddleson, J.

    1985-01-01

    An approximate method for determining the characteristics associated with one-dimensional particulate two-phase flow models is presented. The method is based on iteration and is valid for small particulate volume fractions. The method is applied to several special cases involving incompressible particles suspended in a gas. The influences of certain changes in the physical model are investigated

  9. The infinite limit as an eliminable approximation for phase transitions

    Science.gov (United States)

    Ardourel, Vincent

    2018-05-01

    It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.

  10. Collective nuclear excitations with Skyrme-second random-phase approximation

    International Nuclear Information System (INIS)

    Gambacurta, D.; Catara, F.; Grasso, M.

    2010-01-01

    Second random-phase approximation (RPA) calculations with a Skyrme force are performed to describe both high- and low-lying excited states in 16 O. The coupling between one particle-one hole and two particle-two hole as well as that between two particle-two hole configurations among themselves are fully taken into account, and the residual interaction is never neglected; we do not resort therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond the standard RPA will be considered in detail in a forthcoming paper. Two approximations are employed here for these rearrangement terms: they are either neglected or evaluated with the RPA procedure. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by the second RPA owing to the huge number of two particle-two hole configurations. A better description of the excitation energies of the low-lying 0 + and 2 + states is obtained with the second RPA than with the RPA.

  11. Synthesis Of Ultrasound Field Sources Based on Phase Screen Approximation

    Directory of Open Access Journals (Sweden)

    Sukhanov Dmitry

    2018-01-01

    Full Text Available Here is proposed the method for synthesizing the sources of an acoustic field on the basis of an approximation of the phase screen. The technology of manufacturing ultrasonic phased arrays providing the formation of a field of a given distribution is proposed. An experimental setup has been developed for the formation of a vortex field at a distance of 10 cm.

  12. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

    International Nuclear Information System (INIS)

    Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao

    2014-01-01

    In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N 4 ). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S ^2 〉 are also developed and tested

  13. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

    Energy Technology Data Exchange (ETDEWEB)

    Peng, Degao; Yang, Yang; Zhang, Peng [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)

    2014-12-07

    In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.

  14. Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

    Science.gov (United States)

    Liu, Li; Mishchenko, Michael I.

    2016-01-01

    We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

  15. Insight into structural phase transitions from the decoupled anharmonic mode approximation.

    Science.gov (United States)

    Adams, Donat J; Passerone, Daniele

    2016-08-03

    We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T  =  0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.

  16. Isoscalar compression modes in relativistic random phase approximation

    International Nuclear Information System (INIS)

    Ma, Zhong-yu; Van Giai, Nguyen.; Wandelt, A.; Vretenar, D.; Ring, P.

    2001-01-01

    Monopole and dipole compression modes in nuclei are analyzed in the framework of a fully consistent relativistic random phase approximation (RRPA), based on effective mean-field Lagrangians with nonlinear meson self-interaction terms. The large effect of Dirac sea states on isoscalar strength distribution functions is illustrated for the monopole mode. The main contribution of Fermi and Dirac sea pair states arises through the exchange of the scalar meson. The effect of vector meson exchange is much smaller. For the monopole mode, RRPA results are compared with constrained relativistic mean-field calculations. A comparison between experimental and calculated energies of isoscalar giant monopole resonances points to a value of 250-270 MeV for the nuclear matter incompressibility. A large discrepancy remains between theoretical predictions and experimental data for the dipole compression mode

  17. Atomic structure calculations using the relativistic random phase approximation

    International Nuclear Information System (INIS)

    Cheng, K.T.; Johnson, W.R.

    1981-01-01

    A brief review is given for the relativistic random phase approximation (RRPA) applied to atomic transition problems. Selected examples of RRPA calculations on discrete excitations and photoionization are given to illustrate the need of relativistic many-body theories in dealing with atomic processes where both relativity and correlation are important

  18. Beyond chemical accuracy: The pseudopotential approximation in diffusion Monte Carlo calculations of the HCP to BCC phase transition in beryllium.

    Energy Technology Data Exchange (ETDEWEB)

    Shulenburger, Luke [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mattsson, Thomas Kjell Rene [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Desjarlais, Michael Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-01-01

    Motivated by the disagreement between recent diffusion Monte Carlo calculations of the phase transition pressure between the ambient and beta-Sn phases of silicon and experiments, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an opportunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotential approximation and after removing this we find excellent agreement with experiment for the ambient HCP phase and results similar to careful calculations using density functional theory for the phase transition pressure.

  19. Cold pasta phase in the extended Thomas-Fermi approximation

    Science.gov (United States)

    Avancini, S. S.; Bertolino, B. P.

    2015-10-01

    In this paper, we aim to obtain more accurate values for the transition density to the homogenous phase in the nuclear pasta that occurs in the inner crust of neutron stars. To that end, we use the nonlinear Walecka model at zero temperature and an approach based on the extended Thomas-Fermi (ETF) approximation.

  20. Cold pasta phase in the extended Thomas–Fermi approximation

    International Nuclear Information System (INIS)

    Avancini, S.S.; Bertolino, B.P.

    2015-01-01

    In this paper, we aim to obtain more accurate values for the transition density to the homogenous phase in the nuclear pasta that occurs in the inner crust of neutron stars. To that end, we use the nonlinear Walecka model at zero temperature and an approach based on the extended Thomas–Fermi (ETF) approximation. (author)

  1. Collapse of the random-phase approximation: Examples and counter-examples from the shell model

    International Nuclear Information System (INIS)

    Johnson, Calvin W.; Stetcu, Ionel

    2009-01-01

    The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a 'phase transition' in the literature). The order of the transition is important when one applies the random-phase approximation (RPA) to the of the Hartree-Fock wave function: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as 'collapse' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time nontrivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.

  2. Calculating beta decay in the deformed self-consistent quasiparticle random phase approximation

    Energy Technology Data Exchange (ETDEWEB)

    Engel, Jonathan, E-mail: engelj@physics.unc.edu [Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255 (United States); Mustonen, M. T., E-mail: mika.mustonen@yale.edu [Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255 (United States); Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06052 (United States)

    2016-06-21

    We discuss a recent global calculation of beta-decay rates in the self-consistent Skyrme quasiparticle random phase approximation (QRPA), with axially symmetric nuclear deformation treated explicitly. The calculation makes makes use of the finite-amplitude method, first proposed by Nakatsukasa and collaborators, to reduce computation time. The results are comparable in quality to those of several other global QRPA calculations. The QRPA may have reached the limit of its accuracy.

  3. Self-consistent random phase approximation - application to systems of strongly correlated fermions; Approximation des phases aleatoires self-consistante - applications a des systemes de fermions fortement correles

    Energy Technology Data Exchange (ETDEWEB)

    Jemai, M

    2004-07-01

    In the present thesis we have applied the self consistent random phase approximation (SCRPA) to the Hubbard model with a small number of sites (a chain of 2, 4, 6,... sites). Earlier SCRPA had produced very good results in other models like the pairing model of Richardson. It was therefore interesting to see what kind of results the method is able to produce in the case of a more complex model like the Hubbard model. To our great satisfaction the case of two sites with two electrons (half-filling) is solved exactly by the SCRPA. This may seem a little trivial but the fact is that other respectable approximations like 'GW' or the approach with the Gutzwiller wave function yield results still far from exact. With this promising starting point, the case of 6 sites at half filling was considered next. For that case, evidently, SCRPA does not any longer give exact results. However, they are still excellent for a wide range of values of the coupling constant U, covering for instance the phase transition region towards a state with non zero magnetisation. We consider this as a good success of the theory. Non the less the case of 4 sites (a plaquette), as indeed all cases with 4n sites at half filling, turned out to have a problem because of degeneracies at the Hartree Fock level. A generalisation of the present method, including in addition to the pairs, quadruples of Fermions operators (called second RPA) is proposed to also include exactly the plaquette case in our approach. This is therefore a very interesting perspective of the present work. (author)

  4. Extending the random-phase approximation for electronic correlation energies: the renormalized adiabatic local density approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2012-01-01

    The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...

  5. Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

    KAUST Repository

    Zhu, Guangpu

    2018-04-17

    In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

  6. Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

    KAUST Repository

    Zhu, Guangpu; Kou, Jisheng; Sun, Shuyu; Yao, Jun; Li, Aifen

    2018-01-01

    In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

  7. Importance of self-consistency in relativistic continuum random-phase approximation calculations

    International Nuclear Information System (INIS)

    Yang Ding; Cao Ligang; Tian Yuan; Ma Zhongyu

    2010-01-01

    A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

  8. Matrix model approximations of fuzzy scalar field theories and their phase diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)

    2015-12-29

    We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.

  9. The phase transition lines in pair approximation for the basic reinfection model SIRI

    International Nuclear Information System (INIS)

    Stollenwerk, Nico; Martins, Jose; Pinto, Alberto

    2007-01-01

    For a spatial stochastic epidemic model we investigate in the pair approximation scheme the differential equations for the moments. The basic reinfection model of susceptible-infected-recovered-reinfected or SIRI type is analysed, its phase transition lines calculated analytically in this pair approximation

  10. Random phase approximation in relativistic approach

    International Nuclear Information System (INIS)

    Ma Zhongyu; Yang Ding; Tian Yuan; Cao Ligang

    2009-01-01

    Some special issues of the random phase approximation(RPA) in the relativistic approach are reviewed. A full consistency and proper treatment of coupling to the continuum are responsible for the successful application of the RPA in the description of dynamical properties of finite nuclei. The fully consistent relativistic RPA(RRPA) requires that the relativistic mean filed (RMF) wave function of the nucleus and the RRPA correlations are calculated in a same effective Lagrangian and the consistent treatment of the Dirac sea of negative energy states. The proper treatment of the single particle continuum with scattering asymptotic conditions in the RMF and RRPA is discussed. The full continuum spectrum can be described by the single particle Green's function and the relativistic continuum RPA is established. A separable form of the paring force is introduced in the relativistic quasi-particle RPA. (authors)

  11. Separable pairing force for relativistic quasiparticle random-phase approximation

    International Nuclear Information System (INIS)

    Tian Yuan; Ma Zhongyu; Ring, Peter

    2009-01-01

    We have introduced a separable pairing force, which was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. This separable pairing force is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing properties in the ground state of finite nuclei on almost the same footing as the original Gogny interaction. In this work we investigate excited states using the Relativistic Quasiparticle Random-Phase Approximation (RQRPA) with the same separable pairing force. For consistency the Goldstone modes and the convergence with various cutoff parameters in this version of RQRPA are studied. The first excited 2 + states for the chain of Sn isotopes with Z=50 and the chain of isotones with N=82 isotones are calculated in RQRPA together with the 3 - states of Sn isotopes. By comparing our results with experimental data and with the results of the original Gogny force we find that this simple separable pairing interaction is very successful in depicting the pairing properties of vibrational excitations.

  12. First results from GERDA Phase II

    Science.gov (United States)

    Agostini, M.; Allardt, M.; Bakalyarov, A. M.; Balata, M.; Barabanov, I.; Baudis, L.; Bauer, C.; Bellotti, E.; Belogurov, S.; Belyaev, S. T.; Benato, G.; Bettini, A.; Bezrukov, L.; Bode, T.; Borowicz, D.; Brudanin, V.; Brugnera, R.; Caldwell, A.; Cattadori, C.; Chernogorov, A.; D'Andrea, V.; Demidova, E. V.; Di Marco, N.; Domula, A.; Doroshkevich, E.; Egorov, V.; Falkenstein, R.; Frodyma, N.; Gangapshev, A.; Garfagnini, A.; Gooch, C.; Grabmayr, P.; Gurentsov, V.; Gusev, K.; Hakenmüller, J.; Hegai, A.; Heisel, M.; Hemmer, S.; Hofmann, W.; Hult, M.; Inzhechik, L. V.; Janicskó Csáthy, J.; Jochum, J.; Junker, M.; Kazalov, V.; Kihm, T.; Kirpichnikov, I. V.; Kirsch, A.; Kish, A.; Klimenko, A.; Kneißl, R.; Knöpfle, K. T.; Kochetov, O.; Kornoukhov, V. N.; Kuzminov, V. V.; Laubenstein, M.; Lazzaro, A.; Lebedev, V. I.; Lehnert, B.; Liao, H. Y.; Lindner, M.; Lippi, I.; Lubashevskiy, A.; Lubsandorzhiev, B.; Lutter, G.; Macolino, C.; Majorovits, B.; Maneschg, W.; Medinaceli, E.; Miloradovic, M.; Mingazheva, R.; Misiaszek, M.; Moseev, P.; Nemchenok, I.; Palioselitis, D.; Panas, K.; Pandola, L.; Pelczar, K.; Pullia, A.; Riboldi, S.; Rumyantseva, N.; Sada, C.; Salamida, F.; Salathe, M.; Schmitt, C.; Schneider, B.; Schönert, S.; Schreiner, J.; Schulz, O.; Schütz, A.-K.; Schwingenheuer, B.; Selivanenko, O.; Shevchik, E.; Shirchenko, M.; Simgen, H.; Smolnikov, A.; Stanco, L.; Vanhoefer, L.; Vasenko, A. A.; Veresnikova, A.; von Sturm, K.; Wagner, V.; Wegmann, A.; Wester, T.; Wiesinger, C.; Wojcik, M.; Yanovich, E.; Zhitnikov, I.; Zhukov, S. V.; Zinatulina, D.; Zuber, K.; Zuzel, G.

    2017-09-01

    Gerda is designed for a background-free search of 76Ge neutrinoless double-β decay, using bare Ge detectors in liquid Ar. The experiment was upgraded after the successful completion of Phase I to double the target mass and further reduce the background. Newly-designed Ge detectors were installed along with LAr scintillation sensors. Phase II of data-taking started in Dec 2015 with approximately 36 kg of Ge detectors and is currently ongoing. The first results based on 10.8 kg· yr of exposure are presented. The background goal of 10-3 cts/(keV· kg· yr) is achieved and a search for neutrinoless double-β decay is performed by combining Phase I and II data. No signal is found and a new limit is set at T1/20ν > 5.3 \\cdot {1025} yr (90% C.L.).

  13. Some results in Diophantine approximation

    DEFF Research Database (Denmark)

    Pedersen, Steffen Højris

    the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

  14. Extended random-phase approximation with three-body ground-state correlations

    International Nuclear Information System (INIS)

    Tohyama, M.; Schuck, P.

    2008-01-01

    An extended random-phase approximation (ERPA) which contains the effects of ground-state correlations up to a three-body level is applied to an extended Lipkin model which contains an additional particle-scattering term. Three-body correlations in the ground state are necessary to preserve the hermiticity of the Hamiltonian matrix of ERPA. Two approximate forms of ERPA which neglect the three-body correlations are also applied to investigate the importance of three-body correlations. It is found that the ground-state energy is little affected by the inclusion of the three-body correlations. On the contrary, three-body correlations for the excited states can become quite important. (orig.)

  15. Self-consistent random phase approximation - application to systems of strongly correlated fermions

    International Nuclear Information System (INIS)

    Jemai, M.

    2004-07-01

    In the present thesis we have applied the self consistent random phase approximation (SCRPA) to the Hubbard model with a small number of sites (a chain of 2, 4, 6,... sites). Earlier SCRPA had produced very good results in other models like the pairing model of Richardson. It was therefore interesting to see what kind of results the method is able to produce in the case of a more complex model like the Hubbard model. To our great satisfaction the case of two sites with two electrons (half-filling) is solved exactly by the SCRPA. This may seem a little trivial but the fact is that other respectable approximations like 'GW' or the approach with the Gutzwiller wave function yield results still far from exact. With this promising starting point, the case of 6 sites at half filling was considered next. For that case, evidently, SCRPA does not any longer give exact results. However, they are still excellent for a wide range of values of the coupling constant U, covering for instance the phase transition region towards a state with non zero magnetisation. We consider this as a good success of the theory. Non the less the case of 4 sites (a plaquette), as indeed all cases with 4n sites at half filling, turned out to have a problem because of degeneracies at the Hartree Fock level. A generalisation of the present method, including in addition to the pairs, quadruples of Fermions operators (called second RPA) is proposed to also include exactly the plaquette case in our approach. This is therefore a very interesting perspective of the present work. (author)

  16. Calculation of thermodynamic properties using the random-phase approximation: alpha-N2

    NARCIS (Netherlands)

    Jansen, A.P.J.; Schoorl, R.

    1988-01-01

    The random-phase approximation (RPA) for molecular crystals is extended in order to calculate thermodynamic properties. A recursion formula for thermodynamic averages of products of mean-field excitation and deexcitation operators is derived. With this formula the thermodynamic average of any

  17. Quantum adiabatic approximation and the geometric phase

    International Nuclear Information System (INIS)

    Mostafazadeh, A.

    1997-01-01

    A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society

  18. Implicit approximate Riemann solver for two fluid two phase flow models

    International Nuclear Information System (INIS)

    Raymond, P.; Toumi, I.; Kumbaro, A.

    1993-01-01

    This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by

  19. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow

    International Nuclear Information System (INIS)

    Toumi, I.; Kumbaro, A.; Paillere, H.

    1999-01-01

    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  20. Communication: Random phase approximation renormalized many-body perturbation theory

    International Nuclear Information System (INIS)

    Bates, Jefferson E.; Furche, Filipp

    2013-01-01

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations

  1. Insight into organic reactions from the direct random phase approximation and its corrections

    Energy Technology Data Exchange (ETDEWEB)

    Ruzsinszky, Adrienn [Department of Physics, Temple University, Philadelphia, Pennsylvania 19122 (United States); Zhang, Igor Ying; Scheffler, Matthias [Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin (Germany)

    2015-10-14

    The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11) represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges.

  2. Insight into organic reactions from the direct random phase approximation and its corrections

    International Nuclear Information System (INIS)

    Ruzsinszky, Adrienn; Zhang, Igor Ying; Scheffler, Matthias

    2015-01-01

    The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11) represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges

  3. Unambiguous results from variational matrix Pade approximants

    International Nuclear Information System (INIS)

    Pindor, Maciej.

    1979-10-01

    Variational Matrix Pade Approximants are studied as a nonlinear variational problem. It is shown that although a stationary value of the Schwinger functional is a stationary value of VMPA, the latter has also another stationary value. It is therefore proposed that instead of looking for a stationary point of VMPA, one minimizes some non-negative functional and then one calculates VMPA at the point where the former has the absolute minimum. This approach, which we call the Method of the Variational Gradient (MVG) gives unambiguous results and is also shown to minimize a distance between the approximate and the exact stationary values of the Schwinger functional

  4. Thermodynamics and structure of liquid metals from a consistent optimized random phase approximation

    International Nuclear Information System (INIS)

    Akinlade, O.; Badirkhan, Z.; Pastore, G.

    2000-05-01

    We study thermodynamics and structural properties of several liquid metals to assess the validity of the generalized non-local model potential (GNMP) of Li et. al. [J.Phys. F16,309 (1986)]. By using a new thermodynamically consistent version of the optimized random phase approximation (ORPA), especially adapted to continuous reference potentials, we improve our previous results obtained within the variational approach based on the Gibbs - Bogoliubov inequality. Hinging on the unified and very accurate evaluation of structure factors and thermodynamic quantities provided by the ORPA, we find that the GNMP yields satisfactory results for the alkali metals, however, those for the polyvalent metals point to a substantial inadequacy of the GNMP for high valence systems. (author)

  5. Random phase approximation applied to solids, molecules, and graphene-metal interfaces

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

    The random phase approximation (RPA) is attracting renewed interest as a universal and accurate method for first-principles total energy calculations. The RPA naturally accounts for long-range dispersive forces without compromising accuracy for short-range interactions making the RPA superior...... to semilocal and hybrid functionals in systems dominated by weak van der Waals or mixed covalent-dispersive interactions. In this work, we present plane-wave-based RPA calculations for a broad collection of systems with bond types ranging from strong covalent to van der Waals. Our main result is the RPA...... the RPA captures both the weak covalent and dispersive forces, which are equally important for these systems. We benchmark our implementation in the GPAW electronic structure code by calculating cohesive energies of graphite and a range of covalently bonded solids and molecules as well as the dissociation...

  6. State equation approximation of transfer matrices and its application to the phase domain calculation of electromagnetic transients

    International Nuclear Information System (INIS)

    Soysal, A.O.; Semlyen, A.

    1994-01-01

    A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time

  7. Roles of antinucleon degrees of freedom in the relativistic random phase approximation

    Science.gov (United States)

    Kurasawa, Haruki; Suzuki, Toshio

    2015-11-01

    The roles of antinucleon degrees of freedom in the relativistic random phase approximation (RPA) are investigated. The energy-weighted sum of the RPA transition strengths is expressed in terms of the double commutator between the excitation operator and the Hamiltonian, as in nonrelativistic models. The commutator, however, should not be calculated in the usual way in the local field theory, because, otherwise, the sum vanishes. The sum value obtained correctly from the commutator is infinite, owing to the Dirac sea. Most of the previous calculations take into account only some of the nucleon-antinucleon states, in order to avoid divergence problems. As a result, RPA states with negative excitation energy appear, which make the sum value vanish. Moreover, disregarding the divergence changes the sign of nuclear interactions in the RPA equation that describes the coupling of the nucleon particle-hole states with the nucleon-antinucleon states. Indeed, the excitation energies of the spurious state and giant monopole states in the no-sea approximation are dominated by these unphysical changes. The baryon current conservation can be described without touching the divergence problems. A schematic model with separable interactions is presented, which makes the structure of the relativistic RPA transparent.

  8. First-order corrections to random-phase approximation GW calculations in silicon and diamond

    NARCIS (Netherlands)

    Ummels, R.T.M.; Bobbert, P.A.; van Haeringen, W.

    1998-01-01

    We report on ab initio calculations of the first-order corrections in the screened interaction W to the random-phase approximation polarizability and to the GW self-energy, using a noninteracting Green's function, for silicon and diamond. It is found that the first-order vertex and self-consistency

  9. Modified random phase approximation for multipole excitations at finite temperature

    International Nuclear Information System (INIS)

    Nguyen Dinh Dang

    1991-01-01

    The modified finite temperature random phase approximation (modified FT-RPA) has been constructed with taking the influence of thermostat on the structure of quansiparticles into account. The modified FT-RPA linear response for electric quadrupole (λ π = 2 + ) and octupole (λ π = 3 - ) excitations in 5 8Ni has been calculated as a function of the nuclear temperature. As compared to the conventional FT-RPA the modified FT-RPA has given a stronger spreading for the strength distribution of quandrupole excitations at finite temperature T ≤ 3MeV. (author). 22 refs; 4 figs; 2 tabs

  10. Hubbard-U corrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations

    DEFF Research Database (Denmark)

    Patrick, Christopher; Thygesen, Kristian Sommer

    2016-01-01

    In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we...... investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transitionmetal compounds ZnS, TiO2, and NiO.We find that the RPA lattice constants are essentially independent of U, despite large changes...... in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U. Our RPA calculations find the rutile phase of TiO2 to be more stable than anatase independent of U, a result which is consistent with experiments...

  11. Relativistic quasiparticle random phase approximation with a separable pairing force

    International Nuclear Information System (INIS)

    Tian Yuan; Ma Zhongyu; Ring Peter

    2009-01-01

    In our previous work, we introduced a separable pairing force for relativistic Hartree-Bogoliubov calculations. This force was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. By using the well known techniques of Talmi and Moshinsky it can be expanded in a series of separable terms and converges quickly after a few terms. It was found that the pairing properties can be depicted on almost the same footing as the original pairing interaction, not only in nuclear matter, but also in finite nuclei. In this study, we construct a relativistic quasiparticle random phase approximation (RQRPA) with this separable pairing interaction and calculate the excitation energies of the first excited 2 + states and reduced B(E2; 0 + →2 + ) transition rates for a chain of Sn isotopes in RQRPA. Compared with the results of the full Gogny force, we find that this simple separable pairing interaction can describe the pairing properties of the excited vibrational states as well as the original pairing interaction. (authors)

  12. Neutrino-nucleus reaction rates based on the relativistic quasiparticle random phase approximation

    International Nuclear Information System (INIS)

    Paar, N.; Vretenar, D.; Marketin, T.; Ring, P.

    2008-01-01

    Neutrino-nucleus cross sections are described in a novel theoretical framework where the weak interaction of leptons with hadrons is expressed in the standard current-current form, the nuclear ground state is described in the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited states are calculated in the relativistic quasiparticle random phase approximation. The model is employed in studies of neutrino-nucleus reactions in several test cases

  13. Finite nucleus Dirac mean field theory and random phase approximation using finite B splines

    International Nuclear Information System (INIS)

    McNeil, J.A.; Furnstahl, R.J.; Rost, E.; Shepard, J.R.; Department of Physics, University of Maryland, College Park, Maryland 20742; Department of Physics, University of Colorado, Boulder, Colorado 80309)

    1989-01-01

    We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic σ-ω model for the closed-shell nuclei 16 O and 40 Ca. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar 1/sup -/ and 3/sup -/ longitudinal form factors of 16 O and 40 Ca. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results

  14. Dispersive and Covalent Interactions between Graphene and Metal Surfaces from the Random Phase Approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Yan, Jun; Mortensen, Jens Jørgen

    2011-01-01

    We calculate the potential energy surfaces for graphene adsorbed on Cu(111), Ni(111), and Co(0001) using density functional theory and the random phase approximation (RPA). For these adsorption systems covalent and dispersive interactions are equally important and while commonly used approximations...... for exchange-correlation functionals give inadequate descriptions of either van der Waals or chemical bonds, RPA accounts accurately for both. It is found that the adsorption is a delicate competition between a weak chemisorption minimum close to the surface and a physisorption minimum further from the surface....

  15. Relativistic continuum random phase approximation in spherical nuclei

    International Nuclear Information System (INIS)

    Daoutidis, Ioannis

    2009-01-01

    Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

  16. Relativistic continuum random phase approximation in spherical nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Daoutidis, Ioannis

    2009-10-01

    Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

  17. Linear-scaling implementation of the direct random-phase approximation

    International Nuclear Information System (INIS)

    Kállay, Mihály

    2015-01-01

    We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor

  18. Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

    Directory of Open Access Journals (Sweden)

    Xiao-Ying Qin

    2014-01-01

    Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

  19. Surface wake in the random-phase approximation

    International Nuclear Information System (INIS)

    Garcia de Abajo, F.J.; Echenique, P.M.

    1993-01-01

    The scalar-electric-potential distribution set up by an ion traveling in the vicinity of a plane solid-vacuum interface, that is, the surface-wake potential, is investigated with the specular-reflection model to describe the response of the surface and with the random-phase approximation for the dielectric function of the bulk material. This permits us to address the study of the low-velocity surface wake: the static potential is found to have a dip at the position of the ion; that dip is shifted towards the direction opposite to the velocity vector for velocities smaller than the threshold of creation of plasmons (∼1.3v F ). Extensive numerical calculations are presented for an ion both inside and outside aluminum. Comparison to the results obtained with the plasmon-pole dielectric function indicates excellent agreement for velocities larger than ∼1.3v F . On the other side, the possibility of surface-wake riding is suggested, by analogy with bulk-wake riding postulated in the past. In it, the electron would be bound in the first trough of the surface-wake potential set up when the ion describes a grazing trajectory. The main feature introduced by the surface with respect to the bulk consists of allowing the use of ions of higher charge, reducing in this way the relative importance of the electron self-energy, and in addition, giving rise to larger binding energies. When the ion beam is directed along a special direction of an oriented crystal surface, the mechanism of resonant coherent excitation could provide a way for experimentally detecting this phenomenon through the emission of the bound electron with well-defined energy and around a preferential direction

  20. Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects.

    Science.gov (United States)

    Mussard, Bastien; Rocca, Dario; Jansen, Georg; Ángyán, János G

    2016-05-10

    Starting from the general expression for the ground state correlation energy in the adiabatic-connection fluctuation-dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case, the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed, and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental for improvement over direct RPA results.

  1. Quantum mechanics of the fractional-statistics gas: Random-phase approximation

    International Nuclear Information System (INIS)

    Dai, Q.; Levy, J.L.; Fetter, A.L.; Hanna, C.B.; Laughlin, R.B.

    1992-01-01

    A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation of Fetter, Hanna, and Laughlin [Phys. Rev. B 39, 9679 (1989)] are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct. Excellent agreement is obtained with the collective-mode dispersion obtained numerically by Xie, He, and Das Sarma [Phys. Rev. Lett. 65, 649 (1990)

  2. Finite-temperature random-phase approximation for spectroscopic properties of neon plasmas

    International Nuclear Information System (INIS)

    Colgan, J.; Collins, L. A.; Fontes, C. J.; Csanak, G.

    2007-01-01

    A finite-temperature random-phase approximation (FTRPA) is applied to calculate oscillator strengths for excitations in hot and dense plasmas. Application of the FTRPA provides a convenient, self-consistent method with which to explore coupled-channel effects of excited electrons in a dense plasma. We present FTRPA calculations that include coupled-channel effects. The inclusion of these effects is shown to cause significant differences in the oscillator strength for a prototypical case of 1 P excitation in neon when compared with single-channel and with average-atom calculations. Trends as a function of temperature and density are also discussed

  3. Optimized random phase approximation for the structure of liquid alkali metals as electron-ion plasmas

    International Nuclear Information System (INIS)

    Senatore, G.; Tosi, M.P.; Trieste Univ.

    1981-08-01

    The purpose of this letter is to stress that the way towards an unconventional optimized-random-phase-approximation (ORPA) approach to the structure of liquid metals is indicated, and in fact already a good first-order solution for such an approach is provided

  4. Domain patterns and hysteresis in phase-transforming solids: analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation

    Czech Academy of Sciences Publication Activity Database

    DeSimone, A.; Kružík, Martin

    2013-01-01

    Roč. 8, č. 2 (2013), s. 481-499 ISSN 1556-1801 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : hysteresis * shape memory Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/kruzik-domain patterns and hysteresis in phase-transforming solids analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation.pdf

  5. Approximation of Measurement Results of “Emergency” Signal Reception Probability

    Directory of Open Access Journals (Sweden)

    Gajda Stanisław

    2017-08-01

    Full Text Available The intended aim of this article is to present approximation results of the exemplary measurements of EMERGENCY signal reception probability. The probability is under-stood as a distance function between the aircraft and a ground-based system under established conditions. The measurements were approximated using the properties of logistic functions. This probability, as a distance function, enables to determine the range of the EMERGENCY signal for a pre-set confidence level.

  6. Collective excitations in the Penson-Kolb model: A generalized random-phase-approximation study

    International Nuclear Information System (INIS)

    Roy, G.K.; Bhattacharyya, B.

    1997-01-01

    The evolution of the superconducting ground state of the half-filled Penson-Kolb model is examined as a function of the coupling constant using a mean-field approach and the generalized random phase approximation (RPA) in two and three dimensions. On-site singlet pairs hop to compete against single-particle motion in this model, giving the coupling constant a strong momentum dependence. There is a pronounced bandwidth enhancement effect that converges smoothly to a finite value in the strong-coupling (Bose) regime. The low-lying collective excitations evaluated in generalized RPA show a linear dispersion and a gradual crossover from the weak-coupling (BCS) limit to the Bose regime; the mode velocity increases monotonically in sharp contrast to the attractive Hubbard model. Analytical results are derived in the asymptotic limits. copyright 1997 The American Physical Society

  7. Scattering phases for particles with nonzero orbital momenta and resonance regimes in the Pais approximation

    International Nuclear Information System (INIS)

    Bruk, Yulii M; Voloshchuk, Aleksandr N

    2012-01-01

    The functional Pais equation for scattering phases with nonzero orbital momenta is solved in the case of low-energy particles. For short-range screened potentials, in particular, Yukawa or Thomas-Fermi potentials, the Pais equation is shown to reduce to transcendental equations. For the potentials varying ∼r - n , n > 0, simple algebraic equations are obtained for determining the phases δ l , l≠0. Possible applications of the Pais approximation to the problem of finding resonance regimes in the scattering of low-energy particles with nonzero orbital momenta are discussed. (methodological notes)

  8. Quantum Chemistry beyond Born–Oppenheimer Approximation on a Quantum Computer: A Simulated Phase Estimation Study

    Czech Academy of Sciences Publication Activity Database

    Veis, Libor; Višňák, Jakub; Nishizawa, H.; Nakai, H.; Pittner, Jiří

    2016-01-01

    Roč. 116, č. 18 (2016), s. 1328-1336 ISSN 0020-7608 R&D Projects: GA ČR GA203/08/0626 Institutional support: RVO:61388955 Keywords : Born-Oppenheimer approximation * nuclear orbital plus molecular orbital method * phase estimation Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.920, year: 2016

  9. A Gaussian Approximation Potential for Silicon

    Science.gov (United States)

    Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

    We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

  10. Electric dipole strength and dipole polarizability in 48Ca within a fully self-consistent second random-phase approximation

    Science.gov (United States)

    Gambacurta, D.; Grasso, M.; Vasseur, O.

    2018-02-01

    The second random-phase-approximation model corrected by a subtraction procedure designed to cure double counting, instabilities, and ultraviolet divergences, is employed for the first time to analyze the dipole strength and polarizability in 48Ca. All the terms of the residual interaction are included, leading to a fully self-consistent scheme. Results are illustrated with two Skyrme parametrizations, SGII and SLy4. Those obtained with the SGII interaction are particularly satisfactory. In this case, the low-lying strength below the neutron threshold is well reproduced and the giant dipole resonance is described in a very satisfactory way especially in its spreading and fragmentation. Spreading and fragmentation are produced in a natural way within such a theoretical model by the coupling of 1 particle-1 hole and 2 particle-2 hole configurations. Owing to this feature, we may provide for the electric polarizability as a function of the excitation energy a curve with a similar slope around the centroid energy of the giant resonance compared to the corresponding experimental results. This represents a considerable improvement with respect to previous theoretical predictions obtained with the random-phase approximation or with several ab-initio models. In such cases, the spreading width of the excitation cannot be reproduced and the polarizability as a function of the excitation energy displays a stiff increase around the predicted centroid energy of the giant resonance.

  11. Right unitarity triangles, stable CP-violating phases and approximate quark-lepton complementarity

    International Nuclear Information System (INIS)

    Xing Zhizhong

    2009-01-01

    Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V are almost the right triangles with α∼90 deg. We highlight a very suggestive parametrization of V and show that its CP-violating phase φ is nearly equal to α (i.e., φ-α∼1.1 deg.). Both φ and α are stable against the renormalizaton-group evolution from the electroweak scale M Z to a superhigh energy scale M X or vice versa, and thus it is impossible to obtain α=90 deg. at M Z from φ=90 deg. at M X . We conjecture that there might also exist a maximal CP-violating phase φ∼90 deg. in the MNS lepton mixing matrix U. The approximate quark-lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U simply due to the smallness of |V ub | and |V e3 |.

  12. Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic broken-symmetry random-phase approximation

    International Nuclear Information System (INIS)

    Strinati, G.C.; Pieri, P.

    2004-01-01

    The linear response to a space- and time-dependent external disturbance of a system of dilute condensed composite bosons at zero temperature, as obtained from the linearized version of the time-dependent Gross-Pitaevskii equation, is shown to result also from the strong-coupling limit of the time-dependent BCS (or broken-symmetry random-phase) approximation for the constituent fermions subject to the same external disturbance. In this way, it is possible to connect excited-state properties of the bosonic and fermionic systems by placing the Gross-Pitaevskii equation in perspective with the corresponding fermionic approximations

  13. An adaptive meshfree method for phase-field models of biomembranes. Part I: Approximation with maximum-entropy basis functions

    OpenAIRE

    Rosolen, A.; Peco, C.; Arroyo, M.

    2013-01-01

    We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp i...

  14. Random-phase-approximation approach to optical and magnetic excitations in the two-dimensional multiband Hubbard model

    International Nuclear Information System (INIS)

    Yonemitsu, K.; Bishop, A.R.

    1992-01-01

    As a convenient qualitative approach to strongly correlated electronic systems, an inhomogeneous Hartree-Fock plus random-phase approximation is applied to response functions for the two-dimensional multiband Hubbard model for cuprate superconductors. A comparison of the results with those obtained by exact diagonalization by Wagner, Hanke, and Scalapino [Phys. Rev. B 43, 10 517 (1991)] shows that overall structures in optical and magnetic particle-hole excitation spectra are well reproduced by this method. This approach is computationally simple, retains conceptual clarity, and can be calibrated by comparison with exact results on small systems. Most importantly, it is easily extended to larger systems and straightforward to incorporate additional terms in the Hamiltonian, such as electron-phonon interactions, which may play a crucial role in high-temperature superconductivity

  15. Benchmark tests and spin adaptation for the particle-particle random phase approximation

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Yang; Steinmann, Stephan N.; Peng, Degao [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Aggelen, Helen van, E-mail: Helen.VanAggelen@UGent.be [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Department of Inorganic and Physical Chemistry, Ghent University, 9000 Ghent (Belgium); Yang, Weitao, E-mail: Weitao.Yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)

    2013-11-07

    The particle-particle random phase approximation (pp-RPA) provides an approximation to the correlation energy in density functional theory via the adiabatic connection [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)]. It has virtually no delocalization error nor static correlation error for single-bond systems. However, with its formal O(N{sup 6}) scaling, the pp-RPA is computationally expensive. In this paper, we implement a spin-separated and spin-adapted pp-RPA algorithm, which reduces the computational cost by a substantial factor. We then perform benchmark tests on the G2/97 enthalpies of formation database, DBH24 reaction barrier database, and four test sets for non-bonded interactions (HB6/04, CT7/04, DI6/04, and WI9/04). For the G2/97 database, the pp-RPA gives a significantly smaller mean absolute error (8.3 kcal/mol) than the direct particle-hole RPA (ph-RPA) (22.7 kcal/mol). Furthermore, the error in the pp-RPA is nearly constant with the number of atoms in a molecule, while the error in the ph-RPA increases. For chemical reactions involving typical organic closed-shell molecules, pp- and ph-RPA both give accurate reaction energies. Similarly, both RPAs perform well for reaction barriers and nonbonded interactions. These results suggest that the pp-RPA gives reliable energies in chemical applications. The adiabatic connection formalism based on pairing matrix fluctuation is therefore expected to lead to widely applicable and accurate density functionals.

  16. Self-consistent Random Phase Approximation applied to a schematic model of the field theory; Approximation des phases aleatoires self-consistante appliquee a un modele schematique de la theorie des champs

    Energy Technology Data Exchange (ETDEWEB)

    Bertrand, Thierry [Inst. de Physique Nucleaire, Lyon-1 Univ., 69 - Villeurbanne (France)

    1998-12-11

    The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum 40 refs., 33 figs., 14 tabs.

  17. A surprise in the first Born approximation for electron scattering

    International Nuclear Information System (INIS)

    Treacy, M.M.J.; Van Dyck, D.

    2012-01-01

    A standard textbook derivation for the scattering of electrons by a weak potential under the first Born approximation suggests that the far-field scattered wave should be in phase with the incident wave. However, it is well known that waves scattered from a weak phase object should be phase-shifted by π/2 relative to the incident wave. A disturbing consequence of this missing phase is that, according to the Optical Theorem, the total scattering cross section would be zero in the first Born approximation. We resolve this mystery pedagogically by showing that the first Born approximation fails to conserve electrons even to first order. Modifying the derivation to conserve electrons introduces the correct phase without changing the scattering amplitude. We also show that the far-field expansion for the scattered waves used in many texts is inappropriate for computing an exit wave from a sample, and that the near-field expansion also give the appropriately phase-shifted result. -- Highlights: ► The first Born approximation is usually invoked as the theoretical physical basis for kinematical electron scattering theory. ► Although it predicts the correct scattering amplitude, it predicts the wrong phase; the scattered wave is missing a prefactor of i. ► We show that this arises because the standard textbook version of the first Born approximation does not conserve electrons. ► We show how this can be fixed.

  18. Dynamic and static correlation functions in the inhomogeneous Hartree-Fock-state approach with random-phase-approximation fluctuations

    International Nuclear Information System (INIS)

    Lorenzana, J.; Grynberg, M.D.; Yu, L.; Yonemitsu, K.; Bishop, A.R.

    1992-11-01

    The ground state energy, and static and dynamic correlation functions are investigated in the inhomogeneous Hartree-Fock (HF) plus random phase approximation (RPA) approach applied to a one-dimensional spinless fermion model showing self-trapped doping states at the mean field level. Results are compared with homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous HF ground state allows the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground state energy agrees well with the exact results at strong and weak coupling limits. We also compare it with a related quasi-boson approach. The instability towards self-trapped behaviour is signaled by a RPA mode with frequency approaching zero. (author). 21 refs, 10 figs

  19. Phase diagram of the Blume-Emery-Griffiths model on the simple cubic lattice calculated by the linear chain approximation

    International Nuclear Information System (INIS)

    Albayrak, Erhan; Keskin, Mustafa

    2000-01-01

    The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made

  20. Phase diagram of the Blume-Emery-Griffiths model on the simple cubic lattice calculated by the linear chain approximation

    CERN Document Server

    Albayrak, E

    2000-01-01

    The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made.

  1. General Rytov approximation.

    Science.gov (United States)

    Potvin, Guy

    2015-10-01

    We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

  2. Random-phase approximation and its extension for the O(2) anharmonic oscillator

    International Nuclear Information System (INIS)

    Aouissat, Z.; Martin, C.

    2004-01-01

    We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations around the static solution in the time-dependent Hartree-Bogolyubov equation. We draw the parallel between the two approaches. (orig.)

  3. Random-phase approximation and its extension for the O(2) anharmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Aouissat, Z. [Institut fuer Kernphysik, Technische Hochschule Darmstadt, Schlossgarten 9, D-64289, Darmstadt (Germany); Martin, C. [Groupe de Physique Theorique, Institut de Physique Nucleaire, F-91406, Orsay Cedex (France)

    2004-02-01

    We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations around the static solution in the time-dependent Hartree-Bogolyubov equation. We draw the parallel between the two approaches. (orig.)

  4. The random phase approximation

    International Nuclear Information System (INIS)

    Schuck, P.

    1985-01-01

    RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more

  5. Application of the resonating Hartree-Fock random phase approximation to the Lipkin model

    International Nuclear Information System (INIS)

    Nishiyama, S.; Ishida, K.; Ido, M.

    1996-01-01

    We have applied the resonating Hartree-Fock (Res-HF) approximation to the exactly solvable Lipkin model by utilizing a newly developed orbital-optimization algorithm. The Res-HF wave function was superposed by two Slater determinants (S-dets) which give two corresponding local energy minima of monopole ''deformations''. The self-consistent Res-HF calculation gives an excellent ground-state correlation energy. There exist excitations due to small vibrational fluctuations of the orbitals and mixing coefficients around their stationary values. They are described by a new approximation called the resonating Hartree-Fock random phase approximation (Res-HF RPA). Matrices of the second-order variation of the Res-HF energy have the same structures as those of the Res-HF RPA's matrices. The quadratic steepest descent of the Res-HF energy in the orbital optimization is considered to include certainly both effects of RPA-type fluctuations up to higher orders and their mode-mode couplings. It is a very important and interesting task to apply the Res-HF RPA to the Lipkin model with the use of the stationary values and to prove the above argument. It turns out that the Res-HF RPA works far better than the usual HF RPA and the renormalized one. We also show some important features of the Res-HF RPA. (orig.)

  6. Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r 6) to O(r 4)

    International Nuclear Information System (INIS)

    Shenvi, Neil; Yang, Yang; Yang, Weitao; Aggelen, Helen van

    2014-01-01

    In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r 6 ), the THC-ppRPA algorithm scales asymptotically as only O(r 4 ), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditional ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations

  7. Quark-diquark approximation of the three-quark structure of a nucleon and the NN phase shifts

    International Nuclear Information System (INIS)

    Efimov, G.V.; Ivanov, M.A.

    1988-01-01

    The quark-diquark approximations of the three-quark structure of a nucleon are considered in the framework of the quark confinement model (QCM) based on definite concepts of the hadronization and quark confinement. The static nucleon characteristics (magnetic moments, ratio G A /G V and strong meson-nucleon coupling constants) are calculated. The behaviour of the electromagnetic and strong nucleon form factors is obtained at the low energy (0≤0 2 =-q 2 2 , where q is a transfer momentum). The one-boson exchange potential is constructed and the NN-phase-shifts are computed. Our results are compared with experiment and the Bonn potential model. 45 refs.; 7 figs.; 3 tabs

  8. Anharmonic phonons and second-order phase-transitions by the stochastic self-consistent harmonic approximation

    Science.gov (United States)

    Mauri, Francesco

    Anharmonic effects can generally be treated within perturbation theory. Such an approach breaks down when the harmonic solution is dynamically unstable or when the anharmonic corrections of the phonon energies are larger than the harmonic frequencies themselves. This situation occurs near lattice-related second-order phase-transitions such as charge-density-wave (CDW) or ferroelectric instabilities or in H-containing materials, where the large zero-point motion of the protons results in a violation of the harmonic approximation. Interestingly, even in these cases, phonons can be observed, measured, and used to model transport properties. In order to treat such cases, we developed a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity in the nonperturbative regime and to obtain, from first-principles, the structural, thermodynamic and vibrational properties of strongly anharmonic systems. I will present applications to the ferroelectric transitions in SnTe, to the CWD transitions in NbS2 and NbSe2 (in bulk and monolayer) and to the hydrogen-bond symmetrization transition in the superconducting hydrogen sulfide system, that exhibits the highest Tc reported for any superconductor so far. In all cases we are able to predict the transition temperature (pressure) and the evolution of phonons with temperature (pressure). This project has received funding from the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore1.

  9. Approximate anlysis of an unreliable $M/M/c$ retrial queue with phase merging algorithm.

    Directory of Open Access Journals (Sweden)

    faiza BELARBI

    2016-06-01

    Full Text Available In this paper, we investigate an approximate analysis of unreliable $M/M/c$ retrial queue with $c\\geq 3$ in which all servers are subject to breakdowns and repairs. Arriving customers that are unable to access a server due to congestion or failure can choose to enter a retrial orbit for an exponentially distributed amount of time and persistently attempt to gain access to a server, or abandon their request and depart the system. Once a customer is admitted to a service station, they remain there for a random duration until service is complete and then depart the system. However, if the server fails during service, i.e., an active breakdown, the customer may choose to abandon the system or proceed directly to the retrial orbit while the server begins repair immediately. In the unreliable model, there are no exact solutions when the number of servers exceeds one. Therefore, we seek to approximate the steady-state joint distribution of the number of customers in orbit and the status of the $c$ servers for the case of Markovian arrival and service times. Our approach to deriving the approximate steady-state probabilities employs a phase-merging algorithm.

  10. Beyond the Random Phase Approximation for the Electron Correlation Energy: The Importance of Single Excitations

    OpenAIRE

    Ren, Xinguo; Rinke, Patrick; Tkatchenko, Alexandre; Scheffler, Matthias

    2010-01-01

    The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice-evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals-leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior ca...

  11. The dilute random field Ising model by finite cluster approximation

    International Nuclear Information System (INIS)

    Benyoussef, A.; Saber, M.

    1987-09-01

    Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs

  12. Approximate solution of space and time fractional higher order phase field equation

    Science.gov (United States)

    Shamseldeen, S.

    2018-03-01

    This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

  13. Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random-phase approximation

    International Nuclear Information System (INIS)

    Paar, N.; Vretenar, D.; Marketin, T.; Ring, P.

    2008-01-01

    Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random-phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on 12 C, 16 O, 56 Fe, and 208 Pb, and results compared with previous studies and available data. Through the use of the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on 16 O and 208 Pb target nuclei are analyzed as functions of the temperature and chemical potential

  14. Self-consistent Random Phase Approximation applied to a schematic model of the field theory

    International Nuclear Information System (INIS)

    Bertrand, Thierry

    1998-01-01

    The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum

  15. Correlated random-phase approximation from densities and in-medium matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)

    2016-07-01

    The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.

  16. Random phase approximations for the screening function in high Tc superconductors

    International Nuclear Information System (INIS)

    Lopez-Aguilar, F.; Costa-Quintana, J.; Sanchez, A.; Puig, T.; Aurell, M.T.; Martinez, L.M.; Munoz, J.S.

    1990-01-01

    This paper reports on the electronic transferences from the CuO 2 sheets toward the CuO 3 linear chain, which locate electrons in the orbitals p y /p z of O4/O1 and d z 2 -y 2 of Cu1, and holes in the orbitals d x 2 -y 2 - P z /p y of Cu2 - P2/O3. These holes states present large interatomic overlapping. In this paper, we determine the screening function within the random phase approximation applied to the high-T c superconductors. This screening function is vanishing for determined values of the frequency which correspond to renormalized plasmon frequencies. These frequencies depends on the band parameters and their knowledge is essential for determining the self energy. This self energy is deduced and it contain independent terms for each of the channels for the localization

  17. Relativistic quasiparticle random-phase approximation calculation of total muon capture rates

    International Nuclear Information System (INIS)

    Marketin, T.; Paar, N.; Niksic, T.; Vretenar, D.

    2009-01-01

    The relativistic proton-neutron quasiparticle random phase approximation (pn-RQRPA) is applied in the calculation of total muon capture rates on a large set of nuclei from 12 C to 244 Pu, for which experimental values are available. The microscopic theoretical framework is based on the relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the pn-RQRPA. The calculation is fully consistent, i.e., the same interactions are used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the pn-RQRPA. The calculated capture rates are sensitive to the in-medium quenching of the axial-vector coupling constant. By reducing this constant from its free-nucleon value g A =1.262 by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.

  18. Monte Carlo simulation and theory in Gaussian approximation of a phase transition in the nuclear spin system of a solid

    Energy Technology Data Exchange (ETDEWEB)

    Merkulov, I A; Papava, Y I; Ponomarenko, V V [Leningradskij Gosudarstvennyj Univ., Leningrad (Russian Federation); Vasiliev, S I [Carleton Univ., Ottawa, ON (Canada). Dept. of Physics

    1988-02-01

    A phase transition of the nuclear spin system of a solid with dipolar and indirect scalar interactions is considered. Monte Carlo simulations of the spin-system isothermic states and of the adiabatic demagnetization process have been made. The structures and energies of the ground states and the values of the critical temperatures, T[sub C], and minimal polarizations, [rho][sub C], at which adiabatic demagnetization leads to spontaneous spin ordering, calculated for the GaAs and CaF[sub 2] nuclear spin systems, are presented. The results of numerical simulations are compared with the experimental data for CaF[sub 2]. The Weiss-field model is extended to the case of adiabatic demagnetization. The fluctuations of the local field are taken into account in the Gaussian approximation. It is shown that the proposed approach allows one to obtain asymptotically correct results both for T >> T[sub C] and T << T[sub C]. The results of the calculations in the Gaussian approximation are compared with the numerical simulations. (10 refs., 9 figs., tab.).

  19. Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r {sup 6}) to O(r {sup 4})

    Energy Technology Data Exchange (ETDEWEB)

    Shenvi, Neil; Yang, Yang; Yang, Weitao [Department of Chemistry, Duke University, Durham, NC 27708 (United States); Aggelen, Helen van [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)

    2014-07-14

    In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r{sup 6}), the THC-ppRPA algorithm scales asymptotically as only O(r{sup 4}), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditional ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations.

  20. Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs

    Science.gov (United States)

    RIngenburg, Michael F.

    Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in

  1. Description of excited states in the nucleus using the Quasiparticle Random-Phase Approximation and the Gogny interaction

    International Nuclear Information System (INIS)

    Lechaftois, Francois

    2016-01-01

    This thesis presents three aspects centered around the QRPA (Quasiparticle Random Phase Approximation). The first consists in the use of an axial code to confront computed data with experimental results and to feed a microscopic reaction code. This step is a chance to analyse low-energy spectroscopy (few tens of MeV) of some nuclei, and more precisely (but not exclusively) the tin isotopic chain (Z=50). The second one relies on the improvement of the formalism to calculate multipolar electromagnetic transition operators, and a method to consolidate the computation of these operators, allowing to ease the programming by unifying the code for different multipolarities. Finally, in order to overcome the axial symmetry constraint, a new triaxial code has been developed. Its assets and development are presented, followed by the first batch of results. (author) [fr

  2. The time-dependent relativistic mean-field theory and the random phase approximation

    International Nuclear Information System (INIS)

    Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang

    2001-01-01

    The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained

  3. Application of the random phase approximation to some atoms with ns2 ground state configurations

    International Nuclear Information System (INIS)

    Wright, L.A.

    1975-01-01

    Atomic bound state properties such as excitation energies and oscillator strengths were calculated by the Random Phase Approximation (RPA), also known as the Time Dependent Hartree-Fock Approximation (TDHFA). The RPA is equivalent to describing excited states as the creation of particle-hole pairs and the application to atoms is important for two reasons: the wide range of densities in an atom will cause the physical interpretation and mathematical approximations to be much different than with a uniform density system, such as an electron gas; this method could detect the existence of collective states in atoms similar to those responsible for the giant dipole resonances in nuclei. The method is shown to be superior to the H-F method in three basic ways: (1) The RPA contains explicit correlations between the excited and ground states. These are not included in the H-F theory. One can apply this method to large atoms since only these correlations are explicitly included. (2) The RPA calculates excitation energies directly without recourse to highly correlated ground state wavefunctions. This is in contrast to the method of configuration mixing which is known to have slow convergence properties. (3) Oscillator strengths and photoionization cross sections can be calculated by finding the eigenvectors corresponding excitation energy eigenvalues. The strength of the RPA is that the excitation energies and oscillator strengths, which are relative quantities, are calculated directly. The results for the oscillator strengths show an improvement of up to 45 percent over the H-F values and an improvement over the RPA done with Hartree wavefunctions by as much as 65 percent. The work was limited to atoms with an ns 2 ground state configuration. These atoms were He, Be, Mg and Ca

  4. Assessment of correlation energies based on the random-phase approximation

    International Nuclear Information System (INIS)

    Paier, Joachim; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias; Scuseria, Gustavo E; Grüneis, Andreas; Kresse, Georg

    2012-01-01

    The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought the Kohn-Sham (KS) density functional theory one step closer towards a universal, ‘general purpose first-principles method’. In an effort to systematically assess the influence of several correlation energy contributions beyond RPA, this paper presents dissociation energies of small molecules and solids, activation energies for hydrogen transfer and non-hydrogen transfer reactions, as well as reaction energies for a number of common test sets. We benchmark EX + RPA and several flavors of energy functionals going beyond it: second-order screened exchange (SOSEX), single-excitation (SE) corrections, renormalized single-excitation (rSE) corrections and their combinations. Both the SE correction and the SOSEX contribution to the correlation energy significantly improve on the notorious tendency of EX + RPA to underbind. Surprisingly, activation energies obtained using EX + RPA based on a KS reference alone are remarkably accurate. RPA + SOSEX + rSE provides an equal level of accuracy for reaction as well as activation energies and overall gives the most balanced performance, because of which it can be applied to a wide range of systems and chemical reactions. (paper)

  5. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation.

    Science.gov (United States)

    van Aggelen, Helen; Yang, Yang; Yang, Weitao

    2014-05-14

    Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H2, and eliminates delocalization errors in H2(+) and other single-bond systems. It gives surprisingly good non-bonded interaction energies--competitive with the ph-RPA--with the correct R(-6) asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.

  6. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation

    International Nuclear Information System (INIS)

    Aggelen, Helen van; Yang, Yang; Yang, Weitao

    2014-01-01

    Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H 2 , and eliminates delocalization errors in H 2 + and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R −6 asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations

  7. Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation

    CERN Document Server

    Casalbuoni, Roberto; Nardulli, Giuseppe; Ruggieri, Marco

    2003-01-01

    We study two aspects of the CFL phase of QCD in the NJL approximation. The first one is the issue of the dependence on \\mu of the ultraviolet cutoff in the gap equation, which is solved allowing a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using the high density effective theory we perform an expansion in the parameter (m_s/\\mu)^2 after checking that its numerical validity is very good already at first order.

  8. Experimental Results on the Level Crossing Intervals of the Phase of Sine Wave Plus Noise

    Science.gov (United States)

    Youssef, Neji; Munakata, Tsutomu; Mimaki, Tadashi

    1993-03-01

    Experimental study was made on the level crossing intervals of a phase process of a sine wave plus narrow-band Gaussian noise. Since successive level crossings of phase do not necessarily occur alternately in the upward and downward direction due to the phase jump beyond 2π, the usual definitions of the probability densities of the level crossing intervals for continuous random processes are not applicable in the case of the phase process. Therefore, the probability densities of level crossing intervals of phase process are newly defined. Measurements of these densities were performed for noise having lowpass spectra of Gaussian and 7th order Butterworth types. Results are given for various values of the signal-to-noise power ratio and of the crossing level, and compared with corresponding approximation developed under the assumption of quasi-independence. The validity of the assumption depends on the spectrum shape of the noise.

  9. Analytical and numerical studies of approximate phase velocity matching based nonlinear S0 mode Lamb waves for the detection of evenly distributed microstructural changes

    International Nuclear Information System (INIS)

    Wan, X; Xu, G H; Tao, T F; Zhang, Q; Tse, P W

    2016-01-01

    Most previous studies on nonlinear Lamb waves are conducted using mode pairs that satisfying strict phase velocity matching and non-zero power flux criteria. However, there are some limitations in existence. First, strict phase velocity matching is not existed in the whole frequency bandwidth; Second, excited center frequency is not always exactly equal to the true phase-velocity-matching frequency; Third, mode pairs are isolated and quite limited in number; Fourth, exciting a single desired primary mode is extremely difficult in practice and the received signal is quite difficult to process and interpret. And few attention has been paid to solving these shortcomings. In this paper, nonlinear S0 mode Lamb waves at low-frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming these limitations. In analytical studies, the secondary amplitudes with the propagation distance considering the fundamental frequency, the maximum cumulative propagation distance (MCPD) with the fundamental frequency and the maximum linear cumulative propagation distance (MLCPD) using linear regression analysis are investigated. Based on analytical results, approximate phase velocity matching is quantitatively characterized as the relative phase velocity deviation less than a threshold value of 1%. Numerical studies are also conducted using tone burst as the excitation signal. The influences of center frequency and frequency bandwidth on the secondary amplitudes and MCPD are investigated. S1–S2 mode with the fundamental frequency at 1.8 MHz, the primary S0 mode at the center frequencies of 100 and 200 kHz are used respectively to calculate the ratios of nonlinear parameter of Al 6061-T6 to Al 7075-T651. The close agreement of the computed ratios to the actual value verifies the effectiveness of nonlinear S0 mode Lamb waves satisfying approximate phase velocity matching for characterizing the material nonlinearity. Moreover, the ratios derived

  10. Rocksalt or cesium chloride: Investigating the relative stability of the cesium halide structures with random phase approximation based methods

    Science.gov (United States)

    Nepal, Niraj K.; Ruzsinszky, Adrienn; Bates, Jefferson E.

    2018-03-01

    The ground state structural and energetic properties for rocksalt and cesium chloride phases of the cesium halides were explored using the random phase approximation (RPA) and beyond-RPA methods to benchmark the nonempirical SCAN meta-GGA and its empirical dispersion corrections. The importance of nonadditivity and higher-order multipole moments of dispersion in these systems is discussed. RPA generally predicts the equilibrium volume for these halides within 2.4% of the experimental value, while beyond-RPA methods utilizing the renormalized adiabatic LDA (rALDA) exchange-correlation kernel are typically within 1.8%. The zero-point vibrational energy is small and shows that the stability of these halides is purely due to electronic correlation effects. The rAPBE kernel as a correction to RPA overestimates the equilibrium volume and could not predict the correct phase ordering in the case of cesium chloride, while the rALDA kernel consistently predicted results in agreement with the experiment for all of the halides. However, due to its reasonable accuracy with lower computational cost, SCAN+rVV10 proved to be a good alternative to the RPA-like methods for describing the properties of these ionic solids.

  11. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  12. Continuum random-phase approximation study of the incoherent μ--e- conversion rate and its spurious 1- admixture

    International Nuclear Information System (INIS)

    Papakonstantinou, P.; Wambach, J.; Kosmas, T.S.; Faessler, A.

    2006-01-01

    The incoherent transition strength of the exotic μ - -e - conversion in the 208 Pb nucleus is investigated by utilizing the continuum random-phase-approximation method, appropriate for the evaluation of the rate that goes to the continuum of the nuclear spectrum. We find that the contribution of resonances lying high in the continuum is not negligible. Special attention is paid to the detailed study of the pronounced 1 - contribution that according to previous calculations, dominates the overall incoherent rate in about all the nuclear targets. The spurious center-of-mass admixture to the partial rate originating from the 1 - excitations is explored, and its elimination is performed by correcting properly the dipole operators. The results found this way show that the greatest portion of the total 1 - contribution to the incoherent rate is spurious

  13. Finite rank separable approximation for Skyrme interactions: spin-isospin excitations

    International Nuclear Information System (INIS)

    Severyukhin, A.P.; Voronov, V.V.; Borzov, I.N.; Nguyen Van Giai

    2012-01-01

    A finite rank separable approximation for the quasiparticle random phase approximation with the Skyrme interactions is applied for the case of charge-exchange nuclear modes. The coupling between one- and two-phonon terms in the wave functions is taken into account. It has been shown that the approximation reproduces reasonably well the full charge-exchange RPA results for the spin-dipole resonances in 132 Sn. As an illustration of the method, the phonon-phonon coupling effect on the β-decay half-life of 78 Ni is considered

  14. Geometrical-optics approximation of forward scattering by coated particles.

    Science.gov (United States)

    Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

    2004-03-20

    By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

  15. Multicritical phase diagrams of the Blume-Emery-Griffiths model with repulsive biquadratic coupling including metastable phases: the pair approximation and the path probability method with pair distribution

    International Nuclear Information System (INIS)

    Keskin, Mustafa; Erdinc, Ahmet

    2004-01-01

    As a continuation of the previously published work, the pair approximation of the cluster variation method is applied to study the temperature dependences of the order parameters of the Blume-Emery-Griffiths model with repulsive biquadratic coupling on a body centered cubic lattice. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. We study the dynamics of the model by the path probability method with pair distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagram in addition to the equilibrium phase diagram and also the first-order phase transition line for the unstable branches of the quadrupole order parameter is superimposed on the phase diagrams. It is found that the metastable phase diagram and the first-order phase boundary for the unstable quadrupole order parameter always exist at the low temperatures which are consistent with experimental and theoretical works

  16. Application of the random phase approximation to complex problems in materials science

    International Nuclear Information System (INIS)

    Schimka, L.

    2012-01-01

    This thesis is devoted to the assessment and application of the random phase approximation (RPA) in the adiabatic-connection fluctuation-dissipation (ACFD) framework in solid state physics. The first part presents a review of density functional theory (DFT) and the ACFD theorem in the RPA. This includes an introduction to the many-body problem as well as a description of the implementation of the RPA in the Vienna Ab-initio Simulation Package (VASP). In the results part, the quality of the RPA is assessed and its performance compared to three (beyond) DFT functionals. The experimental values are corrected for the effect of phonon zero-point vibrational energies which were calculated at the DFT level from ab-initio. We find that the RPA describes all bonding situations very accurately, making it a promising candidate for more complex problems in solid state physics. In light of these findings, we investigate the carbon-water interaction in two specific cases: the adsorption of water on benzene and the adsorption of water on a graphene layer. We compare our results to a different correlated method: diffusion Monte Carlo (DMC). We find very good agreement and thus believe that our values can serve as a benchmark for the development of other DFT functionals to treat water-carbon interfaces. The highlight of this thesis is the successful application of the RPA to the long-standing and (at DFT level) unsolved CO adsorption puzzle. We show results for CO adsorption on Cu, late 4d metals and Pt. RPA is at present the only ab-initio method that describes adsorption and surface energies accurately at the same time and predicts the correct adsorption site in every single case. (author) [de

  17. Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube

    International Nuclear Information System (INIS)

    Nigmatulin, R.I.

    1995-01-01

    The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered

  18. Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube

    Energy Technology Data Exchange (ETDEWEB)

    Nigmatulin, R.I.

    1995-09-01

    The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered.

  19. Electric dipole strength and dipole polarizability in 48Ca within a fully self-consistent second random–phase approximation

    Directory of Open Access Journals (Sweden)

    D. Gambacurta

    2018-02-01

    Full Text Available The second random–phase–approximation model corrected by a subtraction procedure designed to cure double counting, instabilities, and ultraviolet divergences, is employed for the first time to analyze the dipole strength and polarizability in 48Ca. All the terms of the residual interaction are included, leading to a fully self-consistent scheme. Results are illustrated with two Skyrme parametrizations, SGII and SLy4. Those obtained with the SGII interaction are particularly satisfactory. In this case, the low-lying strength below the neutron threshold is well reproduced and the giant dipole resonance is described in a very satisfactory way especially in its spreading and fragmentation. Spreading and fragmentation are produced in a natural way within such a theoretical model by the coupling of 1 particle-1 hole and 2 particle-2 hole configurations. Owing to this feature, we may provide for the electric polarizability as a function of the excitation energy a curve with a similar slope around the centroid energy of the giant resonance compared to the corresponding experimental results. This represents a considerable improvement with respect to previous theoretical predictions obtained with the random–phase approximation or with several ab-initio models. In such cases, the spreading width of the excitation cannot be reproduced and the polarizability as a function of the excitation energy displays a stiff increase around the predicted centroid energy of the giant resonance.

  20. Chiral NNLOsat descriptions of nuclear multipole resonances within the random-phase approximation

    Science.gov (United States)

    Wu, Q.; Hu, B. S.; Xu, F. R.; Ma, Y. Z.; Dai, S. J.; Sun, Z. H.; Jansen, G. R.

    2018-05-01

    We study nuclear multipole resonances in the framework of the random-phase approximation by using the chiral potential NNLOsat. This potential includes two- and three-body terms that have been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main focuses have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, 4He, O 16 ,22 ,24 , and Ca,4840. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential Vlow-k, based on the N3LO two-body potential by Entem and Machleidt [Phys. Rev. C 68, 041001 (2011), 10.1103/PhysRevC.68.041001]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLOsat can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the Vlow-k potential that simultaneously describes the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich O,2422 show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that 22O and 24O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

  1. Reference Determinant Dependence of the Random Phase Approximation in 3d Transition Metal Chemistry.

    Science.gov (United States)

    Bates, J E; Mezei, P D; Csonka, G I; Sun, J; Ruzsinszky, A

    2017-01-10

    Without extensive fitting, accurate prediction of transition metal chemistry is a challenge for semilocal and hybrid density funcitonals. The Random Phase Approximation (RPA) has been shown to yield superior results to semilocal functionals for main group thermochemistry, but much less is known about its performance for transition metals. We have therefore analyzed the behavior of reaction energies, barrier heights, and ligand dissociation energies obtained with RPA and compare our results to several semilocal and hybrid functionals. Particular attention is paid to the reference determinant dependence of RPA. We find that typically the results do not vary much between semilocal or hybrid functionals as a reference, as long as the fraction of exact exchange (EXX) mixing in the hybrid functional is small. For large fractions of EXX mixing, however, the Hartree-Fock-like nature of the determinant can severely degrade the performance. Overall, RPA systematically reduces the errors of semilocal functionals and delivers excellent performance from a single reference determinant for inherently multireference reactions. The behavior of dual hybrids that combine RPA correlation with a hybrid exchange energy was also explored, but ultimately did not lead to a systematic improvement compared to traditional RPA for these systems. We rationalize this conclusion by decomposing the contributions to the reaction energies, and briefly discuss the possible implications for double-hybrid functionals based on RPA. The correlation between EXX mixing and spin-symmetry breaking is also discussed.

  2. Accurate Quasiparticle Spectra from the T-Matrix Self-Energy and the Particle-Particle Random Phase Approximation.

    Science.gov (United States)

    Zhang, Du; Su, Neil Qiang; Yang, Weitao

    2017-07-20

    The GW self-energy, especially G 0 W 0 based on the particle-hole random phase approximation (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.

  3. Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis.

    Science.gov (United States)

    Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg

    2016-12-13

    We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.

  4. β-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation

    International Nuclear Information System (INIS)

    Niksic, T.; Marketin, T.; Vretenar, D.; Paar, N.; Ring, P.

    2005-01-01

    The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of β-decay half-lives of neutron-rich nuclei in the N≅50 and N≅82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogoliubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains but overestimate the lifetimes of Ni isotopes and predict a stable 132 Sn

  5. Scattering Light by а Cylindrical Capsule with Arbitrary End Caps in the Rayleigh-Gans-Debye Approximation

    Directory of Open Access Journals (Sweden)

    K. A. Shapovalov

    2015-01-01

    Full Text Available The paper concerns the light scattering problem of biological objects of complicated structure.It considers optically “soft” (having a refractive index close to that of a surrounding medium homogeneous cylindrical capsules, composed of three parts: central one that is cylindrical and two symmetrical rounding end caps. Such capsules can model more broad class of biological objects than the ordinary shapes of a spheroid or sphere. But, unfortunately, if a particle has other than a regular geometrical shape, then it is very difficult or impossible to solve the scattering problem analytically in its most general form that oblige us to use numerical and approximate analytical methods. The one of such approximate analytical method is the Rayleigh-Gans-Debye approximation (or the first Born approximation.So, the Rayleigh-Gans-Debye approximation is valid for different objects having size from nanometer to millimeter and depending on wave length and refractive index of an object under small phase shift of central ray.The formulas for light scattering amplitude of cylindrical capsule with arbitrary end caps in the Rayleigh-Gans-Debye approximation in scalar form are obtained. Then the light scattering phase function [or element of scattering matrix f11] for natural incident light (unpolarized or arbitrary polarized light is calculated.Numerical results for light scattering phase functions of cylindrical capsule with conical, spheroidal, paraboloidal ends in the Rayleigh-Gans-Debye approximation are compared. Also numerical results for light scattering phase function of cylindrical capsule with conical ends in the Rayleigh-Gans-Debye approximation and in the method of Purcell-Pennypacker (or Discrete Dipole method are compared. The good agreement within an application range of the RayleighGans-Debye approximation is obtained.Further continuation of the work, perhaps, is a consideration of multilayer cylindrical capsule in the Rayleigh

  6. Density functional formulation of the random-phase approximation for inhomogeneous fluids: Application to the Gaussian core and Coulomb particles.

    Science.gov (United States)

    Frydel, Derek; Ma, Manman

    2016-06-01

    Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.

  7. An angularly refineable phase space finite element method with approximate sweeping procedure

    International Nuclear Information System (INIS)

    Kophazi, J.; Lathouwers, D.

    2013-01-01

    An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S n -like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S n scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S 2 sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)

  8. Relativistic Random-Phase Approximation with Density-dependent Meson-nucleon Couplings at Finite Temperature

    International Nuclear Information System (INIS)

    Niu, Y.; Paar, N.; Vretenar, D.; Meng, J.

    2009-01-01

    The fully self-consistent relativistic random-phase approximation (RRPA) framework based on effective interactions with a phenomenological density dependence is extended to finite temperatures. The RRPA configuration space is built from the spectrum of single-nucleon states at finite temperature obtained by the temperature dependent relativistic mean field (RMF-T) theory based on effective Lagrangian with density dependent meson-nucleon vertex functions. As an illustration, the dependence of binding energy, radius, entropy and single particle levels on temperature for spherical nucleus 2 08P b is investigated in RMF-T theory. The finite temperature RRPA has been employed in studies of giant monopole and dipole resonances, and the evolution of resonance properties has been studied as a function of temperature. In addition, exotic modes of excitation have been systematically explored at finite temperatures, with an emphasis on the case of pygmy dipole resonances.(author)

  9. Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

    Science.gov (United States)

    Heßelmann, Andreas

    2015-04-14

    Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

  10. A test of the adhesion approximation for gravitational clustering

    Science.gov (United States)

    Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

    1993-01-01

    We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

  11. SANS [small-angle neutron scattering] evaluation of the RPA [random phase approximation] theory for binary homopolymer mixtures

    International Nuclear Information System (INIS)

    Bates, F.S.; Koehler, W.C.; Wignall, G.D.; Fetters, L.J.

    1986-12-01

    A well characterized binary mixture of normal (protonated) and perdeuterated monodisperse 1,2 polybutenes has been studied by small-angle neutron scattering (SANS). For scattering wavevectors q greater than the inverse radius-of-gyration R/sub g/ -1 , the SANS intensity is quantitatively predicted by the random phase approximation (RPA) theory of deGennes over all measured values of the segment-segment interaction parameter Chi. In the region (Chi s-Chi)Chi s -1 > 0.5 the interaction parameter determined using the RPA theory for q > R/sub g/ -1 is greater than that calculated from the zero-angle intensity based on an Ornstein-Zernike plot, where Chi s represents the limit of single phase stability. These findings indicate a correlation between the critical fluctuation length ξ and R/sub g/ which is not accounted for by the RPA theory

  12. β-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation

    International Nuclear Information System (INIS)

    Niksic, T.; Marketin, T.; Vretenar, D.; Paar, N.; Ring, P.

    2004-01-01

    The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of β-decay half-lives of neutron-rich nuclei in the N∼50 and N∼82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogolyubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable 132 Sn. (orig.)

  13. {beta}-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation

    Energy Technology Data Exchange (ETDEWEB)

    Niksic, T.; Marketin, T.; Vretenar, D. [Zagreb Univ. (Croatia). Faculty of Science, Physics Dept.; Paar, N. [Technische Univ. Darmstadt (Germany). Inst. fuer Kernphysik; Ring, P. [Technische Univ. Muenchen, Garching (Germany). Physik-Department

    2004-12-08

    The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of {beta}-decay half-lives of neutron-rich nuclei in the N{approx}50 and N{approx}82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogolyubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable {sup 132}Sn. (orig.)

  14. Photoelectron spectroscopy and the dipole approximation

    Energy Technology Data Exchange (ETDEWEB)

    Hemmers, O.; Hansen, D.L.; Wang, H. [Univ. of Nevada, Las Vegas, NV (United States)] [and others

    1997-04-01

    Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.

  15. Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients.

    Science.gov (United States)

    Chen, Weitian; Sica, Christopher T; Meyer, Craig H

    2008-11-01

    Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

  16. Approximate Coulomb effects in the three-body scattering problem

    International Nuclear Information System (INIS)

    Haftel, M.I.; Zankel, H.

    1981-01-01

    From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles

  17. Group theoretical treatment of the low-temperature phase transition of the Cd6Ca 1/1-cubic approximant

    International Nuclear Information System (INIS)

    Tamura, R.; Shibata, K.; Nishimoto, K.; Takeuchi, S.; Edagawa, K.; Saitoh, K.; Isobe, M.; Ueda, Y.

    2005-01-01

    An antiparallel orientational transition is reported for an intermetallic compound, i.e., Cd 6 Ca crystal, which is a 1/1-1/1-1/1 crystalline approximant to the icosahedral quasicrystal Cd 5.7 Ca. A group theoretical analysis based on the Landau theory predicts that the space group of the low-temperature phase is either C2/c or C2/m, in good agreement with the observations. Accordingly, two types of orientational orderings of Cd 4 tetrahedra, which are located in the center of icosahedral clusters, may occur below 100 K: In both cases, the Cd 4 tetrahedra are orientationally ordered in an antiparallel fashion along the [110] direction of the high temperature body-centered-cubic phase. Such a transition in a metal is reminiscent of orientational transitions in molecular solids

  18. Calculations of the properties of superconducting alloys via the average T-matrix approximation

    International Nuclear Information System (INIS)

    Chatterjee, P.

    1980-01-01

    The theoretical formula of McMillan, modified via the multiple-scattering theory by Gomersall and Gyorffy, has been very successful in computing the electron-phonon coupling constant (lambda) and the transition temperature (Tsub(c)) of many superconducting elements and compounds. For disordered solids, such as substitutional alloys, however, this theory fails because of the breakdown of the translational symmetry used in the multiple-scattering theory. Under these conditions the problem can still be solved if the t-matrix is averaged in the random phase approximation (average T-matrix approximation). Gomersall and Gyorffy's expression is reformulated for lambda in the random phase approximation. This theory is applied to calculate lambda and Tsub(c) of the binary substitutional NbMo alloy system at different concentrations. The results appear to be in fair agreement with experiments. (author)

  19. Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges

    Science.gov (United States)

    Ismail-Beigi, Sohrab

    2010-05-01

    In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.

  20. Approximate analytic theory of the multijunction grill

    International Nuclear Information System (INIS)

    Hurtak, O.; Preinhaelter, J.

    1991-03-01

    An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs

  1. Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric.

    Science.gov (United States)

    Luenser, Arne; Schurkus, Henry F; Ochsenfeld, Christian

    2017-04-11

    A reformulation of the random phase approximation within the resolution-of-the-identity (RI) scheme is presented, that is competitive to canonical molecular orbital RI-RPA already for small- to medium-sized molecules. For electronically sparse systems drastic speedups due to the reduced scaling behavior compared to the molecular orbital formulation are demonstrated. Our reformulation is based on two ideas, which are independently useful: First, a Cholesky decomposition of density matrices that reduces the scaling with basis set size for a fixed-size molecule by one order, leading to massive performance improvements. Second, replacement of the overlap RI metric used in the original AO-RPA by an attenuated Coulomb metric. Accuracy is significantly improved compared to the overlap metric, while locality and sparsity of the integrals are retained, as is the effective linear scaling behavior.

  2. Plasmon response in K, Na and Li clusters: systematics using the separable random-phase approximation with pseudo-Hamiltonians

    International Nuclear Information System (INIS)

    Kleinig, W.; Nesterenko, V.O.; Reinhard, P.-G.; Serra, Ll.

    1998-01-01

    The systematics of the plasmon response in spherical K, Na and Li clusters in a wide size region (8≤N≤440) is studied. We have considered two simplifying approximations whose validity has been established previously. First, a separable approach to the random-phase approximation is used. This involves an expansion of the residual interaction into a sum of separable terms until convergence is reached. Second, the electron-ion interaction is modelled by using the pseudo-Hamiltonian jellium model (MHJM) which includes nonlocal effects by means of realistic atomic pseudo-Hamiltonians. In cases where nonlocal effects are negligible the Structure Averaged Jellium Model (SAJM) has been used. Good agreement with available experimental data is achieved for K, Na (using the SAJM) and small Li clusters (invoking the PHJM). The trends for peak position and width are generally well reproduced, even up to details of the Landau fragmentation in several clusters. Less good agreement, however, is found for large Li clusters. This remains an open question

  3. Statistics of errors in fibre communication lines with a phase-modulation format and optical phase conjugation

    International Nuclear Information System (INIS)

    Shapiro, Elena G; Fedoruk, Mikhail P

    2011-01-01

    Analytical formulas are derived to approximate the probability density functions of 'zero' and 'one' bits in a linear communication channel with a binary format of optical signal phase modulation. Direct numerical simulation of the propagation of optical pulses in a communication line with optical phase conjugation is performed. The results of the numerical simulation are in good agreement with the analytical approximation. (fibreoptic communication lines)

  4. Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

    Science.gov (United States)

    Yan, Xin-Zhong

    2011-07-01

    The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

  5. Phase integral approximation for coupled ordinary differential equations of the Schroedinger type

    International Nuclear Information System (INIS)

    Skorupski, Andrzej A.

    2008-01-01

    Four generalizations of the phase integral approximation (PIA) to sets of ordinary differential equations of Schroedinger type [u j '' (x)+Σ k=1 N R jk (x)u k (x)=0, j=1,2,...,N] are described. The recurrence relations for higher order corrections are given in a form valid to arbitrary order and for the matrix R(x)[≡(R jk (x))] either Hermitian or non-Hermitian. For Hermitian and negative definite R(x) matrices, a Wronskian conserving PIA theory is formulated, which generalizes Fulling's current conserving theory pertinent to positive definite R(x) matrices. The idea of a modification of the PIA, which is well known for one equation [u '' (x)+R(x)u(x)=0], is generalized to sets. A simplification of Wronskian or current conserving theories is proposed which in each order eliminates one integration from the formulas for higher order corrections. If the PIA is generated by a nondegenerate eigenvalue of the R(x) matrix, the eliminated integration is the only one present. In that case, the simplified theory becomes fully algorithmic and is generalized to non-Hermitian R(x) matrices. The general theory is illustrated by a few examples automatically generated by using the author's program in MATHEMATICA published in e-print arXiv:0710.5406 [math-ph

  6. Dynamical Mean Field Approximation Applied to Quantum Field Theory

    CERN Document Server

    Akerlund, Oscar; Georges, Antoine; Werner, Philipp

    2013-12-04

    We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...

  7. Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation

    International Nuclear Information System (INIS)

    Schurkus, Henry F.; Ochsenfeld, Christian

    2016-01-01

    An atomic-orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling to linear, so that large systems can be studied on simple desktop computers with fully numerically controlled accuracy. Our AO-RPA formulation introduces a contracted double-Laplace transform and employs the overlap-metric resolution-of-the-identity. First timings of our pilot code illustrate the reduced scaling with systems comprising up to 1262 atoms and 10 090 basis functions. 

  8. Low-lying dipole response in the stable 40,48Ca nuclei within the second random-phase approximation

    International Nuclear Information System (INIS)

    Gambacurta, D.; Grasso, M.; Catara, F.

    2012-01-01

    The low-lying dipole strength distributions of 40 CaCa and 48 Ca, in the energy region between 5 and 10 MeV, are studied within the second random phase approximation (RPA) with Skyrme interaction. Standard RPA models do not usually predict any presence of strength in this energy region, while experimentally a significant amount of strength is found. The inclusion of the 2 particle −2 hole configurations allows to obtain a description in a rather good agreement with the experimental data. The properties of the most collective state are analyzed in terms of its 1 particle −1 hole nature and its transition densities.

  9. Low-lying dipole response in the stable 40,48Ca nuclei within the second random-phase approximation

    Science.gov (United States)

    Gambacurta, D.; Grasso, M.; Catara, F.

    2012-10-01

    The low-lying dipole strength distributions of 40CaCa and 48Ca, in the energy region between 5 and 10 MeV, are studied within the second random phase approximation (RPA) with Skyrme interaction. Standard RPA models do not usually predict any presence of strength in this energy region, while experimentally a significant amount of strength is found. The inclusion of the 2 particle -2 hole configurations allows to obtain a description in a rather good agreement with the experimental data. The properties of the most collective state are analyzed in terms of its 1 particle -1 hole nature and its transition densities.

  10. DAMA/LIBRA-phase1 results and perspectives of the phase2

    Directory of Open Access Journals (Sweden)

    Bernabei R.

    2015-01-01

    Full Text Available The results obtained with the total exposure of 1.04 ton × yr collected by DAMA/LIBRA–phase1 deep underground at the Gran Sasso National Laboratory (LNGS of the I.N.F.N. during 7 annual cycles are summarized. The DAMA/LIBRA–phase1 and the former DAMA/NaI data (cumulative exposure 1.33 ton × yr, corresponding to 14 annual cycles give evidence at 9.3 σ C.L. for the presence of Dark Matter (DM particles in the galactic halo, on the basis of the exploited model independent DM annual modulation signature by using highly radio-pure NaI(Tl target. No systematic or side reaction able to mimic the exploited DM signature has been found or suggested by anyone over more than a decade. The same data of DAMA/LIBRA–phase1 have also been analyzed searching for possible DM second-order diurnal effect; at present, the DM diurnal modulation amplitude – expected because of the Earth diurnal motion – evaluated on the basis of the DAMA Dark Matter annual modulation results is below the reached experimental sensitivity. Some of the perspectives of the presently running DAMA/LIBRA–phase2 are outlined.

  11. Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory.

    Science.gov (United States)

    Li, Zhendong; Liu, Wenjian

    2010-08-14

    The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin

  12. Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations.

    Science.gov (United States)

    Ren, Xinguo; Tkatchenko, Alexandre; Rinke, Patrick; Scheffler, Matthias

    2011-04-15

    The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice--evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals--leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions.

  13. Phase 2 microwave concrete decontamination results

    International Nuclear Information System (INIS)

    White, T.L.; Foster, D. Jr.; Wilson, C.T.; Schaich, C.R.

    1995-01-01

    The authors report on the results of the second phase of a four-phase program at Oak Ridge National Laboratory to develop a system to decontaminate concrete using microwave energy. The microwave energy is directed at the concrete surface through the use of an optimized wave guide antenna, or applicator, and this energy rapidly heats the free water present in the interstitial spaces of the concrete matrix. The resulting steam pressure causes the surface to burst in much the same way popcorn pops in a home microwave oven. Each steam explosion removes several square centimeters of concrete surface that are collected by a highly integrated wave guide and vacuum system. The authors call this process the microwave concrete decontamination, or MCD, process. In the first phase of the program the principle of microwaves concrete removal concrete surfaces was demonstrated. In these experiments, concrete slabs were placed on a translator and moved beneath a stationary microwave system. The second phase demonstrated the ability to mobilize the technology to remove the surfaces from concrete floors. Area and volume concrete removal rates of 10.4 cm 2 /s and 4.9 cm 3 /S, respectively, at 18 GHz were demonstrated. These rates are more than double those obtained in Phase 1 of the program. Deeper contamination can be removed by using a longer residence time under the applicator to create multiple explosions in the same area or by taking multiple passes over previously removed areas. Both techniques have been successfully demonstrated. Small test sections of painted and oil-soaked concrete have also been removed in a single pass. Concrete with embedded metal anchors on the surface has also been removed, although with some increased variability of removal depth. Microwave leakage should not pose any operational hazard to personnel, since the observed leakage was much less than the regulatory standard

  14. Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

    International Nuclear Information System (INIS)

    Zhou Shiqi

    2008-01-01

    In this work, a bridge density functional approximation (BDFA) (J. Chem. Phys. 112, 8079 (2000)) for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa (HCRY) fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail. (condensed matter: structure, thermal and mechanical properties)

  15. Sparse approximation with bases

    CERN Document Server

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  16. An Origami Approximation to the Cosmic Web

    Science.gov (United States)

    Neyrinck, Mark C.

    2016-10-01

    The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

  17. Preliminary time-phased TWRS process model results

    International Nuclear Information System (INIS)

    Orme, R.M.

    1995-01-01

    This report documents the first phase of efforts to model the retrieval and processing of Hanford tank waste within the constraints of an assumed tank farm configuration. This time-phased approach simulates a first try at a retrieval sequence, the batching of waste through retrieval facilities, the batching of retrieved waste through enhanced sludge washing, the batching of liquids through pretreatment and low-level waste (LLW) vitrification, and the batching of pretreated solids through high-level waste (HLW) vitrification. The results reflect the outcome of an assumed retrieval sequence that has not been tailored with respect to accepted measures of performance. The batch data, composition variability, and final waste volume projects in this report should be regarded as tentative. Nevertheless, the results provide interesting insights into time-phased processing of the tank waste. Inspection of the composition variability, for example, suggests modifications to the retrieval sequence that will further improve the uniformity of feed to the vitrification facilities. This model will be a valuable tool for evaluating suggested retrieval sequences and establishing a time-phased processing baseline. An official recommendation on tank retrieval sequence will be made in September, 1995

  18. Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase.

    Science.gov (United States)

    Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele

    2014-11-14

    Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

  19. Relaxation and Numerical Approximation of a Two-Fluid Two-Pressure Diphasic Model

    International Nuclear Information System (INIS)

    Ambroso, A.; Chalons, Ch.; Galie, Th.; Chalons, Ch.; Coquel, F.; Coquel, F.

    2009-01-01

    This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach. (authors)

  20. High-K precession modes: Axially symmetric limit of wobbling motion in the cranked random-phase approximation description

    International Nuclear Information System (INIS)

    Shimizu, Yoshifumi R.; Matsuzaki, Masayuki; Matsuyanagi, Kenichi

    2005-01-01

    The rotational band built on the high-K multi-quasiparticle state can be interpreted as a multi-phonon band of the precession mode, which represents the precessional rotation about the axis perpendicular to the direction of the intrinsic angular momentum. By using the axially symmetric limit of the random-phase approximation (RPA) formalism developed for the nuclear wobbling motion, we study the properties of the precession modes in 178 W: the excitation energies, B(E2) and B(M1) values. We show that the excitations of such a specific type of rotation can be well described by the RPA formalism, which gives new insight into the wobbling motion in the triaxial superdeformed nuclei from a microscopic viewpoint

  1. Gaussian and 1/N approximations in semiclassical cosmology

    International Nuclear Information System (INIS)

    Mazzitelli, F.D.; Paz, J.P.

    1989-01-01

    We study the λphi 4 theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field Ω(x) = (λ 2 >)/sup 1/2/ and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation

  2. A comparative study of the second-order Born and Faddeev-Watson approximations for electron-atom collisions

    International Nuclear Information System (INIS)

    Fargher, H.E.; Roberts, M.J.

    1983-01-01

    Simplified versions of the second-order Born and Faddeev-Watson approximations are applied to the excitation of the n=2 levels of atomic hydrogen by the impact of 54.4 eV electrons. The theories are compared with the measurements of differential cross sections and angular correlation parameters. The results indicate that the Born approximation is better at low angles of scattering but that the Faddeev-Watson approximation is better at high angles. The importance of the phases of the two-body T matrices in the Faddeev-Watson approximation is illustrated. (author)

  3. S-wave pion-nucleon phase shifts in PADE approximation

    International Nuclear Information System (INIS)

    Achuthan, P.; Chandramohan, T.; Venkatesan, K.

    1978-01-01

    The two S-wave pion nucleon pahse shifts delta( 1 ) (I = 1/2) and delta( 3 ) (I = 3/2) have been calculated in the Pade approximation using epsilon(700), rho(770), f(1260), Δ(1236) and N(938) for the energy range W = 1085 MeV - 1820 MeV in the centre of mass. Contributions from suitable resonance combinations which agree nearest with the delta( 3 ) experimental values are given. (orig.) [de

  4. Low-lying dipole response in the stable {sup 40,48}Ca nuclei within the second random-phase approximation

    Energy Technology Data Exchange (ETDEWEB)

    Gambacurta, D.; Grasso, M.; Catara, F. [GANIL,CEA/DSM-CNRS/IN2P3, Caen (France); Institut de Physique Nucleaire, Universite Paris-Sud, IN2P3-CNRS, F-91406 Orsay Cedex (France); Dipartimento di Fisica e Astronomia dell' Universita di and INFN Catania (Italy)

    2012-10-20

    The low-lying dipole strength distributions of {sup 40}CaCa and {sup 48}Ca, in the energy region between 5 and 10 MeV, are studied within the second random phase approximation (RPA) with Skyrme interaction. Standard RPA models do not usually predict any presence of strength in this energy region, while experimentally a significant amount of strength is found. The inclusion of the 2 particle -2 hole configurations allows to obtain a description in a rather good agreement with the experimental data. The properties of the most collective state are analyzed in terms of its 1 particle -1 hole nature and its transition densities.

  5. Approximating tunneling rates in multi-dimensional field spaces

    Energy Technology Data Exchange (ETDEWEB)

    Masoumi, Ali; Olum, Ken D.; Wachter, Jeremy M., E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: Jeremy.Wachter@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

    2017-10-01

    Quantum mechanics makes the otherwise stable vacua of a theory metastable through the nucleation of bubbles of the new vacuum. This in turn causes a first order phase transition. These cosmological phase transitions may have played an important role in settling our universe into its current vacuum, and they may also happen in future. The most important frameworks where vacuum decay happens contain a large number of fields. Unfortunately, calculating the tunneling rates in these models is very time-consuming. In this paper we present a simple approximation for the tunneling rate by reducing it to a one-field problem which is easy to calculate. We demonstrate the validity of this approximation using our recent code 'Anybubble' for several classes of potentials.

  6. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

    Science.gov (United States)

    Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian

    2018-05-08

    An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

  7. Numerical method for two-phase flow discontinuity propagation calculation

    International Nuclear Information System (INIS)

    Toumi, I.; Raymond, P.

    1989-01-01

    In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities

  8. Gamow-Teller resonances and a separable approximation for Skyrme tensor interactions

    Directory of Open Access Journals (Sweden)

    Severyukhin A. P.

    2012-12-01

    Full Text Available A finite rank separable approximation for the quasiparticle random phase approximation (QRPA with Skyrme interactions is applied to study properties of the Gamow-Teller (GT resonances in the neutron-rich Cd isotopes. This approximation enables one to reduce considerably the dimension of matrix that must be diagonalized to perform QRPA calculations in a very large configuration space. Our results from the SGII Skyrme interaction with the tensor interactions and the density-dependent zero-range pairing interaction show that the GT distribution is noticeably modified when the tensor correlations are taken into account. In particular, for 130Cd the dominant peak is moved 3.6 MeV downward and 10% of the GT distribution is shifted to the high excitation energy region near E=50MeV.

  9. γ-decay of {}_{8}^{16}{{\\rm{O}}}_{8}\\,{and}\\,{}_{7}^{16}{{\\rm{N}}}_{9} in proton-neutron Tamm-Dancoff and random phase approximations with optimized surface δ interaction

    Science.gov (United States)

    Pahlavani, M. R.; Firoozi, B.

    2016-09-01

    γ-ray transitions from excited states of {}16{{N}} and {}16{{O}} isomers that appear in the γ spectrum of the {}616{{{C}}}10\\to {}716{{{N}}}9\\to {}816{{{O}}}8 beta decay chain are investigated. The theoretical approach used in this research starts with a mean-field potential consisting of a phenomenological Woods-Saxon potential including spin-orbit and Coulomb terms (for protons) in order to obtain single-particle energies and wave functions for nucleons in a nucleus. A schematic residual surface delta interaction is then employed on the top of the mean field and is treated within the proton-neutron Tamm-Dancoff approximation (pnTDA) and the proton-neutron random phase approximation. The goal is to use an optimized surface delta interaction interaction, as a residual interaction, to improve the results. We have used artificial intelligence algorithms to establish a good agreement between theoretical and experimental energy spectra. The final results of the ‘optimized’ calculations are reasonable via this approach.

  10. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  11. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Science.gov (United States)

    Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

  12. Dynamical spin susceptibility in the TD-LDA and QSGW approximations

    Energy Technology Data Exchange (ETDEWEB)

    Schilfgaarde, Mark Van [Arizona State Univ., Mesa, AZ (United States); Kotani, Takao [Arizona State Univ., Mesa, AZ (United States)

    2012-10-15

    Abstract. This project was aimed at building the transverse dynamical spin susceptibility with the TD-LDA and the recently-developed Quasparticle Self-Consisent Approximations, which determines an optimum quasiparticle picture in a self-consistent manner within the GW approximation. Our main results were published into two papers, (J. Phys. Cond. Matt. 20, 95214 (2008), and Phys. Rev. B83, 060404(R) (2011). In the first paper we present spin wave dispersions for MnO, NiO, and -MnAs based on quasiparticle self-consistent GW approximation (QSGW). For MnO and NiO, QSGW results are in rather good agreement with experiments, in contrast to the LDA and LDA+U descriptions. For -MnAs, we find a collinear ferromagnetic ground state in QSGW, while this phase is unstable in the LDA. In the second, we apply TD-LDA to the CaFeAs2 the first attempt the first ab initio calculation of dynamical susceptibililty in a system with complex electronic structure Magnetic excitations in the striped phase of CaFe2As2 are studied as a function of local moment amplitude. We find a new kind of excitation: sharp resonances of Stoner-like (itinerant) excitations at energies comparable to the ´eel temperature, originating largely from a narrow band of Fe d states near the Fermi level, and coexisting with more conventional (localized) spin waves. Both kinds of excitations can show multiple branches, highlighting the inadequacy of a description based on a localized spin model.

  13. Approximate representation of optimal strategies from influence diagrams

    DEFF Research Database (Denmark)

    Jensen, Finn V.

    2008-01-01

    , and where the policy functions for the decisions have so large do- mains that they cannot be represented directly in a strategy tree. The approach is to have separate ID representations for each decision variable. In each representation the actual information is fully exploited, however the representation...... of policies for future decisions are approximations. We call the approximation information abstraction. It consists in introducing a dummy structure connecting the past with the decision. We study how to specify, implement and learn information abstraction.......There are three phases in the life of a decision problem, specification, solution, and rep- resentation of solution. The specification and solution phases are off-line, while the rep- resention of solution often shall serve an on-line situation with rather tough constraints on time and space. One...

  14. Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

    Science.gov (United States)

    Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

    2018-06-01

    An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

  15. Ordered cones and approximation

    CERN Document Server

    Keimel, Klaus

    1992-01-01

    This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

  16. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N

    1991-01-01

    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  17. Integrated thermal treatment system sudy: Phase 2, Results

    Energy Technology Data Exchange (ETDEWEB)

    Feizollahi, F.; Quapp, W.J.

    1995-08-01

    This report presents the second phase of a study on thermal treatment technologies. The study consists of a systematic assessment of nineteen thermal treatment alternatives for the contact-handled mixed low-level waste (MLLW) currently stored in the US Department of Energy complex. The treatment alternatives consist of widely varying technologies for safely destroying the hazardous organic components, reducing the volume, and preparing for final disposal of the MLLW. The alternatives considered in Phase 2 were innovative thermal treatments with nine types of primary processing units. Other variations in the study examined the effect of combustion gas, air pollution control system design, and stabilization technology for the treatment residues. The Phase 1 study, the results of which have been published as an interim report, examined ten initial thermal treatment alternatives. The Phase 2 systems were evaluated in essentially the same manner as the Phase 2 systems. The assumptions and methods were the same as for the Phase 1 study. The quantities, and physical and chemical compositions, of the input waste used in he Phase 2 systems differ from those in the Phase 1 systems, which were based on a preliminary waste input database developed at the onset of the Integrated Thermal Treatment System study. The inventory database used in the Phase 2 study incorporates the latest US Department of Energy information. All systems, both primary treatment systems and subsystem inputs, have now been evaluated using the same waste input (2,927 lb/hr).

  18. Integrated thermal treatment system sudy: Phase 2, Results

    International Nuclear Information System (INIS)

    Feizollahi, F.; Quapp, W.J.

    1995-08-01

    This report presents the second phase of a study on thermal treatment technologies. The study consists of a systematic assessment of nineteen thermal treatment alternatives for the contact-handled mixed low-level waste (MLLW) currently stored in the US Department of Energy complex. The treatment alternatives consist of widely varying technologies for safely destroying the hazardous organic components, reducing the volume, and preparing for final disposal of the MLLW. The alternatives considered in Phase 2 were innovative thermal treatments with nine types of primary processing units. Other variations in the study examined the effect of combustion gas, air pollution control system design, and stabilization technology for the treatment residues. The Phase 1 study, the results of which have been published as an interim report, examined ten initial thermal treatment alternatives. The Phase 2 systems were evaluated in essentially the same manner as the Phase 2 systems. The assumptions and methods were the same as for the Phase 1 study. The quantities, and physical and chemical compositions, of the input waste used in he Phase 2 systems differ from those in the Phase 1 systems, which were based on a preliminary waste input database developed at the onset of the Integrated Thermal Treatment System study. The inventory database used in the Phase 2 study incorporates the latest US Department of Energy information. All systems, both primary treatment systems and subsystem inputs, have now been evaluated using the same waste input (2,927 lb/hr)

  19. Semiclassical initial value approximation for Green's function.

    Science.gov (United States)

    Kay, Kenneth G

    2010-06-28

    A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.

  20. Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix

    International Nuclear Information System (INIS)

    Griffin, J.J.; Dworzecka, M.

    1982-01-01

    The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases

  1. An Approximate Method for Solving Optimal Control Problems for Discrete Systems Based on Local Approximation of an Attainability Set

    Directory of Open Access Journals (Sweden)

    V. A. Baturin

    2017-03-01

    Full Text Available An optimal control problem for discrete systems is considered. A method of successive improvements along with its modernization based on the expansion of the main structures of the core algorithm about the parameter is suggested. The idea of the method is based on local approximation of attainability set, which is described by the zeros of the Bellman function in the special problem of optimal control. The essence of the problem is as follows: from the end point of the phase is required to find a path that minimizes functional deviations of the norm from the initial state. If the initial point belongs to the attainability set of the original controlled system, the value of the Bellman function equal to zero, otherwise the value of the Bellman function is greater than zero. For this special task Bellman equation is considered. The support approximation and Bellman equation are selected. The Bellman function is approximated by quadratic terms. Along the allowable trajectory, this approximation gives nothing, because Bellman function and its expansion coefficients are zero. We used a special trick: an additional variable is introduced, which characterizes the degree of deviation of the system from the initial state, thus it is obtained expanded original chain. For the new variable initial nonzero conditions is selected, thus obtained trajectory is lying outside attainability set and relevant Bellman function is greater than zero, which allows it to hold a non-trivial approximation. As a result of these procedures algorithms of successive improvements is designed. Conditions for relaxation algorithms and conditions for the necessary conditions of optimality are also obtained.

  2. Main results of the german risk study, phase B

    International Nuclear Information System (INIS)

    Heuser, F.W.

    1988-01-01

    Work on the German Risk Study is under contract of the Federal Ministry of Research and Technology. The reference plant for the analysis is the Biblis nuclear power plant, Unit B, a KWU pressurized water reactor of the 1300 MWel class. The plant is in operation since 1976. First results on Phase A of the study have been published in 1979. Investigations on Phase B have been foreseen to endeepen the analysis. The principal purpose of these investigations is to improve and to optimize the plant's safety features on a more realistic basis. Main objectives of Phase B are: - Completeness of accident event tree analysis taking into account further accident initiating events. - Identification and analyses of accident management measures which are adequate to minimize accidental risk. - improvement of the analysis on an as far as possible realistic basis, thereby taking into account recent results of safety research. The paper deals with the most important results of the plant analyses (level 1 and level 2) which have been performed within the scope of Phases B of the study

  3. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow; Solveurs de Riemann approches et schemas de decentrement de flux pour les ecoulements diphasiques

    Energy Technology Data Exchange (ETDEWEB)

    Toumi, I.; Kumbaro, A.; Paillere, H

    1999-07-01

    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  4. Approximate Model Checking of PCTL Involving Unbounded Path Properties

    Science.gov (United States)

    Basu, Samik; Ghosh, Arka P.; He, Ru

    We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the existing statistical methods either consider a restricted subset of PCTL, specifically, the subset that can only express bounded until properties; or rely on user-specified finite bound on the sample path length. We propose a new method that does not have such restrictions and can be effectively used to reason about unbounded until properties. We approximate probabilistic characteristics of an unbounded until property by that of a bounded until property for a suitably chosen value of the bound. In essence, our method is a two-phase process: (a) the first phase is concerned with identifying the bound k 0; (b) the second phase computes the probability of satisfying the k 0-bounded until property as an estimate for the probability of satisfying the corresponding unbounded until property. In both phases, it is sufficient to verify bounded until properties which can be effectively done using existing statistical techniques. We prove the correctness of our technique and present its prototype implementations. We empirically show the practical applicability of our method by considering different case studies including a simple infinite-state model, and large finite-state models such as IPv4 zeroconf protocol and dining philosopher protocol modeled as Discrete Time Markov chains.

  5. When Density Functional Approximations Meet Iron Oxides.

    Science.gov (United States)

    Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong

    2016-10-11

    Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.

  6. Universality Results for Multi-phase Hele-Shaw Flows

    Science.gov (United States)

    Daripa, Prabir

    2013-03-01

    Saffman-Taylor instability is a well known viscosity driven instability of an interface separating two immiscible fluids. We study linear stability of displacement processes in a Hele-Shaw cell involving an arbitrary number of immiscible fluid phases. This is a problem involving many interfaces. Universal stability results have been obtained for this multi-phase immiscible flow in the sense that the results hold for arbitrary number of interfaces. These stability results have been applied to design displacement processes that are considerably less unstable than the pure Saffman-Taylor case. In particular, we derive universal formula which gives specific values of the viscosities of the fluid layers corresponding to smallest unstable band. Other similar universal results will also be presented. The talk is based on the following paper. This work was supported by the Qatar National Research Fund (a member of The Qatar Foundation).

  7. Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice

    Science.gov (United States)

    Willatt, Michael J.; Ceriotti, Michele; Althorpe, Stuart C.

    2018-03-01

    Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a "planetary" model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the "planet"). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The "planetary" fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.

  8. Some remarks on off-shell scattering in the eikonal approximation and applications to semi-inclusive reactions

    International Nuclear Information System (INIS)

    Rinat, A.S.; Taragin, M.F.

    1997-01-01

    Using the Abel inversion for the eikonal phase as function of the interaction we derive simple integral relations between half and on-shell eikonal phases. A frequently used short-range approximation for the half off-shell phase and profile appears supported by the above-mentioned relation. We work out some examples and also address the half off-shell eikonal phase pertinent to a diffractive amplitude. The latter is relevant for a calculation of selected transparencies T of nuclei for a proton, knocked-out in selected semi-inclusive A(e,e'p)X reactions. Some numerical results for T are given. (orig.)

  9. Relativistic time-dependent local-density approximation theory and applications to atomic physics

    International Nuclear Information System (INIS)

    Parpia, F.Z.

    1984-01-01

    A time-dependent linear-response theory appropriate to the relativistic local-density approximation (RLDA) to quantum electrodynamics (QED) is developed. The resulting theory, the relativistic time-dependent local-density approximation (RTDLDA) is specialized to the treatment of electric excitations in closed-shell atoms. This formalism is applied to the calculation of atomic photoionization parameters in the dipole approximation. The static-field limit of the RTDLDA is applied to the calculation of dipole polarizabilities. Extensive numerical calculations of the photoionization parameters for the rare gases neon, argon, krypton, and xenon, and for mercury from the RTDLDA are presented and compared in detail with the results of other theories, in particular the relativistic random-phase approximation (RRPA), and with experimental measurements. The predictions of the RTDLDA are comparable with the RRPA calculations made to date. This is remarkable in that the RTDLDA entails appreciably less computational effort. Finally, the dipole polarizabilities predicted by the static-field RTDLDA are compared with other determinations of these quantities. In view of its simplicity, the static-field RTDLDA demonstrates itself to be one of the most powerful theories available for the calculation of dipole polarizabilities

  10. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  11. Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals

    Science.gov (United States)

    Mejia-Rodriguez, Daniel; Trickey, S. B.

    2017-11-01

    We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic-energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization, but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, Tao-Perdew-Staroverov-Scuseria, and strongly constrained and appropriately normed functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.

  12. Accuracy of the adiabatic-impulse approximation for closed and open quantum systems

    Science.gov (United States)

    Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo

    2018-03-01

    We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.

  13. Limitations of shallow nets approximation.

    Science.gov (United States)

    Lin, Shao-Bo

    2017-10-01

    In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

  14. Beam phase space and emittance

    International Nuclear Information System (INIS)

    Buon, J.

    1990-12-01

    The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation and to treat two particular examples

  15. Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

    Science.gov (United States)

    Eshuis, Henk; Yarkony, Julian; Furche, Filipp

    2010-06-01

    The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4 log N) operations and O(N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

  16. Rapid and Robust Cross-Correlation-Based Seismic Phase Identification Using an Approximate Nearest Neighbor Method

    Science.gov (United States)

    Tibi, R.; Young, C. J.; Gonzales, A.; Ballard, S.; Encarnacao, A. V.

    2016-12-01

    The matched filtering technique involving the cross-correlation of a waveform of interest with archived signals from a template library has proven to be a powerful tool for detecting events in regions with repeating seismicity. However, waveform correlation is computationally expensive, and therefore impractical for large template sets unless dedicated distributed computing hardware and software are used. In this study, we introduce an Approximate Nearest Neighbor (ANN) approach that enables the use of very large template libraries for waveform correlation without requiring a complex distributed computing system. Our method begins with a projection into a reduced dimensionality space based on correlation with a randomized subset of the full template archive. Searching for a specified number of nearest neighbors is accomplished by using randomized K-dimensional trees. We used the approach to search for matches to each of 2700 analyst-reviewed signal detections reported for May 2010 for the IMS station MKAR. The template library in this case consists of a dataset of more than 200,000 analyst-reviewed signal detections for the same station from 2002-2014 (excluding May 2010). Of these signal detections, 60% are teleseismic first P, and 15% regional phases (Pn, Pg, Sn, and Lg). The analyses performed on a standard desktop computer shows that the proposed approach performs the search of the large template libraries about 20 times faster than the standard full linear search, while achieving recall rates greater than 80%, with the recall rate increasing for higher correlation values. To decide whether to confirm a match, we use a hybrid method involving a cluster approach for queries with two or more matches, and correlation score for single matches. Of the signal detections that passed our confirmation process, 52% were teleseismic first P, and 30% were regional phases.

  17. Hopping system control with an approximated dynamics model and upper-body motion

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Hyang Jun; Oh, Jun Ho [KAIST, Daejeon (Korea, Republic of)

    2015-11-15

    A hopping system is highly non-linear due to the nature of its dynamics, which has alternating phases in a cycle, flight and stance phases and related transitions. Every control method that stabilizes the hopping system satisfies the Poincaré stability condition. At the Poincaré section, a hopping system cycle is considered as discrete sectional data set. By controlling the sectional data in a discrete control form, we can generate a stable hopping cycle. We utilize phase-mapping matrices to build a Poincaré return map by approximating the dynamics of the hopping system with SLIP model. We can generate various Poincaré stable gait patterns with the approximated discrete control form which uses upper-body motions as inputs.

  18. Aging of snubbers in nuclear service: Phase I study results and Phase II plans

    International Nuclear Information System (INIS)

    Goodman, R.L.; Bush, S.H.; Page, R.E.

    1988-01-01

    Two major research areas were investigated in the Phase I snubber aging studies. The first area involved a preliminary evaluation of the effects of various aging mechanisms on snubber operation; failure modes of mechanisms were identified and their contributions to aging degradation were assessed relative to other failure modes. The second area involved estimating the efficacy of existing tests and examinations that are intended to determine the effects of aging and degradation. Available data on snubber behavior and operating experience were reviewed, using licensee event reports and other historical data for the 10-year period from 1973 through 1983. Value-impact was considered in terms of (1) exposure of workers to radioactive environments for examination/testing and (2) the cost for expansion of the snubber testing program due to failed snubbers. Results from the Phase I studies identified the need to modify or improve examination and testing procedures to enhance snubber reliability. Based on the results of the Phase I snubber studies, the seals and fluids were identified as the two principal elements affected by aging degradation in hydraulic snubbers. Phase II work, which was initiated in FY 1987, will develop cooperative activities between PNL and operating utilities through the Snubber Utility Group (SNUG), who will work to establish a strong data and experience base for both hydraulic and mechanical snubbers based on actual operating and maintenance history at nuclear power plants. Application guidelines for snubbers will be recommended based on the study results

  19. On Born approximation in black hole scattering

    Science.gov (United States)

    Batic, D.; Kelkar, N. G.; Nowakowski, M.

    2011-12-01

    A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

  20. Hot accreting white dwarfs in the quasi-static approximation

    International Nuclear Information System (INIS)

    Iben, I. Jr.

    1982-01-01

    Properties of white dwarfs which are accreting hydrogen-rich matter at rates in the range 1.5 x 10 -9 to 2.5 x 10 -7 M/sub sun/ yr -1 are investigated in several approximations. Steady-burning models, in which matter is processed through nuclear-burning shells as rapidly as it is accreted, provide a framework for understanding the properties of models in which thermal pulses induced by hydrogen burning and helium burning are allowed to occur. In these latter models, the underlying carbon-oxygen core is chosen to be in a cycle-averaged steady state with regard to compressional heating and neutrino losses. Several of these models are evolved in the quasi-static approximation. Combining results obtained in the steady-burning approximation with those obtained in the quasi-static approximation, expressions are obtained for estimating, as functions of accretion rate and white dwarf mass, the thermal pulse recurrence period and the duration of hydrogen-burning phases. The time spent by an accreting model burning hydrogen as a large star of giant dimensions versus time spent burning hydrogen as a hot dwarf is also estimated as a function of model mass and accretion rate. Finally, suggestions for detecting observational counterparts of the theoretical models and suggestions for further theoretical investigations are offered. Subject headings: stars: accretion: stars: interiors: stars: novae: stars: symbiotic: stars: white dwarfs

  1. On the phase lag of turbulent dissipation in rotating tidal flows

    Science.gov (United States)

    Zhang, Qianjiang; Wu, Jiaxue

    2018-03-01

    Field observations of rotating tidal flows in a shallow tidally swept sea reveal that a notable phase lag of both shear production and turbulent dissipation increases with height above the seafloor. These vertical delays of turbulent quantities are approximately equivalent in magnitude to that of squared mean shear. The shear production approximately equals turbulent dissipation over the phase-lag column, and thus a main mechanism of phase lag of dissipation is mean shear, rather than vertical diffusion of turbulent kinetic energy. By relating the phase lag of dissipation to that of the mean shear, a simple formulation with constant eddy viscosity is developed to describe the phase lag in rotating tidal flows. An analytical solution indicates that the phase lag increases linearly with height subjected to a combined effect of tidal frequency, Coriolis parameter and eddy viscosity. The vertical diffusion of momentum associated with eddy viscosity produces the phase lag of squared mean shear, and resultant delay of turbulent quantities. Its magnitude is inhibited by Earth's rotation. Furthermore, a theoretical formulation of the phase lag with a parabolic eddy viscosity profile can be constructed. A first-order approximation of this formulation is still a linear function of height, and its magnitude is approximately 0.8 times that with constant viscosity. Finally, the theoretical solutions of phase lag with realistic viscosity can be satisfactorily justified by realistic phase lags of dissipation.

  2. Blind sensor calibration using approximate message passing

    International Nuclear Information System (INIS)

    Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka

    2015-01-01

    The ubiquity of approximately sparse data has led a variety of communities to take great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them to real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing us to treat large sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure. (paper)

  3. Zr-Fe-Sn Ternary System Phase Diagrams- New Experimental Results

    International Nuclear Information System (INIS)

    Nieva, N; Gomez, A; Arias, D

    2004-01-01

    New experimental results for the Zr-Fe-Sn ternary system are presented in this paper. The phases present and equilibrium relations for the 900 o C isothermal on the central zone of the Gibbs triangle are analysed. A set of ternary alloys was designed and obtained, and they were analysed by semi quantitative SEM- EDS, XRD, and metallographic samples. The resulting ternary phase diagrams are presented here (JCH)

  4. Nuclear Hartree-Fock approximation testing and other related approximations

    International Nuclear Information System (INIS)

    Cohenca, J.M.

    1970-01-01

    Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

  5. Microscopic mean field approximation and beyond with the Gogny force

    Directory of Open Access Journals (Sweden)

    Péru S.

    2014-03-01

    Full Text Available Fully consistent axially-symmetric-deformed quasiparticle random phase approximation calculations have been performed with the D1S Gogny force. A brief review on the main results obtained in this approach is presented. After a reminder on the method and on the first results concerning giant resonances in deformed Mg and Si isotopes, the multipole responses up to octupole in the deformed and heavy nucleus 238U are discussed. In order to analyse soft dipole modes in exotic nuclei, the dipole responses have been studied in Ne isotopes and in N=16 isotopes, for which results are presented. In these nuclei, the QRPA results on the low lying 2+ states are compared to the 5-Dimensional Collective Hamiltonian ones.

  6. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  7. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-01

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  8. Neutron wave reflexions in interface media with transport equation P1 approximation

    International Nuclear Information System (INIS)

    Oliveira Vellozo, S. de.

    1977-01-01

    The propagation of neutron waves in non multiplying media is investigated employing the Telegrapher's equation obtained from the P 1 approximation of the time, space and energy dependent Boltzmann equation. Solution of the problem of propagation of sinusoidally modulated source incident on one face of the medium is obtained by analysing the Fourier component of a pulsed source introduced, for the corresponding frequency. The amplitude and the phase of the flux are computed as a function of frequency in media consisting of one, two and three regions in order to study the effects of reflection at the interfaces. The results are compared with those from the Diffusion approximation obtained by neglecting the term involving the second order time derivative. (author)

  9. Approximations of Fuzzy Systems

    Directory of Open Access Journals (Sweden)

    Vinai K. Singh

    2013-03-01

    Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

  10. Lowest lying 2+ and 3- vibrational states in Pb, Sn, and Ni isotopes in relativistic quasiparticle random-phase approximation

    International Nuclear Information System (INIS)

    Ansari, A.; Ring, P.

    2006-01-01

    The excitation energies and electric multipole decay rates of the lowest lying 2 + and 3 - vibrational states in Pb, Sn, and Ni nuclei are calculated following relativistic quasiparticle random-phase approximation formalism based on the relativistic Hartree-Bogoliubov mean field. Two sets of Lagrangian parameters, NL1 and NL3, are used to investigate the effect of the nuclear force. Overall there is good agreement with the available experimental data for a wide range of mass numbers considered here, and the NL3 set seems to be a better choice. However, strictly speaking, these studies point toward the need of a new set of force parameters that could produce more realistic single-particle levels, at least in vicinity of the Fermi surface, of a wide range of nuclear masses

  11. Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning

    International Nuclear Information System (INIS)

    Serna, J I; Monz, M; Kuefer, K H; Thieke, C

    2009-01-01

    One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide on the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to ensure that all clinically meaningful plans are covered and that as many clinically irrelevant plans as possible are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that constitutes the first phase. It is possible that two plans on the Pareto surface have a small, clinically insignificant difference in one criterion and a significant difference in another criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, the so-called trade-off bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects. The proposed scheme is applied to two artificial cases and one clinical case of a paraspinal tumor. For all cases, the quality of the Pareto surface approximation is measured with respect to the number of computed plans, and the range of values occurring in the approximation for different criteria is compared. Through enforcing trade-off bounds, the scheme disregards clinically irrelevant plans during the approximation. Thereby, the number of plans necessary to achieve a good approximation quality can be significantly reduced. Thus, trade-off bounds are an effective tool to focus the planning and to reduce computation time.

  12. Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning.

    Science.gov (United States)

    Serna, J I; Monz, M; Küfer, K H; Thieke, C

    2009-10-21

    One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide on the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to ensure that all clinically meaningful plans are covered and that as many clinically irrelevant plans as possible are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that constitutes the first phase. It is possible that two plans on the Pareto surface have a small, clinically insignificant difference in one criterion and a significant difference in another criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, the so-called trade-off bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects. The proposed scheme is applied to two artificial cases and one clinical case of a paraspinal tumor. For all cases, the quality of the Pareto surface approximation is measured with respect to the number of computed plans, and the range of values occurring in the approximation for different criteria is compared. Through enforcing trade-off bounds, the scheme disregards clinically irrelevant plans during the approximation. Thereby, the number of plans necessary to achieve a good approximation quality can be significantly reduced. Thus, trade-off bounds are an effective tool to focus the planning and to reduce computation time.

  13. Characteristics and stability analyses of transient one-dimensional two-phase flow equations and their finite difference approximations

    International Nuclear Information System (INIS)

    Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W.; Hughes, E.D.

    1975-01-01

    Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)

  14. Phase retrieval for X-ray in-line phase contrast imaging

    International Nuclear Information System (INIS)

    Scattarella, F.; Bellotti, R.; Tangaro, S.; Gargano, G.; Giannini, C.

    2011-01-01

    A review article about phase retrieval problem in X-ray phase contrast imaging is presented. A simple theoretical framework of Fresnel diffraction imaging by X-rays is introduced. A review of the most important methods for phase retrieval in free-propagation-based X-ray imaging and a new method developed by our collaboration are shown. The proposed algorithm, Combined Mixed Approach (CMA) is based on a mixed transfer function and transport of intensity approach, and it requires at most an initial approximate estimate of the average phase shift introduced by the object as prior knowledge. The accuracy with which this initial estimate is known determines the convenience speed of algorithm. The new proposed algorithm is based on the retrieval of both the object phase and its complex conjugate. The results obtained by the algorithm on simulated data have shown that the obtained reconstructed phase maps are characterized by particularly low normalized mean square errors. The algorithm was also tested on noisy experimental phase contrast data, showing a good efficiency in recovering phase information and enhancing the visibility of details inside soft tissues.

  15. Particle in a standing wave field; beyond the oscillation center approximation

    International Nuclear Information System (INIS)

    Schmidt, G.

    1982-01-01

    The ponderomotive force arises in plasma physics as a weak field approximation on particle dynamics. Recent advances in stochasticity theory lead to the conclusion that for sufficiently strong fields, the ponderomotive potential well disappears, and significant portions of phase space are filled with stochastic trajectories. This is illustrated by numerically studying the phase space behavior of the oscillation center. (author)

  16. Wave vector modification of the infinite order sudden approximation

    International Nuclear Information System (INIS)

    Sachs, J.G.; Bowman, J.M.

    1980-01-01

    A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities P/sub n/1→nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when Δn=such thatub f/-n/sub i/ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison

  17. Wave vector modification of the infinite order sudden approximation

    Science.gov (United States)

    Sachs, Judith Grobe; Bowman, Joel M.

    1980-10-01

    A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities Pn1→nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when Δn=‖nf-ni‖ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.

  18. Miscellaneous results on the electroweak phase transition

    International Nuclear Information System (INIS)

    Ilgenfritz, E.M.; Schiller, A.

    1994-12-01

    We present new 4-D Monte Carlo results characterizing the strength of the finite temperature phase transition for Higgs/W mass ratios 1.0 and 0.6, obtained on isotropic lattices mainly with N s = 16, N t = 2. We discuss the distribution of a gauge invariant block spin order parameter, estimating the Higgs condensate Φ c at T c . We use the Potvin/Rebbi method in order to find the interface tension α/T c 3 . We demonstrate how the multi-histogram method (giving free energy differences) can be used to avoid the limiting procedure δ K → 0. From pure-phase histograms at K c , extrapolated with the help of this method, we estimate the latent heat Δε/T c 4 . Actual time series at lower Higgs mass require blocking in order to determine the jump of the lattice observables. (orig.)

  19. Ancilla-approximable quantum state transformations

    International Nuclear Information System (INIS)

    Blass, Andreas; Gurevich, Yuri

    2015-01-01

    We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation

  20. Ancilla-approximable quantum state transformations

    Energy Technology Data Exchange (ETDEWEB)

    Blass, Andreas [Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Gurevich, Yuri [Microsoft Research, Redmond, Washington 98052 (United States)

    2015-04-15

    We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.

  1. Intermolecular interactions in the condensed phase

    DEFF Research Database (Denmark)

    Christensen, Anders S.; Kromann, Jimmy Charnley; Jensen, Jan Halborg

    2017-01-01

    To facilitate further development of approximate quantum mechanical methods for condensed phase applications, we present a new benchmark dataset of intermolecular interaction energies in the solution phase for a set of 15 dimers, each containing one charged monomer. The reference interaction energy...... and solution phases. As most approximate QM methods are parametrized and evaluated using data measured or calculated in the gas phase, the dataset represents an important first step toward calibrating QM based methods for application in the condensed phase where polarization and exchange repulsion need...

  2. Quantum phase transition with dissipative frustration

    Science.gov (United States)

    Maile, D.; Andergassen, S.; Belzig, W.; Rastelli, G.

    2018-04-01

    We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.

  3. Phase Transition Couplings in the Higgsed Monopole Model

    CERN Document Server

    Laperashvili, L V

    1999-01-01

    Using a one-loop approximation for the effective potential in the Higgs model of electrodynamics for a charged scalar field, we argue for the existence of a triple point for the renormalized (running) values of the selfinteraction beta-function as a typical quantity we estimate that the one-loop approximation is valid with accuracy of deviations not more than 30% in the region of the parameters: $0.2 \\stackrel{<}{\\sim}{\\large \\alpha, \\tilde{\\alpha}} corresponds to the above-mentioned region of $\\alpha, \\tilde \\alpha$. Under the point of view that the Higgs particle is a monopole with a magnetic charge g, the obtained electric fine structure constant turns out to be to the $\\alpha_{crit}^{lat}\\approx{0.20}$ which in a U(1) lattice gauge theory corresponds to the phase transition between the "Coulomb" and confinement phases. Such a result is very encouraging for the idea of an approximate "universality" (regularization independence) of gauge couplings at the phase transition point. This idea was suggested by...

  4. Evaluation of Gaussian approximations for data assimilation in reservoir models

    KAUST Repository

    Iglesias, Marco A.

    2013-07-14

    implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil-water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification. © 2013 Springer Science+Business Media Dordrecht.

  5. Phase transitions in local equation-of-state approximation and anomalies of spatial charge profiles in non-uniform plasma

    Science.gov (United States)

    Chigvintsev, A. Yu; Zorina, I. G.; Noginova, L. Yu; Iosilevskiy, I. L.

    2018-01-01

    Impressive appearance of discontinuities in equilibrium spatial charge profiles in non-uniform Coulomb systems is under discussions in wide number of thermoelectrostatics problems. Such discontinuities are considered as peculiar micro-level manifestation of phase transitions and intrinsic macro-level non-ideality effects in local equation of state (EOS), which should be used for description of non-ideal ionic subsystem in frames of local-density (or “pseudofluid”, or “jellium” etc) approximation. Such discontinuities were discussed already by the authors for electronic subsystems. Special emphasis is made in present paper on the mentioned above non-ideality effects in non-uniform ionic subsystems, such as micro-ions profile within screening “cloud” around macro-ion in complex (dusty, colloid etc) plasmas, equilibrium charge profile in ionic traps or (and) in the neighborhood vicinity of “charged wall” etc). Multiphase EOS for simplified ionic model of classical charged hard spheres on uniformly compressible electrostatic compensating background was constructed and several illustrative examples of discussed discontinuous ionic profiles were calculated.

  6. Assessing the performance of the random phase approximation for exchange and superexchange coupling constants in magnetic crystalline solids

    DEFF Research Database (Denmark)

    Olsen, Thomas

    2017-01-01

    The random phase approximation (RPA) for total energies has previously been shown to provide a qualitatively correct description of static correlation in molecular systems, where density functional theory (DFT) with local functionals are bound to fail. This immediately poses the question of whether...... the RPA is also able to capture the correct physics of strongly correlated solids such asMott insulators. Due to strong electron localization, magnetic interactions in such systems are dominated by superexchange, which in the simplest picture can be regarded as the analog of static correlation...... for molecules. In this paper, we investigate the performance of the RPA for evaluating both superexchange and direct exchange interactions in the magnetic solids NiO, MnO, Na3Cu2SbO6, Sr2CuO3, Sr2CuTeO6, and a monolayer of CrI3, which were chosen to represent a broad variety of magnetic interactions...

  7. Scattering in particle-hole space: simple approximations to nuclear RPA calculations in the continuum

    International Nuclear Information System (INIS)

    Toledo Piza, A.F.R. de.

    1987-01-01

    The Random Phase Approximation (RPA) treatment of nuclear small amplitude vibrations including particle-hole continua is handled in terms of previously developed techniques to treat single-particle resonances in a reaction theoretical framework. A hierarchy of interpretable approximations is derived and a simple working approximation is proposed which involves a numerical effort no larger than that involved in standard, discrete RPA calculations. (Author) [pt

  8. Two correlated quasiparticles states in the principal series approximation

    International Nuclear Information System (INIS)

    Dukelsky, J.; Dussel, G.G.; Sofia, H.M.

    1983-01-01

    The principal series approximation is extended to the description of two correlated quasiparticles states, enabling a treatment of these states that takes into account the coupling among the two particle Green's function and the particle-hole one. This description is related to a random phase approximation treatment of collective states in open shell nuclei that includes simultaneously the particle-particle and particle-hole versions of the nuclear residual Hamiltonian. Using separable interactions it is found that the inclusion of the particle-particle part of the Hamiltonians greatly changes the properties of the 2 + states in the Sn isotopes

  9. Approximation and hardness results for the maximum edge q-coloring problem

    DEFF Research Database (Denmark)

    Adamaszek, Anna Maria; Popa, Alexandru

    2016-01-01

    We consider the problem of coloring edges of a graph subject to the following constraints: for every vertex v, all the edges incident with v have to be colored with at most q colors. The goal is to find a coloring satisfying the above constraints and using the maximum number of colors. Notice...... ϵ>0 and any q≥2 assuming the unique games conjecture (UGC), or 1+−ϵ for any ϵ>0 and any q≥3 (≈1.19 for q=2) assuming P≠NP. These results hold even when the considered graphs are bipartite. On the algorithmic side, we restrict to the case q=2, since this is the most important in practice and we show...... a 5/3-approximation algorithm for graphs which have a perfect matching....

  10. The geometric phase in quantum physics

    International Nuclear Information System (INIS)

    Bohm, A.

    1993-03-01

    After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase

  11. Theoretical study of titanium phases; Etude theorique des phases du titane

    Energy Technology Data Exchange (ETDEWEB)

    Trinite, V

    2006-10-15

    The aim of this work is to obtain a good understanding of the phase diagram of titanium within density functional theory. This diagram is composed of the alpha phase, the high pressure omega phase and the high temperature beta phase. This requires the differences in total energy to be predicted with a great precision, because these differences are around 50 meV. I find the omega phase to be the most stable one by ab initio calculation at zero temperature and pressure, in contradiction to the experimental results. I find this inversion of the stability also appears in titanium dioxide and zirconium. I have analyzed all the approximations brought into play in the ab initio approach. I have estimated the zero point energy and studied the impact of including the semi-core states as well as the effect of the exchange-correlation functionals. The conclusion is that the usual approximations for the exchange-correlation generate the biggest part of the error. A possible correction is to take into account the electronic self-interaction. I have apply this correction to the semi-core states and find a systematic improvement of the cell parameters, but no improvement on the phase stability. So I can conclude that a better description of the exchange interaction on the localized 3d states is needed. Although the standard functionals of exchange-correlation are not accurate enough to predict the phase diagrams of titanium, they perform well in describing physical properties less demanding in terms of precision, like elastic constants. However, I find important that the predicted equilibrium volume must be precise, as these properties are found strongly dependent on the volume. (author)

  12. Quantum mean-field approximations for nuclear bound states and tunneling

    International Nuclear Information System (INIS)

    Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge

    1979-01-01

    A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems

  13. Approximation for limit cycles and their isochrons.

    Science.gov (United States)

    Demongeot, Jacques; Françoise, Jean-Pierre

    2006-12-01

    Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).

  14. KAERI results for BN600 full MOX benchmark (Phase 4)

    International Nuclear Information System (INIS)

    Lee, Kibog Lee

    2003-01-01

    The purpose of this document is to report the results of KAERI's calculation for the Phase-4 of BN-600 full MOX fueled core benchmark analyses according to the RCM report of IAEA CRP Action on U pdated Codes and Methods to Reduce the Calculational Uncertainties of the LMFR Reactivity Effects. T he BN-600 full MOX core model is based on the specification in the document, F ull MOX Model (Phase4. doc ) . This document addresses the calculational methods employed in the benchmark analyses and benchmark results carried out by KAERI

  15. Approximate entropy—a new statistic to quantify arc and welding process stability in short-circuiting gas metal arc welding

    International Nuclear Information System (INIS)

    Cao Biao; Xiang Yuanpeng; Lü Xiaoqing; Zeng Min; Huang Shisheng

    2008-01-01

    Based on the phase state reconstruction of welding current in short-circuiting gas metal arc welding using carbon dioxide as shielding gas, the approximate entropy of welding current as well as its standard deviation has been calculated and analysed to investigate their relation with the stability of electric arc and welding process. The extensive experimental and calculated results show that the approximate entropy of welding current is significantly and positively correlated with arc and welding process stability, whereas its standard deviation is correlated with them negatively. A larger approximate entropy and a smaller standard deviation imply a more stable arc and welding process, and vice versa. As a result, the approximate entropy of welding current promises well in assessing and quantifying the stability of electric arc and welding process in short-circuiting gas metal arc welding

  16. Results of FY 2002 of feasibility study on commercialized fast reactor cycle systems. Phase 2

    International Nuclear Information System (INIS)

    2003-06-01

    Japan Nuclear Cycle Development Institute (JNC) and Japan Atomic Power Company (JAPC, that is the representative of the electric utilities in Japan) established a new organization to develop a commercialized fast reactor (FR) cycle system on July 1, 1999 and feasibility study (F/S) was undertaken in order to determine the promising concepts and to define the necessary R and D tasks. During Phase 1 (JFY 1999 and 2000), a number of candidate concepts were screened from various options, featuring innovative technologies. In the F/S, the options were evaluated and conceptual designs were examined considering the attainable perspectives for following: 1) ensuring safety, 2) economic competitiveness to future LWRs, 3) efficient utilization of resources, 4) reduction of environmental burden and 5) enhancement of nuclear non-proliferation. The F/S should also guide the necessary R and D to commercialize FR cycle system. To begin with the study of feasible candidate concepts screened in Phase I, Phase 2 started in the plan for five years in 2001. This aims at clarifying several feasible candidate concepts and deciding the research plan after Phase 3 as taking into consideration the innovative technology. As for this plan, an interim report will be carried out in 2003 as one pause and the prospect to clarify the feasible candidates will be expected. Furthermore, after the completion of this research and investigation program, research and development activities will be carried out under a rolling plan in which reviews will be carried out approximately every five years. The objective of these R and D activities is to make a proposal regarding highly attractive and competitive FR cycle system technology that assures safety by 2015. This report summarizes the results of F/S of Phase 2 in 2002. In 2002, the second year of Phase 2, the study was advanced along with the plan which was evaluated by the committee for the Evaluation. Then, in the study of FR system and fuel cycle

  17. Signals of a phase transition in nuclear multifragmentation: molecular-dynamics approximation

    International Nuclear Information System (INIS)

    Kiselev, S.M.

    1989-01-01

    The signals of a liquid-gas-like phase transition proposed recently by X.Campi are analyzed for the reactions Ca+Ca at E/A=400, 800MeV, Nb+Nb at E/A=150, 400,650,800MeV, La+La at E/A=800 MeV and Ne+U at E/A=400 MeV simulated on the basis of the molecular-dynamical model. For the symmetrical systems at E/A≥400 MeV the manifestations of a phase transition are conditioned by the peripheral collisions whereas for the reactions Nb+Nb at E/A=150 MeV and Ne+U at E/A=400 MeV the quasicentral events are a main source of the signals. The manifestations depend weakly on the projectile energy and become more pronounced for a more heavy nuclear system. 15 refs.; 3 figs

  18. Dataset concerning the analytical approximation of the Ae3 temperature

    Directory of Open Access Journals (Sweden)

    B.L. Ennis

    2017-02-01

    The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of the approximation method used to derive and validate the coefficients has also been included. For discussion and application of this model, please refer to the full length article entitled “The role of aluminium in chemical and phase segregation in a TRIP-assisted dual phase steel” 10.1016/j.actamat.2016.05.046 (Ennis et al., 2016 [1].

  19. Approximation for the adjoint neutron spectrum

    International Nuclear Information System (INIS)

    Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

    2002-01-01

    The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)

  20. Approximated treatment of the Pauli principle effects in elastic collisons

    International Nuclear Information System (INIS)

    Schechter, H.

    1984-08-01

    Exact microscopic methods like the RGM (Resonanting Group Method) and the GCM (Generator Coordinate Method) and approximate methods like the OCM (Orthogonality Condition Model) are used to study the effects of Pauli Principle in α- 16 O elastic scattering. Using V2 and BL nucleon-nucleon interactions, nucleus-nucleus effective potentials are obtained from RGM 'exact' wave functions and also from an approximate method developed previoulsy. Using these potentials in the OCM Saito Equation phase-shifts are calculated for partial waves Λ = 0, 1, ... 11, in the energy range 0 [pt

  1. Gaussian-approximation formalism for evaluating decay of NMR spin echoes

    International Nuclear Information System (INIS)

    Recchia, C.H.; Gorny, K.; Pennington, C.H.

    1996-01-01

    We present a formalism for evaluating the amplitude of the NMR spin echo and stimulated echo as a function of pulse spacings, for situations in which the nuclear spins experience an effective longitudinal magnetic field h z (t) resulting from an arbitrary number of independent sources, each characterized by its own arbitrary time correlation function. The distribution of accumulated phase angles for the ensemble of nuclear spins at the time of the echo is approximated as a Gaussian. The development of the formalism is motivated by the need to understand the transverse relaxation of 89 Y in YBa 2 Cu 3 O 7 , in which the 89 Y experiences 63,65 Cu dipolar fields which fluctuate due to 63,65 Cu T 1 processes. The formalism is applied successfully to this example, and to the case of nuclei diffusing in a spatially varying magnetic field. Then we examine a situation in which the approximation fails emdash the classic problem of chemical exchange in dimethylformamide, where the methyl protons experience a chemical shift which fluctuates between two discrete values. In this case the Gaussian approximation yields a monotonic decay of the echo amplitude with increasing pulse spacing, while the exact solution yields distinct open-quote open-quote beats close-quote close-quote in the echo height, which we confirm experimentally. In light of this final example the limits of validity of the approximation are discussed. copyright 1996 The American Physical Society

  2. Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

    Science.gov (United States)

    Bardhan, Jaydeep P; Knepley, Matthew G

    2011-09-28

    We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

  3. Local density approximations for relativistic exchange energies

    International Nuclear Information System (INIS)

    MacDonald, A.H.

    1986-01-01

    The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

  4. First results of GERDA Phase II and consistency with background models

    Science.gov (United States)

    Agostini, M.; Allardt, M.; Bakalyarov, A. M.; Balata, M.; Barabanov, I.; Baudis, L.; Bauer, C.; Bellotti, E.; Belogurov, S.; Belyaev, S. T.; Benato, G.; Bettini, A.; Bezrukov, L.; Bode1, T.; Borowicz, D.; Brudanin, V.; Brugnera, R.; Caldwell, A.; Cattadori, C.; Chernogorov, A.; D'Andrea, V.; Demidova, E. V.; Di Marco, N.; Domula, A.; Doroshkevich, E.; Egorov, V.; Falkenstein, R.; Frodyma, N.; Gangapshev, A.; Garfagnini, A.; Gooch, C.; Grabmayr, P.; Gurentsov, V.; Gusev, K.; Hakenmüller, J.; Hegai, A.; Heisel, M.; Hemmer, S.; Hofmann, W.; Hult, M.; Inzhechik, L. V.; Janicskó Csáthy, J.; Jochum, J.; Junker, M.; Kazalov, V.; Kihm, T.; Kirpichnikov, I. V.; Kirsch, A.; Kish, A.; Klimenko, A.; Kneißl, R.; Knöpfle, K. T.; Kochetov, O.; Kornoukhov, V. N.; Kuzminov, V. V.; Laubenstein, M.; Lazzaro, A.; Lebedev, V. I.; Lehnert, B.; Liao, H. Y.; Lindner, M.; Lippi, I.; Lubashevskiy, A.; Lubsandorzhiev, B.; Lutter, G.; Macolino, C.; Majorovits, B.; Maneschg, W.; Medinaceli, E.; Miloradovic, M.; Mingazheva, R.; Misiaszek, M.; Moseev, P.; Nemchenok, I.; Palioselitis, D.; Panas, K.; Pandola, L.; Pelczar, K.; Pullia, A.; Riboldi, S.; Rumyantseva, N.; Sada, C.; Salamida, F.; Salathe, M.; Schmitt, C.; Schneider, B.; Schönert, S.; Schreiner, J.; Schulz, O.; Schütz, A.-K.; Schwingenheuer, B.; Selivanenko, O.; Shevzik, E.; Shirchenko, M.; Simgen, H.; Smolnikov, A.; Stanco, L.; Vanhoefer, L.; Vasenko, A. A.; Veresnikova, A.; von Sturm, K.; Wagner, V.; Wegmann, A.; Wester, T.; Wiesinger, C.; Wojcik, M.; Yanovich, E.; Zhitnikov, I.; Zhukov, S. V.; Zinatulina, D.; Zuber, K.; Zuzel, G.

    2017-01-01

    The GERDA (GERmanium Detector Array) is an experiment for the search of neutrinoless double beta decay (0νββ) in 76Ge, located at Laboratori Nazionali del Gran Sasso of INFN (Italy). GERDA operates bare high purity germanium detectors submersed in liquid Argon (LAr). Phase II of data-taking started in Dec 2015 and is currently ongoing. In Phase II 35 kg of germanium detectors enriched in 76Ge including thirty newly produced Broad Energy Germanium (BEGe) detectors is operating to reach an exposure of 100 kg·yr within about 3 years data taking. The design goal of Phase II is to reduce the background by one order of magnitude to get the sensitivity for T1/20ν = O≤ft( {{{10}26}} \\right){{ yr}}. To achieve the necessary background reduction, the setup was complemented with LAr veto. Analysis of the background spectrum of Phase II demonstrates consistency with the background models. Furthermore 226Ra and 232Th contamination levels consistent with screening results. In the first Phase II data release we found no hint for a 0νββ decay signal and place a limit of this process T1/20ν > 5.3 \\cdot {1025} yr (90% C.L., sensitivity 4.0·1025 yr). First results of GERDA Phase II will be presented.

  5. Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions

    Science.gov (United States)

    Garza, Alejandro J.; Bulik, Ireneusz W.; Alencar, Ana G. Sousa; Sun, Jianwei; Perdew, John P.; Scuseria, Gustavo E.

    2016-04-01

    Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add - without introducing double counting, self-interaction, or increase in cost - the missing correlation to these methods via meta-GGA (generalised gradient approximation) density functionals (Tao-Perdew-Staroverov-Scuseria and strongly constrained and appropriately normed). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with density functional theory and the direct random phase approximation, respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.

  6.  Higher Order Improvements for Approximate Estimators

    DEFF Research Database (Denmark)

    Kristensen, Dennis; Salanié, Bernard

    Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...

  7. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey; Alkhalifah, Tariq Ali

    2013-01-01

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  8. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey

    2013-11-21

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  9. The Phase Envelope of Multicomponent Mixtures in the Presence of a Capillary Pressure Difference

    DEFF Research Database (Denmark)

    Sandoval Lemus, Diego Rolando; Yan, Wei; Michelsen, Michael Locht

    2016-01-01

    for test mixtures with wide ranges of compositions at different capillary radii and vapor fractions. The calculation results show that the phase envelope changes everywhere except at the critical point. The bubble point and the lower branch of the dew point show a decrease in the saturation pressure......, whereas the upper branch of the dew point shows an increase. The cricondentherm is shifted to a higher temperature. We also presented a mathematical analysis of the phase envelope shift due to capillary pressure based on linear approximations. The resulting linear approximation equations can predict...... the magnitude of shift, and the approximation is close for the change in the bubble point pressure....

  10. Magnetocaloric effect (MCE): Microscopic approach within Tyablikov approximation for anisotropic ferromagnets

    Energy Technology Data Exchange (ETDEWEB)

    Kotelnikova, O.A.; Prudnikov, V.N. [Physical Faculty, Lomonosov State University, Department of Magnetism, Moscow (Russian Federation); Rudoy, Yu.G., E-mail: rudikar@mail.ru [People' s Friendship University of Russia, Department of Theoretical Physics, Moscow (Russian Federation)

    2015-06-01

    The aim of this paper is to generalize the microscopic approach to the description of the magnetocaloric effect (MCE) started by Kokorina and Medvedev (E.E. Kokorina, M.V. Medvedev, Physica B 416 (2013) 29.) by applying it to the anisotropic ferromagnet of the “easy axis” type in two settings—with external magnetic field parallel and perpendicular to the axis of easy magnetization. In the last case there appears the field induced (or spin-reorientation) phase transition which occurs at the critical value of the external magnetic field. This value is proportional to the exchange anisotropy constant at low temperatures, but with the rise of temperature it may be renormalized (as a rule, proportional to the magnetization). We use the explicit form of the Hamiltonian of the anisotropic ferromagnet and apply widely used random phase approximation (RPA) (known also as Tyablikov approximation in the Green function method) which is more accurate than the well known molecular field approximation (MFA). It is shown that in the first case the magnitude of MCE is raised whereas in the second one the MCE disappears due to compensation of the critical field renormalized with the magnetization.

  11. Approximate circuits for increased reliability

    Science.gov (United States)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  12. The phase diagram of scalar field theory on the fuzzy disc

    Energy Technology Data Exchange (ETDEWEB)

    Rea, Simone; Sämann, Christian [Maxwell Institute for Mathematical Sciences, Department of Mathematics,Heriot-Watt University,Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom)

    2015-11-17

    Using a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second and third order phase transitions between them. In particular, we find that the second order phase transition happens approximately at a fixed ratio of the two coupling constants defining the potential. We compute this ratio analytically in the limit of large coupling constants. Our results qualitatively agree with previously obtained numerical results.

  13. The Wigner transform and the semi-classical approximations

    International Nuclear Information System (INIS)

    Shlomo, S.

    1985-01-01

    The Wigner transform provides a reformulation of quantum mechanics in terms of classical concepts. Some properties of the Wigner transform of the density matrix which justify its interpretation as the quantum-mechanical analog of the classical phase-space distribution function are presented. Considering some applications, it is demonstrated that the Wigner distribution function serves as a good starting point for semi-classical approximations to properties of the (nuclear) many-body system

  14. A cluster approximation for the transfer-matrix method

    International Nuclear Information System (INIS)

    Surda, A.

    1990-08-01

    A cluster approximation for the transfer-method is formulated. The calculation of the partition function of lattice models is transformed to a nonlinear mapping problem. The method yields the free energy, correlation functions and the phase diagrams for a large class of lattice models. The high accuracy of the method is exemplified by the calculation of the critical temperature of the Ising model. (author). 14 refs, 2 figs, 1 tab

  15. Phase transitions in de Sitter space

    Directory of Open Access Journals (Sweden)

    Alexander Vilenkin

    1983-10-01

    Full Text Available An effective potential in de Sitter space is calculated for a model of two interacting scalar fields in one-loop approximation and in a self-consistent approximation which takes into account an infinite set of diagrams. Various approaches to renormalization in de Sitter space are discussed. The results are applied to analyze the phase transition in the Hawking-Moss version of the inflationary universe scenario. Requiring that inflation is sufficiently large, we derive constraints on the parameters of the model.

  16. Recognition of computerized facial approximations by familiar assessors.

    Science.gov (United States)

    Richard, Adam H; Monson, Keith L

    2017-11-01

    Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in

  17. Beam phase space and emittance

    International Nuclear Information System (INIS)

    Buon, J.

    1992-02-01

    The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation, with three particular examples, and to introduce a beam envelope-ellipse and the β-function, emphasing the statistical features of its properties. (author) 14 refs.; 11 figs

  18. Approximation of the semi-infinite interval

    Directory of Open Access Journals (Sweden)

    A. McD. Mercer

    1980-01-01

    Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

  19. Exact and approximate multiple diffraction calculations

    International Nuclear Information System (INIS)

    Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

    1976-08-01

    A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

  20. Improved Dutch Roll Approximation for Hypersonic Vehicle

    Directory of Open Access Journals (Sweden)

    Liang-Liang Yin

    2014-06-01

    Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.

  1. Can biological homochirality result from a phase transition?

    Science.gov (United States)

    Figureau, A; Duval, E; Boukenter, A

    1995-06-01

    The problem of chiral purity in living organisms is still one of the prominent difficulties in the study of the origins of life. In particular the parity non-conservation known to occur in weak interactions could not be related to this lack of symmetry: these physical forces, though universal, are very weak and up to now no amplification process had been proposed. In 1991, A. Salam remarked that, due to the attractive character of the parity violating force in electro-weak interactions, a phase transition at low temperature should exist, leading eventually to enantiomeric purity. We undertook then a series of experimental tests, looking for a sizeable change in the optical activity of cystine molecules. We found no evidence for the phase transition down to 0.01 K. The interpretation of these negative results will be discussed, and future experiments proposed.

  2. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-01-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  3. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-09-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  4. Phase contrast STEM for thin samples: Integrated differential phase contrast.

    Science.gov (United States)

    Lazić, Ivan; Bosch, Eric G T; Lazar, Sorin

    2016-01-01

    It has been known since the 1970s that the movement of the center of mass (COM) of a convergent beam electron diffraction (CBED) pattern is linearly related to the (projected) electrical field in the sample. We re-derive a contrast transfer function (CTF) for a scanning transmission electron microscopy (STEM) imaging technique based on this movement from the point of view of image formation and continue by performing a two-dimensional integration on the two images based on the two components of the COM movement. The resulting integrated COM (iCOM) STEM technique yields a scalar image that is linear in the phase shift caused by the sample and therefore also in the local (projected) electrostatic potential field of a thin sample. We confirm that the differential phase contrast (DPC) STEM technique using a segmented detector with 4 quadrants (4Q) yields a good approximation for the COM movement. Performing a two-dimensional integration, just as for the COM, we obtain an integrated DPC (iDPC) image which is approximately linear in the phase of the sample. Beside deriving the CTFs of iCOM and iDPC, we clearly point out the objects of the two corresponding imaging techniques, and highlight the differences to objects corresponding to COM-, DPC-, and (HA) ADF-STEM. The theory is validated with simulations and we present first experimental results of the iDPC-STEM technique showing its capability for imaging both light and heavy elements with atomic resolution and a good signal to noise ratio (SNR). Copyright © 2015 Elsevier B.V. All rights reserved.

  5. Approximating The DCM

    DEFF Research Database (Denmark)

    Madsen, Rasmus Elsborg

    2005-01-01

    The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...

  6. Depressurisation studies. Phase 2: results of Tests 127 and 128

    International Nuclear Information System (INIS)

    Edwards, A.R.; Borgartz, B.O.; Goodman, R.M.E.; O'Brien, T.P.; Rawlingson, M.

    1978-06-01

    A basic experimental programme involving the sudden depressurisation of a simple pipe system containing water at 3.45 to 17.24MPa pressure and temperature in the range of 200 to 250 0 C has been concluded. Measurements were made of the transient density, pressure, and temperature variations in a two phase fluid in the system during discharge. Phase 1 tests investigated blowdown from straight pipes 4m long with constant internal diameters of 73 and 32 mm. Phase 2 tests incorporated a reservoir added to the 32mm pipe. In this, the second of three reports on Phase 2 tests, the test assembly, instrumentation and experimental procedure are briefly described. The conditions and results are reported for two of the tests in which the liquid in the long discharge pipe was initially subcooled by 10 0 C and 15 0 C while the reservoir was at saturation conditions with a steam dome present. (UK)

  7. On the phase structure of lattice SU(2) Gauge-Higgs theory

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Mitryushkin, V.K.; Zadorozhnyj, A.M.; Ilchev, A.S.

    1985-01-01

    The results on the phase structure of SU(2) gauge theory coupled with radially active Higgs fields are iscussed. It is shown that obtained results are not in contradiction with the known ones. The first order phase transitions observed are confirmed by the Monte Carlo calcUlations and by the analysis of an approximate effective potential

  8. Comparison of the Born series and rational approximants in potential scattering. [Pade approximants, Yikawa and exponential potential

    Energy Technology Data Exchange (ETDEWEB)

    Garibotti, C R; Grinstein, F F [Rosario Univ. Nacional (Argentina). Facultad de Ciencias Exactas e Ingenieria

    1976-05-08

    It is discussed the real utility of Born series for the calculation of atomic collision processes in the Born approximation. It is suggested to make use of Pade approximants and it is shown that this approach provides very fast convergent sequences over all the energy range studied. Yukawa and exponential potential are explicitly considered and the results are compared with high-order Born approximation.

  9. EXPERIMENTAL RESULTS OF THE NEPHELINE PHASE III STUDY

    Energy Technology Data Exchange (ETDEWEB)

    Fox, K.; Edwards, T.

    2009-11-09

    This study is the third phase in a series of experiments designed to reduce conservatism in the model that predicts the formation of nepheline, a crystalline phase that can reduce the durability of high level waste glass. A Phase I study developed a series of glass compositions that were very durable while their nepheline discriminator values were well below the current nepheline discriminator limit of 0.62, where nepheline is predicted to crystallize upon slow cooling. A Phase II study selected glass compositions to identify any linear effects of composition on nepheline crystallization and that were restricted to regions that fell within the validation ranges of the Defense Waste Processing Facility (DWPF) Product Composition Control System (PCCS) models. However, it was not possible to identify any linear effects of composition on chemical durability performance for this set of study glasses. The results of the Phase II study alone were not sufficient to recommend modification of the current nepheline discriminator. It was recommended that the next series of experiments continue to focus not only on compositional regions where the PCCS models are considered applicable (i.e., the model validation ranges), but also be restricted to compositional regions where the only constraint limiting processing is the current nepheline discriminator. Two methods were used in selecting glasses for this Phase III nepheline study. The first was based on the relationship of the current nepheline discriminator model to the other DWPF PCCS models, and the second was based on theory of crystallization in mineral and glass melts. A series of 29 test glass compositions was selected for this study using a combination of the two approaches. The glasses were fabricated and characterized in the laboratory. After reviewing the data, the study glasses generally met the target compositions with little issue. Product Consistency Test results correlated well with the crystallization analyses in

  10. Lattice energies of molecular solids from the random phase approximation with singles corrections

    Czech Academy of Sciences Publication Activity Database

    Klimeš, Jiří

    2016-01-01

    Roč. 145, č. 9 (2016), 094506 ISSN 0021-9606 EU Projects: European Commission(XE) 658705 - NEW4NEW Grant - others:GA MŠk(CZ) LM2010005 Institutional support: RVO:61388955 Keywords : Approximation algorithms * Bins * Hydrogen bonds Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.965, year: 2016

  11. An approximate analysis of expected cycle time in business process execution

    NARCIS (Netherlands)

    Ha, B.H.; Reijers, H.A.; Bae, J.; Bae, H.; Eder, J.; Dustdar, S

    2006-01-01

    The accurate prediction of business process performance during its design phase can facilitate the assessment of existing processes and the generation of alternatives. In this paper, an approximation method to estimate the cycle time of a business process is introduced. First, we propose a process

  12. Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation

    KAUST Repository

    Li, Muxingzi

    2017-04-24

    Optical Coherence Tomography (OCT) is a coherence-gated, micrometer-resolution imaging technique that focuses a broadband near-infrared laser beam to penetrate into optical scattering media, e.g. biological tissues. The OCT resolution is split into two parts, with the axial resolution defined by half the coherence length, and the depth-dependent lateral resolution determined by the beam geometry, which is well described by a Gaussian beam model. The depth dependence of lateral resolution directly results in the defocusing effect outside the confocal region and restricts current OCT probes to small numerical aperture (NA) at the expense of lateral resolution near the focus. Another limitation on OCT development is the presence of a mixture of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous papers have adopted the first Born approximation with the assumption of small perturbation of the incident field in inhomogeneous media. The Rytov method of the same order with smooth phase perturbation assumption benefits from a wider spatial range of validity. A deconvolution method for solving the inverse problem associated with the first Rytov approximation is developed, significantly reducing the defocusing effect through depth and therefore extending the feasible range of NA.

  13. Results from a model system of superconducting solenoids and phase shifting bridge for pulsed power studies for proposed tokamak EF coils

    International Nuclear Information System (INIS)

    Fuja, R.E.; Kustom, R.L.; Smith, R.P.

    1977-01-01

    A matched pair of superconducting solenoids and a phase-shifting bridge circuit has been constructed to study energy storage and transfer for application to tokamak EF coils. The intrinsically stable solenoids, each with 4 H self-inductance, incorporate sufficient cooling to allow charging at several hundred volts, corresponding to B approximately equal 1 T/sec. The three-phase inductor-convertor capacitive bridge network operating at up to 150 V rms transfers energy reversibly and at controllable rates from the storage coil to the load coil

  14. Coexistence of spin-triplet superconductivity with magnetism within a single mechanism for orbitally degenerate correlated electrons: statistically consistent Gutzwiller approximation

    International Nuclear Information System (INIS)

    Zegrodnik, M; Spałek, J; Bünemann, J

    2013-01-01

    An orbitally degenerate two-band Hubbard model is analyzed with the inclusion of the Hund's rule-induced spin-triplet even-parity paired states and their coexistence with magnetic ordering. The so-called statistically consistent Gutzwiller approximation (SGA) has been applied to the case of a square lattice. The superconducting gaps, the magnetic moment and the free energy are analyzed as a function of the Hund's rule coupling strength and the band filling. Also, the influence of the intersite hybridization on the stability of paired phases is discussed. In order to examine the effect of correlations the results are compared with those calculated earlier within the Hartree–Fock (HF) approximation combined with the Bardeen–Cooper–Schrieffer (BCS) approach. Significant differences between the two methods used (HF + BCS versus SGA + real-space pairing) appear in the stability regions of the considered phases. Our results supplement the analysis of this canonical model used widely in the discussions of pure magnetic phases with the detailed elaboration of the stability of the spin-triplet superconducting states and the coexistent magnetic-superconducting states. At the end, we briefly discuss qualitatively the factors that need to be included for a detailed quantitative comparison with the corresponding experimental results. (paper)

  15. Phase diagrams for surface alloys

    DEFF Research Database (Denmark)

    Christensen, Asbjørn; Ruban, Andrei; Stoltze, Per

    1997-01-01

    We discuss surface alloy phases and their stability based on surface phase diagrams constructed from the surface energy as a function of the surface composition. We show that in the simplest cases of pseudomorphic overlayers there are four generic classes of systems, characterized by the sign...... is based on density-functional calculations using the coherent-potential approximation and on effective-medium theory. We give self-consistent density-functional results for the segregation energy and surface mixing energy for all combinations of the transition and noble metals. Finally we discuss...

  16. The approximation function of bridge deck vibration derived from the measured eigenmodes

    Directory of Open Access Journals (Sweden)

    Sokol Milan

    2017-12-01

    Full Text Available This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approximate the displacement vibration function by a sum of sine functions whose periodicity is determined by spectral analysis adapted for non-uniformly sampled data and where the parameters of scale and phase are estimated as usual by the least-squares method. Moreover, this periodic component is supplemented by a cubic regression spline (fitted on its residuals that captures individual displacements between piers. The statistical evaluation of the stiffness parameter is performed using more vertical modes obtained from experimental results. The previous method (Sokol and Flesch, 2005, which was derived for near the pier areas, has been enhanced to the whole length of the bridge. The experimental data describing the mode shapes are not appropriate for direct use. Especially the higher derivatives calculated from these data are very sensitive to data precision.

  17. Effects of thermal and particle-number fluctuations on the giant isovector dipole modes for the 58Ni nucleus in the finite-temperature random-phase approximation

    International Nuclear Information System (INIS)

    Nguyen Dinhdang; Nguyen Zuythang

    1988-01-01

    Using the realistic single-particle energy spectrum obtained in the Woods-Saxon nucleon mean-field potential, we calculate the BCS pairing gap for 58 Ni as a function of temperature taking into account the thermal and particle-number fluctuations. The strength distributions of the electric dipole transitions and the centroids of the isovector giant dipole resonance (IV-GDR) are computed in the framework of the finite-temperature random-phase approximation (RPA) based on the Hamiltonian of the quasiparticle-phonon nuclear model with separate dipole forces. It is shown that the change of the pairing gap at finite temperature can noticeably influence the IV-GDR localisation in realistic nuclei. By taking both thermal and quasiparticle fluctuations in the pairing gap into account the effect of the phase transition from superfluid to normal in the temperature dependence of the IV-GDR centroid is completely smeared out. (author)

  18. On Covering Approximation Subspaces

    Directory of Open Access Journals (Sweden)

    Xun Ge

    2009-06-01

    Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

  19. Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

    Science.gov (United States)

    Kim, SungKun; Lee, Hunpyo

    2017-06-01

    Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

  20. BWR Full Integral Simulation Test (FIST). Phase I test results

    International Nuclear Information System (INIS)

    Hwang, W.S.; Alamgir, M.; Sutherland, W.A.

    1984-09-01

    A new full height BWR system simulator has been built under the Full-Integral-Simulation-Test (FIST) program to investigate the system responses to various transients. The test program consists of two test phases. This report provides a summary, discussions, highlights and conclusions of the FIST Phase I tests. Eight matrix tests were conducted in the FIST Phase I. These tests have investigated the large break, small break and steamline break LOCA's, as well as natural circulation and power transients. Results and governing phenomena of each test have been evaluated and discussed in detail in this report. One of the FIST program objectives is to assess the TRAC code by comparisons with test data. Two pretest predictions made with TRACB02 are presented and compared with test data in this report

  1. Saddlepoint approximation methods in financial engineering

    CERN Document Server

    Kwok, Yue Kuen

    2018-01-01

    This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...

  2. Studies of Ionic Photoionization Using Relativistic Random Phase Approximation and Relativistic Multichannel Quantum Defect Theory

    Science.gov (United States)

    Haque, Ghousia Nasreen

    The absorption of electromagnetic radiation by positive ions is one of the fundamental processes of nature which occurs in every intensely hot environment. Due to the difficulties in producing sufficient densities of ions in a laboratory, there are very few measurements of ionic photoabsorption parameters. On the theoretical side, some calculations have been made of a few major photoionization parameters, but generally speaking, most of the work done so far has employed rather simple single particle models and any theoretical work which has adequately taken into account intricate atomic many-body and relativistic effects is only scanty. In the present work, several complex aspects of atomic/ionic photoabsorption parameters have been studied. Non -resonant photoionization in neon and argon isonuclear as well as isoelectronic sequences has been studied using a very sophisticated technique, namely the relativistic random phase approximation (RRPA). This technique takes into account relativistic effects as well as an important class of major many-body effects on the same footing. The present calculations confirmed that gross features of photoionization parameters calculated using simpler models were not an artifact of the simple model. Also, the present RRPA calculations on K^+ ion and neutral Ar brought out the relative importance of various many-body effects such the inter-channel coupling. Inter-channel coupling between discrete bound state photoexcitation channels from an inner atomic/ionic level and photoionization continuum channels from an outer atomic/ionic level leads to the phenomena of autoionization resonances in the photoionization process. These resonances lead to very complex effects in the atomic/ionic photoabsorption spectra. These resonances have been calculated and studied in the present work in the neon and magnesium isoelectronic sequences using the relativistic multi-channel quantum defect theory (RMQDT) within the framework of the RRPA. The

  3. The comparing results of carcinoma between three-phase and delayed whole body bone scan

    International Nuclear Information System (INIS)

    Si Hongwei; Li Xianfeng

    2004-01-01

    Purpose: Three phase bone scan is an imaging technology in nuclear medicine, which composed of blood flow phase, blood pool phase and delayed phase and the last one is often performed in routine works in department of nuclear medicine. The purpose of this study is to evaluate the merit of three-phase bone scan.Methods: In this study, we chose 54 patients who were having an regional pain which caused by benign or malignant carcinoma that diagnosed by CT, X-ray, ECT, MRI or other examinations. The imaging were acquired simultaneously from both anterior and posterior views, after a bolus injection of 1110 MBq technetium-99m-labelled methylene diphosphonate (MDP), blood phase contains 20 frame sand 3 seconds per frame, blood pool phase contains 5 frames and 1 minute per frame, delayed phase was performed 2.5 hour later. According to the results of three-phase bone scan, the patients were divided into 2 groups: normal and abnormal groups. The abnormal group includes early phase positive,delay positive and all three phase positive sets. The comparing among the 3 sets were analyzed by chi-square test and other statistic means.Results: There were 54 patients who had suffered lung cancer, breast cancer and other cancer,involved in this study, 34 males and 20 females, ranged age 17 to 88 years, were normal in 15 cases,positive in 22 cases, the results in delayed phase were positive in 9 cases, blood flow and blood pool phase showed blood flow changes in 4 cases and soft tissue tumors were seen in 4 cases. Three phase bone scan was more sensitive than delayed whole body bone scan in detecting the abnormal sites (p 0.05) The sensitivity of detecting tumors in blood flow and blood pool phase,delayed phase were respectively lower than in three phase bone scan (p<0.001).Conclusion: It is more sensitivity of detecting tumor lesions in three phase bone scan than in delayed phase whole body bone scan and the changes of blood flow and soft tissue can be seen in three phase bone scan

  4. On exact and approximate exchange-energy densities

    DEFF Research Database (Denmark)

    Springborg, Michael; Dahl, Jens Peder

    1999-01-01

    Based on correspondence rules between quantum-mechanical operators and classical functions in phase space we construct exchange-energy densities in position space. Whereas these are not unique but depend on the chosen correspondence rule, the exchange potential is unique. We calculate this exchange......-energy density for 15 closed-shell atoms, and compare it with kinetic- and Coulomb-energy densities. It is found that it has a dominating local-density character, but electron-shell effects are recognizable. The approximate exchange-energy functionals that have been proposed so far are found to account only...

  5. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  6. Approximate number and approximate time discrimination each correlate with school math abilities in young children.

    Science.gov (United States)

    Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

    2016-01-01

    What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright

  7. Phase diagram study of a dimerized spin-S zig–zag ladder

    International Nuclear Information System (INIS)

    Matera, J M; Lamas, C A

    2014-01-01

    The phase diagram of a frustrated spin-S zig–zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar–Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for S = 1/2, and spiral phases can appear for large S. The phase diagram is characterized by means of a generalization of the usual mean field approximation. The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the random phase approximation. Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like the Density Matrix Renormalization Group are also presented. (paper)

  8. Large-N -approximated field theory for multipartite entanglement

    Science.gov (United States)

    Facchi, P.; Florio, G.; Parisi, G.; Pascazio, S.; Scardicchio, A.

    2015-12-01

    We try to characterize the statistics of multipartite entanglement of the random states of an n -qubit system. Unable to solve the problem exactly we generalize it, replacing complex numbers with real vectors with Nc components (the original problem is recovered for Nc=2 ). Studying the leading diagrams in the large-Nc approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-Nc limit.

  9. Phases of a polar spin-1 Bose gas in a magnetic field

    International Nuclear Information System (INIS)

    Kis-Szabo, Krisztian; Szepfalusy, Peter; Szirmai, Gergely

    2007-01-01

    The two Bose-Einstein condensed phases of a polar spin-1 gas at nonzero magnetizations and temperatures are investigated. The Hugenholtz-Pines theorem is generalized to this system. Crossover to a quantum phase transition is also studied. Results are discussed in a mean field approximation

  10. Some relations between entropy and approximation numbers

    Institute of Scientific and Technical Information of China (English)

    郑志明

    1999-01-01

    A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

  11. A Note on Holography and Phase Transitions

    Directory of Open Access Journals (Sweden)

    Marc Bellon

    2011-01-01

    Full Text Available Focusing on the connection between the Landau theory of second-order phase transitions and the holographic approach to critical phenomena, we study diverse field theories in an anti de Sitter black hole background. Through simple analytical approximations, solutions to the equations of motion can be obtained in closed form which give rather good approximations of the results obtained using more involved numerical methods. The agreement we find stems from rather elementary considerations on perturbation of Schrödinger equations.

  12. Self-similar factor approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.; Sornette, D.

    2003-01-01

    The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

  13. First-principles study of electronic and structural properties and examining the effect of pressure on structure and energy gap in In N phases

    International Nuclear Information System (INIS)

    Bouchani, A.; Arabi, H.; Abolhasani, M. R.

    2007-01-01

    The electronic and structural properties of both zinc-blende and wurtzite phases of In N were investigated by using full potential augmented plane wave method within density functional theory. For exchange correlation potential, local density approximation, generalized gradient approximation and an alternative form of generalized gradient approximation proposed by Engel and Vosko (EV-generalized gradient approximation ) have been used. Results obtained for band structure of these compounds have been compared with experimental results as well as other theoretical work and closer to experimental data. The lattice constants, bulk modulus are calculated for each of both phases. We have also investigated the structural transitions of In N and have calculated the transition pressure between zinc-blende and rock salt phases.

  14. A unified approach to the Darwin approximation

    International Nuclear Information System (INIS)

    Krause, Todd B.; Apte, A.; Morrison, P. J.

    2007-01-01

    There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

  15. Effects of the menstrual cycle phases on the tilt testing results in vasovagal patients.

    Science.gov (United States)

    Zyśko, Dorota; Gajek, Jacek; Terpiłowski, Lukasz; Agrawal, Anil Kumar; Wróblewski, Paweł; Rudnicki, Jerzy

    2012-08-01

    The aim of the study was to assess the distribution of positive tilt testing (TT) throughout the menstrual cycle and to determine if the phase of menstrual cycle contributes to the duration of the loss of consciousness. TT results of 183 premenopausal women, aged 29.5 ± 9.8 years, were studied. The menstrual cycle was divided into four phases based on the first day of the last menstrual bleeding: perimenstrual (M), preovulatory (F), periovulatory (O) and postovulatory (L). Positive TT results were equally distributed. In patients with TT in O phase, the highest percentage of NTG provocation was needed. Patients in L phase had significantly lower incidence of cardioinhibitory reaction. The longest duration of loss of consciousness was in the M phase. Multiple regression analysis revealed that the duration of loss of consciousness during positive TT was significantly associated with higher number of syncopal events, TT performed in M phase and lower heart rate at TT termination. Cardiodepressive type of neurocardiogenic reaction was more frequent during M and O phase than during L phase. The distribution of positive TT results as well as syncope and presyncope does not differ throughout the menstrual cycle. Diagnostic TT in premenopausal women with unexplained syncope could be performed irrespective of the phase of menstrual cycle. TT has similar sensitivity throughout the menstrual cycle. During the postovulatory phase, cardioinhibitory reaction is less frequent than in M and O phases. The duration of loss of consciousness is longer during the M phase of the menstrual cycle independently of the higher syncope number and lower heart rate at TT termination.

  16. Modulated Pade approximant

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1980-01-01

    In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

  17. Real-time dynamics of matrix quantum mechanics beyond the classical approximation

    Science.gov (United States)

    Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

    2018-03-01

    We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

  18. Appendix to the report from the low-residue soldering task force: Phase 2 results

    Energy Technology Data Exchange (ETDEWEB)

    Iman, R.L.; Anderson, D.J.; Huffman, D.D. [and others

    1995-12-01

    The LRSTF report for Phase I of its evaluation of low-residue soldering was issued in June 1995. This Appendix summarizes the results of follow-on testing performed in Phase II and compares electrical test results for both phases. Deliberate decisions were made by the LRSTF in Phase I to challenge the design guideline limits in MILSTD-275, Printed Wiring for Electronic Equipment The LRSTF considered this approach to produce a ``worst case`` design and provide useful information about the robustness of LR soldering processes. As such, good design practices were sometimes deliberately violated in designing the LRSTF board. This approach created some anomalies for both LR boards and RMA/cleaned controls. Phase II testing verified that problems that affected both RMA/cleaned and LR boards in Phase I were design related.

  19. Spectral decomposition of single-tone-driven quantum phase modulation

    International Nuclear Information System (INIS)

    Capmany, Jose; Fernandez-Pousa, Carlos R

    2011-01-01

    Electro-optic phase modulators driven by a single radio-frequency tone Ω can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of ℎΩ. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F 1 , the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F 1 is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation.

  20. Spectral decomposition of single-tone-driven quantum phase modulation

    Energy Technology Data Exchange (ETDEWEB)

    Capmany, Jose [ITEAM Research Institute, Univ. Politecnica de Valencia, 46022 Valencia (Spain); Fernandez-Pousa, Carlos R, E-mail: c.pousa@umh.es [Signal Theory and Communications, Department of Physics and Computer Science, Univ. Miguel Hernandez, 03202 Elche (Spain)

    2011-02-14

    Electro-optic phase modulators driven by a single radio-frequency tone {Omega} can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of {h_bar}{Omega}. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F{sub 1}, the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F{sub 1} is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation.

  1. Approximation methods in probability theory

    CERN Document Server

    Čekanavičius, Vydas

    2016-01-01

    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

  2. Slit-scanning differential phase-contrast mammography: first experimental results

    Science.gov (United States)

    Roessl, Ewald; Daerr, Heiner; Koehler, Thomas; Martens, Gerhard; van Stevendaal, Udo

    2014-03-01

    The demands for a large field-of-view (FOV) and the stringent requirements for a stable acquisition geometry rank among the major obstacles for the translation of grating-based, differential phase-contrast techniques from the laboratory to clinical applications. While for state-of-the-art Full-Field-Digital Mammography (FFDM) FOVs of 24 cm x 30 cm are common practice, the specifications for mechanical stability are naturally derived from the detector pixel size which ranges between 50 and 100 μm. However, in grating-based, phasecontrast imaging, the relative placement of the gratings in the interferometer must be guaranteed to within micro-meter precision. In this work we report on first experimental results on a phase-contrast x-ray imaging system based on the Philips MicroDose L30 mammography unit. With the proposed approach we achieve a FOV of about 65 mm x 175 mm by the use of the slit-scanning technique. The demand for mechanical stability on a micrometer scale was relaxed by the specific interferometer design, i.e., a rigid, actuator-free mount of the phase-grating G1 with respect to the analyzer-grating G2 onto a common steel frame. The image acquisition and formation processes are described and first phase-contrast images of a test object are presented. A brief discussion of the shortcomings of the current approach is given, including the level of remaining image artifacts and the relatively inefficient usage of the total available x-ray source output.

  3. Edge effects in phase-shifting masks for 0.25-µm lithography

    Science.gov (United States)

    Wong, Alfred K. K.; Neureuther, Andrew R.

    1993-03-01

    The impact on image quality of scattering from phase-shifter edges and of interactions between phase-shifter and chrome edges is assessed using rigorous electromagnetic simulation. Effects of edge taper in phase-shift masks, spacing between phase-shifter and chrome edges, small outrigger features with a trench phase-shifter, and of the repair of phase defects by etching to 360 degree(s) are considered. Near field distributions and diffraction efficiencies are examined and images are compared with more approximate results from the commonly used Hopkins' theory of imaging.

  4. Spline approximation, Part 1: Basic methodology

    Science.gov (United States)

    Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

    2018-04-01

    In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

  5. Calculation of static characteristics of linear step motors for control rod drives of nuclear reactors - an approximate approach

    International Nuclear Information System (INIS)

    Khan, S.H.; Ivanov, A.A.

    1993-01-01

    This paper describes an approximate method for calculating the static characteristics of linear step motors (LSM), being developed for control rod drives (CRD) in large nuclear reactors. The static characteristic of such an LSM which is given by the variation of electromagnetic force with armature displacement determines the motor performance in its standing and dynamic modes. The approximate method of calculation of these characteristics is based on the permeance analysis method applied to the phase magnetic circuit of LSM. This is a simple, fast and efficient analytical approach which gives satisfactory results for small stator currents and weak iron saturation, typical to the standing mode of operation of LSM. The method is validated by comparing theoretical results with experimental ones. (Author)

  6. 'LTE-diffusion approximation' for arc calculations

    International Nuclear Information System (INIS)

    Lowke, J J; Tanaka, M

    2006-01-01

    This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode

  7. A phase space approach to wave propagation with dispersion.

    Science.gov (United States)

    Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

    2015-08-01

    A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

  8. Main results on the RF amplitude and phase regulation systems in operation at GANIL

    International Nuclear Information System (INIS)

    Joubert, A.; Ducoudret, B.; Labiche, J.C.; Loyant, J.M.

    1984-06-01

    The general features of the amplitude and phase regulations and their control systems are briefly reviewed. These feedback control systems are fully under the control of the main computer aided by dedicated CAMAC microprocessors for actions such as starting, parameters tuning or phase stability surveying. Numerous results obtained with spectrum analysis method give the actual RF purity and the residual modulation and crossmodulation noise level for all RF signals picked up in the RF resonators. A typical value for the noise immunity is 80 dB below the carrier at 100 Hz deviation. Another set of results gives the actual long term phase drift between resonators (< 0.2 RF degree within 6 hours). The stability of the RF phases is confirmed by on line beam phase measurements

  9. Approximation Properties of Certain Summation Integral Type Operators

    Directory of Open Access Journals (Sweden)

    Patel P.

    2015-03-01

    Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

  10. DAMA/LIBRA results and perspectives of phase 2

    Energy Technology Data Exchange (ETDEWEB)

    Bernabei, R. [Dip. di Fisica, Univ. “Tor Vergata”, I-00133 Rome (Italy); INFN, sez. Roma “Tor Vergata”, I-00133 Rome (Italy); Belli, P., E-mail: pierluigi.belli@roma2.infn.it [Dip. di Fisica, Univ. “Tor Vergata”, I-00133 Rome (Italy); INFN, sez. Roma “Tor Vergata”, I-00133 Rome (Italy); Cappella, F. [Dip. di Fisica, Univ. di Roma “La Sapienza”, I-00185 Rome (Italy); INFN, sez. Roma, I-00185 Rome (Italy); Caracciolo, V.; Cerulli, R. [Laboratori Nazionali del Gran Sasso, I.N.F.N., Assergi (Italy); Dai, C.J. [IHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039 (China); D' Angelo, A. [Dip. di Fisica, Univ. di Roma “La Sapienza”, I-00185 Rome (Italy); INFN, sez. Roma, I-00185 Rome (Italy); D' Angelo, S.; Di Marco, A. [Dip. di Fisica, Univ. “Tor Vergata”, I-00133 Rome (Italy); INFN, sez. Roma “Tor Vergata”, I-00133 Rome (Italy); He, H.L. [IHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039 (China); Incicchitti, A. [Dip. di Fisica, Univ. di Roma “La Sapienza”, I-00185 Rome (Italy); INFN, sez. Roma, I-00185 Rome (Italy); Ma, X.H. [IHEP, Chinese Academy, P.O. Box 918/3, Beijing 100039 (China); Montecchia, F. [Dip. di Fisica, Univ. “Tor Vergata”, I-00133 Rome (Italy); INFN, sez. Roma “Tor Vergata”, I-00133 Rome (Italy); Dip. di Ingegneria Civile e Ingegneria Informatica, Univ. “Tor Vergata”, I-00133 Rome (Italy); and others

    2014-04-01

    The DAMA/LIBRA experiment, running at the Gran Sasso National Laboratory of the INFN, has a sensitive mass of about 250 kg highly radiopure NaI(Tl). It is mainly devoted to the investigation of Dark Matter (DM) particles in the Galactic halo by exploiting the model independent DM annual modulation signature. The present DAMA/LIBRA experiment and the former DAMA/NaI one (the first generation experiment having an exposed mass of about 100 kg) have released so far results corresponding to a total exposure of 1.17 ton×year over 13 annual cycles. They provide a model independent evidence of the presence of DM particles in the galactic halo at 8.9σ C.L. After the upgrade at fall 2010 when all the PMTs have been replaced with new ones having higher quantum efficiency, the feasibility to decrease the software energy threshold has been demonstrated and the set-up is running in this new configuration, named DAMA/LIBRA–phase2. The perspectives of DAMA/LIBRA–phase2 will be shortly summarized.

  11. DAMA/LIBRA results and perspectives of phase 2

    International Nuclear Information System (INIS)

    Bernabei, R.; Belli, P.; Cappella, F.; Caracciolo, V.; Cerulli, R.; Dai, C.J.; D'Angelo, A.; D'Angelo, S.; Di Marco, A.; He, H.L.; Incicchitti, A.; Ma, X.H.; Montecchia, F.

    2014-01-01

    The DAMA/LIBRA experiment, running at the Gran Sasso National Laboratory of the INFN, has a sensitive mass of about 250 kg highly radiopure NaI(Tl). It is mainly devoted to the investigation of Dark Matter (DM) particles in the Galactic halo by exploiting the model independent DM annual modulation signature. The present DAMA/LIBRA experiment and the former DAMA/NaI one (the first generation experiment having an exposed mass of about 100 kg) have released so far results corresponding to a total exposure of 1.17 ton×year over 13 annual cycles. They provide a model independent evidence of the presence of DM particles in the galactic halo at 8.9σ C.L. After the upgrade at fall 2010 when all the PMTs have been replaced with new ones having higher quantum efficiency, the feasibility to decrease the software energy threshold has been demonstrated and the set-up is running in this new configuration, named DAMA/LIBRA–phase2. The perspectives of DAMA/LIBRA–phase2 will be shortly summarized

  12. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  13. Initial results of strand produced in Phase 2 of the SSCL Vendor Qualification Program

    International Nuclear Information System (INIS)

    Erdmann, M.; Capone, D. II; Coleman, S.; Jones, B.; Seuntjens, J.

    1993-05-01

    In 1991, the Superconducting Super Collider Laboratory (SSCL) instituted a program to qualify specific superconductor manufacturers for production of cable acceptable for use in both Collider Dipole (CDM) and Quadrupole (CQM) magnets. The SSCL Vendor Qualification Program (VQP) was designed with two Phases. Phase 1 was divided into two additional phases, 1A and 1B, which ran concurrently. In Phase 1B, each vendor was directed to manufacture roughly 3000 kg of cable using a ''baseline'' process. The baseline process was agreed to by both the SSCL and the vendor at the beginning of the VQP. In this phase, process control was closely monitored with the use of statistical methods and each vendor was graded based on these results. Phase 1A, known as the R ampersand D phase, was developed to allow each vendor an opportunity to optimize and improve on their baseline process in terms of both cost and manufacturability. In this phase, multifilament billets were designed to explore several key variables such as alternate alloy sources, process modifications and improved billet designs. At the end of Phase 1, the results from both 1A and 1B were evaluated at a review between the SSCL and each vendor, and a final Phase 2 process was generated and fixed using the best results. In Phase 2, each vendor is required to manufacture roughly 6000 kg of superconducting cable under a firm fixed price contract which can then be used to create an accurate price estimate for competitive bidding on the full rate production CDM and CQM contracts. At the end of Phase 2, each vendor must meet the minimum requirements outlined in the contract to become a qualified superconducting cable supplier. For one requirement, critical process variables identified by the SSCL Conductor Department at the beginning of the VQP will be evaluated to determine the quality and uniformity of the material produced during Phase 2 of the program

  14. Phase III Simplified Integrated Test (SIT) results - Space Station ECLSS testing

    Science.gov (United States)

    Roberts, Barry C.; Carrasquillo, Robyn L.; Dubiel, Melissa Y.; Ogle, Kathryn Y.; Perry, Jay L.; Whitley, Ken M.

    1990-01-01

    During 1989, phase III testing of Space Station Freedom Environmental Control and Life Support Systems (ECLSS) began at Marshall Space Flight Center (MSFC) with the Simplified Integrated Test. This test, conducted at the MSFC Core Module Integration Facility (CMIF), was the first time the four baseline air revitalization subsystems were integrated together. This paper details the results and lessons learned from the phase III SIT. Future plans for testing at the MSFC CMIF are also discussed.

  15. An acoustic-convective splitting-based approach for the Kapila two-phase flow model

    Energy Technology Data Exchange (ETDEWEB)

    Eikelder, M.F.P. ten, E-mail: m.f.p.teneikelder@tudelft.nl [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Daude, F. [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); IMSIA, UMR EDF-CNRS-CEA-ENSTA 9219, Université Paris Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau (France); Koren, B.; Tijsseling, A.S. [Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

    2017-02-15

    In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.

  16. Results from phase I of the GERDA experiment

    Science.gov (United States)

    Wester, Thomas

    2015-10-01

    The GERmanium Detector Array Gerda at the Laboratori Nazionali del Gran Sasso of the INFN in Italy is an experiment dedicated to the search for the neutrinoless double beta (0νββ) decay in 76Ge. The experiment employs high purity germanium detectors enriched in 76Ge inside a 64 m3 cryostat filled with liquid argon. Gerda was planned in two phases of data taking with the goal to reach a half-life sensitivity in the order of 1026 yr. Phase I of Gerda was running from November 2011 until May 2013. With about 18 kg total detector mass, data with an exposure of 21.6 kg.yr was collected and a background index of 0.01 cts/(keV.kg.yr) was achieved in the region of interest. No signal was found for the 0νββ decay and a new limit of T1/2 > 2.1 . 1025 yr (90% C.L.) was obtained, strongly disfavoring the previous claim of observation. Furthermore, the 2νββ decay half-life of 76Ge was measured with unprecedented precision. Other results include new half-life limits of the order of 1023 yr for Majoron emitting double beta decay modes with spectral indices n = 1, 2, 3, 7 and new limits in the order of 1023 yr for 2νββ decays to the first 3 excited states of 76Se. In Phase II, currently in preparation, the detector mass will be doubled while reducing the background index by a factor of 10.

  17. Hydrodynamics of phase transition fronts and the speed of sound in the plasma

    International Nuclear Information System (INIS)

    Leitao, Leonardo; Mégevand, Ariel

    2015-01-01

    The growth of bubbles in cosmological first-order phase transitions involves nontrivial hydrodynamics. For that reason, the study of the propagation of phase transition fronts often requires several approximations. A frequently used approximation consists in describing the two phases as being composed only of radiation and vacuum energy (the so-called bag equation of state). We show that, in realistic models, the speed of sound in the low-temperature phase is generally smaller than that of radiation, and we study the hydrodynamics in such a situation. We find in particular that a new kind of hydrodynamical solution may be possible, which does not arise in the bag model. We obtain analytic results for the efficiency of the transfer of latent heat to bulk motions of the plasma, as a function of the speed of sound in each phase

  18. Hydrodynamics of phase transition fronts and the speed of sound in the plasma

    Energy Technology Data Exchange (ETDEWEB)

    Leitao, Leonardo, E-mail: lleitao@mdp.edu.ar; Mégevand, Ariel, E-mail: megevand@mdp.edu.ar

    2015-02-15

    The growth of bubbles in cosmological first-order phase transitions involves nontrivial hydrodynamics. For that reason, the study of the propagation of phase transition fronts often requires several approximations. A frequently used approximation consists in describing the two phases as being composed only of radiation and vacuum energy (the so-called bag equation of state). We show that, in realistic models, the speed of sound in the low-temperature phase is generally smaller than that of radiation, and we study the hydrodynamics in such a situation. We find in particular that a new kind of hydrodynamical solution may be possible, which does not arise in the bag model. We obtain analytic results for the efficiency of the transfer of latent heat to bulk motions of the plasma, as a function of the speed of sound in each phase.

  19. Short overview of PSA quantification methods, pitfalls on the road from approximate to exact results

    International Nuclear Information System (INIS)

    Banov, Reni; Simic, Zdenko; Sterc, Davor

    2014-01-01

    Over time the Probabilistic Safety Assessment (PSA) models have become an invaluable companion in the identification and understanding of key nuclear power plant (NPP) vulnerabilities. PSA is an effective tool for this purpose as it assists plant management to target resources where the largest benefit for plant safety can be obtained. PSA has quickly become an established technique to numerically quantify risk measures in nuclear power plants. As complexity of PSA models increases, the computational approaches become more or less feasible. The various computational approaches can be basically classified in two major groups: approximate and exact (BDD based) methods. In recent time modern commercially available PSA tools started to provide both methods for PSA model quantification. Besides availability of both methods in proven PSA tools the usage must still be taken carefully since there are many pitfalls which can drive to wrong conclusions and prevent efficient usage of PSA tool. For example, typical pitfalls involve the usage of higher precision approximation methods and getting a less precise result, or mixing minimal cuts and prime implicants in the exact computation method. The exact methods are sensitive to selected computational paths in which case a simple human assisted rearrangement may help and even switch from computationally non-feasible to feasible methods. Further improvements to exact method are possible and desirable which opens space for a new research. In this paper we will show how these pitfalls may be detected and how carefully actions must be done especially when working with large PSA models. (authors)

  20. Asymptotically stable phase synchronization revealed by autoregressive circle maps

    Science.gov (United States)

    Drepper, F. R.

    2000-11-01

    A specially designed of nonlinear time series analysis is introduced based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying autoregressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, invertibility enforcing phase space map allows us to detect conditional asymptotic stability of coupled phases. This comparatively general synchronization criterion unites two existing generalizations of the old concept and can successfully be applied, e.g., to phases obtained from electrocardiogram and airflow recordings characterizing cardiorespiratory interaction.

  1. Phase diagram of an extended Agassi model

    Science.gov (United States)

    García-Ramos, J. E.; Dukelsky, J.; Pérez-Fernández, P.; Arias, J. M.

    2018-05-01

    Background: The Agassi model [D. Agassi, Nucl. Phys. A 116, 49 (1968), 10.1016/0375-9474(68)90482-X] is an extension of the Lipkin-Meshkov-Glick (LMG) model [H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. 62, 188 (1965), 10.1016/0029-5582(65)90862-X] that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960s by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss [J. Phys. G: Nucl. Phys. 12, 805 (1986), 10.1088/0305-4616/12/9/006] generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.

  2. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  3. Final model independent result of DAMA/LIBRA-phase1

    Energy Technology Data Exchange (ETDEWEB)

    Bernabei, R.; D' Angelo, S.; Di Marco, A. [Universita di Roma ' ' Tor Vergata' ' , Dipartimento di Fisica, Rome (Italy); INFN, sez. Roma ' ' Tor Vergata' ' , Rome (Italy); Belli, P. [INFN, sez. Roma ' ' Tor Vergata' ' , Rome (Italy); Cappella, F.; D' Angelo, A.; Prosperi, D. [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, sez. Roma, Rome (Italy); Caracciolo, V.; Castellano, S.; Cerulli, R. [INFN, Laboratori Nazionali del Gran Sasso, Assergi (Italy); Dai, C.J.; He, H.L.; Kuang, H.H.; Ma, X.H.; Sheng, X.D.; Wang, R.G. [Chinese Academy, IHEP, Beijing (China); Incicchitti, A. [INFN, sez. Roma, Rome (Italy); Montecchia, F. [INFN, sez. Roma ' ' Tor Vergata' ' , Rome (Italy); Universita di Roma ' ' Tor Vergata' ' , Dipartimento di Ingegneria Civile e Ingegneria Informatica, Rome (Italy); Ye, Z.P. [Chinese Academy, IHEP, Beijing (China); University of Jing Gangshan, Jiangxi (China)

    2013-12-15

    The results obtained with the total exposure of 1.04 ton x yr collected by DAMA/LIBRA-phase1 deep underground at the Gran Sasso National Laboratory (LNGS) of the I.N.F.N. during 7 annual cycles (i.e. adding a further 0.17 ton x yr exposure) are presented. The DAMA/LIBRA-phase1 data give evidence for the presence of Dark Matter (DM) particles in the galactic halo, on the basis of the exploited model independent DM annual modulation signature by using highly radio-pure NaI(Tl) target, at 7.5{sigma} C.L. Including also the first generation DAMA/NaI experiment (cumulative exposure 1.33 ton x yr, corresponding to 14 annual cycles), the C.L. is 9.3{sigma} and the modulation amplitude of the single-hit events in the (2-6) keV energy interval is: (0.0112{+-}0.0012) cpd/kg/keV; the measured phase is (144{+-}7) days and the measured period is (0.998{+-}0.002) yr, values well in agreement with those expected for DM particles. No systematic or side reaction able to mimic the exploited DM signature has been found or suggested by anyone over more than a decade. (orig.)

  4. JNC results of BN-600 benchmark calculation (phase 3)

    International Nuclear Information System (INIS)

    Ishikawa, M.

    2002-01-01

    The present work is the result of phase 3 BN-600 core benchmark problem, meaning burnup and heterogeneity. Analytical method applied consisted of: JENDL-3.2 nuclear data library, group constants (70 group, ABBN type self shielding transport factors), heterogeneous cell model for fuel and control rod, basic diffusion calculation (CITATION code), transport theory and mesh size correction (NSHEX code based on SN transport nodal method developed by JNC). Burnup and heterogeneity calculation results are presented obtained by applying both diffusion and transport approach for beginning and end of cycle

  5. Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation

    KAUST Repository

    Negara, Ardiansyah; Salama, Amgad; Sun, Shuyu

    2015-01-01

    Numerical investigations of two-phase flows in anisotropic porous media have been conducted. In the flow model, the permeability has been considered as a full tensor and is implemented in the numerical scheme using the multipoint flux approximation within the framework of finite difference method. In addition, the experimenting pressure field approach is used to obtain the solution of the pressure field, which makes the matrix of coefficient of the global system easily constructed. A number of numerical experiments on the flow of two-phase system in two-dimensional porous medium domain are presented. In this work, the gravity is included in the model to capture the possible buoyancy-driven effects due to density differences between the two phases. Different anisotropy scenarios have been considered. From the numerical results, interesting patterns of the flow, pressure, and saturation fields emerge, which are significantly influenced by the anisotropy of the absolute permeability field. It is found that the two-phase system moves along the principal direction of anisotropy. Furthermore, the effects of anisotropy orientation on the flow rates and the cross flow index are also discussed in the paper.

  6. Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation

    KAUST Repository

    Negara, Ardiansyah

    2015-03-04

    Numerical investigations of two-phase flows in anisotropic porous media have been conducted. In the flow model, the permeability has been considered as a full tensor and is implemented in the numerical scheme using the multipoint flux approximation within the framework of finite difference method. In addition, the experimenting pressure field approach is used to obtain the solution of the pressure field, which makes the matrix of coefficient of the global system easily constructed. A number of numerical experiments on the flow of two-phase system in two-dimensional porous medium domain are presented. In this work, the gravity is included in the model to capture the possible buoyancy-driven effects due to density differences between the two phases. Different anisotropy scenarios have been considered. From the numerical results, interesting patterns of the flow, pressure, and saturation fields emerge, which are significantly influenced by the anisotropy of the absolute permeability field. It is found that the two-phase system moves along the principal direction of anisotropy. Furthermore, the effects of anisotropy orientation on the flow rates and the cross flow index are also discussed in the paper.

  7. MPPT for PM wind generator using gradient approximation

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Ying-Yi; Lu, Shiue-Der; Chiou, Ching-Sheng [Department of Electrical Engineering, Chung Yuan Christian University, 200, Chung-Pei Road, Chung Li 320 (China)

    2009-01-15

    This paper applies new maximum-power-point tracking (MPPT) algorithms to a wind-turbine generator system (WTGS). In this paper, the WTGS is a direct-drive system and includes the wind-turbine, permanent-magnet (PM) synchronous generator, three-phase full bridge rectifier, buck-boost converter and load. The new MPPT method uses gradient approximation (GA) algorithm. Three methods based on GA for achieving MPPT are discussed in this paper: (1) full-sensor control with anemometer and tachometer, (2) rule-based method and (3) adaptive duty cycle method. The third method has merits of no PID parameters, proportional constant, anemometer, tachometer and characteristics of WTGS required. This method enables the permanent-magnet synchronous generator (PMSG) to operate at variable speeds to achieve good performance. Simulation results show that the tip-speed ratio (TSR) and power coefficient obtained by the adaptive duty cycle method with GA can be almost identical to the optimal values. (author)

  8. MPPT for PM wind generator using gradient approximation

    International Nuclear Information System (INIS)

    Hong, Y.-Y.; Lu, S.-D.; Chiou, C.-S.

    2009-01-01

    This paper applies new maximum-power-point tracking (MPPT) algorithms to a wind-turbine generator system (WTGS). In this paper, the WTGS is a direct-drive system and includes the wind-turbine, permanent-magnet (PM) synchronous generator, three-phase full bridge rectifier, buck-boost converter and load. The new MPPT method uses gradient approximation (GA) algorithm. Three methods based on GA for achieving MPPT are discussed in this paper: (1) full-sensor control with anemometer and tachometer, (2) rule-based method and (3) adaptive duty cycle method. The third method has merits of no PID parameters, proportional constant, anemometer, tachometer and characteristics of WTGS required. This method enables the permanent-magnet synchronous generator (PMSG) to operate at variable speeds to achieve good performance. Simulation results show that the tip-speed ratio (TSR) and power coefficient obtained by the adaptive duty cycle method with GA can be almost identical to the optimal values

  9. Independent center, independent electron approximation for dynamics of molecules and clusters

    International Nuclear Information System (INIS)

    McGuire, J.H.; Straton, J.C.; Wang, J.; Wang, Y.D.; Weaver, O.L.; Corchs, S.E.; Rivarola, R.D.

    1996-01-01

    A formalism is developed for evaluating probabilities and cross sections for multiple-electron transitions in scattering of molecules and clusters by charged collision partners. First, the molecule is divided into subclusters each made up of identical centers (atoms). Within each subcluster coherent scattering from identical centers may lead to observable phase terms and a geometrical structure factor. Then, using a mean field approximation to describe the interactions between centers we obtain A I ∼ summation k product ke iδ k I A Ik . Second, the independent electron approximation for each center may be obtained by neglecting the correlation between electrons in each center. The probability amplitude for each center is then a product of single electron transition probability amplitudes, a Ik i , i.e. A Ik ≅ product iaik i . Finally, the independent subcluster approximation is introduced by neglecting the interactions between different subclusters in the molecule or cluster. The total probability amplitude then reduces to a simple product of amplitudes for each subcluster, A≅ product IAI . Limitations of this simple approximation are discussed. copyright 1996 American Institute of Physics

  10. No surprise in the first Born approximation for electron scattering

    International Nuclear Information System (INIS)

    Lentzen, M.

    2014-01-01

    In a recent article it is argued that the far-field expansion of electron scattering, a pillar of electron diffraction theory, is wrong (Treacy and Van Dyck, 2012 [1]). It is further argued that in the first Born approximation of electron scattering the intensity of the electron wave is not conserved to first order in the scattering potential. Thus a “mystery of the missing phase” is investigated, and the supposed flaw in scattering theory is seeked to be resolved by postulating a standing spherical electron wave (Treacy and Van Dyck, 2012 [1]). In this work we show, however, that these theses are wrong. A review of the essential parts of scattering theory with careful checks of the underlying assumptions and limitations for high-energy electron scattering yields: (1) the traditional form of the far-field expansion, comprising a propagating spherical wave, is correct; (2) there is no room for a missing phase; (3) in the first Born approximation the intensity of the scattered wave is conserved to first order in the scattering potential. The various features of high-energy electron scattering are illustrated by wave-mechanical calculations for an explicit target model, a Gaussian phase object, and for a Si atom, considering the geometric conditions in high-resolution transmission electron microscopy. - Highlights: Treacy and Van Dyck (2012) argue that the far-field expansion of electron scattering is wrong. The chief theses of that former work are wrong. There is no room for the missing phase proposed by Treacy and Van Dyck. There is no violation of the intensity conservation to first order in the scattering potential. Calculations for a phase object and an atomic target confirm traditional scattering theory

  11. Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

    KAUST Repository

    Djebbi, Ramzi

    2014-02-18

    Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.

  12. Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

    KAUST Repository

    Djebbi, Ramzi; Alkhalifah, Tariq Ali

    2014-01-01

    Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.

  13. Leptonic CP violation induced by approximately μ-τ symmetric seesaw mechanism

    International Nuclear Information System (INIS)

    Baba, Teppei; Yasue, Masaki

    2008-01-01

    Assuming a minimal seesaw model with two heavy neutrinos (N), we examine effects of leptonic CP violation induced by approximate μ-τ symmetric interactions. As long as N is subject to the μ-τ symmetry, we can choose CP phases of Dirac mass terms without loss of generality in such a way that these phases arise from μ-τ symmetry breaking interactions. In the case that no phase is present in heavy neutrino mass terms, leptonic CP phases are controlled by two phases α and β. The similar consideration is extended to N blind to the μ-τ symmetry. It is argued that N subject (blind) to the μ-τ symmetry necessarily describes the normal (inverted) mass hierarchy. We restrict ourselves to μ-τ symmetric textures giving the tribimaximal mixing and calculate flavor neutrino masses to estimate CP-violating Dirac and Majorana phases as well as neutrino mixing angles as functions of α and β. Since α and β are generated by μ-τ symmetry breaking interactions, the CP-violating Majorana phase tends to be suppressed and is found to be at most O(0.1) radian. On the other hand, the CP-violating Dirac phase tends to show a proportionality to α or to β.

  14. Electronic structure and phase equilibria in ternary substitutional alloys

    International Nuclear Information System (INIS)

    Traiber, A.J.S.; Allen, S.M.; Waterstrat, R.M.

    1996-01-01

    A reliable, consistent scheme to study phase equilibria in ternary substitutional alloys based on the tight-binding approximation is presented. With electronic parameters from linear muffin-tin orbital calculations, the computed density of states and band structures compare well with those from more accurate abinitio calculations. Disordered alloys are studied within the tight-binding coherent-potential approximation extended to alloys; energetics of ordered systems are obtained through effective pair interactions computed with the general perturbation method; and partially ordered alloys are studied with a novel simplification of the molecular coherent-potential approximation combined with the general perturbation method. The formalism is applied to bcc-based Zr-Ru-Pd alloys which are promising candidates for medical implant devices. Using energetics obtained from the above scheme, we apply the cluster- variation method to study phase equilibria for particular pseudo- binary alloys and show that results are consistent with observed behavior of electronic specific heat coefficient with composition for Zr 0.5 (Ru, Pd) 0.5

  15. Results on Neutrinoless Double-Beta Decay from Gerda Phase I

    Science.gov (United States)

    Macolino, Carla

    2014-12-01

    The GERmanium Detector Array, GERDA, is designed to search for neutrinoless double-beta (0νββ) decay of 76Ge and it is installed in the Laboratori Nazionali del Gran Sasso (LNGS) of INFN, Italy. In this review, the detection principle and detector setup of GERDA are described. Also, the main physics results by GERDA Phase I, are discussed. They include the measurement of the half-life of 2νββ decay, the background decomposition of the energy spectrum and the techniques for the discrimination of the background, based on the pulse shape of the signal. In the last part of this review, the estimation of a limit on the half-life of 0νββ (T0ν 1/2>2.1ḑot 1025 yr at 90% C.L.) and the comparison with previous results are discussed. GERDA data from Phase I strongly disfavor the recent claim of 0νββ discovery, based on data from the Heidelberg-Moscow experiment.

  16. Looking for the Phase Transition—Recent NA61/SHINE Results

    Directory of Open Access Journals (Sweden)

    Ludwik Turko

    2018-03-01

    Full Text Available The fixed-target NA61/SHINE experiment at the CERN Super Proton Synchrotron (SPS seeks to find the critical point (CR of strongly interacting matter as well as the properties of the onset of deconfinement. The experiment provides a scan of measurements of particle spectra and fluctuations in proton–proton, proton–nucleus, and nucleus–nucleus interactions as functions of collision energy and system size, corresponding to a two-dimensional phase diagram (T- μ B . New NA61/SHINE results are shown here, including transverse momentum and multiplicity fluctuations in Ar+Sc collisions as compared to NA61 p+p and Be+Be data, as well earlier NA49 A+A results. Recently, a preliminary effect of change in the system size dependence, labelled as the “percolation threshold” or the “onset of fireball”, was observed in NA61/SHINE data. This effect is closely related to the vicinity of the hadronic phase space transition region and will be discussed in the text.

  17. Results from phase I of the GERDA experiment

    International Nuclear Information System (INIS)

    Wester, Thomas

    2015-01-01

    The GERmanium Detector Array Gerda at the Laboratori Nazionali del Gran Sasso of the INFN in Italy is an experiment dedicated to the search for the neutrinoless double beta (0νββ) decay in 76 Ge. The experiment employs high purity germanium detectors enriched in 76 Ge inside a 64 m 3 cryostat filled with liquid argon. Gerda was planned in two phases of data taking with the goal to reach a half-life sensitivity in the order of 10 26 yr. Phase I of Gerda was running from November 2011 until May 2013. With about 18 kg total detector mass, data with an exposure of 21.6 kg·yr was collected and a background index of 0.01 cts/(keV·kg·yr) was achieved in the region of interest. No signal was found for the 0νββ decay and a new limit of T 1/2 > 2.1 · 10 25 yr (90% C.L.) was obtained, strongly disfavoring the previous claim of observation. Furthermore, the 2νββ decay half-life of 76 Ge was measured with unprecedented precision. Other results include new half-life limits of the order of 10 23 yr for Majoron emitting double beta decay modes with spectral indices n = 1, 2, 3, 7 and new limits in the order of 10 23 yr for 2νββ decays to the first 3 excited states of 76 Se. In Phase II, currently in preparation, the detector mass will be doubled while reducing the background index by a factor of 10

  18. Results from phase I of the GERDA experiment

    Energy Technology Data Exchange (ETDEWEB)

    Wester, Thomas [Institute of Nuclear and Particle Physics, TU Dresden, Zellescher Weg 19, Germany thomas.wester@tu-dresden.de (Germany)

    2015-10-28

    The GERmanium Detector Array Gerda at the Laboratori Nazionali del Gran Sasso of the INFN in Italy is an experiment dedicated to the search for the neutrinoless double beta (0νββ) decay in {sup 76}Ge. The experiment employs high purity germanium detectors enriched in {sup 76}Ge inside a 64 m{sup 3} cryostat filled with liquid argon. Gerda was planned in two phases of data taking with the goal to reach a half-life sensitivity in the order of 10{sup 26} yr. Phase I of Gerda was running from November 2011 until May 2013. With about 18 kg total detector mass, data with an exposure of 21.6 kg·yr was collected and a background index of 0.01 cts/(keV·kg·yr) was achieved in the region of interest. No signal was found for the 0νββ decay and a new limit of T{sub 1/2} > 2.1 · 10{sup 25} yr (90% C.L.) was obtained, strongly disfavoring the previous claim of observation. Furthermore, the 2νββ decay half-life of {sup 76}Ge was measured with unprecedented precision. Other results include new half-life limits of the order of 10{sup 23} yr for Majoron emitting double beta decay modes with spectral indices n = 1, 2, 3, 7 and new limits in the order of 10{sup 23} yr for 2νββ decays to the first 3 excited states of {sup 76}Se. In Phase II, currently in preparation, the detector mass will be doubled while reducing the background index by a factor of 10.

  19. Loss-induced limits to phase measurement precision with maximally entangled states

    International Nuclear Information System (INIS)

    Rubin, Mark A.; Kaushik, Sumanth

    2007-01-01

    The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values L of the loss, phase measurement precision degrades with increasing number N of entangled photons for N sufficiently large. For L above a critical value of approximately 0.785, phase measurement precision degrades with increasing N for all values of N. For L near zero, phase measurement precision improves with increasing N down to a limiting precision of approximately 1.018L radians, attained at N approximately equal to 2.218/L, and degrades as N increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons N T is also examined. For L above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing N, the number of entangled photons employed in a single measurement, for all values of N. For L near zero this ratio is optimized by using approximately N=1.279/L entangled photons in each measurement, yielding a precision of approximately 1.340√(L/N T ) radians

  20. Uniform analytic approximation of Wigner rotation matrices

    Science.gov (United States)

    Hoffmann, Scott E.

    2018-02-01

    We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

  1. Stochastic quantization and mean field approximation

    International Nuclear Information System (INIS)

    Jengo, R.; Parga, N.

    1983-09-01

    In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)

  2. A stochastic phase-field model determined from molecular dynamics

    KAUST Repository

    von Schwerin, Erik

    2010-03-17

    The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.

  3. A stochastic phase-field model determined from molecular dynamics

    KAUST Repository

    von Schwerin, Erik; Szepessy, Anders

    2010-01-01

    The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.

  4. High Rate User Ka-Band Phased Array Antenna Test Results

    Science.gov (United States)

    Caroglanian, Armen; Perko, Kenneth; Seufert, Steve; Dod, Tom; Warshowsky, Jay; Day, John H. (Technical Monitor)

    2001-01-01

    The High Rate User Phased Array Antenna (HRUPAA) is a Ka-Band planar phased array designed by the Harris Corporation for the NASA Goddard Space Flight Center. The HRUPAA permits a satellite to downlink data either to a ground station or through the Tracking and Data Relay Satellite System (TDRSS). The HRUPAA is scanned electronically by ground station / user satellite command over a 120 degree cone angle. The phased array has the advantage of not imparting attitude disturbances to the user spacecraft. The 288-element transmit-only array has distributed RF amplifiers integrated behind each of the printed patch antenna elements. The array has 33 dBW EIRP and is left-hand circularly polarized. An engineering model of a partially populated array has been developed and delivered to NASA Goddard Space Flight Center. This report deals with the testing of the engineering model at the Goddard Antenna Range near-field and compact range facilities. The antenna specifications are described first, followed by the test plan and test results.

  5. Results on neutrinoless double beta decay from GERDA phase I

    CERN Multimedia

    CERN. Geneva

    2013-01-01

    After motivating searches of double beta decay and lepton number violation details about the construction, operation and analysis of GERDA will be given. Results of the recently completed phase I of data taking will then be presented and interpreted. Finally an outlook on future plans will be given.

  6. Development of the relativistic impulse approximation

    International Nuclear Information System (INIS)

    Wallace, S.J.

    1985-01-01

    This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references

  7. Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

    Directory of Open Access Journals (Sweden)

    Giorgos Minas

    2017-07-01

    Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

  8. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  9. Reliability of the one-crossing approximation in describing the Mott transition

    International Nuclear Information System (INIS)

    Vildosola, V; Roura-Bas, P; Pourovskii, L V; Manuel, L O

    2015-01-01

    We assess the reliability of the one-crossing approximation (OCA) approach in a quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds and nanoscale systems. However, several recent studies in the framework of impurity models pointed out serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal–insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behaviour is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations of the system away from the particle-hole symmetric case are also presented and discussed. (paper)

  10. Reliability of the one-crossing approximation in describing the Mott transition

    Science.gov (United States)

    Vildosola, V.; Pourovskii, L. V.; Manuel, L. O.; Roura-Bas, P.

    2015-12-01

    We assess the reliability of the one-crossing approximation (OCA) approach in a quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds and nanoscale systems. However, several recent studies in the framework of impurity models pointed out serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behaviour is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations of the system away from the particle-hole symmetric case are also presented and discussed.

  11. Experimental Investigation of Triplet Correlation Approximations for Fluid Water.

    Science.gov (United States)

    Pallewela, Gayani N; Ploetz, Elizabeth A; Smith, Paul E

    2018-08-25

    Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.

  12. THREE-MOMENT BASED APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING SYSTEMS

    Directory of Open Access Journals (Sweden)

    T. I. Aliev

    2014-03-01

    Full Text Available The paper deals with the problem of approximation of probability distributions of random variables defined in positive area of real numbers with coefficient of variation different from unity. While using queueing systems as models for computer networks, calculation of characteristics is usually performed at the level of expectation and variance. At the same time, one of the main characteristics of multimedia data transmission quality in computer networks is delay jitter. For jitter calculation the function of packets time delay distribution should be known. It is shown that changing the third moment of distribution of packets delay leads to jitter calculation difference in tens or hundreds of percent, with the same values of the first two moments – expectation value and delay variation coefficient. This means that delay distribution approximation for the calculation of jitter should be performed in accordance with the third moment of delay distribution. For random variables with coefficients of variation greater than unity, iterative approximation algorithm with hyper-exponential two-phase distribution based on three moments of approximated distribution is offered. It is shown that for random variables with coefficients of variation less than unity, the impact of the third moment of distribution becomes negligible, and for approximation of such distributions Erlang distribution with two first moments should be used. This approach gives the possibility to obtain upper bounds for relevant characteristics, particularly, the upper bound of delay jitter.

  13. Odour reduction strategies for biosolids produced from a Western Australian wastewater treatment plant: results from Phase I laboratory trials.

    Science.gov (United States)

    Gruchlik, Yolanta; Heitz, Anna; Joll, Cynthia; Driessen, Hanna; Fouché, Lise; Penney, Nancy; Charrois, Jeffrey W A

    2013-01-01

    This study investigated sources of odours from biosolids produced from a Western Australian wastewater treatment plant and examined possible strategies for odour reduction, specifically chemical additions and reduction of centrifuge speed on a laboratory scale. To identify the odorous compounds and assess the effectiveness of the odour reduction measures trialled in this study, headspace solid-phase microextraction gas chromatography-mass spectrometry (HS SPME-GC-MS) methods were developed. The target odour compounds included volatile sulphur compounds (e.g. dimethyl sulphide, dimethyl disulphide and dimethyl trisulphide) and other volatile organic compounds (e.g. toluene, ethylbenzene, styrene, p-cresol, indole and skatole). In our laboratory trials, aluminium sulphate added to anaerobically digested sludge prior to dewatering offered the best odour reduction strategy amongst the options that were investigated, resulting in approximately 40% reduction in the maximum concentration of the total volatile organic sulphur compounds, relative to control.

  14. Face Recognition using Approximate Arithmetic

    DEFF Research Database (Denmark)

    Marso, Karol

    Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

  15. Limitations of the acoustic approximation for seismic crosshole tomography

    Science.gov (United States)

    Marelli, Stefano; Maurer, Hansruedi

    2010-05-01

    implemented by setting the shear wave velocity to almost zero (Vs ~ 0). This approach was checked against a purely acoustic 2D pseudo-spectral time-domain modelling code and found to yield very similar results. In a variety of numerical 2D and 3D experiments, we propagated both acoustic only and full elastic waves through models of increasing complexity. We first investigated three basic simple-shaped anomalies embedded in a homogeneous background, including i) a vertical layer ii) a horizontal layer and iii) two-rectangular blocks. Maximum velocity contrast in these models is about 50% We then tested a more complex model representing a realistic-scale, engineered-nuclear waste repository-like structure, embedded in a granite host rock. Velocity contrasts were chosen to be much higher in this model. Our results indicate that for the simplest models (horizontal and vertical layers) the acoustic approximation is reasonable for the early portions of the seismograms, but for even only moderately complex subsurface models involving several interfaces (e.g. the two block anomalies), the acoustic approximation breaks down and fails to account for the synthesised wavefields. We attribute this failure to the presence of significant P-to-S mode conversions at each interface. Comparable observations were found for both the 2D and the 3D simulations. The main advantage of seismic waveform inversion is that subtle changes in amplitude and phase of the waveforms can be exploited for constructing subsurface models at sub-wavelength resolution. The significant deficiencies of the acoustic approximation for crosshole problems, even in the presence of relatively minor anomalies, therefore strongly question the usefulness of acoustic waveform transmission tomography. Consequently, efforts have to be made to implement the computationally much more challenging elastic waveform inversion scheme.

  16. Approximating centrality in evolving graphs: toward sublinearity

    Science.gov (United States)

    Priest, Benjamin W.; Cybenko, George

    2017-05-01

    The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

  17. Preliminary results of a test of a longitudinal phase-space monitor

    International Nuclear Information System (INIS)

    Kikutani, Eiji; Funakoshi, Yoshihiro; Kawamoto, Takashi; Mimashi, Toshihiro

    1994-01-01

    A prototype of a longitudinal phase-space monitor has been developed in TRISTAN Main Ring at KEK. The principle of the monitor and its basic components are explained. Also a result of a preliminary beam test is given. (author)

  18. Discovering approximate-associated sequence patterns for protein-DNA interactions

    KAUST Repository

    Chan, Tak Ming

    2010-12-30

    Motivation: The bindings between transcription factors (TFs) and transcription factor binding sites (TFBSs) are fundamental protein-DNA interactions in transcriptional regulation. Extensive efforts have been made to better understand the protein-DNA interactions. Recent mining on exact TF-TFBS-associated sequence patterns (rules) has shown great potentials and achieved very promising results. However, exact rules cannot handle variations in real data, resulting in limited informative rules. In this article, we generalize the exact rules to approximate ones for both TFs and TFBSs, which are essential for biological variations. Results: A progressive approach is proposed to address the approximation to alleviate the computational requirements. Firstly, similar TFBSs are grouped from the available TF-TFBS data (TRANSFAC database). Secondly, approximate and highly conserved binding cores are discovered from TF sequences corresponding to each TFBS group. A customized algorithm is developed for the specific objective. We discover the approximate TF-TFBS rules by associating the grouped TFBS consensuses and TF cores. The rules discovered are evaluated by matching (verifying with) the actual protein-DNA binding pairs from Protein Data Bank (PDB) 3D structures. The approximate results exhibit many more verified rules and up to 300% better verification ratios than the exact ones. The customized algorithm achieves over 73% better verification ratios than traditional methods. Approximate rules (64-79%) are shown statistically significant. Detailed variation analysis and conservation verification on NCBI records demonstrate that the approximate rules reveal both the flexible and specific protein-DNA interactions accurately. The approximate TF-TFBS rules discovered show great generalized capability of exploring more informative binding rules. © The Author 2010. Published by Oxford University Press. All rights reserved.

  19. Development of an elevated temperature aluminum alloy containing Al3X-type dispersed phases

    International Nuclear Information System (INIS)

    Zedalis, M.S.

    1985-01-01

    The extents of solid solubility in the equilibrium, tetragonal Al 3 X-type dispersed phases (X represents binary and ternary combinations of Hf, Ti, V, and Zr) were examined using powder x-ray diffraction methods. Minimum lattice disregistry (delta) with the Al(ss) matrix was achieved by maximizing the amount of Ti or V added to the Al 3 Hf and/or Al 3 Zr phases without forming a co-intermetallic compound exhibiting a DO 22 crystal structure. In comparison to Al 3 Zr, with a (delta) equal to 2.88%, the addition of V to Al 3 Zr in the ratio 7:1, i.e., Al 3 (v/sub 0.875/Zr/sub 0.125/), results in a decrease in (delta) by approximately 17%. Electron diffraction revealed that the addition of V to the metastable cubic (L1 2 ) Al 3 Zr phase also resulted in a reduction in the lattice disregistry across the precipitate/matrix boundary. In comparison with the cubic Al 3 Zr phase, with a (delta) of approximately 1.0%, the Al 3 (V/sub 0.875/Zr/sub 0.125/) phase exhibits a mismatch of approximately -0.14%. The cubic Al 3 (V/sub 0.875/Zr/sub 0.125/) phase was observed by TEM to be substantially more stable, i.e., resist transformation to the equilibrium tetragonal phase, when compared to the cubic Al 3 Zr phase. It is proposed that a reduction in lattice disregistry results in a decrease in the strain energy component of the system's total free energy. A systematic decrease in the coarsening rate with a reduction in the lattice disregistry for the cubic Al 3 Zr, Al 3 (V/sub 0.725/Zr/sub 0.275/) and Al 3 (V/sub 0.875/Zr/sub 0.125/) and tetragonal Al 3 Zr and Al 3 (V/sub 0.875/Zr/sub 0.125/) phases is proposed to be representative of a decrease in the interfacial energy across the precipitate/matrix boundary

  20. INL Results for Phases I and III of the OECD/NEA MHTGR-350 Benchmark

    Energy Technology Data Exchange (ETDEWEB)

    Gerhard Strydom; Javier Ortensi; Sonat Sen; Hans Hammer

    2013-09-01

    The Idaho National Laboratory (INL) Very High Temperature Reactor (VHTR) Technology Development Office (TDO) Methods Core Simulation group led the construction of the Organization for Economic Cooperation and Development (OECD) Modular High Temperature Reactor (MHTGR) 350 MW benchmark for comparing and evaluating prismatic VHTR analysis codes. The benchmark is sponsored by the OECD's Nuclear Energy Agency (NEA), and the project will yield a set of reference steady-state, transient, and lattice depletion problems that can be used by the Department of Energy (DOE), the Nuclear Regulatory Commission (NRC), and vendors to assess their code suits. The Methods group is responsible for defining the benchmark specifications, leading the data collection and comparison activities, and chairing the annual technical workshops. This report summarizes the latest INL results for Phase I (steady state) and Phase III (lattice depletion) of the benchmark. The INSTANT, Pronghorn and RattleSnake codes were used for the standalone core neutronics modeling of Exercise 1, and the results obtained from these codes are compared in Section 4. Exercise 2 of Phase I requires the standalone steady-state thermal fluids modeling of the MHTGR-350 design, and the results for the systems code RELAP5-3D are discussed in Section 5. The coupled neutronics and thermal fluids steady-state solution for Exercise 3 are reported in Section 6, utilizing the newly developed Parallel and Highly Innovative Simulation for INL Code System (PHISICS)/RELAP5-3D code suit. Finally, the lattice depletion models and results obtained for Phase III are compared in Section 7. The MHTGR-350 benchmark proved to be a challenging simulation set of problems to model accurately, and even with the simplifications introduced in the benchmark specification this activity is an important step in the code-to-code verification of modern prismatic VHTR codes. A final OECD/NEA comparison report will compare the Phase I and III

  1. Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

    Science.gov (United States)

    Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K.N.; Stamnes, K.

    2016-01-01

    The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

  2. A material optimization model to approximate energy bounds for cellular materials under multiload conditions

    DEFF Research Database (Denmark)

    Guedes, J.M.; Rodrigues, H.C.; Bendsøe, Martin P.

    2003-01-01

    This paper describes a computational model, based on inverse homogenization and topology design, for approximating energy bounds for two-phase composites under multiple load cases. The approach allows for the identification of possible single-scale cellular materials that give rise to the optimal...

  3. Wigner’s phase-space function and atomic structure: II. Ground states for closed-shell atoms

    DEFF Research Database (Denmark)

    Springborg, Michael; Dahl, Jens Peder

    1987-01-01

    We present formulas for reduced Wigner phase-space functions for atoms, with an emphasis on the first-order spinless Wigner function. This function can be written as the sum of separate contributions from single orbitals (the natural orbitals). This allows a detailed study of the function. Here we...... display and analyze the function for the closed-shell atoms helium, beryllium, neon, argon, and zinc in the Hartree-Fock approximation. The quantum-mechanical exact results are compared with those obtained with the approximate Thomas-Fermi description of electron densities in phase space....

  4. Analysis of free-surface flows through energy considerations: Single-phase versus two-phase modeling.

    Science.gov (United States)

    Marrone, Salvatore; Colagrossi, Andrea; Di Mascio, Andrea; Le Touzé, David

    2016-05-01

    The study of energetic free-surface flows is challenging because of the large range of interface scales involved due to multiple fragmentations and reconnections of the air-water interface with the formation of drops and bubbles. Because of their complexity the investigation of such phenomena through numerical simulation largely increased during recent years. Actually, in the last decades different numerical models have been developed to study these flows, especially in the context of particle methods. In the latter a single-phase approximation is usually adopted to reduce the computational costs and the model complexity. While it is well known that the role of air largely affects the local flow evolution, it is still not clear whether this single-phase approximation is able to predict global flow features like the evolution of the global mechanical energy dissipation. The present work is dedicated to this topic through the study of a selected problem simulated with both single-phase and two-phase models. It is shown that, interestingly, even though flow evolutions are different, energy evolutions can be similar when including or not the presence of air. This is remarkable since, in the problem considered, with the two-phase model about half of the energy is lost in the air phase while in the one-phase model the energy is mainly dissipated by cavity collapses.

  5. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-10-01

    The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

  6. Gravitational recoil from binary black hole mergers: The close-limit approximation

    International Nuclear Information System (INIS)

    Sopuerta, Carlos F.; Yunes, Nicolas; Laguna, Pablo

    2006-01-01

    The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. Due to the relevance of this phenomenon in astrophysics, in particular, for galaxy merger scenarios, there have been several attempts to estimate the magnitude of this velocity. Since the main contribution to the recoil comes from the last orbit and plunge, an approximation valid at the last stage of coalescence is well motivated for this type of calculation. In this paper, we present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of ∼57 km/s for a symmetric mass ratio η=M 1 M 2 /(M 1 +M 2 ) 2 ∼0.19 and an initial proper separation of 4M, where M is the total Arnowitt-Deser-Misner (ADM) mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. Therefore, it cannot account for the contributions due to inspiral and initial merger. If we supplement this estimate with post-Newtonian (PN) calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around 80 km/s. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of 214-240 km/s. We also provide nonlinear fits to these estimated upper and lower bounds. These

  7. Phase diagrams of the ternary alloy with a single-ion anisotropy in the mean-field approximation

    International Nuclear Information System (INIS)

    Dely, J.; Bobak, A.

    2006-01-01

    The phase diagram of the AB p C 1-p ternary alloy consisting of Ising spins S A =32, S B =2, and S C =52 is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The effect of the single-ion anisotropy on the phase diagrams is discussed by changing values of the parameters in the model Hamiltonian and comparison is made with the recently reported finite-temperature phase diagrams for the ternary alloy having spin S B =1

  8. Phase transformations and resulting microstructures in Ti - 47 Al -2 Cr alloy

    International Nuclear Information System (INIS)

    Ghasemi-Armaki, H.; Heshmati-Manesh, S.; Jafarian, H. R.; Nili-Ahmadabadi, M.

    2008-01-01

    During the last three decades, intermetallic alloys have focused attention because of their high strength to weight ratio and good creep resistance. Titanium aluminide alloys based on γ-Ti Al are potential candidates to replace Ni-based super alloys currently used in jet engine components at high temperatures because of their low density, high melting temperature, good elevated-temperature strength and modulus retention, high resistance to oxidation and hydrogen absorption, and excellent creep properties. One of the major concerns in these alloys is their poor ductility at room and intermediate temperatures which has been improved slightly by microstructure modifications through heat treatment. Thus, modification of microstructure during cooling and CCT diagram in these alloys is of vital importance. In this study, Ti - 47 Al - 2 Cr intermetallic alloy has been prepared by remelting 4 times with a vacuum arc remelting furnace. Homogenizing treatment was done at 1125 d eg C for 72 h in a sealed vacuum quartz tube. All heat treatments on the samples were carried out in a vacuum heat treatment furnace under a pressure of 10 -1 bar. The atmosphere inside the furnace was changed to that of high purity argon for each heat treatment as an added precaution against oxidation. In this paper, phase transformations in a γ-Ti Al based intermetallic alloy containing chromium were investigated. Heat treatments on samples of this alloy at temperatures above Tα and subsequent cooling with various cooling rates resulted in variety of microstructures. The schematic CCT diagram for this alloy was drawn from microstructural studies using microscopy routs and X-ray diffraction. Then, cyclic heat treatment with grain refining purpose was conducted on a sample of this alloy having massive gamma microstructure. During cyclic heat treatment, gradual dissociation of the gamma phase resulted in the formation of a Widmanstaetten type structure. Trend of microstructure evolution and

  9. Phase transitions in field theory

    International Nuclear Information System (INIS)

    Carvalho, C.A.A. de; Bollini, C.G.; Giambiagi, J.J.

    1984-01-01

    By means of an example for which the effective potential is explicitly calculable (up to the one loop approximation), it is discussed how a phase transition takes place as the temperature is increased and pass from spontaneously broken symmetry to a phase in which the symmetry is restored. (Author) [pt

  10. Nuclear ``pasta'' phase within density dependent hadronic models

    Science.gov (United States)

    Avancini, S. S.; Brito, L.; Marinelli, J. R.; Menezes, D. P.; de Moraes, M. M. W.; Providência, C.; Santos, A. M.

    2009-03-01

    In the present paper, we investigate the onset of the “pasta” phase with different parametrizations of the density dependent hadronic model and compare the results with one of the usual parametrizations of the nonlinear Walecka model. The influence of the scalar-isovector virtual δ meson is shown. At zero temperature, two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature, only the coexistence phases method is used. npe matter with fixed proton fractions and in β equilibrium are studied. We compare our results with restrictions imposed on the values of the density and pressure at the inner edge of the crust, obtained from observations of the Vela pulsar and recent isospin diffusion data from heavy-ion reactions, and with predictions from spinodal calculations.

  11. Nuclear 'pasta' phase within density dependent hadronic models

    International Nuclear Information System (INIS)

    Avancini, S. S.; Marinelli, J. R.; Menezes, D. P.; Moraes, M. M. W. de; Brito, L.; Providencia, C.; Santos, A. M.

    2009-01-01

    In the present paper, we investigate the onset of the 'pasta' phase with different parametrizations of the density dependent hadronic model and compare the results with one of the usual parametrizations of the nonlinear Walecka model. The influence of the scalar-isovector virtual δ meson is shown. At zero temperature, two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature, only the coexistence phases method is used. npe matter with fixed proton fractions and in β equilibrium are studied. We compare our results with restrictions imposed on the values of the density and pressure at the inner edge of the crust, obtained from observations of the Vela pulsar and recent isospin diffusion data from heavy-ion reactions, and with predictions from spinodal calculations

  12. OECD/NEA Burnup Credit Calculational Criticality Benchmark Phase I-B Results

    International Nuclear Information System (INIS)

    DeHart, M.D.

    1993-01-01

    Burnup credit is an ongoing technical concern for many countries that operate commercial nuclear power reactors. In a multinational cooperative effort to resolve burnup credit issues, a Burnup Credit Working Group has been formed under the auspices of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development. This working group has established a set of well-defined calculational benchmarks designed to study significant aspects of burnup credit computational methods. These benchmarks are intended to provide a means for the intercomparison of computer codes, methods, and data applied in spent fuel analysis. The benchmarks have been divided into multiple phases, each phase focusing on a particular feature of burnup credit analysis. This report summarizes the results and findings of the Phase I-B benchmark, which was proposed to provide a comparison of the ability of different code systems and data libraries to perform depletion analysis for the prediction of spent fuel isotopic concentrations. Results included here represent 21 different sets of calculations submitted by 16 different organizations worldwide, and are based on a limited set of nuclides determined to have the most important effect on the neutron multiplication factor of light-water-reactor spent fuel. A comparison of all sets of results demonstrates that most methods are in agreement to within 10% in the ability to estimate the spent fuel concentrations of most actinides. All methods are within 11% agreement about the average for all fission products studied. Furthermore, most deviations are less than 10%, and many are less than 5%. The exceptions are 149 Sm, 151 Sm, and 155 Gd

  13. Effective interactions approach to phase stability in alloys under irradiation

    International Nuclear Information System (INIS)

    Enrique, R.A.; Bellon, P.

    1999-01-01

    Phase stability in alloys under irradiation is studied considering effective thermodynamic potentials. A simple kinetic model of a binary alloy with phase separation is investigated. Time evolution in the alloy results form two competing dynamics: thermal diffusion, and irradiation induced ballistic exchanges. The dynamical (steady state) phase diagram is evaluated exactly performing Kinetic Monte Carlo simulations. The solution is then compared to two theoretical frameworks: the effective quasi-interactions model as proposed by Vaks and Kamishenko, and the effective free energy model as proposed by Martin. New developments of these models are proposed to allow for quantitative comparisons. Both theoretical frameworks yield fairly good approximations to the dynamical phase diagram

  14. Effective interactions approach to phase stability in alloys under irradiation

    International Nuclear Information System (INIS)

    Enrique, R.A.; Bellon, P.

    1999-01-01

    Phase stability in alloys under irradiation is studied considering effective thermodynamic potentials. A simple kinetic model of a binary alloy with phase separation is investigated. Time evolution in the alloy results from two competing dynamics: thermal diffusion, and irradiation induced ballistic exchanges The dynamical (steady state) phase diagram is evaluated exactly performing Kinetic Monte Carlo simulations. The solution is then compared to two theoretical frameworks: the effective quasi-interactions model as proposed by Vaks and Kamishenko, and the effective free energy model as proposed by Martin. New developments of these models are proposed to allow for quantitative comparisons. Both theoretical frameworks yield fairly good approximations to the dynamical phase diagram

  15. Towards the theory of the electroweak phase transition

    International Nuclear Information System (INIS)

    Dine, M.; Leigh, R.G.; Huet, P.; Linde, A.; Linde, D.

    1992-01-01

    We investigate various problems related to the theory of the electroweak phase transition. This includes determination of the nature of the phase transition, discussion of the possible role of the higher-order radiative corrections, and the theory of the formation and evolution of bubbles of the new phase. We show, in particular, that no dangerous linear terms in the scalar field φ appear in the expression for the effective potential. We have found that, for the Higgs-boson mass smaller than the masses of W and Z bosons, the phase transition is of the first order. However, its strength is approximately 2/3 times less than what follows from the one-loop approximation. The phase transition occurs due to production and expansion of critical bubbles. Subcritical bubbles may be important only if the phase transition is very weakly first order. A general analytic expression for the probability of the bubble formation is obtained, which may be used for study of tunneling in a wide class of theories. The bubble-wall velocity depends on many factors, including the ratio of the mean free path of the particles to the thickness of the wall. Thin walls in the electroweak theory have a nonrelativistic velocity, whereas thick walls may be relativistic. A decrease of the cubic term by the factor 2/3 rules our baryogenesis in the minimal version of the electroweak theory. Even though we concentrate in this paper on the phase transition in this theory, most of our results can be applied to more general models as well, where baryogenesis is possible

  16. Foot trajectory approximation using the pendulum model of walking.

    Science.gov (United States)

    Fang, Juan; Vuckovic, Aleksandra; Galen, Sujay; Conway, Bernard A; Hunt, Kenneth J

    2014-01-01

    Generating a natural foot trajectory is an important objective in robotic systems for rehabilitation of walking. Human walking has pendular properties, so the pendulum model of walking has been used in bipedal robots which produce rhythmic gait patterns. Whether natural foot trajectories can be produced by the pendulum model needs to be addressed as a first step towards applying the pendulum concept in gait orthosis design. This study investigated circle approximation of the foot trajectories, with focus on the geometry of the pendulum model of walking. Three able-bodied subjects walked overground at various speeds, and foot trajectories relative to the hip were analysed. Four circle approximation approaches were developed, and best-fit circle algorithms were derived to fit the trajectories of the ankle, heel and toe. The study confirmed that the ankle and heel trajectories during stance and the toe trajectory in both the stance and the swing phases during walking at various speeds could be well modelled by a rigid pendulum. All the pendulum models were centred around the hip with pendular lengths approximately equal to the segment distances from the hip. This observation provides a new approach for using the pendulum model of walking in gait orthosis design.

  17. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung

    2013-02-16

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  18. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung; Liang, Faming; Chen, Yuguo; Yu, Kai

    2013-01-01

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  19. Phase diagram Fe-Sn-Sr. New experimental results

    International Nuclear Information System (INIS)

    Nieva, N; Jimenez, M.J; Gomez, A; Corvalan Moya, C; Arias, D

    2012-01-01

    Zr-based alloys are widely used in nuclear industry due to their specific characteristics. The information of the phase diagrams of the ternary system Fe-Zr-Sn is scarce. In this work we investigate, in a experimental way, the central and the Fe-Sn binary adjacent regions of the Fe-Sn-Zr Gibbs triangle at the temperature of 800 o C. For the experimental work, a set of seven ternary alloys was designed, produced and examined by different complementary techniques. There were performed two types of heat treatments: one of medium and another of long duration. We present a new proposal for the 800 o C isothermal section. The boundaries of the identified phases and the fields of one, two and three phases are indicated in the diagram

  20. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  1. Phases of phosphatidyl ethanolamine monolayers studied by synchrotron x-ray scattering

    DEFF Research Database (Denmark)

    Helm, C.A.; Tippmann-Krayer, P.; Möhwald, H.

    1991-01-01

    For the first time, phospholid monolayers at the air/water interface have been studied by x-ray diffraction and reflection all along the isotherm from the laterally isotropic fluid (the so-called LE phase) to the ordered phases. The model used to analyze the data, and the accuracy of the parameters...... deduced, were tested by comparing the results obtained with two lipids having the same head group but different chain lengths. Compression of the fluid phase leads predominantly to a change of thickness of the hydrophobic moiety, much less of its density, with the head group extension remaining constant....... The main transition involves a considerable increase (approximately 10%) of the electron density in the hydrophobic region, a dehydration of the head group and a positional ordering of the aliphatic tails, albeit with low coherence lengths (approximately 10 spacings). On further compression of the film...

  2. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  3. Magnetic Phase Transitions of CeSb. I

    DEFF Research Database (Denmark)

    Fischer, Pernille Hertz; Lebech, Bente; Meier, G.

    1978-01-01

    The magnetic ordering of the anomalous antiferromagnet CeSb, which has a NaCl crystal structure, was determined in zero applied magnetic field by means of neutron diffraction investigations of single crystals and powder. Below the Neel temperature TN of (16.1+or-0.1)K, there exist six partially...... a first-order phase transition at TN. At approximately TN/2 there is a first-order phase transition to a FCC type IA low-temperature configuration. The unusual magnetic properties of CeSb, which result from anisotropic exchange and crystalline electric field effects, resemble those of certain actinide Na...

  4. Results from phase 2 of the radioiodine test facility experimental program

    Energy Technology Data Exchange (ETDEWEB)

    Ball, J M; Kupferschmid, W C.H.; Wren, J C [Atomic Energy of Canada Ltd., Pinawa, MB (Canada). Whiteshell Labs.

    1996-12-01

    A series of intermediate-scale experiments were conducted in the Radioiodine Test Facility (RTF) in a vinyl-painted, zinc-primer coated, carbon steel vessel in order to assess the effects of vinyl surfaces on iodine volatility in both the presence and absence of radiation. This test series, Phase 2 of a larger, comprehensive program assessing a variety of containment surfaces, also examined the effects of organic (i.e., methyl ethyl ketone) and inorganic (i.e., hydrazine) additives, pH, and venting on the aqueous chemistry and volatility of solutions initially containing cesium iodide. These tests have clearly demonstrated that organics are released to the aqueous phase from the vinyl coating and that, under radiation conditions, these organics can have a significant effect on the formation of volatile iodine species. In particular, the RTF results suggest that radiolytic decomposition of the released organics results in dramatic reductions in pH and dissolved oxygen concentration, which in turn are responsible for increased formation of molecular iodine and organic iodides. When the pH was maintained at 10 (Test 3), much lower iodine volatility was observed; low iodine volatility was also observed in the absence of radiation. This test series also demonstrated that vinyl surfaces, particularly those in contact with the gas phase, were a sink for iodine. (author) 4 figs., 6 tabs., 17 refs.

  5. Results from phase 2 of the radioiodine test facility experimental program

    International Nuclear Information System (INIS)

    Ball, J.M.; Kupferschmid, W.C.H.; Wren, J.C.

    1996-01-01

    A series of intermediate-scale experiments were conducted in the Radioiodine Test Facility (RTF) in a vinyl-painted, zinc-primer coated, carbon steel vessel in order to assess the effects of vinyl surfaces on iodine volatility in both the presence and absence of radiation. This test series, Phase 2 of a larger, comprehensive program assessing a variety of containment surfaces, also examined the effects of organic (i.e., methyl ethyl ketone) and inorganic (i.e., hydrazine) additives, pH, and venting on the aqueous chemistry and volatility of solutions initially containing cesium iodide. These tests have clearly demonstrated that organics are released to the aqueous phase from the vinyl coating and that, under radiation conditions, these organics can have a significant effect on the formation of volatile iodine species. In particular, the RTF results suggest that radiolytic decomposition of the released organics results in dramatic reductions in pH and dissolved oxygen concentration, which in turn are responsible for increased formation of molecular iodine and organic iodides. When the pH was maintained at 10 (Test 3), much lower iodine volatility was observed; low iodine volatility was also observed in the absence of radiation. This test series also demonstrated that vinyl surfaces, particularly those in contact with the gas phase, were a sink for iodine. (author) 4 figs., 6 tabs., 17 refs

  6. Nonstandard approximation schemes for lower dimensional quantum field theories

    International Nuclear Information System (INIS)

    Fitzpatrick, D.A.

    1981-01-01

    The purpose of this thesis has been to apply two different nonstandard approximation schemes to a variety of lower-dimensional schemes. In doing this, we show their applicability where (e.g., Feynman or Rayleigh-Schroedinger) approximation schemes are inapplicable. We have applied the well-known mean-field approximation scheme by Guralnik et al. to general lower dimensional theories - the phi 4 field theory in one dimension, and the massive and massless Thirring models in two dimensions. In each case, we derive a bound-state propagator and then expand the theory in terms of the original and bound-state propagators. The results obtained can be compared with previously known results thereby show, in general, reasonably good convergence. In the second half of the thesis, we develop a self-consistent quantum mechanical approximation scheme. This can be applied to any monotonic polynomial potential. It has been applied in detail to the anharmonic oscillator, and the results in several analytical domains are very good, including extensive tables of numerical results

  7. APPECT: An Approximate Backbone-Based Clustering Algorithm for Tags

    DEFF Research Database (Denmark)

    Zong, Yu; Xu, Guandong; Jin, Pin

    2011-01-01

    algorithm for Tags (APPECT). The main steps of APPECT are: (1) we execute the K-means algorithm on a tag similarity matrix for M times and collect a set of tag clustering results Z={C1,C2,…,Cm}; (2) we form the approximate backbone of Z by executing a greedy search; (3) we fix the approximate backbone...... as the initial tag clustering result and then assign the rest tags into the corresponding clusters based on the similarity. Experimental results on three real world datasets namely MedWorm, MovieLens and Dmoz demonstrate the effectiveness and the superiority of the proposed method against the traditional...... Agglomerative Clustering on tagging data, which possess the inherent drawbacks, such as the sensitivity of initialization. In this paper, we instead make use of the approximate backbone of tag clustering results to find out better tag clusters. In particular, we propose an APProximate backbonE-based Clustering...

  8. Discommensurates and incommensurate phases

    International Nuclear Information System (INIS)

    Gordon, Mirta Beatriz

    1983-01-01

    In its first part, this research thesis reports the study of the commensurate-incommensurate (C-I) transition of single layers of rare gases adsorbed on graphite. The anharmonicity of the interaction between adatoms could explain experimental results corresponding to krypton. The author also studied the orientation instability of the single layer with respect to the chemical potential. Near the C-I transition, walls or discommensurates are oriented in substrate symmetry directions which are determined. The effect of substrate deformation on C-I transition is also studied. In the second part, the author studied the phase diagram at low temperature of the anisotropic Ising model with competing interactions for the approximation of the mean field. Finally, the author presents a phenomenological model of Cerium Antimony which reproduces a large part of its phase diagram [fr

  9. Phase contrast STEM for thin samples: Integrated differential phase contrast

    International Nuclear Information System (INIS)

    Lazić, Ivan; Bosch, Eric G.T.; Lazar, Sorin

    2016-01-01

    It has been known since the 1970s that the movement of the center of mass (COM) of a convergent beam electron diffraction (CBED) pattern is linearly related to the (projected) electrical field in the sample. We re-derive a contrast transfer function (CTF) for a scanning transmission electron microscopy (STEM) imaging technique based on this movement from the point of view of image formation and continue by performing a two-dimensional integration on the two images based on the two components of the COM movement. The resulting integrated COM (iCOM) STEM technique yields a scalar image that is linear in the phase shift caused by the sample and therefore also in the local (projected) electrostatic potential field of a thin sample. We confirm that the differential phase contrast (DPC) STEM technique using a segmented detector with 4 quadrants (4Q) yields a good approximation for the COM movement. Performing a two-dimensional integration, just as for the COM, we obtain an integrated DPC (iDPC) image which is approximately linear in the phase of the sample. Beside deriving the CTFs of iCOM and iDPC, we clearly point out the objects of the two corresponding imaging techniques, and highlight the differences to objects corresponding to COM-, DPC-, and (HA) ADF-STEM. The theory is validated with simulations and we present first experimental results of the iDPC-STEM technique showing its capability for imaging both light and heavy elements with atomic resolution and a good signal to noise ratio (SNR). - Highlights: • First DPC-based atomic resolution images of potential and charge density are obtained. • This is enabled by integration and differentiation of 2D DPC signals, respectively. • Integrated DPC (iDPC) based on 4 quadrant imaging is compared to iCOM imaging. • Noise analysis and comparison with standard STEM imaging modes is provided. • iDPC allows direct imaging of light (C, N, O …) and heavy (Ga, Au …) atoms together.

  10. Phase contrast STEM for thin samples: Integrated differential phase contrast

    Energy Technology Data Exchange (ETDEWEB)

    Lazić, Ivan, E-mail: ivan.lazic@fei.com; Bosch, Eric G.T.; Lazar, Sorin

    2016-01-15

    It has been known since the 1970s that the movement of the center of mass (COM) of a convergent beam electron diffraction (CBED) pattern is linearly related to the (projected) electrical field in the sample. We re-derive a contrast transfer function (CTF) for a scanning transmission electron microscopy (STEM) imaging technique based on this movement from the point of view of image formation and continue by performing a two-dimensional integration on the two images based on the two components of the COM movement. The resulting integrated COM (iCOM) STEM technique yields a scalar image that is linear in the phase shift caused by the sample and therefore also in the local (projected) electrostatic potential field of a thin sample. We confirm that the differential phase contrast (DPC) STEM technique using a segmented detector with 4 quadrants (4Q) yields a good approximation for the COM movement. Performing a two-dimensional integration, just as for the COM, we obtain an integrated DPC (iDPC) image which is approximately linear in the phase of the sample. Beside deriving the CTFs of iCOM and iDPC, we clearly point out the objects of the two corresponding imaging techniques, and highlight the differences to objects corresponding to COM-, DPC-, and (HA) ADF-STEM. The theory is validated with simulations and we present first experimental results of the iDPC-STEM technique showing its capability for imaging both light and heavy elements with atomic resolution and a good signal to noise ratio (SNR). - Highlights: • First DPC-based atomic resolution images of potential and charge density are obtained. • This is enabled by integration and differentiation of 2D DPC signals, respectively. • Integrated DPC (iDPC) based on 4 quadrant imaging is compared to iCOM imaging. • Noise analysis and comparison with standard STEM imaging modes is provided. • iDPC allows direct imaging of light (C, N, O …) and heavy (Ga, Au …) atoms together.

  11. Dynamical Vertex Approximation for the Hubbard Model

    Science.gov (United States)

    Toschi, Alessandro

    A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.

  12. Commissioning and first results from the CMS phase-1 upgrade pixel detector

    CERN Document Server

    Sonneveld, Jorine Mirjam

    2017-01-01

    The phase~1 upgrade of the CMS pixel detector has been designed to maintain the tracking performance at instantaneous luminosities of $2 \\times 10^{34} \\mathrm{~cm}^{-2} \\mathrm{~s}^{-1}$. Both barrel and endcap disk systems now feature one extra layer (4 barrel layers and 3 endcap disks), and a digital readout that provides a large enough bandwidth to read out its 124M pixel channels (87.7 percent more pixels compared to the previous system). The backend control and readout systems have been upgraded accordingly from VME-based to micro-TCA-based ones. The detector is now also fitted with a bi-phase CO$_2$ cooling system that reduces the material budget in the tracking region. The detector has been installed inside CMS at the start of 2017 and is now taking data. These proceedings discuss experiences in the commissioning and operation of the CMS phase~1 pixel detector. The first results from the CMS phase~1 pixel detector with this year's LHC proton-proton collision data are presented. ...

  13. Geometric convergence of some two-point Pade approximations

    International Nuclear Information System (INIS)

    Nemeth, G.

    1983-01-01

    The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)

  14. Approximation properties of haplotype tagging

    Directory of Open Access Journals (Sweden)

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  15. Lattice quantum chromodynamics with approximately chiral fermions

    International Nuclear Information System (INIS)

    Hierl, Dieter

    2008-05-01

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  16. Lattice quantum chromodynamics with approximately chiral fermions

    Energy Technology Data Exchange (ETDEWEB)

    Hierl, Dieter

    2008-05-15

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  17. Plutonium immobilization program - Cold pour Phase 1 test results

    International Nuclear Information System (INIS)

    Hamilton, L.

    2000-01-01

    The Plutonium Immobilization Project will disposition excess weapons grade plutonium. It uses the can-in-canister approach that involves placing plutonium-ceramic pucks in sealed cans that are then placed into Defense Waste Processing Facility canisters. These canisters are subsequently filled with high-level radioactive waste glass. This process puts the plutonium in a stable form and makes it unattractive for reuse. A cold (non-radioactive) glass pour program was performed to develop and verify the baseline design for the canister and internal hardware. This paper describes the Phase 1 scoping test results

  18. Plutonium Immobilization Program - Cold pour Phase 1 test results

    International Nuclear Information System (INIS)

    Hamilton, L.

    2000-01-01

    The Plutonium Immobilization Project will disposition excess weapons grade plutonium. It uses the can-in-canister approach that involves placing plutonium-ceramic pucks in sealed cans that are then placed into Defense Waste Processing Facility canisters. These canisters are subsequently filled with high-level radioactive waste glass. This process puts the plutonium in a stable form and makes it unattractive for reuse. A cold (non-radioactive) glass pour program was performed to develop and verify the baseline design for the canister and internal hardware. This paper describes the Phase 1 scoping test results

  19. Main results of the German risk study - phase B

    International Nuclear Information System (INIS)

    Heuser, F.W.

    1987-01-01

    To start the author introduces briefly some comments on main tasks and objectives of risk analysises which at least after the Chernobyl accident should be emphasized more explicitly. Following on some main results of the system - and accident event tree analysis of the German Risk Study, Phase B, are summarized. The second part of this paper deals with the analysis of core melt accidents performed in context of the study. Hetero investigations on the hydrogen problem and investigations on containment venting after a core melt accident will be discussed in more detail

  20. Static quadrupolar susceptibility for a Blume–Emery–Griffiths model based on the mean-field approximation

    Energy Technology Data Exchange (ETDEWEB)

    Pawlak, A., E-mail: pawlak@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61–614 Poznań (Poland); Gülpınar, G. [Department of Physics, Dokuz Eylül University, 35160 İzmir (Turkey); Erdem, R. [Department of Physics, Akdeniz University, 07058 Antalya (Turkey); Ağartıoğlu, M. [Institute of Science, Dokuz Eylül University, 35160 İzmir (Turkey)

    2015-12-01

    The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume–Emery–Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic–paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like. - Highlights: • MFA calculation of the quadrupolar and dipolar susceptibility in BEG model is given • The crystal-field variation of susceptibilities near the multi-critical points is examined • There are broad peaks in the quadrupolar susceptibility in the vicinity of CP • These maxima are remembrances of the very strong quadrupolar Fluctuations.

  1. OECD/NEA Burnup Credit Calculational Criticality Benchmark Phase I-B Results

    Energy Technology Data Exchange (ETDEWEB)

    DeHart, M.D.

    1993-01-01

    Burnup credit is an ongoing technical concern for many countries that operate commercial nuclear power reactors. In a multinational cooperative effort to resolve burnup credit issues, a Burnup Credit Working Group has been formed under the auspices of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development. This working group has established a set of well-defined calculational benchmarks designed to study significant aspects of burnup credit computational methods. These benchmarks are intended to provide a means for the intercomparison of computer codes, methods, and data applied in spent fuel analysis. The benchmarks have been divided into multiple phases, each phase focusing on a particular feature of burnup credit analysis. This report summarizes the results and findings of the Phase I-B benchmark, which was proposed to provide a comparison of the ability of different code systems and data libraries to perform depletion analysis for the prediction of spent fuel isotopic concentrations. Results included here represent 21 different sets of calculations submitted by 16 different organizations worldwide, and are based on a limited set of nuclides determined to have the most important effect on the neutron multiplication factor of light-water-reactor spent fuel. A comparison of all sets of results demonstrates that most methods are in agreement to within 10% in the ability to estimate the spent fuel concentrations of most actinides. All methods are within 11% agreement about the average for all fission products studied. Furthermore, most deviations are less than 10%, and many are less than 5%. The exceptions are {sup 149}Sm, {sup 151}Sm, and {sup 155}Gd.

  2. An improved saddlepoint approximation.

    Science.gov (United States)

    Gillespie, Colin S; Renshaw, Eric

    2007-08-01

    Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.

  3. Phase accuracy evaluation for phase-shifting fringe projection profilometry based on uniform-phase coded image

    Science.gov (United States)

    Zhang, Chunwei; Zhao, Hong; Zhu, Qian; Zhou, Changquan; Qiao, Jiacheng; Zhang, Lu

    2018-06-01

    Phase-shifting fringe projection profilometry (PSFPP) is a three-dimensional (3D) measurement technique widely adopted in industry measurement. It recovers the 3D profile of measured objects with the aid of the fringe phase. The phase accuracy is among the dominant factors that determine the 3D measurement accuracy. Evaluation of the phase accuracy helps refine adjustable measurement parameters, contributes to evaluating the 3D measurement accuracy, and facilitates improvement of the measurement accuracy. Although PSFPP has been deeply researched, an effective, easy-to-use phase accuracy evaluation method remains to be explored. In this paper, methods based on the uniform-phase coded image (UCI) are presented to accomplish phase accuracy evaluation for PSFPP. These methods work on the principle that the phase value of a UCI can be manually set to be any value, and once the phase value of a UCI pixel is the same as that of a pixel of a corresponding sinusoidal fringe pattern, their phase accuracy values are approximate. The proposed methods provide feasible approaches to evaluating the phase accuracy for PSFPP. Furthermore, they can be used to experimentally research the property of the random and gamma phase errors in PSFPP without the aid of a mathematical model to express random phase error or a large-step phase-shifting algorithm. In this paper, some novel and interesting phenomena are experimentally uncovered with the aid of the proposed methods.

  4. Project Half Double: Current Results of Phase 1 and Phase 2, December 2017

    DEFF Research Database (Denmark)

    Svejvig, Per; Thorp Adland, Karoline; Zippora Klein, Judith Birte

    ’s competitiveness and play an important role in the battle for jobs and future welfare. The overall goal is to deliver “Projects in half the time with double the impact” where projects in half the time should be understood as half the time to impact (benefit realization, effect is achieved) and not as half the time...... of Project Half Double was initiated in June 2015. It is a two-phase project: phase 1 took place from June 2015 to June 2016 with seven pilot projects, and phase 2 is in progress from July 2016 to July 2018 with 10 pilot projects. The Half Double consortium: Implement Consulting Group is the project leader....... 2016, Svejvig et al. 2017). This report’s target group inludes practitioners in Danish industry and society in general. The editorial team from Aarhus University prepared the report from October 2017 to December 2017, which means that data about pilot projects from December 2017 is not included....

  5. Application of phase contrast imaging to mammography

    International Nuclear Information System (INIS)

    Tohyama, Keiko; Yamada, Katsuhiko; Katafuchi, Tetsuro; Matsuo, Satoru; Morishita, Junji

    2005-01-01

    Phase contrast images were obtained experimentally by using a customized mammography unit with a nominal focal spot size of 100 μm and variable source-to-image distances of up to 1.5 m. The purpose of this study was to examine the applicability and potential usefulness of phase contrast imaging for mammography. A mammography phantom (ACR156 RMI phantom) was imaged, and its visibility was examined. The optical density of the phantom images was adjusted to approximately 1.3 for both the contact and phase contrast images. Forty-one observers (18 medical doctors and 23 radiological technologists) participated in visual evaluation of the images. Results showed that, in comparison with the images of contact mammography, the phantom images of phase contrast imaging demonstrated statistically significantly superior visibility for fibers, clustered micro-calcifications, and masses. Therefore, phase contrast imaging obtained by using the customized mammography unit would be useful for improving diagnostic accuracy in mammography. (author)

  6. Does Concurrent Radiochemotherapy Affect Cosmetic Results in the Adjuvant Setting After Breast-Conserving Surgery? Results of the ARCOSEIN Multicenter, Phase III Study: Patients' and Doctors' Views

    International Nuclear Information System (INIS)

    Toledano, Alain H.; Bollet, Marc A.; Fourquet, Alain; Azria, David; Gligorov, Joseph; Garaud, Pascal; Serin, Daniel; Bosset, Jean-Francois; Miny-Buffet, Joelle; Favre, Anne; Le Foch, Olivier; Calais, Gilles

    2007-01-01

    Purpose: To evaluate the cosmetic results of sequential vs. concurrent adjuvant chemotherapy with radiotherapy after breast-conserving surgery for breast cancer, and to compare ratings by patients and physicians. Methods and Materials: From 1996 to 2000, 716 patients with Stage I-II breast cancers were included in a multicenter, Phase III trial (the ARCOSEIN study) comparing, after breast-conserving surgery with axillary dissection, sequential treatment with chemotherapy first followed by radiotherapy vs. chemotherapy administered concurrently with radiotherapy. Cosmetic results with regard to both the overall aspect of the breast and specific changes (color, scar) were evaluated in a total of 214 patients (107 in each arm) by means of questionnaires to both the patient and a physician whose rating was blinded to treatment allocation. Results: Patients' overall satisfaction with cosmesis was not statistically different between the two arms, with approximately 92% with at least satisfactory results (p = 0.72), although differences between the treated and untreated breasts were greater after the concurrent regimen (29% vs. 14% with more than moderate differences; p 0.0015). Physician assessment of overall cosmesis was less favorable, with lower rates of at least satisfactory results in the concurrent arm (60% vs. 85%; p = 0.001). Consequently, the concordance for overall satisfaction with cosmesis between patients and doctors was only fair (κ = 0.62). Conclusion: After breast-conserving surgery, the concurrent use of chemotherapy with radiotherapy is significantly associated with greater differences between the breasts. These differences do not translate into patients' lessened satisfaction with cosmesis

  7. Efficient solution of parabolic equations by Krylov approximation methods

    Science.gov (United States)

    Gallopoulos, E.; Saad, Y.

    1990-01-01

    Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

  8. Offshore Code Comparison Collaboration within IEA Wind Task 23: Phase IV Results Regarding Floating Wind Turbine Modeling; Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Jonkman, J.; Larsen, T.; Hansen, A.; Nygaard, T.; Maus, K.; Karimirad, M.; Gao, Z.; Moan, T.; Fylling, I.

    2010-04-01

    Offshore wind turbines are designed and analyzed using comprehensive simulation codes that account for the coupled dynamics of the wind inflow, aerodynamics, elasticity, and controls of the turbine, along with the incident waves, sea current, hydrodynamics, and foundation dynamics of the support structure. This paper describes the latest findings of the code-to-code verification activities of the Offshore Code Comparison Collaboration, which operates under Subtask 2 of the International Energy Agency Wind Task 23. In the latest phase of the project, participants used an assortment of codes to model the coupled dynamic response of a 5-MW wind turbine installed on a floating spar buoy in 320 m of water. Code predictions were compared from load-case simulations selected to test different model features. The comparisons have resulted in a greater understanding of offshore floating wind turbine dynamics and modeling techniques, and better knowledge of the validity of various approximations. The lessons learned from this exercise have improved the participants' codes, thus improving the standard of offshore wind turbine modeling.

  9. Polynomial approximation on polytopes

    CERN Document Server

    Totik, Vilmos

    2014-01-01

    Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

  10. Polynomial approximation of functions in Sobolev spaces

    International Nuclear Information System (INIS)

    Dupont, T.; Scott, R.

    1980-01-01

    Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces

  11. The generalized approximation method and nonlinear heat transfer equations

    Directory of Open Access Journals (Sweden)

    Rahmat Khan

    2009-01-01

    Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.

  12. Kullback-Leibler divergence and the Pareto-Exponential approximation.

    Science.gov (United States)

    Weinberg, G V

    2016-01-01

    Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.

  13. Inertial parameters in the interacting boson fermion approximation

    International Nuclear Information System (INIS)

    Dukelsky, J.; Lima, C.

    1986-06-01

    The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors) [pt

  14. On badly approximable complex numbers

    DEFF Research Database (Denmark)

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  15. Phase calibration approaches for radar interferometry and imaging configurations: equatorial spread F results

    Directory of Open Access Journals (Sweden)

    J. L. Chau

    2008-08-01

    Full Text Available In recent years, more and more radar systems with multiple-receiver antennas are being used to study the atmospheric and ionospheric irregularities with either interferometric and/or imaging configurations. In such systems, one of the major challenges is to know the phase offsets between the different receiver channels. Such phases are intrinsic to the system and are due to different cable lengths, filters, attenuators, amplifiers, antenna impedance, etc. Moreover, such phases change as function of time, on different time scales, depending on the specific installation. In this work, we present three approaches using natural targets (radio stars, meteor-head and meteor trail echoes that allow either an absolute or relative phase calibration. In addition, we present the results of using an artificial source (radio beacon for a continuous calibration that complements the previous approaches. These approaches are robust and good alternatives to other approaches, e.g. self-calibration techniques using known data features, or for multiple-receiver configurations constantly changing their receiving elements. In order to show the good performance of the proposed phase calibration techniques, we present new radar imaging results of equatorial spread F (ESF irregularities. Finally we introduce a new way to represent range-time intensity (RTI maps color coded with the Doppler information. Such modified map allows the identification and interpretation of geophysical phenomena, previously hidden in conventional RTI maps, e.g. the time and altitude of occurrence of ESF irregularities pinching off from the bottomside and their respective Doppler velocity.

  16. Results of the Gallium-Clad Phase 3 and Phase 4 tasks (canceled prior to completion)

    International Nuclear Information System (INIS)

    Morris, R.N.

    1998-08-01

    This report summarizes the results of the Gallium-Clad interactions Phase 3 and 4 tasks. Both tasks were to involve examining the out-of-pile stability of residual gallium in short fuel rods with an imposed thermal gradient. The thermal environment was to be created by an electrical heater in the center of the fuel rod and coolant flow on the rod outer cladding. Both tasks were canceled due to difficulties with fuel pellet fabrication, delays in the preparation of the test apparatus, and changes in the Fissile Materials Disposition program budget

  17. Approximal morphology as predictor of approximal caries in primary molar teeth

    DEFF Research Database (Denmark)

    Cortes, A; Martignon, S; Qvist, V

    2018-01-01

    consent was given, participated. Upper and lower molar teeth of one randomly selected side received a 2-day temporarily separation. Bitewing radiographs and silicone impressions of interproximal area (IPA) were obtained. One-year procedures were repeated in 52 children (84%). The morphology of the distal...... surfaces of the first molar teeth and the mesial surfaces on the second molar teeth (n=208) was scored from the occlusal aspect on images from the baseline resin models resulting in four IPA variants: concave-concave; concave-convex; convex-concave, and convex-convex. Approximal caries on the surface...

  18. Comparison of reporting phase I trial results in ClinicalTrials.gov and matched publications.

    Science.gov (United States)

    Shepshelovich, D; Goldvaser, H; Wang, L; Abdul Razak, A R; Bedard, P L

    2017-12-01

    Background Data on completeness of reporting of phase I cancer clinical trials in publications are lacking. Methods The ClinicalTrials.gov database was searched for completed adult phase I cancer trials with reported results. PubMed was searched for matching primary publications published prior to November 1, 2016. Reporting in primary publications was compared with the ClinicalTrials.gov database using a 28-point score (2=complete; 1=partial; 0=no reporting) for 14 items related to study design, outcome measures and safety profile. Inconsistencies between primary publications and ClinicalTrials.gov were recorded. Linear regression was used to identify factors associated with incomplete reporting. Results After a review of 583 trials in ClinicalTrials.gov , 163 matching primary publications were identified. Publications reported outcomes that did not appear in ClinicalTrials.gov in 25% of trials. Outcomes were upgraded, downgraded or omitted in publications in 47% of trials. The overall median reporting score was 23/28 (interquartile range 21-25). Incompletely reported items in >25% publications were: inclusion criteria (29%), primary outcome definition (26%), secondary outcome definitions (53%), adverse events (71%), serious adverse events (80%) and dates of study start and database lock (91%). Higher reporting scores were associated with phase I (vs phase I/II) trials (ppublication in journals with lower impact factor (p=0.004). Conclusions Reported results in primary publications for early phase cancer trials are frequently inconsistent or incomplete compared with ClinicalTrials.gov entries. ClinicalTrials.gov may provide more comprehensive data from new cancer drug trials.

  19. Casimir interaction between a cylinder and a plate at finite temperature: Exact results and comparison to proximity force approximation

    International Nuclear Information System (INIS)

    Teo, L. P.

    2011-01-01

    We study the finite temperature Casimir interaction between a cylinder and a plate using the exact formula derived from the Matsubara representation and the functional determinant representation. We consider the scalar field with Dirichlet and Neumann boundary conditions. The asymptotic expansions of the Casimir free energy and the Casimir force when the separation a between the cylinder and the plate is small are derived. As in the zero temperature case, it is found that the leading terms of the Casimir free energy and the Casimir force agree with those derived from the proximity force approximation when rT>>1, where r is the radius of the cylinder. Specifically, when aT 5/2 whereas, for the Casimir force, it is of order T 7/2 . In this case, the leading terms are independent of the separation a. When 1 3/2 , whereas, for the force, it is inversely proportional to a 5/2 . The first order corrections to the proximity force approximations in different temperature regions are computed using the perturbation approach. In the zero temperature case, the results agree with those derived in [M. Bordag, Phys. Rev. D 73, 125018 (2006)].

  20. Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation

    Directory of Open Access Journals (Sweden)

    Feng Lian

    2012-01-01

    Full Text Available The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD filter and its extended Kalman (EK filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.

  1. Square well approximation to the optical potential

    International Nuclear Information System (INIS)

    Jain, A.K.; Gupta, M.C.; Marwadi, P.R.

    1976-01-01

    Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)

  2. Integrated thermal treatment system study -- Phase 2 results. Revision 1

    Energy Technology Data Exchange (ETDEWEB)

    Feizollahi, F.; Quapp, W.J.

    1996-02-01

    This report presents the second phase of a study on thermal treatment technologies. The study consists of a systematic assessment of nineteen thermal treatment alternatives for the contact-handled mixed low-level waste (MLLW) currently stored in the US Department of Energy complex. The treatment alternatives consist of widely varying technologies for safely destroying the hazardous organic components, reducing the volume, and preparing for final disposal of the MLLW. The alternatives considered in Phase 2 were innovative thermal treatments with nine types of primary processing units. Other variations in the study examined the effect of combustion gas, air pollution control system design, and stabilization technology for the treatment residues. The Phase 1 study examined ten initial thermal treatment alternatives. The Phase 2 systems were evaluated in essentially the same manner as the Phase 1 systems. The alternatives evaluated were: rotary kiln, slagging kiln, plasma furnace, plasma gasification, molten salt oxidation, molten metal waste destruction, steam gasification, Joule-heated vitrification, thermal desorption and mediated electrochemical oxidation, and thermal desorption and supercritical water oxidation. The quantities, and physical and chemical compositions, of the input waste used in the Phase 2 systems differ from those in the Phase 1 systems, which were based on a preliminary waste input database developed at the onset of the Integrated Thermal Treatment System study. The inventory database used in the Phase 2 study incorporates the latest US Department of Energy information. All systems, both primary treatment systems and subsystem inputs, have now been evaluated using the same waste input (2,927 lb/hr). 28 refs., 88 figs., 41 tabs.

  3. Integrated thermal treatment system study -- Phase 2 results. Revision 1

    International Nuclear Information System (INIS)

    Feizollahi, F.; Quapp, W.J.

    1996-02-01

    This report presents the second phase of a study on thermal treatment technologies. The study consists of a systematic assessment of nineteen thermal treatment alternatives for the contact-handled mixed low-level waste (MLLW) currently stored in the US Department of Energy complex. The treatment alternatives consist of widely varying technologies for safely destroying the hazardous organic components, reducing the volume, and preparing for final disposal of the MLLW. The alternatives considered in Phase 2 were innovative thermal treatments with nine types of primary processing units. Other variations in the study examined the effect of combustion gas, air pollution control system design, and stabilization technology for the treatment residues. The Phase 1 study examined ten initial thermal treatment alternatives. The Phase 2 systems were evaluated in essentially the same manner as the Phase 1 systems. The alternatives evaluated were: rotary kiln, slagging kiln, plasma furnace, plasma gasification, molten salt oxidation, molten metal waste destruction, steam gasification, Joule-heated vitrification, thermal desorption and mediated electrochemical oxidation, and thermal desorption and supercritical water oxidation. The quantities, and physical and chemical compositions, of the input waste used in the Phase 2 systems differ from those in the Phase 1 systems, which were based on a preliminary waste input database developed at the onset of the Integrated Thermal Treatment System study. The inventory database used in the Phase 2 study incorporates the latest US Department of Energy information. All systems, both primary treatment systems and subsystem inputs, have now been evaluated using the same waste input (2,927 lb/hr). 28 refs., 88 figs., 41 tabs

  4. Deterministic quantum controlled-PHASE gates based on non-Markovian environments

    Science.gov (United States)

    Zhang, Rui; Chen, Tian; Wang, Xiang-Bin

    2017-12-01

    We study the realization of the quantum controlled-PHASE gate in an atom-cavity system beyond the Markovian approximation. The general description of the dynamics for the atom-cavity system without any approximation is presented. When the spectral density of the reservoir has the Lorentz form, by making use of the memory backflow from the reservoir, we can always construct the deterministic quantum controlled-PHASE gate between a photon and an atom, no matter the atom-cavity coupling strength is weak or strong. While, the phase shift in the output pulse hinders the implementation of quantum controlled-PHASE gates in the sub-Ohmic, Ohmic or super-Ohmic reservoirs.

  5. An overview on polynomial approximation of NP-hard problems

    Directory of Open Access Journals (Sweden)

    Paschos Vangelis Th.

    2009-01-01

    Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

  6. Function approximation using combined unsupervised and supervised learning.

    Science.gov (United States)

    Andras, Peter

    2014-03-01

    Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

  7. Nuclear data processing, analysis, transformation and storage with Pade-approximants

    International Nuclear Information System (INIS)

    Badikov, S.A.; Gay, E.V.; Guseynov, M.A.; Rabotnov, N.S.

    1992-01-01

    A method is described to generate rational approximants of high order with applications to neutron data handling. The problems considered are: The approximations of neutron cross-sections in resonance region producing the parameters for Adler-Adler type formulae; calculations of resulting rational approximants' errors given in analytical form allowing to compute the error at any energy point inside the interval of approximation; calculations of the correlation coefficient of error values in two arbitrary points provided that experimental errors are independent and normally distributed; a method of simultaneous generation of a few rational approximants with identical set of poles; functionals other than LSM; two-dimensional approximation. (orig.)

  8. Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman; Spall, J. C.

    1998-01-01

    simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

  9. Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation

    Institute of Scientific and Technical Information of China (English)

    Cornelis KRAAIKAMP; Ionica SMEETS

    2011-01-01

    In 2004,Tong found bounds for the approximation quality of a regular continued fraction convergent to a rational number,expressed in bounds for both the previous and next approximation.The authors sharpen his results with a geometric method and give both sharp upper and lower bounds.The asymptotic frequencies that these bounds occur are also calculated.

  10. Approximating Preemptive Stochastic Scheduling

    OpenAIRE

    Megow Nicole; Vredeveld Tjark

    2009-01-01

    We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

  11. On the chiral phase transition in the linear sigma model

    International Nuclear Information System (INIS)

    Tran Huu Phat; Nguyen Tuan Anh; Le Viet Hoa

    2003-01-01

    The Cornwall- Jackiw-Tomboulis (CJT) effective action for composite operators at finite temperature is used to investigate the chiral phase transition within the framework of the linear sigma model as the low-energy effective model of quantum chromodynamics (QCD). A new renormalization prescription for the CJT effective action in the Hartree-Fock (HF) approximation is proposed. A numerical study, which incorporates both thermal and quantum effect, shows that in this approximation the phase transition is of first order. However, taking into account the higher-loop diagrams contribution the order of phase transition is unchanged. (author)

  12. Approximate kernel competitive learning.

    Science.gov (United States)

    Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

    2015-03-01

    Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

  13. Approximated calculation of the vacuum wave function and vacuum energy of the LGT with RPA method

    International Nuclear Information System (INIS)

    Hui Ping

    2004-01-01

    The coupled cluster method is improved with the random phase approximation (RPA) to calculate vacuum wave function and vacuum energy of 2 + 1 - D SU(2) lattice gauge theory. In this calculating, the trial wave function composes of single-hollow graphs. The calculated results of vacuum wave functions show very good scaling behaviors at weak coupling region l/g 2 >1.2 from the third order to the sixth order, and the vacuum energy obtained with RPA method is lower than the vacuum energy obtained without RPA method, which means that this method is a more efficient one

  14. First test results for an adjustable phase undulator

    International Nuclear Information System (INIS)

    Carr, R.; Nuhn, H.D.; Corbett, J.

    1992-01-01

    An Adjustable Phase Undulator (APU) was installed and tested on the beamline 5 of the SPEAR storage ring. The APU has the same magnetic structure as a conventional adjustable gap undulator (AGU), but its magnetic field is varied by changing the longitudinal position between the rows of magnets, while keeping the gap between them fixed. The tests described here show that this undulator performs according to theoretical predictions and numerical models. The main reason to consider a phase adjustable design is the substantial reduction in size, complexity, and cost over comparable conventional designs. (author) 4 refs.; 3 figs

  15. Study of SmS properties in the low pressure phase (black phase)

    International Nuclear Information System (INIS)

    Bordier, G.

    1986-01-01

    SmS was studied for the transition from low pressure phase (black phase) to high pressure phase with an intermediate valence. But the study of the black phase is very rich. The variations of electron transport properties with pressure at low temperature show a semi-metal phase located, in the pressure-temperature diagram in the black phase for pressure over 4 kbars, corresponding to the phase B'of the doping-temperature diagram. Electron spin resonance shows a lack of sulfur and nearby this defect a samarium ion, magnetically coupled with the matrix, presents a divalent trivalent transition. Resonance lines are broadened with temperature. Conductivity relaxations occur at low pressure and low temperature by trapping a conduction electron, by magnetic exchange giving a bounded magnetic polaron. The relaxation time at null magnetic field is activated. An approximation of trapping barrier and critical field corresponding the maximum magnetoresistance is given by a model [fr

  16. Quantum teleportation via noisy bipartite and tripartite accelerating quantum states: beyond the single mode approximation

    Science.gov (United States)

    Zounia, M.; Shamirzaie, M.; Ashouri, A.

    2017-09-01

    In this paper quantum teleportation of an unknown quantum state via noisy maximally bipartite (Bell) and maximally tripartite (Greenberger-Horne-Zeilinger (GHZ)) entangled states are investigated. We suppose that one of the observers who would receive the sent state accelerates uniformly with respect to the sender. The interactions of the quantum system with its environment during the teleportation process impose noises. These (unital and nonunital) noises are: phase damping, phase flip, amplitude damping and bit flip. In expressing the modes of the Dirac field used as qubits, in the accelerating frame, the so-called single mode approximation is not imposed. We calculate the fidelities of teleportation, and discuss their behaviors using suitable plots. The effects of noise, acceleration and going beyond the single mode approximation are discussed. Although the Bell states bring higher fidelities than GHZ states, the global behaviors of the two quantum systems with respect to some noise types, and therefore their fidelities, are different.

  17. Lognormal Approximations of Fault Tree Uncertainty Distributions.

    Science.gov (United States)

    El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

    2018-01-26

    Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

  18. Improved WKB approximation for quantum tunneling: Application to heavy-ion fusion

    Energy Technology Data Exchange (ETDEWEB)

    Toubiana, A.J. [Universidade Federal do Rio de Janeiro, Departamento de Engenharia Nuclear, Escola Politecnica, C.P. 68529, Rio de Janeiro, RJ (Brazil); Ecole CentraleSupelec, Gif-sur-Yvette (France); Paris Saclay, Saint-Aubin (France); Canto, L.F. [Universidade Federal do Rio de Janeiro, Instituto de Fisica, C.P. 68528, Rio de Janeiro (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Hussein, M.S. [Universidade de Sao Paulo, Instituto de Estudos Avancados, C.P. 72012, Sao Paulo, SP (Brazil); Universidade de Sao Paulo, Instituto de Fisica, C.P. 66318, Sao Paulo, SP (Brazil); Instituto Tecnologico de Aeronautica, CTA, Departamento de Fisica, Sao Jose dos Campos, Sao Paulo, SP (Brazil)

    2017-02-15

    In this paper we revisit the one-dimensional tunnelling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum-mechanical results. We find that the extended Kemble's approximation reproduces the results of quantum mechanics with great accuracy. (orig.)

  19. Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA

    International Nuclear Information System (INIS)

    Sheshadri, K.; Pandit, R.; Krishnamurthy, H.R.; Ramakrishnan, T.V.

    1993-01-01

    The bosonic Hubbard model is studied via a simple mean-field theory. At zero temperature, in addition to yielding a phase diagram that is qualitatively correct, namely a superfluid phase for non-integer fillings and a Mott transition from a superfluid to an insulating phase for integer fillings, this theory gives results that are in good agreement with Monte Carlo simulations. In particular, the superfluid fraction obtained as a function of the interaction strength U for both integer and non-integer fillings is close to the simulation results. In all phases the excitation spectra are obtained by using the random phase approximation (RPA): the spectrum has a gap in the insulating phase and is gapless (and linear at small wave vectors) in the superfluid phase. Analytic results are presented in the limits of large U and small superfluid density. Finite-temperature phase diagrams and the Mott-insulator-normal-phase crossover are also described. (orig.)

  20. Approximate cohomology in Banach algebras | Pourabbas ...

    African Journals Online (AJOL)

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  1. An overview on Approximate Bayesian computation*

    Directory of Open Access Journals (Sweden)

    Baragatti Meïli

    2014-01-01

    Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.

  2. First-principles calculations on the four phases of BaTiO3.

    Science.gov (United States)

    Evarestov, Robert A; Bandura, Andrei V

    2012-04-30

    The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO(3) crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange-correlation density functional theory (DFT) functionals for four stable phases of BaTiO(3). A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO(3). The comparative phonon symmetry analysis in BaTiO(3) four phases has been made basing on the site symmetry and irreducible representation indexes for the first time. Copyright © 2012 Wiley Periodicals, Inc.

  3. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  4. Forms of Approximate Radiation Transport

    CERN Document Server

    Brunner, G

    2002-01-01

    Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.

  5. Approximate estimation of system reliability via fault trees

    International Nuclear Information System (INIS)

    Dutuit, Y.; Rauzy, A.

    2005-01-01

    In this article, we show how fault tree analysis, carried out by means of binary decision diagrams (BDD), is able to approximate reliability of systems made of independent repairable components with a good accuracy and a good efficiency. We consider four algorithms: the Murchland lower bound, the Barlow-Proschan lower bound, the Vesely full approximation and the Vesely asymptotic approximation. For each of these algorithms, we consider an implementation based on the classical minimal cut sets/rare events approach and another one relying on the BDD technology. We present numerical results obtained with both approaches on various examples

  6. Quenched Approximation to ΔS = 1 K Decay

    International Nuclear Information System (INIS)

    Christ, Norman H.

    2005-01-01

    The importance of explicit quark loops in the amplitudes contributing to ΔS = 1, K meson decays raises potential ambiguities when these amplitudes are evaluated in the quenched approximation. Using the factorization of these amplitudes into short- and long-distance parts provided by the standard low-energy effective weak Hamiltonian, we argue that the quenched approximation can be conventionally justified if it is applied to the long-distance portion of each amplitude. The result is a reasonably well-motivated definition of the quenched approximation that is close to that employed in the RBC and CP-PACS calculations of these quantities

  7. Approximate viability for nonlinear evolution inclusions with application to controllability

    Directory of Open Access Journals (Sweden)

    Omar Benniche

    2016-12-01

    Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.

  8. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  9. Approximation of ruin probabilities via Erlangized scale mixtures

    DEFF Research Database (Denmark)

    Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue

    2018-01-01

    In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....

  10. A simple approximation method for dilute Ising systems

    International Nuclear Information System (INIS)

    Saber, M.

    1996-10-01

    We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs

  11. Function approximation of tasks by neural networks

    International Nuclear Information System (INIS)

    Gougam, L.A.; Chikhi, A.; Mekideche-Chafa, F.

    2008-01-01

    For several years now, neural network models have enjoyed wide popularity, being applied to problems of regression, classification and time series analysis. Neural networks have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. The latter is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. In a previous contribution, we have used a well known simplified architecture to show that it provides a reasonably efficient, practical and robust, multi-frequency analysis. We have investigated the universal approximation theory of neural networks whose transfer functions are: sigmoid (because of biological relevance), Gaussian and two specified families of wavelets. The latter have been found to be more appropriate to use. The aim of the present contribution is therefore to use a m exican hat wavelet a s transfer function to approximate different tasks relevant and inherent to various applications in physics. The results complement and provide new insights into previously published results on this problem

  12. A first-principle study on the phase transition, electronic structure, and mechanical properties of three-phase ZrTi2 alloy under high pressure*

    Science.gov (United States)

    Yuan, Xiao-Li; Xue, Mi-An; Chen, Wen; An, Tian-Qing

    2016-11-01

    We employed density-functional theory (DFT) within the generalized gradient approximation (GGA) to investigate the ZrTi2 alloy, and obtained its structural phase transition, mechanical behavior, Gibbs free energy as a function of pressure, P-V equation of state, electronic and Mulliken population analysis results. The lattice parameters and P-V EOS for α, β and ω phases revealed by our calculations are consistent with other experimental and computational values. The elastic constants obtained suggest that ω-ZrTi2 and α-ZrTi2 are mechanically stable, and that β-ZrTi2 is mechanically unstable at 0 GPa, but becomes more stable with increasing pressure. Our calculated results indicate a phase transition sequence of α → ω → β for ZrTi2. Both the bulk modulus B and shear modulus G increase linearly with increasing pressure for three phases. The G/B values illustrated good ductility of ZrTi2 alloy for three phases, with ωJournal web page at http://dx.doi.org/10.1140/epjb/e2016-70218-0

  13. Approximations for Markovian multi-class queues with preemptive priorities

    NARCIS (Netherlands)

    van der Heijden, Matthijs C.; van Harten, Aart; Sleptchenko, Andrei

    2004-01-01

    We discuss the approximation of performance measures in multi-class M/M/k queues with preemptive priorities for large problem instances (many classes and servers) using class aggregation and server reduction. We compared our approximations to exact and simulation results and found that our approach

  14. Approximation theorems by Meyer-Koenig and Zeller type operators

    International Nuclear Information System (INIS)

    Ali Ozarslan, M.; Duman, Oktay

    2009-01-01

    This paper is mainly connected with the approximation properties of Meyer-Koenig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based on q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results.

  15. Approximate and renormgroup symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  16. Implications of protein polymorphism on protein phase behaviour

    NARCIS (Netherlands)

    Stegen, J.; Schoot, van der P.P.A.M.

    2015-01-01

    The phase behaviour of small globular proteins is often modeled by approximating them as spherical particles with fixed internal structure. However, changes in the local environment of a protein can lead to changes in its conformation rendering this approximation invalid. We present a simple

  17. Approximate approaches to the one-dimensional finite potential well

    International Nuclear Information System (INIS)

    Singh, Shilpi; Pathak, Praveen; Singh, Vijay A

    2011-01-01

    The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m i ) is taken to be distinct from mass outside (m o ). A relevant parameter is the mass discontinuity ratio β = m i /m o . To correctly account for the mass discontinuity, we apply the BenDaniel-Duke boundary condition. We obtain approximate solutions for two cases: when the well is shallow and when the well is deep. We compare the approximate results with the exact results and find that higher-order approximations are quite robust. For the shallow case, the approximate solution can be expressed in terms of a dimensionless parameter σ l = 2m o V 0 L 2 /ℎ 2 (or σ = β 2 σ l for the deep case). We show that the lowest-order results are related by a duality transform. We also discuss how the energy upscales with L (E∼1/L γ ) and obtain the exponent γ. Exponent γ → 2 when the well is sufficiently deep and β → 1. The ratio of the masses dictates the physics. Our presentation is pedagogical and should be useful to students on a first course on elementary quantum mechanics or low-dimensional semiconductors.

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

    Science.gov (United States)

    Samanta, G. C.; Myrzakulov, R.

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

  19. Interacting-fermion approximation in the two-dimensional ANNNI model

    International Nuclear Information System (INIS)

    Grynberg, M.D.; Ceva, H.

    1990-12-01

    We investigate the effect of including domain-walls interactions in the two-dimensional axial next-nearest-neighbor Ising or ANNNI model. At low temperatures this problem is reduced to a one-dimensional system of interacting fermions which can be treated exactly. It is found that the critical boundaries of the low-temperature phases are in good agreement with those obtained using a free-fermion approximation. In contrast with the monotonic behavior derived from the free-fermion approach, the wall density or wave number displays reentrant phenomena when the ratio of the next-nearest-neighbor and nearest-neighbor interactions is greater than one-half. (author). 17 refs, 2 figs

  20. Derivation of the RPA (Random Phase Approximation) Equation of ATDDFT (Adiabatic Time Dependent Density Functional Ground State Response Theory) from an Excited State Variational Approach Based on the Ground State Functional.

    Science.gov (United States)

    Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen

    2014-09-09

    The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.

  1. Cosmological applications of Padé approximant

    International Nuclear Information System (INIS)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation

  2. Cosmological applications of Padé approximant

    Science.gov (United States)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

  3. Consistent Atomic Geometries and Electronic Structure of Five Phases of Potassium Niobate from Density-Functional Theory

    Directory of Open Access Journals (Sweden)

    Falko Schmidt

    2017-01-01

    Full Text Available We perform a comprehensive theoretical study of the structural and electronic properties of potassium niobate (KNbO3 in the cubic, tetragonal, orthorhombic, monoclinic, and rhombohedral phase, based on density-functional theory. The influence of different parametrizations of the exchange-correlation functional on the investigated properties is analyzed in detail, and the results are compared to available experimental data. We argue that the PBEsol and AM05 generalized gradient approximations as well as the RTPSS meta-generalized gradient approximation yield consistently accurate structural data for both the external and internal degrees of freedom and are overall superior to the local-density approximation or other conventional generalized gradient approximations for the structural characterization of KNbO3. Band-structure calculations using a HSE-type hybrid functional further indicate significant near degeneracies of band-edge states in all phases which are expected to be relevant for the optical response of the material.

  4. Simultaneous perturbation stochastic approximation for tidal models

    KAUST Repository

    Altaf, M.U.

    2011-05-12

    The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.

  5. Simultaneous perturbation stochastic approximation for tidal models

    KAUST Repository

    Altaf, M.U.; Heemink, A.W.; Verlaan, M.; Hoteit, Ibrahim

    2011-01-01

    The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.

  6. On the mathematical treatment of the Born-Oppenheimer approximation

    International Nuclear Information System (INIS)

    Jecko, Thierry

    2014-01-01

    Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

  7. On the mathematical treatment of the Born-Oppenheimer approximation

    Energy Technology Data Exchange (ETDEWEB)

    Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

    2014-05-15

    Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

  8. Approximate method in estimation sensitivity responses to variations in delayed neutron energy spectra

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, J; Shin, H S; Song, T Y; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1998-12-31

    Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)

  9. Approximate method in estimation sensitivity responses to variations in delayed neutron energy spectra

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, J.; Shin, H. S.; Song, T. Y.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1997-12-31

    Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)

  10. Expectation Consistent Approximate Inference

    DEFF Research Database (Denmark)

    Opper, Manfred; Winther, Ole

    2005-01-01

    We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

  11. Methods of Approximation Theory in Complex Analysis and Mathematical Physics

    CERN Document Server

    Saff, Edward

    1993-01-01

    The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...

  12. Approximation and Computation

    CERN Document Server

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

    Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

  13. Vacancy-rearrangement theory in the first Magnus approximation

    International Nuclear Information System (INIS)

    Becker, R.L.

    1984-01-01

    In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub α/-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references

  14. OECD/NEA burnup credit calculational criticality benchmark Phase I-B results

    Energy Technology Data Exchange (ETDEWEB)

    DeHart, M.D.; Parks, C.V. [Oak Ridge National Lab., TN (United States); Brady, M.C. [Sandia National Labs., Las Vegas, NV (United States)

    1996-06-01

    In most countries, criticality analysis of LWR fuel stored in racks and casks has assumed that the fuel is fresh with the maximum allowable initial enrichment. This assumption has led to the design of widely spaced and/or highly poisoned storage and transport arrays. If credit is assumed for fuel burnup, initial enrichment limitations can be raised in existing systems, and more compact and economical arrays can be designed. Such reliance on the reduced reactivity of spent fuel for criticality control is referred to as burnup credit. The Burnup Credit Working Group, formed under the auspices of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development, has established a set of well-defined calculational benchmarks designed to study significant aspects of burnup credit computational methods. These benchmarks are intended to provide a means for the intercomparison of computer codes, methods, and data applied in spent fuel analysis. The benchmarks have been divided into multiple phases, each phase focusing on a particular feature of burnup credit analysis. This report summarizes the results and findings of the Phase I-B benchmark, which was proposed to provide a comparison of the ability of different code systems and data libraries to perform depletion analysis for the prediction of spent fuel isotopic concentrations. Results included here represent 21 different sets of calculations submitted by 16 different organizations worldwide and are based on a limited set of nuclides determined to have the most important effect on the neutron multiplication factor of light-water-reactor spent fuel. A comparison of all sets of results demonstrates that most methods agree to within 10% in the ability to estimate the spent fuel concentrations of most actinides. All methods agree within 11% about the average for all fission products studied. Most deviations are less than 10%, and many are less than 5%. The exceptions are Sm 149, Sm 151, and Gd 155.

  15. OECD/NEA burnup credit calculational criticality benchmark Phase I-B results

    International Nuclear Information System (INIS)

    DeHart, M.D.; Parks, C.V.; Brady, M.C.

    1996-06-01

    In most countries, criticality analysis of LWR fuel stored in racks and casks has assumed that the fuel is fresh with the maximum allowable initial enrichment. This assumption has led to the design of widely spaced and/or highly poisoned storage and transport arrays. If credit is assumed for fuel burnup, initial enrichment limitations can be raised in existing systems, and more compact and economical arrays can be designed. Such reliance on the reduced reactivity of spent fuel for criticality control is referred to as burnup credit. The Burnup Credit Working Group, formed under the auspices of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development, has established a set of well-defined calculational benchmarks designed to study significant aspects of burnup credit computational methods. These benchmarks are intended to provide a means for the intercomparison of computer codes, methods, and data applied in spent fuel analysis. The benchmarks have been divided into multiple phases, each phase focusing on a particular feature of burnup credit analysis. This report summarizes the results and findings of the Phase I-B benchmark, which was proposed to provide a comparison of the ability of different code systems and data libraries to perform depletion analysis for the prediction of spent fuel isotopic concentrations. Results included here represent 21 different sets of calculations submitted by 16 different organizations worldwide and are based on a limited set of nuclides determined to have the most important effect on the neutron multiplication factor of light-water-reactor spent fuel. A comparison of all sets of results demonstrates that most methods agree to within 10% in the ability to estimate the spent fuel concentrations of most actinides. All methods agree within 11% about the average for all fission products studied. Most deviations are less than 10%, and many are less than 5%. The exceptions are Sm 149, Sm 151, and Gd 155

  16. Perturbation methods and closure approximations in nonlinear systems

    International Nuclear Information System (INIS)

    Dubin, D.H.E.

    1984-01-01

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

  17. Intensity-based hierarchical elastic registration using approximating splines.

    Science.gov (United States)

    Serifovic-Trbalic, Amira; Demirovic, Damir; Cattin, Philippe C

    2014-01-01

    We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces. The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model. The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method. The proposed hierarchical elastic image registration approach incorporates the GEBS

  18. Constrained Optimization via Stochastic approximation with a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman

    1997-01-01

    This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....

  19. Pade approximant calculations for neutron escape probability

    International Nuclear Information System (INIS)

    El Wakil, S.A.; Saad, E.A.; Hendi, A.A.

    1984-07-01

    The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)

  20. Analytical models approximating individual processes: a validation method.

    Science.gov (United States)

    Favier, C; Degallier, N; Menkès, C E

    2010-12-01

    Upscaling population models from fine to coarse resolutions, in space, time and/or level of description, allows the derivation of fast and tractable models based on a thorough knowledge of individual processes. The validity of such approximations is generally tested only on a limited range of parameter sets. A more general validation test, over a range of parameters, is proposed; this would estimate the error induced by the approximation, using the original model's stochastic variability as a reference. This method is illustrated by three examples taken from the field of epidemics transmitted by vectors that bite in a temporally cyclical pattern, that illustrate the use of the method: to estimate if an approximation over- or under-fits the original model; to invalidate an approximation; to rank possible approximations for their qualities. As a result, the application of the validation method to this field emphasizes the need to account for the vectors' biology in epidemic prediction models and to validate these against finer scale models. Copyright © 2010 Elsevier Inc. All rights reserved.