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Sample records for theory ii approximation

  1. Quantal density functional theory II. Approximation methods and applications

    International Nuclear Information System (INIS)

    Sahni, Viraht

    2010-01-01

    This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

  2. Intelligent control-II: review of fuzzy systems and theory of approximate reasoning

    International Nuclear Information System (INIS)

    Nagrial, M.H.

    2004-01-01

    Fuzzy systems are knowledge-based or rule-based systems. The heart of a fuzzy systems knowledge base consisting of the so-called fuzzy IF -THEN rules. This paper reviews various aspects of fuzzy IF-THEN rules. The theory of approximate reasoning, which provides a powerful framework for reasoning the imprecise and uncertain information, , is also reviewed. Additional properties of fuzzy systems are also discussed. (author)

  3. 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...

  4. 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.

  5. 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

  6. 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.

  7. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  8. Mathematical analysis, approximation theory and their applications

    CERN Document Server

    Gupta, Vijay

    2016-01-01

    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  9. Theory for site-site pair distribution functions of molecular fluids. II. Approximations for the Percus--Yevick site-site direct correlation functions

    International Nuclear Information System (INIS)

    Johnson, E.

    1977-01-01

    A theory for site-site pair distribution functions of molecular fluids is derived from the Ornstein-Zernike equation. Atom-atom pair distribution functions of this theory which were obtained by using different approximations for the Percus-Yevick site-site direct correlation functions are compared

  10. Methods of Fourier analysis and approximation theory

    CERN Document Server

    Tikhonov, Sergey

    2016-01-01

    Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

  11. Shape theory categorical methods of approximation

    CERN Document Server

    Cordier, J M

    2008-01-01

    This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and

  12. High energy approximations in quantum field theory

    International Nuclear Information System (INIS)

    Orzalesi, C.A.

    1975-01-01

    New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt

  13. VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II

    International Nuclear Information System (INIS)

    Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

    1977-11-01

    The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently

  14. VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II. [LMFBR

    Energy Technology Data Exchange (ETDEWEB)

    Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

    1977-11-01

    The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.

  15. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  16. 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

  17. 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

  18. Some approximate calculations in SU2 lattice mean field theory

    International Nuclear Information System (INIS)

    Hari Dass, N.D.; Lauwers, P.G.

    1981-12-01

    Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)

  19. Scattering theory and effective medium approximations to heterogeneous materials

    International Nuclear Information System (INIS)

    Gubernatis, J.E.

    1977-01-01

    The formal analogy existing between problems studied in the microscopic theory of disordered alloys and problems concerned with the effective (macroscopic) behavior of heterogeneous materials is discussed. Attention is focused on (1) analogous approximations (effective medium approximations) developed for the microscopic problems by scattering theory concepts and techniques, but for the macroscopic problems principally by intuitive means, (2) the link, provided by scattering theory, of the intuitively developed approximations to a well-defined perturbative analysis, (3) the possible presence of conditionally convergent integrals in effective medium approximations

  20. 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. ...

  1. Variational, projection methods and Pade approximants in scattering theory

    International Nuclear Information System (INIS)

    Turchetti, G.

    1980-12-01

    Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt

  2. Modification of linear response theory for mean-field approximations

    NARCIS (Netherlands)

    Hütter, M.; Öttinger, H.C.

    1996-01-01

    In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

  3. 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...

  4. Semiclassical approximation to time-dependent Hartree--Fock theory

    International Nuclear Information System (INIS)

    Dworzecka, M.; Poggioli, R.

    1976-01-01

    Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form

  5. Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation

    Energy Technology Data Exchange (ETDEWEB)

    Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)

    1975-01-04

    Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.

  6. Optical approximation in the theory of geometric impedance

    International Nuclear Information System (INIS)

    Stupakov, G.; Bane, K.L.F.; Zagorodnov, I.

    2007-02-01

    In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance. (orig.)

  7. 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

  8. 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

  9. Approximate models for broken clouds in stochastic radiative transfer theory

    International Nuclear Information System (INIS)

    Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas

    2014-01-01

    This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models

  10. 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

  11. Lattice approximation of gauge theories with Dirac Kaehler fermions

    International Nuclear Information System (INIS)

    Joos, H.

    1988-01-01

    A program which tries to overcome the systematic difficulties caused by the lattice fermion problem by the consideration of models which describe Dirac fields by differential forms is reported. In the first lecture the formalism is developped and applied to the formulation of geometric QCD and of a Geometric Standard Model. The second lecture treats the characteristic symmetry problems which appear in the lattice approximation of geometric field theories. In the last lecture strong coupling dynamics of geometric QCD are considered with the final aim of a derivation of the quark model for the hadron spectrum. (author) [pt

  12. Complete hierarchies of efficient approximations to problems in entanglement theory

    International Nuclear Information System (INIS)

    Eisert, Jens; Hyllus, Philipp; Guehne, Otfried; Curty, Marcos

    2004-01-01

    We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multiparty entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multiparty entanglement, (D) the test whether states are multiparty entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree 3 or less. We then apply very recently established known methods from the theory of semidefinite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of efficiently decidable sufficient criteria for multiparticle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach

  13. ANALYTIC APPROXIMATION OF CARBON CONDENSATION ISSUES IN TYPE II SUPERNOVAE

    Energy Technology Data Exchange (ETDEWEB)

    Clayton, Donald D., E-mail: claydonald@gmail.com [Department of Physics and Astronomy, Clemson University, Clemson, SC (United States)

    2013-01-01

    I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if {sup 56}Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel and Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.

  14. Approximation scheme for strongly coupled plasmas: Dynamical theory

    International Nuclear Information System (INIS)

    Golden, K.I.; Kalman, G.

    1979-01-01

    The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability α (k, ω) at long wavelengths in strongly coupled one-component plasmas. Development of the scheme is carried out in two stages. The first stage follows the earlier Golden-Kalman-Silevitch (GKS) velocity-average approximation approach, but goes much further in its application of the nonlinear fluctuation-dissipation theorem to dynamical calculations. The result is the simple expression for α (k, ω), αatsub GKSat(k, ω) 4 moment sum rule. In the second stage, the above dynamical expression is made self-consistent at long wavelengths by postulating that a decomposition of the quadratic polarizabilities in terms of linear ones, which prevails in the k → 0 limit for weak coupling, can be relied upon as a paradigm for arbitrary coupling. The result is a relatively simple quadratic integral equation for α. Its evaluation in the weak-coupling limit and its comparison with known exact results in that limit reveal that almost all important correlational and long-time effects are reproduced by our theory with very good numerical accuracy over the entire frequency range; the only significant defect of the approximation seems to be the absence of the ''dominant'' γ ln γ -1 (γ is the plasma parameter) contribution to Im α

  15. The quasi-diffusive approximation in transport theory: Local solutions

    International Nuclear Information System (INIS)

    Celaschi, M.; Montagnini, B.

    1995-01-01

    The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

  16. Theory of magnetohydrodynamic waves: The WKB approximation revisited

    International Nuclear Information System (INIS)

    Barnes, A.

    1992-01-01

    Past treatments of the eikonal or WKB theory of the propagation of magnetohydrodynamics waves have assumed a strictly isentropic background. IF in fact there is a gradient in the background entropy, then in second order in the WKB ordering, adiabatic fluctuations (in the Lagrangian sense) are not strictly isentropic in the Eulerian sense. This means that in the second order of the WKB expansion, which determines the variation of wave amplitude along rays, the violation of isentropy must be accounted for. The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments

  17. PWL approximation of nonlinear dynamical systems, part II: identification issues

    International Nuclear Information System (INIS)

    De Feo, O; Storace, M

    2005-01-01

    This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator)

  18. Self-consistent approximations beyond the CPA: Part II

    International Nuclear Information System (INIS)

    Kaplan, T.; Gray, L.J.

    1982-01-01

    This paper concentrates on a self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl. The construction of the augmented space formalism for a binary alloy is sketched, and the notation to be used derived. Using the operator methods of the augmented space, the self-consistent approximation is derived for the average Green's function, and for evaluating the self-energy, taking into account the scattering by clusters of excitations. The particular cluster approximation desired is derived by treating the scattering by the excitations with S /SUB T/ exactly. Fourier transforms on the disorder-space clustersite labels solve the self-consistent set of equations. Expansion to short range order in the alloy is also discussed. A method to reduce the problem to a computationally tractable form is described

  19. Usefulness of bound-state approximations in reaction theory

    International Nuclear Information System (INIS)

    Adhikari, S.K.

    1981-01-01

    A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process

  20. A new perturbative approximation applied to supersymmetric quantum field theory

    International Nuclear Information System (INIS)

    Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.; Los Alamos National Lab.

    1988-01-01

    We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not known of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

  1. Pade approximants in field theory: pion and kaon systems

    International Nuclear Information System (INIS)

    Zinn-Justin, J.

    1969-01-01

    We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances (ρ, K * (890), φ, K * (1420), f 0 , f', A 2 ) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the ρ and f 0 agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [fr

  2. Analytic approximations to hamiltonian lattice field theories. Pt. 2

    International Nuclear Information System (INIS)

    Surany, P.

    1983-01-01

    It is shown that at weak coupling physical quantities in hamiltonian U(1) lattice gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d - 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions. Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2 + 1 U(1) gauge theory confines electric charges at all non-vanishing coupling. (orig.)

  3. WKB approximation and tunneling in theories with noncanonical kinetic terms

    Science.gov (United States)

    González, Mariana Carrillo; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark

    2017-09-01

    Tunneling is a fascinating aspect of quantum mechanics that renders the local minima of a potential meta-stable, with important consequences for particle physics, for the early hot stage of the universe, and more speculatively, for the behavior of the putative multiverse. While this phenomenon has been studied extensively for systems which have canonical kinetic terms, many theories of fundamental physics contain fields with noncanonical kinetic structures. It is therefore desirable to have a detailed framework for calculating tunneling rates and initial states after tunneling for these theories. In this work we present such a rigorous formulation and illustrate its use by applying it to a number of examples.

  4. How Do Wings Generate Lift? 2. Myths, Approximate Theories and ...

    Indian Academy of Sciences (India)

    A cambered surface that is moving forward in a fluid generateslift. To explain this interesting fact in terms of simplermodels, some preparatory concepts were discussed in thefirst part of this article. We also agreed on what is an acceptableexplanation. Then some popular models were discussed.Some quantitative theories ...

  5. 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.

  6. A look inside the theory of the linear approximation

    OpenAIRE

    Bel, Ll.

    2006-01-01

    We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This allows to introduce geometrical objects that are not invariant under General gauge transformations but they are under Special ones. We develop then a formalism that strengthens the analogy of the formalisms of the electromagnetic and the gravitational theo...

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

    CERN Document Server

    Rassias, Michael

    2014-01-01

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

  8. Intelligent mathematics II applied mathematics and approximation theory

    CERN Document Server

    Duman, Oktay

    2016-01-01

    This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.

  9. Approximate theory the electromagnetic energy of solenoid in special relativity

    International Nuclear Information System (INIS)

    Prastyaningrum, I; Kartikaningsih, S.

    2017-01-01

    Solenoid is a device that is often used in electronic devices. A solenoid is electrified will cause a magnetic field. In our analysis, we just focus on the electromagnetic energy for solenoid form. We purpose to analyze by the theoretical approach in special relativity. Our approach is begun on the Biot Savart law and Lorentz force. Special theory relativity can be derived from the Biot Savart law, and for the energy can be derived from Lorentz for, by first determining the momentum equation. We choose the solenoid form with the goal of the future can be used to improve the efficiency of the electrical motor. (paper)

  10. New approximation for Glauber theory on stripping of relativistic deuterons

    International Nuclear Information System (INIS)

    Nissen-Meyer, S.A.

    1978-03-01

    The momentum distribution of forward protons from relativistic collisions of deuterons with nuclei is computed from a Glauber theoretical Ansatz of Bertocchi and Tekou. The outgoing proton-neutron scattering state (disintegrated deuteron) with a plane wave minus the components of this plane wave along the deuteron bound state vector is approximated. With no fitted parameters good agreement is found with data from the reaction d + C 12 → p + X in the region corresponding to nonrelativistic Fermi momenta in the forward direction. At more relativistic Fermi momenta, the model deviates more from the data, which can be due to incorrect choice of the short distance part of the deuteron wave function as well as off-shell effects in the deuteron

  11. Progress in approximation theory and applicable complex analysis in memory of Q.I. Rahman

    CERN Document Server

    Mohapatra, Ram; Qazi, Mohammed; Schmeisser, Gerhard

    2017-01-01

    Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and appl...

  12. Post-Newtonian approximation of the maximum four-dimensional Yang-Mills gauge theory

    International Nuclear Information System (INIS)

    Smalley, L.L.

    1982-01-01

    We have calculated the post-Newtonian approximation of the maximum four-dimensional Yang-Mills theory proposed by Hsu. The theory contains torsion; however, torsion is not active at the level of the post-Newtonian approximation of the metric. Depending on the nature of the approximation, we obtain the general-relativistic values for the classical Robertson parameters (γ = β = 1), but deviations for the Nordtvedt effect and violations of post-Newtonian conservation laws. We conclude that in its present form the theory is not a viable theory of gravitation

  13. New perspectives on approximation and sampling theory Festschrift in honor of Paul Butzer's 85th birthday

    CERN Document Server

    Schmeisser, Gerhard

    2014-01-01

    Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer’s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate...

  14. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  15. Critical region of a type II superconducting film near Hsub(c2): rational approximants

    International Nuclear Information System (INIS)

    Ruggeri, G.J.

    1979-01-01

    The high-temperature perturbative expansions for the thermal quantities of a type II superconducting film are extrapolated to the critical region near Hsub(c2) by means of new rational approximants of the Pade type. The new approximants are forced to reproduce the leading correction to the flux lattice contribution on the low-temperature side of the transition. Compared to those previously considered in the literature: (i) the mutual consistency of the approximants is improved; and (ii) they are nearer to the exact solution of the zero-dimensional Landau-Ginsburg model. (author)

  16. Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

    DEFF Research Database (Denmark)

    Zhang, H.W.; Schäffer, Hemming Andreas

    2007-01-01

    An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

  17. Semiclassical approximations in a mean-field theory with collision terms

    International Nuclear Information System (INIS)

    Galetti, D.

    1986-01-01

    Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt

  18. New Trends in Approximation Theory : in Memory of André Boivin

    CERN Document Server

    Manolaki, Myrto; Gauthier, Paul

    2018-01-01

    The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of...

  19. Approximate design theory for a simple block design with random block effects

    OpenAIRE

    Christof, Karin

    1985-01-01

    Approximate design theory for a simple block design with random block effects / K. Christof ; F. Pukelsheim. - In: Linear statistical inference / ed. by T. Calinski ... - Berlin u. a. : Springer, 1985. - S. 20-28. - (Lecture notes in statistics ; 35)

  20. Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation

    DEFF Research Database (Denmark)

    Popov, Vladislav; Lavrinenko, Andrei; Novitsky, Andrey

    2016-01-01

    that the zeroth-, first-, and second-order approximations of the operator effective medium theory correspond to electric dipoles, chirality, and magnetic dipoles plus electric quadrupoles, respectively. We discover that the spatially dispersive bianisotropic effective medium obtained in the second...

  1. A variational approach to operator and matrix Pade approximation. Applications to potential scattering and field theory

    International Nuclear Information System (INIS)

    Mery, P.

    1977-01-01

    The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed

  2. Numerical Test of Different Approximations Used in the Transport Theory of Energetic Particles

    Science.gov (United States)

    Qin, G.; Shalchi, A.

    2016-05-01

    Recently developed theories for perpendicular diffusion work remarkably well. The diffusion coefficients they provide agree with test-particle simulations performed for different turbulence setups ranging from slab and slab-like models to two-dimensional and noisy reduced MHD turbulence. However, such theories are still based on different analytical approximations. In the current paper we use a test-particle code to explore the different approximations used in diffusion theory. We benchmark different guiding center approximations, simplifications of higher-order correlations, and the Taylor-Green-Kubo formula. We demonstrate that guiding center approximations work very well as long as the particle's unperturbed Larmor radius is smaller than the perpendicular correlation length of the turbulence. Furthermore, the Taylor-Green-Kubo formula and the definition of perpendicular diffusion coefficients via mean square displacements provide the same results. The only approximation that was used in the past in nonlinear diffusion theory that fails is to replace fourth-order correlations by a product of two second-order correlation functions. In more advanced nonlinear theories, however, this type of approximation is no longer used. Therefore, we confirm the validity of modern diffusion theories as a result of the work presented in the current paper.

  3. Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

    International Nuclear Information System (INIS)

    Hees, Hendrik van; Knoll, Joern

    2002-01-01

    The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept

  4. Renormalization of self-consistent approximation schemes at finite temperature II: applications to the sunset diagram

    International Nuclear Information System (INIS)

    Hees, H. van; Knoll, J.

    2001-01-01

    The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)

  5. Continuum orbital approximations in weak-coupling theories for inelastic electron scattering

    International Nuclear Information System (INIS)

    Peek, J.M.; Mann, J.B.

    1977-01-01

    Two approximations, motivated by heavy-particle scattering theory, are tested for weak-coupling electron-atom (ion) inelastic scattering theory. They consist of replacing the one-electron scattering orbitals by their Langer uniform approximations and the use of an average trajectory approximation which entirely avoids the necessity for generating continuum orbitals. Numerical tests for a dipole-allowed and a dipole-forbidden event, based on Coulomb-Born theory with exchange neglected, reveal the error trends. It is concluded that the uniform approximation gives a satisfactory prediction for traditional weak-coupling theories while the average approximation should be limited to collision energies exceeding at least twice the threshold energy. The accuracy for both approximations is higher for positive ions than for neutral targets. Partial-wave collision-strength data indicate that greater care should be exercised in using these approximations to predict quantities differential in the scattering angle. An application to the 2s 2 S-2p 2 P transition in Ne VIII is presented

  6. Modified method of perturbed stationary states. II. Semiclassical and low-velocity quantal approximations

    International Nuclear Information System (INIS)

    Green, T.A.

    1978-10-01

    For one-electron heteropolar systems, the wave-theoretic Lagrangian of Paper I 2 is simplified in two distinct approximations. The first is semiclassical; the second is quantal, for velocities below those for which the semiclassical treatment is reliable. For each approximation, unitarity and detailed balancing are discussed. Then, the variational method as described by Demkov is used to determine the coupled equations for the radial functions and the Euler-Lagrange equations for the translational factors which are part of the theory. Specific semiclassical formulae for the translational factors are given in a many-state approximation. Low-velocity quantal formulae are obtained in a one-state approximation. The one-state results of both approximations agree with an earlier determination by Riley. 14 references

  7. Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation

    Science.gov (United States)

    Doremus, R. H.

    1982-01-01

    It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.

  8. Padé approximations for Painlevé I and II transcendents

    Science.gov (United States)

    Novokshenov, V. Yu.

    2009-06-01

    We use a version of the Fair-Luke algorithm to find the Padé approximate solutions of the Painlevé I and II equations. We find the distributions of poles for the well-known Ablowitz-Segur and Hastings-McLeod solutions of the Painlevé II equation. We show that the Boutroux tritronquée solution of the Painleé I equation has poles only in the critical sector of the complex plane. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behavior at infinity in the complex plane.

  9. Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

    Science.gov (United States)

    Chen, Zhenhua; Hoffmann, Mark R

    2012-07-07

    A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4

  10. Many-body perturbation theory using the density-functional concept: beyond the GW approximation.

    Science.gov (United States)

    Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

    2005-05-13

    We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.

  11. Hard Thermal Loop approximation in the Light Front Quantum Field Theory

    International Nuclear Information System (INIS)

    Silva, Charles da Rocha; Perez, Silvana

    2011-01-01

    Full text: In this paper we generalize the Hard Thermal Loop approximation (HTL) for the Thermal Light Front Quantum Field Theory. This technique was developed by Braaten e Pisarski [PRL. 63 (1989) 1129, Nucl. Phys. B337 (1990) 569], for the Thermal Quantum Field Theory at equal time and is particularly useful to solve problems of convergence of the amplitudes within Quantum Chromodynamics, caused by the inherently nonperturbative behavior. The HTL approximation satisfies simple Ward identities, is ultraviolet finite and gauge independent. Here we use the light front generalized coordinates (GLFC) proposed by one of us (V. S. Alves, Ashok Das, e Silvana Perez [PRD. 66, (2002) 125008]) and analyze the one loop amplitudes for the λφ3 theory and the Quantum Electrodynamics in (3+1) dimensions at finite temperature in the HTL approximation. For the scalar theory, we evaluate the two-point function, recovering the usual dispersion relations. We also analyze the rotational invariance of the model. We then consider the Quantum Electrodynamics in (3+1) dimensions and calculate the polarization tensor and the vertex function at finite temperature in the HTL approximation. In future, our interest will be to apply the Generalized Light Front formalism to understand the confinement mechanism which occurs in the Quantum Chromodynamics. There is an expectation that the Light Front Quantum Field Theory formalism is more appropriate to study this problems. (author)

  12. Hard Thermal Loop approximation in the Light Front Quantum Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Silva, Charles da Rocha [Instituto Federal de Educacao, Ciencia e Tecnologia do Para (IFPA), Belem, PA (Brazil); Universidade Federal do Para (UFPA), Belem, PA (Brazil); Perez, Silvana [Universidade Federal do Para (UFPA), Belem, PA (Brazil)

    2011-07-01

    Full text: In this paper we generalize the Hard Thermal Loop approximation (HTL) for the Thermal Light Front Quantum Field Theory. This technique was developed by Braaten e Pisarski [PRL. 63 (1989) 1129, Nucl. Phys. B337 (1990) 569], for the Thermal Quantum Field Theory at equal time and is particularly useful to solve problems of convergence of the amplitudes within Quantum Chromodynamics, caused by the inherently nonperturbative behavior. The HTL approximation satisfies simple Ward identities, is ultraviolet finite and gauge independent. Here we use the light front generalized coordinates (GLFC) proposed by one of us (V. S. Alves, Ashok Das, e Silvana Perez [PRD. 66, (2002) 125008]) and analyze the one loop amplitudes for the {lambda}{phi}3 theory and the Quantum Electrodynamics in (3+1) dimensions at finite temperature in the HTL approximation. For the scalar theory, we evaluate the two-point function, recovering the usual dispersion relations. We also analyze the rotational invariance of the model. We then consider the Quantum Electrodynamics in (3+1) dimensions and calculate the polarization tensor and the vertex function at finite temperature in the HTL approximation. In future, our interest will be to apply the Generalized Light Front formalism to understand the confinement mechanism which occurs in the Quantum Chromodynamics. There is an expectation that the Light Front Quantum Field Theory formalism is more appropriate to study this problems. (author)

  13. 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.

  14. Motion of spinning particles. Post-Newtonian approximation in the Einstein-Cartan theory

    Energy Technology Data Exchange (ETDEWEB)

    Boccaletti, D; Agostini, W; Festa, P [Rome Univ. (Italy). Ist. di Matematica

    1979-01-11

    The equations of motion of spinning particles are obtained in the post-Newtonian approximation of the Einstein-Cartan theory. The starting point of the calculation is the Hehl combined equation and a semi-classical model is assumed for the system of spinning particles. Comparison is made with an analogous quantum result obtained in the context of Gupta quantization of the linearized Einstein theory.

  15. Comparison of approximate methods for multiple scattering in high-energy collisions. II

    International Nuclear Information System (INIS)

    Nolan, A.M.; Tobocman, W.; Werby, M.F.

    1976-01-01

    The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass

  16. Phonons: Theory and experiments II. Volume 2

    International Nuclear Information System (INIS)

    Bruesch, P.

    1986-01-01

    The present second volume titled as ''Phonons: Theory and Experiments II'', contains, a thorough study of experimental techniques and the interpretation of experimental results. This three-volume set tries to bridge the gap between theory and experiment, and is addressed to those working in both camps in the vast field of dynamical properties of solids. Topics presented in the second volume include; infrared-, Raman and Brillouin spectroscopy, interaction of X-rays with phonons, and inelastic neutron scattering. In addition an account is given of some other techniques, including ultrasonic methods, inelastic electron tunneling spectroscopy, point contact spectroscopy, and spectroscopy of surface phonons, thin films and adsorbates. Both experimental aspects and theoretical concepts necessary for the interpretation of experimental data are discussed. An attempt is made to present the descriptive as well as the analytical aspects of the topics. Simple models are often used to illustrate the basic concepts and more than 100 figures are included to illustrate both theoretical and experimental results. Many chapters contain a number of problems with hints and results giving additional information

  17. Finite-measuring approximation of operators of scattering theory in representation of wave packets

    International Nuclear Information System (INIS)

    Kukulin, V.I.; Rubtsova, O.A.

    2004-01-01

    Several types of the packet quantization of the continuos spectrum in the scattering theory quantum problems are considered. Such a quantization leads to the convenient finite-measuring (i.e. matrix) approximation of the integral operators in the scattering theory and it makes it possible to reduce the solution of the singular integral equations, complying with the scattering theory, to the convenient purely algebraic equations on the analytical basis, whereby all the singularities are separated in the obvious form. The main attention is paid to the problems of the method practical realization [ru

  18. Local density approximation for exchange in excited-state density functional theory

    OpenAIRE

    Harbola, Manoj K.; Samal, Prasanjit

    2004-01-01

    Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.

  19. 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

  20. ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

    Science.gov (United States)

    Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

    2008-12-01

    We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

  1. Fundamentals and approximations of multilevel resonance theory for reactor physics applications

    International Nuclear Information System (INIS)

    Moore, M.S.

    1980-01-01

    The formal theory of nuclear reactions leads to any of a number of alternative representations for describing resonance behavior. None of these is satisfactory for applications, and, depending on the problem to be addressed, approximate expressions are used. The specializations and approximations found to be most useful by evaluators are derived from R-matrix theory and are discussed from the viewpoint of convenience in numerical calculations. Finally, we illustrate the application of the theory by reviewing a particular example: the spin-separated neutron-induced cross sections of 235 U in the resolved and unresolved resonance regions and the use of these results in the U.S. evaluated nuclear data file ENDF/B. (author)

  2. Coulomb couplings in solubilised light harvesting complex II (LHCII): challenging the ideal dipole approximation from TDDFT calculations.

    Science.gov (United States)

    López-Tarifa, P; Liguori, Nicoletta; van den Heuvel, Naudin; Croce, Roberta; Visscher, Lucas

    2017-07-19

    The light harvesting complex II (LHCII), is a pigment-protein complex responsible for most of the light harvesting in plants. LHCII harvests sunlight and transfers excitation energy to the reaction centre of the photo-system, where the water oxidation process takes place. The energetics of LHCII can be modulated by means of conformational changes allowing a switch from a harvesting to a quenched state. In this state, the excitation energy is no longer transferred but converted into thermal energy to prevent photooxidation. Based on molecular dynamics simulations at the microsecond time scale, we have recently proposed that the switch between different fluorescent states can be probed by correlating shifts in the chromophore-chromophore Coulomb interactions to particular protein movements. However, these findings are based upon calculations in the ideal point dipole approximation (IDA) where the Coulomb couplings are simplified as first order dipole-dipole interactions, also assuming that the chromophore transition dipole moments lay in particular directions of space with constant moduli (FIX-IDA). In this work, we challenge this approximation using the time-dependent density functional theory (TDDFT) combined with the frozen density embedding (FDE) approach. Our aim is to establish up to which limit FIX-IDA can be applied and which chromophore types are better described under this approximation. For that purpose, we use the classical trajectories of solubilised light harvesting complex II (LHCII) we have recently reported [Liguori et al., Sci. Rep., 2015, 5, 15661] and selected three pairs of chromophores containing chlorophyll and carotenoids (Chl and Car): Chla611-Chla612, Chlb606-Chlb607 and Chla612-Lut620. Using the FDE in the Tamm-Dancoff approximation (FDEc-TDA), we show that IDA is accurate enough for predicting Chl-Chl Coulomb couplings. However, the FIX-IDA largely overestimates Chl-Car interactions mainly because the transition dipole for the Cars is not

  3. The Pade approximate method for solving problems in plasma kinetic theory

    International Nuclear Information System (INIS)

    Jasperse, J.R.; Basu, B.

    1992-01-01

    The method of Pade Approximates has been a powerful tool in solving for the time dependent propagator (Green function) in model quantum field theories. We have developed a modified Pade method which we feel has promise for solving linearized collisional and weakly nonlinear problems in plasma kinetic theory. In order to illustrate the general applicability of the method, in this paper we discuss Pade solutions for the linearized collisional propagator and the collisional dielectric function for a model collisional problem. (author) 3 refs., 2 tabs

  4. On the independent particle approximation of Gauge theories: a simple example

    International Nuclear Information System (INIS)

    Palladino, B.E.

    1992-08-01

    In this work, the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1+1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed. (author)

  5. Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory.

    Science.gov (United States)

    Sharpe, Daniel J; Levy, Mel; Tozer, David J

    2018-02-13

    Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.

  6. Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

    Science.gov (United States)

    Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

    2015-04-21

    We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

  7. Implementation of the CCGM approximation for surface diffraction using Wigner R-matrix theory

    International Nuclear Information System (INIS)

    Lauderdale, J.G.; McCurdy, C.W.

    1983-01-01

    The CCGM approximation for surface scattering proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)] is implemented for realistic surface interaction potentials using Wigner R-matrix theory. The resulting procedure is highly efficient computationally and is in no way limited to hard wall or purely repulsive potentials. Comparison is made with the results of close-coupling calculations of other workers which include the same diffraction channels in order to fairly evaluate the CCGM approximation which is an approximation to the coupled channels Lippman--Schwinger equation for the T matrix. The shapes of selective adsorption features, whether maxima or minima, in the scattered intensity are well represented in this approach for cases in which the surface corrugation is not too strong

  8. Mode-coupling theory and bunch lengthening in SPEAR II

    International Nuclear Information System (INIS)

    Suzuki, T.; Chin, Y.; Satoh, K.

    1983-01-01

    A mode-coupling theory of bunched-beam instabilities is developed for a Gaussian bunch. The theory converts Sacherer's integral equation with mode coupling into a matrix eigenvalue problem. The present theory assumes well-defined azimuthal modes and takes into account radial modes which are expressed as superpositions of orthogonal functions. The theory is applied to bunch lengthening observed at SPEAR II. The theory explains qualitative features of the experimental results fairly well, but quantitative agreement is not too good. This is ascribed to insufficient knowledge of the coupling impedance of SPEAR II or to the possibility that such effects as radiation damping and quantum excitation should be included. (author)

  9. Heterotic/Type-II duality and its field theory avatars

    International Nuclear Information System (INIS)

    Kiritsis, Elias

    1999-01-01

    In these lecture notes, I will describe heterotic/type-II duality in six and four dimensions. When supersymmetry is the maximal N=4 it will be shown that the duality reduces in the field theory limit to the Montonen-Olive duality of N=4 Super Yang-Mills theory. We will consider further compactifications of type II theory on Calabi-Yau manifolds. We will understand the physical meaning of geometric conifold singularities and the dynamics of conifold transitions. When the CY manifold is a K3 fibration we will argue that the type-II ground-state is dual to the heterotic theory compactified on K3xT 2 . This allows an exact computation of the low effective action. Taking the field theory limit, α ' →0, we will recover the Seiberg-Witten non-perturbative solution of N=2 gauge theory

  10. PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

    Energy Technology Data Exchange (ETDEWEB)

    Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)

    2015-07-20

    A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

  11. Approximate self-consistent potentials for density-functional-theory exchange-correlation functionals

    International Nuclear Information System (INIS)

    Cafiero, Mauricio; Gonzalez, Carlos

    2005-01-01

    We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials

  12. Theory of superfluidity of helium II near the lambda point

    International Nuclear Information System (INIS)

    Ginzburg, V.L.; Sobyanin, A.A.

    1982-01-01

    The present state of the Psi theory of superfluidity of helium II near the lambda point is reviewed. The basic assumptions underlying this theory and the limits of its applicability are discussed. The results of the solution of some problems in the framework of the theory are presented and compared with experimental data. The necessity and possibility of further comparison of the theory with experiment are emphasized

  13. Derivation of fluid dynamics from kinetic theory with the 14-moment approximation

    International Nuclear Information System (INIS)

    Denicol, G.S.; Molnar, E.; Niemi, H.; Rischke, D.H.

    2012-01-01

    We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case. (orig.)

  14. Reggeon field theory at D = 2 in two-loop approximation

    International Nuclear Information System (INIS)

    Eremyan, Sh.S.; Nazaryan, A.E.

    1982-01-01

    A general method of constructing an explicit representation is developed for the pomeron propagator in the presence of additional parameters, such as the pomeron production threshold xi 0 , momentum transfer K vector or the intercept shift delta 0 . The method is shown to be applicable in both one-loop and two-loop approximations. The obtained general formulae allow to consider the pomeron propagator in both asymptotic region and the region of the perturbation theory applicability. Besides, they provide the smooth matching of both these regions. The observed values are calculated, and the results connected with asymptotically high energies are discussed

  15. Many-body perturbation theory using the density-functional concept: beyond the GW approximation

    OpenAIRE

    Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

    2005-01-01

    We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...

  16. Hartree-type approximation applied to a phi4 field theory

    International Nuclear Information System (INIS)

    Chang, S.-J.

    1976-01-01

    Recently, there has been considerable interest in studying the relativistic field theories by means of nonperturbative method. These studies are partially motivated by the now fashionable physical picture that the hadrons are created from an 'abnormal vacuum state'. This abnormal vacuum state is the ground state associated with a spontaneously broken symmetry and is usually characterized by the non-vanishing expectation value of one or more scale fields. Presently, nearly all understandings of hadrons in the above description are based on semi-classical calculations. It is important to know how significant are the effects of the quantum corrections. Some results on the quantum fluctuations in a phi 4 field theory based in a self-consistent Hartree-type approximation are described. (Auth.)

  17. Kinematic approximation in the theory of stimulated nuclear polarization in radical recombination

    International Nuclear Information System (INIS)

    Mikhailov, S.A.; Purtov, P.A.

    1989-01-01

    Within the kinematic approximation, we have developed the theory of stimulated nuclear polarization (SNP) in reactions of geminal recombination of radicals in a strong d.c. magnetic field. We have obtained analytical formulas which are applicable for analysis of SNP effects occurring when the reactions are carried out in nonviscous solutions. The result is represented in the form of integrals with respect to the Green's function determining the kinematics of reagent approach. As an illustration of the proposed theory, we have calculated the polarization of nuclei formed in the reaction products of p-benzoquinone in CD 3 OD and in C 6 D 6 with addition of phenol, and we compare with experiment

  18. Renormalization in self-consistent approximation schemes at finite temperature I: theory

    International Nuclear Information System (INIS)

    Hees, H. van; Knoll, J.

    2001-07-01

    Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

  19. General theory for calculating disorder-averaged Green's function correlators within the coherent potential approximation

    Science.gov (United States)

    Zhou, Chenyi; Guo, Hong

    2017-01-01

    We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.

  20. Biophysics and the microscopic theory of He II

    International Nuclear Information System (INIS)

    Chela-Flores, J.; Ghassib, H.B.

    1985-08-01

    Bose-Einstein condensation and solitonic propagation have recently been shown to be intimately related in biosystems. From our previous demonstration of the existence of solitons in a dilute Bose gas we set out the basis for a full microscopic theory of He II. This is used to understand recent experiments in He II, which are in apparent contradiction. New experiments are suggested by the microscopic theory. (author)

  1. 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

  2. Introduction to string and superstring theory II

    International Nuclear Information System (INIS)

    Peskin, M.E.

    1987-03-01

    Conformal field theory is reviewed, then conformal invariance is used to rederive the basic results on the embedding dimensionality for bosonic and fermionic strings. The spectrum of the bosonic and the computation of scattering amplitudes are discussed. The formalism used is extended to clarify the origin of Yang-Mills gauge invariance in the open bosonic string theory. The question of the general-coordinate gauge invariance of string theory is addressed, presenting two disparate viewpoints on this question. A brief introduction is then given of the reduction from the idealized string theory in 10 extended dimensions to more realistic solutions in which all but 4 of these dimensions are compactified. The state of knowledge about the space-time supersymmetry of the superstring from the covariant viewpoint is outlined. An approach for identifying possible 6-dimensional spaces which might represent the form of the compact dimensions is discussed, and the orbifold scheme of compactification is presented. 77 refs., 18 figs

  3. Introduction to string and superstring theory II

    Energy Technology Data Exchange (ETDEWEB)

    Peskin, M.E.

    1987-03-01

    Conformal field theory is reviewed, then conformal invariance is used to rederive the basic results on the embedding dimensionality for bosonic and fermionic strings. The spectrum of the bosonic and the computation of scattering amplitudes are discussed. The formalism used is extended to clarify the origin of Yang-Mills gauge invariance in the open bosonic string theory. The question of the general-coordinate gauge invariance of string theory is addressed, presenting two disparate viewpoints on this question. A brief introduction is then given of the reduction from the idealized string theory in 10 extended dimensions to more realistic solutions in which all but 4 of these dimensions are compactified. The state of knowledge about the space-time supersymmetry of the superstring from the covariant viewpoint is outlined. An approach for identifying possible 6-dimensional spaces which might represent the form of the compact dimensions is discussed, and the orbifold scheme of compactification is presented. 77 refs., 18 figs. (LEW)

  4. 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

  5. Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas?

    International Nuclear Information System (INIS)

    White, R D; Robson, R E; Schmidt, B; Morrison, Michael A

    2003-01-01

    The 'two-term' approximation (representation of the electron distribution by the first two terms of an expansion in spherical harmonics in velocity space) continues to occupy a central role in the low-temperature plasma physics literature, in spite of the mass of evidence illustrating its inadequacy in the swarm (free diffusion) limit for many molecular gases. Part of the problem lies in the failure of many authors to specify quantitatively what they mean when they say that the two-term approximation is 'acceptable'. Thus for example, an error of 10% in transport coefficients may well be acceptable in many plasma applications, but for analysis of highly accurate swarm experiments to compare with ab initio and beam-derived cross-sections, 0.1% or less is required, making 'multi-term' analysis mandatory. While reconciliation of the swarm and plasma literature along the lines of two different accuracy regimes may thus be possible, we dispute claims that the two-term approximation is generally satisfactory for inversion of swarm experiment data to obtain electron impact cross-sections. The unsatisfactory nature of other assumptions implicit in much of the modern plasma kinetic theory literature is also discussed

  6. Deep-inelastic structure functions in an approximation to the bag theory

    International Nuclear Information System (INIS)

    Jaffe, R.L.

    1975-01-01

    A cavity approximation to the bag theory developed earlier is extended to the treatment of forward virtual Compton scattering. In the Bjorken limit and for small values of ω (ω = vertical-bar2p center-dot q/q 2 vertical-bar) it is argued that the operator nature of the bag boundaries might be ignored. Structure functions are calculated in one and three dimensions. Bjorken scaling is obtained. The model provides a realization of light-cone current algebra and possesses a parton interpretation. The structure functions show a quasielastic peak. The spreading of the structure functions about the peak is associated with confinement. As expected, Regge behavior is not obtained for large ω. The ''momentum sum rule'' is saturated, indicating that the hadron's charged constituents carry all the momentum in this model. νW/subL/ is found to scale and is calculable. Application of the model to the calculation of spin-dependent and chiral-symmetry--violating structure functions is proposed. The nature of the intermediate states in this approximation is discussed. Problems associated with the cavity approximation are also discussed

  7. Lagrangian intersection Floer theory anomaly and obstruction, part II

    CERN Document Server

    Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru

    2009-01-01

    This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...

  8. Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

    Science.gov (United States)

    Gould, Tim; Kronik, Leeor; Pittalis, Stefano

    2018-05-01

    By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

  9. Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

    Science.gov (United States)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  10. Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

    Science.gov (United States)

    Lao, Ka Un; Herbert, John M

    2012-03-22

    We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

  11. Transverse signal decay under the weak field approximation: Theory and validation.

    Science.gov (United States)

    Berman, Avery J L; Pike, G Bruce

    2018-07-01

    To derive an expression for the transverse signal time course from systems in the motional narrowing regime, such as water diffusing in blood. This was validated in silico and experimentally with ex vivo blood samples. A closed-form solution (CFS) for transverse signal decay under any train of refocusing pulses was derived using the weak field approximation. The CFS was validated via simulations of water molecules diffusing in the presence of spherical perturbers, with a range of sizes and under various pulse sequences. The CFS was compared with more conventional fits assuming monoexponential decay, including chemical exchange, using ex vivo blood Carr-Purcell-Meiboom-Gill data. From simulations, the CFS was shown to be valid in the motional narrowing regime and partially into the intermediate dephasing regime, with increased accuracy with increasing Carr-Purcell-Meiboom-Gill refocusing rate. In theoretical calculations of the CFS, fitting for the transverse relaxation rate (R 2 ) gave excellent agreement with the weak field approximation expression for R 2 for Carr-Purcell-Meiboom-Gill sequences, but diverged for free induction decay. These same results were confirmed in the ex vivo analysis. Transverse signal decay in the motional narrowing regime can be accurately described analytically. This theory has applications in areas such as tissue iron imaging, relaxometry of blood, and contrast agent imaging. Magn Reson Med 80:341-350, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

  12. Quantum theory of anharmonic oscillators - a variational and systematic general approximation method

    International Nuclear Information System (INIS)

    Yamazaki, K.; Kyoto Univ.

    1984-01-01

    The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)

  13. Site-occupation embedding theory using Bethe ansatz local density approximations

    Science.gov (United States)

    Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

    2018-06-01

    Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

  14. Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

    Energy Technology Data Exchange (ETDEWEB)

    Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

    1976-04-01

    Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

  15. Morphing Continuum Theory: A First Order Approximation to the Balance Laws

    Science.gov (United States)

    Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

    2017-11-01

    Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

  16. Defects and diffusion, theory & simulation II

    CERN Document Server

    Fisher, David J

    2010-01-01

    This second volume in a new series covering entirely general results in the fields of defects and diffusion includes 356 abstracts of papers which appeared between the end of 2009 and the end of 2010. As well as the abstracts, the volume includes original papers on theory/simulation, semiconductors and metals: ""Predicting Diffusion Coefficients from First Principles ..."" (Mantina, Chen & Liu), ""Gouge Assessment for Pipes ..."" (Meliani, Pluvinage & Capelle), ""Simulation of the Impact Behaviour of ... Hollow Sphere Structures"" (Ferrano, Speich, Rimkus, Merkel & Öchsner), ""Elastic-Plastic

  17. Comparison of approximations in density functional theory calculations: Energetics and structure of binary oxides

    Science.gov (United States)

    Hinuma, Yoyo; Hayashi, Hiroyuki; Kumagai, Yu; Tanaka, Isao; Oba, Fumiyasu

    2017-09-01

    High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include C u2O , A g2O , MgO, ZnO, CdO, SnO, PbO, A l2O3 , G a2O3 , I n2O3 , L a2O3 , B i2O3 , Si O2 , Sn O2 , Pb O2 , Ti O2 , Zr O2 , Hf O2 , V2O5 , N b2O5 , T a2O5 , Mo O3 , and W O3 . Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and -0.04 eV, respectively, and root

  18. Pade approximants in field theory: pion and kaon systems; Approximants de pade en theorie des champs: systeme de pions et de kaons

    Energy Technology Data Exchange (ETDEWEB)

    Zinn-Justin, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1969-07-01

    We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the {rho} and f{sub 0} agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [French] Nous avons construit les approximants de Pade de la matrice S a partir de la serie formelle des perturbations, dans le cas des systemes a deux corps de pions et de kaons. Le probleme depend de trois parametres. Nous avons obtenu les sept resonances meson-meson a deux corps ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) a quelques pour cent de leurs masses experimentales. Les trajectoires de Regge sont trouvees croissantes, les intercepts du {rho} et du f{sub 0} sont en bon accord avec l'experience. Dans les appendices nous donnons quelques proprietes et applications des approximants de Pade. (auteur)

  19. Pade approximants in field theory: pion and kaon systems; Approximants de pade en theorie des champs: systeme de pions et de kaons

    Energy Technology Data Exchange (ETDEWEB)

    Zinn-Justin, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1969-07-01

    We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the {rho} and f{sub 0} agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [French] Nous avons construit les approximants de Pade de la matrice S a partir de la serie formelle des perturbations, dans le cas des systemes a deux corps de pions et de kaons. Le probleme depend de trois parametres. Nous avons obtenu les sept resonances meson-meson a deux corps ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) a quelques pour cent de leurs masses experimentales. Les trajectoires de Regge sont trouvees croissantes, les intercepts du {rho} et du f{sub 0} sont en bon accord avec l'experience. Dans les appendices nous donnons quelques proprietes et applications des approximants de Pade. (auteur)

  20. Early Tests of Piagetian Theory Through World War II.

    Science.gov (United States)

    Beins, Bernard C

    2016-01-01

    Psychologists recognized the importance of Jean Piaget's theory from its inception. Within a year of the appearance of his first book translated into English, The Language and Thought of the Child (J. Piaget, 1926) , it had been reviewed and welcomed; shortly thereafter, psychologists began testing the tenets of the theory empirically. The author traces the empirical testing of his theory in the 2 decades following publication of his initial book. A review of the published literature through the World War II era reveals that the research resulted in consistent failure to support the theoretical mechanisms that Piaget proposed. Nonetheless, the theory ultimately gained traction to become the bedrock of developmental psychology. Reasons for its persistence may include a possible lack of awareness by psychologists about the lack of empirical support, its breadth and complexity, and a lack of a viable alternate theory. As a result, the theory still exerts influence in psychology even though its dominance has diminished.

  1. Orbifolds of M-theory and type II string theories in two dimensions

    International Nuclear Information System (INIS)

    Roy, S.

    1997-01-01

    We consider several orbifold compactifications of M-theory and theircorresponding type II duals in two space-time dimensions. In particular, we show that while the orbifold compactification of M-theory on T 9 /J 9 is dual to the orbifold compactification of type IIB string theory on T 8 /I 8 , the same orbifold T 8 /I 8 of type IIA string theory is dual to M-theory compactified on a smooth product manifold K3 x T 5 . Similarly, while the orbifold compactification of M-theory on (K3 x T 5 )/σ. J 5 is dual to the orbifold compactification of type IIB string theory on (K3 x T 4 )/σ.I 4 , the same orbifold of type IIA string theory is dual to the orbifold T 4 x (K3 x S 1 )/σ.J 1 of M-theory. The spectrum of various orbifold compactifications of M-theory and type II string theories on both sides are compared giving evidence in favor of these duality conjectures. We also comment on a connection between the Dasgupta-Mukhi-Witten conjecture and the Dabholkar-Park-Sen conjecture for the six-dimensional orbifold models of type IIB string theory and M-theory. (orig.)

  2. Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering

    Science.gov (United States)

    Tang, K. T.; Karplus, M.

    1970-10-01

    A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.

  3. Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

    Energy Technology Data Exchange (ETDEWEB)

    Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)

    2016-09-15

    Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the

  4. Relational quadrilateralland II: The Quantum Theory

    Science.gov (United States)

    Anderson, Edward; Kneller, Sophie

    2014-04-01

    We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.

  5. Stellar explosion in the weak field approximation of the Brans-Dicke theory

    International Nuclear Information System (INIS)

    Hamity, Victor H; Barraco, Daniel E

    2005-01-01

    We treat a very crude model of an exploding star, in the weak field approximation of the Brans-Dicke theory, in a scenario that resembles some characteristic data of a type Ia supernova. The most noticeable feature, in the electromagnetic component, is the relationship between the absolute magnitude at maximum brightness of the star and the decline rate in one magnitude from that maximum. This characteristic has become one of the most accurate methods to measure luminosity distances to objects at cosmological distances (Phillips M M 1993 Astrophys. J. 413 L105; see www.all-science-fair-projects.com/ science f air p rojects e ncyclopedia/Supernova, for a brief description of supernovae types). An interesting result is that the active mass associated with the scalar field is totally radiated to infinity, representing a mass loss in the ratio of the 'tensor' component to the scalar component of 1 to (2ω + 3) (ω is the Brans-Dicke parameter), in agreement with a general result of Hawking (1972 Commun. Math. Phys. 25 167). Then, this model shows explicitly, in a dynamical case, the mechanism of the radiation of a scalar field, which is necessary to understand the Hawking result

  6. The Application of Approximate Entropy Theory in Defects Detecting of IGBT Module

    Directory of Open Access Journals (Sweden)

    Shengqi Zhou

    2012-01-01

    Full Text Available Defect is one of the key factors in reducing the reliability of the insulated gate bipolar transistor (IGBT module, so developing the diagnostic method for defects inside the IGBT module is an important measure to avoid catastrophic failure and improves the reliability of power electronic converters. For this reason, a novel diagnostic method based on the approximate entropy (ApEn theory is presented in this paper, which can provide statistical diagnosis and allow the operator to replace defective IGBT modules timely. The proposed method is achieved by analyzing the cross ApEn of the gate voltages before and after the occurring of defects. Due to the local damage caused by aging, the intrinsic parasitic parameters of packaging materials or silicon chips inside the IGBT module such as parasitic inductances and capacitances may change over time, which will make remarkable variation in the gate voltage. That is to say the gate voltage is close coupled with the defects. Therefore, the variation is quantified and used as a precursor parameter to evaluate the health status of the IGBT module. Experimental results validate the correctness of the proposed method.

  7. Study of λφ4 theory in the coupled independent double-oscillator approximation

    International Nuclear Information System (INIS)

    Bray, H.; Stevenson, P.M.

    1992-01-01

    A scalar field can be viewed as an infinite set of coupled oscillators, one at each lattice point in space, as the lattice spacing goes to zero. Λφ 4 theory considers the case when each oscillator is given a potential of the form V(φ) = 1/2m 2 φ 2 + λφ 4 . The question the authors wish to investigate is whether or not such a potential can cause spontaneous symmetry breaking. They approach this problem by defining an open-quotes effective potentialclose quotes which takes into account the quantum effects of the oscillators. This is useful because a double well effective potential would imply spontaneous symmetry breaking. They consider a variational calculation with a trial wavefunctional that is a product of independent double-oscillator wavefunctions. Each double-oscillator wavefunction is defined to be the sum of two Gaussians with the same widths, centered around φ o . They then define the effective potential at φ o to be the energy density resulting from this variational calculation, where the separation and the width of the Gaussians are the parameters which are allowed to vary. They call this the open-quotes Coupled Independent Double-Oscillator Approximation.close quotes The goal of this research is to compute this effective potential, renormalize the variables, and to gain additional insight into whether or not spontaneous symmetry breaking occurs

  8. 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

  9. Cosmological models in globally geodesic coordinates. II. Near-field approximation

    International Nuclear Information System (INIS)

    Liu Hongya

    1987-01-01

    A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel'dovich, as its near-field approximation in the observer's globally geodesic coordinate system

  10. Exotic dual of type II double field theory

    Directory of Open Access Journals (Sweden)

    Eric A. Bergshoeff

    2017-04-01

    Full Text Available We perform an exotic dualization of the Ramond–Ramond fields in type II double field theory, in which they are encoded in a Majorana–Weyl spinor of O(D,D. Starting from a first-order master action, the dual theory in terms of a tensor–spinor of O(D,D is determined. This tensor–spinor is subject to an exotic version of the (self-duality constraint needed for a democratic formulation. We show that in components, reducing O(D,D to GL(D, one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory.

  11. Spin-Density Functionals from Current-Density Functional Theory and Vice Versa: A Road towards New Approximations

    International Nuclear Information System (INIS)

    Capelle, K.; Gross, E.

    1997-01-01

    It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional. copyright 1997 The American Physical Society

  12. Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

    International Nuclear Information System (INIS)

    Kushner, Harold J.

    2012-01-01

    This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

  13. Quantum theory of atom-surface scattering: exact solutions and evaluation of approximations

    International Nuclear Information System (INIS)

    Chiroli, C.; Levi, A.C.

    1976-01-01

    In a recent article a hard corrugated surface was proposed as a simple model for atom-surface scattering. The problem was not solved exactly, however, but several alternative approximations were considered. Since these three similar, but inequivalent, approximations were proposed, the problem arose to evaluate these approximations in order to choose between them. In the present letter some exact calculations are presented which make this choice rationally possible. (Auth.)

  14. Theory of electron cyclotron heating in the Constance II experiment

    International Nuclear Information System (INIS)

    Mauel, M.E.

    1981-03-01

    The bounce-averaged quasi-linear equation for a non-relativistic mirror-confined plasma interacting with electromagnetic waves is derived for use in the study of ECRH of the Constance II mirror experiment. The derivations follows the more formal examples given by Berk for electrostatic waves and Bernstein and Baxter for relativistic plasmas. The validity of the theory is discussed by examining individual particle orbits in an EM field. The local dispersion relation is found while deriving a self-consistent WKB theory which can be used to estimate the power transferred from the launching horn to the plasma

  15. 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

  16. Theory of inelastic electron tunneling from a localized spin in the impulsive approximation.

    Science.gov (United States)

    Persson, Mats

    2009-07-31

    A simple expression for the conductance steps in inelastic electron tunneling from spin excitations in a single magnetic atom adsorbed on a nonmagnetic metal surface is derived. The inelastic coupling between the tunneling electron and the spin is via the exchange coupling and is treated in an impulsive approximation using the Tersoff-Hamann approximation for the tunneling between the tip and the sample.

  17. Random matrix theory and acoustic resonances in plates with an approximate symmetry

    DEFF Research Database (Denmark)

    Andersen, Anders Peter; Ellegaard, C.; Jackson, A.D.

    2001-01-01

    We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and...

  18. Magnetic exchange couplings from noncollinear perturbation theory: dinuclear CuII complexes.

    Science.gov (United States)

    Phillips, Jordan J; Peralta, Juan E

    2014-08-07

    To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.

  19. A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations

    Energy Technology Data Exchange (ETDEWEB)

    Gorenflo, Norbert [Beuth Hochschule fuer Technik Berlin (Germany). Fachbereich II; Kunik, Matthias [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik

    2009-07-01

    We present a new and self-contained theory for mapping properties of the boundary operators for slit diffraction occurring in Sommerfeld's diffraction theory, covering two different cases of the polarisation of the light. This theory is entirely developed in the context of the boundary operators with a Hankel kernel and not based on the corresponding mixed boundary value problem for the Helmholtz equation. For a logarithmic approximation of the Hankel kernel we also study the corresponding mapping properties and derive explicit solutions together with certain regularity results. (orig.)

  20. Analytical mass formula and nuclear surface properties in the ETF approximation. Part II: asymmetric nuclei

    Science.gov (United States)

    Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

    2016-08-01

    We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

  1. T-dualization of type II superstring theory in double space

    Energy Technology Data Exchange (ETDEWEB)

    Nikolic, B.; Sazdovic, B. [University of Belgrade, Institute of Physics Belgrade, Belgrade (Serbia)

    2017-03-15

    In this article we offer a new interpretation of the T-dualization procedure of type II superstring theory in the double space framework. We use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms. T-dualization along any subset of the initial coordinates, x{sup a}, is equivalent to the permutation of this subset with subset of the corresponding T-dual coordinates, y{sub a}, in double space coordinate Z{sup M} = (x{sup μ}, y{sub μ}). Requiring that the T-dual transformation law after the exchange x{sup a} <-> y{sub a} has the same form as the initial one, we obtain the T-dual NS-NS and NS-R background fields. The T-dual R-R field strength is determined up to one arbitrary constant under some assumptions. The compatibility between supersymmetry and T-duality produces a change of bar spinors and R-R field strength. If we dualize an odd number of dimensions x{sup a}, such a change flips type IIA/B to type II B/A. If we T-dualize the time-like direction, one imaginary unit i maps type II superstring theories to type II{sup *} ones. (orig.)

  2. Nonlinear many-body reaction theories from nuclear mean field approximations

    International Nuclear Information System (INIS)

    Griffin, J.J.

    1983-01-01

    Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

  3. Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

    Science.gov (United States)

    Fries, T. P.; Schöllhammer, D.

    2017-11-01

    A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.

  4. Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation

    International Nuclear Information System (INIS)

    Sanders, Sören; Holthaus, Martin

    2017-01-01

    We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose–Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions. (paper)

  5. Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation

    Science.gov (United States)

    Sanders, Sören; Holthaus, Martin

    2017-11-01

    We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose-Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.

  6. The soliton solution of the PHI24 field theory in the Hartree approximation

    International Nuclear Information System (INIS)

    Altenbokum, M.

    1984-01-01

    In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de

  7. Comparison of the Debye–Hückel and the Mean Spherical Approximation Theories for Electrolyte Solutions

    DEFF Research Database (Denmark)

    Maribo-Mogensen, Bjørn; Kontogeorgis, Georgios M.; Thomsen, Kaj

    2012-01-01

    The thermodynamics of electrolyte solutions has been investigated by many scientists throughout the last century. While several theories have been presented, the most popular models for the electrostatic interactions are based on the Debye–Hückel and mean spherical approximation (MSA) theories....... In this paper we investigate the differences between the Debye–Hückel and the MSA theories, and comparisons of the numerical results for the Helmholtz energy and its derivatives with respect to temperature, volume and composition are presented. The investigation shows that the nonrestricted primitive MSA...... theory performs similarly to Debye–Hückel, despite the differences in the derivation. We furthermore show that the static permittivity is a key parameter for both models and that in many cases it completely dominates the results obtained from the two models. Consequently, we conclude that the simpler...

  8. Laser driven electron-positron pair creation-kinetic theory versus analytical approximations

    International Nuclear Information System (INIS)

    Smolyansky, S.A.; Prozorkevich, A.V.; Bonitz, M.

    2013-01-01

    The dynamical Schwinger effect of vacuum pair creation driven by an intense external laser pulse is studied on the basis of quantum kinetic theory. The numerical solutions of these kinetic equations exhibit a complex time dependence which makes an analysis of the physical processes difficult. In particular, the question of secondary effects, such as creation of secondary annihilation photons from the focus spot of the colliding laser beams, remains an important open problem. In the present work we, therefore, develop a perturbation theory which is able to capture the dominant time dependence of the produced electron-positron pair density. The theory shows excellent agreement with the exact kinetic results during the laser pulse, but fails to reproduce the residual pair density remaining in the system after termination of the pulse. (copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  9. Breakdown of the standard perturbation theory and moving boundary approximation for "pulled" fronts

    NARCIS (Netherlands)

    U. M. Ebert (Ute); W. van Saarloos

    2000-01-01

    htmlabstractA moving boundary approximation or similar perturbative schemes for the response of a coherent structure like a front, vortex or pulse to external forces and noise can generally be derived if two conditions are obeyed: (i) there must be a separation of the time scales of the dynamics on

  10. Breakdown of the standard perturbation theory and moving boundary approximation for pulled fronts

    NARCIS (Netherlands)

    U. M. Ebert (Ute); W. van Saarloos

    2000-01-01

    textabstractThe derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales of the dynamics on the inner and outer scale and

  11. Type II Superstring Field Theory: Geometric Approach and Operadic Description

    CERN Document Server

    Jurco, Branislav

    2013-01-01

    We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a $\\mathcal{N}=1$ generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.

  12. ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION

    Energy Technology Data Exchange (ETDEWEB)

    Heng, Kevin; Mendonça, João M.; Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch [University of Bern, Center for Space and Habitability, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

    2014-11-01

    We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior), and solutions for the temperature-pressure profiles. Generally, the problem is mathematically underdetermined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat, and the properties of scattering in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.

  13. Theory of hot and rotating nuclei within the static path approximation

    International Nuclear Information System (INIS)

    Ansari, A.

    1995-01-01

    For the description of hot and rotating nuclei the static path approximation to the path integral representation of the partition function is at present the best practicable approach incorporating rigorously the statistical fluctuations in nuclear shape degrees of freedom. The paper briefly discusses the method and present a few of the recent results on level densities and GDR (giant dipole resonance) γ-absorption cross sections. (author). 22 refs., 2 figs

  14. Towards a comprehensive theory for He II: II. A temperature-dependent field-theoretic approach

    International Nuclear Information System (INIS)

    Chela-Flores, J.; Ghassib, H.B.

    1982-09-01

    New experimental aspects of He II are used as a guide towards a comprehensive theory in which non-zero temperature U(1) and SU(2) gauge fields are incorporated into a gauge hierarchy of effective Lagrangians. We conjecture that an SU(n) gauge-theoretic description of the superfluidity of 4 He may be obtained in the limit n→infinity. We indicate, however, how experiments may be understood in the zeroth, first and second order of the hierarchy. (author)

  15. Theory of magnetic neutron small-angle scattering using the dynamical theory of diffraction instead of the Born approximation. I

    International Nuclear Information System (INIS)

    Schaerpf, O.

    1978-01-01

    Two ways are given for solving the problem of the dependence of the refraction on the direction of magnetization on both sides of the refractive boundary, one applying the Halpern magnetic scattering vector, the other applying the dynamical theory of diffraction. They lead to different results. Experimental investigation of refraction by magnetic boundaries shows no dependence of the angle of deflection on the relative angles of magnetization in adjacent domains. This behaviour is only described correctly by the dynamical theory, which far from Laue reflections leads to a treatment by the Schoedinger equation with a spin-dependent potential dependent on the average continuous homogenous magnetic induction, both for the law of refraction and for the precession of the spin. The results of this treatment are discussed as a consequence of the behaviour of the spin of the neutrons. This gives some insight about how and why, with refraction, the intensities of the direct and deflected beams depend on the magnetization directions in adjacent domains. The dynamical theory also shows that the Halpern magnetic scattering vector applies only with Laue or Bragg reflections and not with transmission far from those reflections. (Auth.)

  16. A quantal transport theory for nuclear collective motion: the merits of a locally harmonic approximation

    International Nuclear Information System (INIS)

    Hofmann, H.

    1997-01-01

    A transport theory is developed for collective motion of systems such as an atomic nucleus, which may be considered as a typical representative of a self-bound micro-system. Albeit for pragmatic reasons, collective variables are introduced as shape parameters, self-consistency with respect to the nucleonic degrees of freedom has been implemented at various important stages. This feature leads to subsidiary conditions which are obeyed locally for both the average motion as well as for the quantized Hamiltonian constructed through a Bohm-Pines procedure. Furthermore, self-consistency governs the definition of the transport coefficients appearing in the equations for collective motion. The latter is associated to the time evolution of the density in collective phase space, for which the concept of the Wigner function is employed. Global motion is described by propagating the system in successive time laps which are macroscopically small, but microscopically large. This enables one to exploit linearization procedures and to take advantage of the benefits of linear response theory. A microscopic damping mechanism is introduced by dressing the energies of the independent particle model by complex self-energies, the parameters of which are determined from optical model considerations. Numerical evaluations of transport coefficients are described and tested for the case of fission in the light of recent experimental findings. The theory allows one to extend both Kramers' picture of this process as well as his equation for the density distribution into the quantum regime. (orig.)

  17. Variational calculations in gauge theories with approximate projection on gauge invariant states

    International Nuclear Information System (INIS)

    Heinemann, C.; Martin, C.; Vautherin, D.; Iancu, E.

    1999-01-01

    Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. The minimization with respect to the kernel and center of the Gaussian leads to a gap type equation which is free of the difficulties generally encountered with negative modes. We show that the divergences in the expectation value of the energy density are only logarithmic and can be removed by a renormalization of the coupling constant. The renormalized energy density has a minimum which corresponds to a vanishing background magnetic field. We obtain an estimate for the gluon condensate. (authors)

  18. Theory and application of an approximate model of saltwater upconing in aquifers

    Science.gov (United States)

    McElwee, C.; Kemblowski, M.

    1990-01-01

    Motion and mixing of salt water and fresh water are vitally important for water-resource development throughout the world. An approximate model of saltwater upconing in aquifers is developed, which results in three non-linear coupled equations for the freshwater zone, the saltwater zone, and the transition zone. The description of the transition zone uses the concept of a boundary layer. This model invokes some assumptions to give a reasonably tractable model, considerably better than the sharp interface approximation but considerably simpler than a fully three-dimensional model with variable density. We assume the validity of the Dupuit-Forchheimer approximation of horizontal flow in each layer. Vertical hydrodynamic dispersion into the base of the transition zone is assumed and concentration of the saltwater zone is assumed constant. Solute in the transition zone is assumed to be moved by advection only. Velocity and concentration are allowed to vary vertically in the transition zone by using shape functions. Several numerical techniques can be used to solve the model equations, and simple analytical solutions can be useful in validating the numerical solution procedures. We find that the model equations can be solved with adequate accuracy using the procedures presented. The approximate model is applied to the Smoky Hill River valley in central Kansas. This model can reproduce earlier sharp interface results as well as evaluate the importance of hydrodynamic dispersion for feeding salt water to the river. We use a wide range of dispersivity values and find that unstable upconing always occurs. Therefore, in this case, hydrodynamic dispersion is not the only mechanism feeding salt water to the river. Calculations imply that unstable upconing and hydrodynamic dispersion could be equally important in transporting salt water. For example, if groundwater flux to the Smoky Hill River were only about 40% of its expected value, stable upconing could exist where

  19. 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

  20. Analysis of EBR-II neutron and photon physics by multidimensional transport-theory techniques

    International Nuclear Information System (INIS)

    Jacqmin, R.P.; Finck, P.J.; Palmiotti, G.

    1994-01-01

    This paper contains a review of the challenges specific to the EBR-II core physics, a description of the methods and techniques which have been developed for addressing these challenges, and the results of some validation studies relative to power-distribution calculations. Numerical tests have shown that the VARIANT nodal code yields eigenvalue and power predictions as accurate as finite difference and discrete ordinates transport codes, at a small fraction of the cost. Comparisons with continuous-energy Monte Carlo results have proven that the errors introduced by the use of the diffusion-theory approximation in the collapsing procedure to obtain broad-group cross sections, kerma factors, and photon-production matrices, have a small impact on the EBR-II neutron/photon power distribution

  1. On the Application of Iterative Methods of Nondifferentiable Optimization to Some Problems of Approximation Theory

    Directory of Open Access Journals (Sweden)

    Stefan M. Stefanov

    2014-01-01

    Full Text Available We consider the data fitting problem, that is, the problem of approximating a function of several variables, given by tabulated data, and the corresponding problem for inconsistent (overdetermined systems of linear algebraic equations. Such problems, connected with measurement of physical quantities, arise, for example, in physics, engineering, and so forth. A traditional approach for solving these two problems is the discrete least squares data fitting method, which is based on discrete l2-norm. In this paper, an alternative approach is proposed: with each of these problems, we associate a nondifferentiable (nonsmooth unconstrained minimization problem with an objective function, based on discrete l1- and/or l∞-norm, respectively; that is, these two norms are used as proximity criteria. In other words, the problems under consideration are solved by minimizing the residual using these two norms. Respective subgradients are calculated, and a subgradient method is used for solving these two problems. The emphasis is on implementation of the proposed approach. Some computational results, obtained by an appropriate iterative method, are given at the end of the paper. These results are compared with the results, obtained by the iterative gradient method for the corresponding “differentiable” discrete least squares problems, that is, approximation problems based on discrete l2-norm.

  2. 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

  3. Enhanced gauge symmetry in type II string theory

    International Nuclear Information System (INIS)

    Katz, S.; Ronen Plesser, M.

    1996-01-01

    We show how enhanced gauge symmetry in type II string theory compactified on a Calabi-Yau threefold arises from singularities in the geometry of the target space. When the target space of the type IIA string acquires a genus g curve C of A N-1 singularities, we find that an SU(N) gauge theory with g adjoint hypermultiplets appears at the singularity. The new massless states correspond to solitons wrapped about the collapsing cycles, and their dynamics is described by a twisted supersymmetric gauge theory on C x R 4 . We reproduce this result from an analysis of the S-dual D-manifold. We check that the predictions made by this model about the nature of the Higgs branch, the monodromy of period integrals, and the asymptotics of the one-loop topological amplitude are in agreement with geometrical computations. In one of our examples we find that the singularity occurs at strong coupling in the heterotic dual proposed by Kachru and Vafa. (orig.)

  4. Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

    International Nuclear Information System (INIS)

    Akhiezer, A.I.; Shul'ga, N.F.

    1991-01-01

    The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)

  5. Towards a unification of the hierarchical reference theory and the self-consistent Ornstein-Zernike approximation.

    Science.gov (United States)

    Reiner, A; Høye, J S

    2005-12-01

    The hierarchical reference theory and the self-consistent Ornstein-Zernike approximation are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase coexistence and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal, we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity, we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable mean spherical approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions that any closure to the Ornstein-Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.

  6. Speeding up equation of motion coupled cluster theory with the chain of spheres approximation

    International Nuclear Information System (INIS)

    Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert

    2016-01-01

    In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel’s test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm −1 (59 μHartree) for excitation energies and 6.799 cm −1 (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core

  7. Speeding up equation of motion coupled cluster theory with the chain of spheres approximation

    Energy Technology Data Exchange (ETDEWEB)

    Dutta, Achintya Kumar; Neese, Frank, E-mail: frank.neese@cec.mpg.de; Izsák, Róbert, E-mail: robert.izsak@cec.mpg.de [Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr (Germany)

    2016-01-21

    In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel’s test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm{sup −1} (59 μHartree) for excitation energies and 6.799 cm{sup −1} (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.

  8. Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities

    Energy Technology Data Exchange (ETDEWEB)

    Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp [Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Champagne, Benoît; Botek, Edith [Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur (Belgium)

    2015-01-22

    We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.

  9. Total-energy Assisted Tight-binding Method Based on Local Density Approximation of Density Functional Theory

    Science.gov (United States)

    Fujiwara, Takeo; Nishino, Shinya; Yamamoto, Susumu; Suzuki, Takashi; Ikeda, Minoru; Ohtani, Yasuaki

    2018-06-01

    A novel tight-binding method is developed, based on the extended Hückel approximation and charge self-consistency, with referring the band structure and the total energy of the local density approximation of the density functional theory. The parameters are so adjusted by computer that the result reproduces the band structure and the total energy, and the algorithm for determining parameters is established. The set of determined parameters is applicable to a variety of crystalline compounds and change of lattice constants, and, in other words, it is transferable. Examples are demonstrated for Si crystals of several crystalline structures varying lattice constants. Since the set of parameters is transferable, the present tight-binding method may be applicable also to molecular dynamics simulations of large-scale systems and long-time dynamical processes.

  10. 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.

  11. Leptogenesis in unified theories with Type II see-saw

    International Nuclear Information System (INIS)

    Antusch, Stefan; King, Steve F.

    2006-01-01

    In some classes of flavour models based on unified theories with a type I see-saw mechanism, the prediction for the mass of the lightest right-handed neutrino is in conflict with the lower bound from the requirement of successful thermal leptogenesis. We investigate how lifting the absolute neutrino mass scale by adding a type II see-saw contribution proportional to the unit matrix can solve this problem. Generically, lifting the neutrino mass scale increases the prediction for the mass of the lightest right-handed neutrino while the decay asymmetry is enhanced and washout effects are reduced, relaxing the lower bound on the mass of the lightest right-handed neutrino from thermal leptogenesis. For instance in classes of unified theories where the lightest right-handed neutrino dominates the type I see-saw contribution, we find that thermal leptogenesis becomes possible if the neutrino mass scale is larger than about 0.15 eV, making this scenario testable by neutrinoless double beta decay experiments in the near future

  12. Methods of approximation theory

    National Research Council Canada - National Science Library

    Stepane︠t︡s, A. I

    2005-01-01

    .... Korneichuk, Α. V. Efimov, S. A. Telyakovskii, etc. In the same years, the concept of (φ, β) -derivative defined for a given function / by a given sequence of numbers ψ = ψ (k), k = 1 , 2 , . . . , and numbers β was formed. The ordinary rth derivative, r = 1 , 2 , . . . , of a periodic function is a particular case of the (φ, /3)-derivative for y(k...

  13. 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.

  14. Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF

    Science.gov (United States)

    Li, Chen; Requist, Ryan; Gross, E. K. U.

    2018-02-01

    We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation—an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).

  15. Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response

    Science.gov (United States)

    Caricato, Marco

    2018-04-01

    We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

  16. Ab initio quasi-particle approximation bandgaps of silicon nanowires calculated at density functional theory/local density approximation computational effort

    Energy Technology Data Exchange (ETDEWEB)

    Ribeiro, M., E-mail: ribeiro.jr@oorbit.com.br [Office of Operational Research for Business Intelligence and Technology, Principal Office, Buffalo, Wyoming 82834 (United States)

    2015-06-21

    Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost.

  17. Ab initio quasi-particle approximation bandgaps of silicon nanowires calculated at density functional theory/local density approximation computational effort

    International Nuclear Information System (INIS)

    Ribeiro, M.

    2015-01-01

    Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost

  18. Origin of the Anomalous Color of Egyptian and Han Blue Historical Pigments: Going beyond the Complex Approximation in Ligand Field Theory

    Science.gov (United States)

    García-Fernandez, Pablo; Moreno, Miguel; Aramburu, José Antonio

    2016-01-01

    The complex approximation is widely used in the framework of the Ligand Field Theory for explaining the optical properties of crystalline coordination compounds. Here, we show that there are essential features of these systems that cannot be understood with the usual approximation that only considers an isolated complex at the correct equilibrium…

  19. 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...

  20. A Study on the Model of Detecting the Liquid Level of Sealed Containers Based on Kirchhoff Approximation Theory

    Directory of Open Access Journals (Sweden)

    Bin Zhang

    2017-06-01

    Full Text Available By simulating the sound field of a round piston transducer with the Kirchhoff integral theorem and analyzing the shape of ultrasound beams and propagation characteristics in a metal container wall, this study presents a model for calculating the echo sound pressure by using the Kirchhoff paraxial approximation theory, based on which and according to different ultrasonic impedance between gas and liquid media, a method for detecting the liquid level from outside of sealed containers is proposed. Then, the proposed method is evaluated through two groups of experiments. In the first group, three kinds of liquid media with different ultrasonic impedance are used as detected objects; the echo sound pressure is calculated by using the proposed model under conditions of four sets of different wall thicknesses. The changing characteristics of the echo sound pressure in the entire detection process are analyzed, and the effects of different ultrasonic impedance of liquids on the echo sound pressure are compared. In the second group, taking water as an example, two transducers with different radii are selected to measure the liquid level under four sets of wall thickness. Combining with sound field characteristics, the influence of different size transducers on the pressure calculation and detection resolution are discussed and analyzed. Finally, the experimental results indicate that measurement uncertainly is better than ±5 mm, which meets the industrial inspection requirements.

  1. A Study on the Model of Detecting the Liquid Level of Sealed Containers Based on Kirchhoff Approximation Theory.

    Science.gov (United States)

    Zhang, Bin; Song, Wen-Ai; Wei, Yue-Juan; Zhang, Dong-Song; Liu, Wen-Yi

    2017-06-15

    By simulating the sound field of a round piston transducer with the Kirchhoff integral theorem and analyzing the shape of ultrasound beams and propagation characteristics in a metal container wall, this study presents a model for calculating the echo sound pressure by using the Kirchhoff paraxial approximation theory, based on which and according to different ultrasonic impedance between gas and liquid media, a method for detecting the liquid level from outside of sealed containers is proposed. Then, the proposed method is evaluated through two groups of experiments. In the first group, three kinds of liquid media with different ultrasonic impedance are used as detected objects; the echo sound pressure is calculated by using the proposed model under conditions of four sets of different wall thicknesses. The changing characteristics of the echo sound pressure in the entire detection process are analyzed, and the effects of different ultrasonic impedance of liquids on the echo sound pressure are compared. In the second group, taking water as an example, two transducers with different radii are selected to measure the liquid level under four sets of wall thickness. Combining with sound field characteristics, the influence of different size transducers on the pressure calculation and detection resolution are discussed and analyzed. Finally, the experimental results indicate that measurement uncertainly is better than ±5 mm, which meets the industrial inspection requirements.

  2. The use of approximation formulae in calculations of acid-base equilibria-II: salts of mono- and diprotic acids.

    Science.gov (United States)

    Narasaki, H

    1980-02-01

    The pH of solutions of salts of mono- and diprotic acids is calculated by use of approximation formulae and the theoretically exact equations. The regions for useful application of the approximation formulae (error monoprotic acids, areas are symmetrically equal to those of the acids. For salts of diprotic acids the ranges generally depend on K(2)/K(1).

  3. Four-dimensional boson field theory. II. Existence

    International Nuclear Information System (INIS)

    Baker, G.A. Jr.

    1986-01-01

    The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high-temperature expansions of the corresponding continuous-spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free

  4. Understanding Ion Binding Affinity and Selectivity in β-Parvalbumin Using Molecular Dynamics and Mean Spherical Approximation Theory.

    Science.gov (United States)

    Kucharski, Amir N; Scott, Caitlin E; Davis, Jonathan P; Kekenes-Huskey, Peter M

    2016-08-25

    Parvalbumin (PV) is a globular calcium (Ca(2+))-selective protein expressed in a variety of biological tissues. Our computational studies of the rat β-parvalbumin (β-PV) isoform seek to elucidate the molecular thermodynamics of Ca(2+) versus magnesium (Mg(2+)) binding at the protein's two EF-hand motifs. Specifically, we have utilized molecular dynamics (MD) simulations and a mean-field electrolyte model (mean spherical approximation (MSA) theory) to delineate how the EF-hand scaffold controls the "local" thermodynamics of Ca(2+) binding selectivity over Mg(2+). Our MD simulations provide the probability density of metal-chelating oxygens within the EF-hand scaffolds for both Ca(2+) and Mg(2+), as well the conformational strain induced by Mg(2+) relative to Ca(2+) binding. MSA theory utilizes the binding domain oxygen and charge distributions to predict the chemical potential of ion binding, as well as their corresponding concentrations within the binding domain. We find that the electrostatic and steric contributions toward ion binding were similar for Mg(2+) and Ca(2+), yet the latter was 5.5 kcal/mol lower in enthalpy when internal strain within the EF hand was considered. We therefore speculate that beyond differences in dehydration energies for the Ca(2+) versus Mg(2+), strain induced in the β-PV EF hand by cation binding significantly contributes to the nearly 10,000-fold difference in binding affinity reported in the literature. We further complemented our analyses of local factors governing cation binding selectivity with whole-protein (global) contributions, such as interhelical residue-residue contacts and solvent exposure of hydrophobic surface. These contributions were found to be comparable for both Ca(2+)- and Mg(2+)-bound β-PV, which may implicate local factors, EF-hand strain, and dehydration, in providing the primary means of selectivity. We anticipate these methods could be used to estimate metal binding thermodynamics across a broad range of

  5. Diophantine approximation

    CERN Document Server

    Schmidt, Wolfgang M

    1980-01-01

    "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

  6. SU(4) x U(1) gauge theory. II. CP nonconservation

    International Nuclear Information System (INIS)

    Deshpande, N.G.; Hwa, R.C.; Mannheim, P.D.

    1979-01-01

    We exploit the higher symmetry inherent in an SU(4) x U(1) gauge theory to construct a spontaneously broken theory of CP nonconservation. Higgs multiplets in the adjoint representation of SU(4) contain both even and odd CP fields; thus, requiring the simultaneous nonvanishing of the vacuum expectation values of these fields leads to CP noninvariance of the vacuum. We find that all the CP-nonconserving effects are mediated in our theory by the superheavy gauge bosons of the broken SU(4) x U(1) symmetry. In fact, the very existence of CP violation sets an upper limit on the masses of these bosons. In our model the dominant CP effect lies in the neutral kaon system and is found to arise through a direct (ΔS = 2) K 1 -K 2 transition. The model has all the features of a superweak theory, with a neutron electric dipole moment substantially smaller than 10 -24 e cm

  7. An Opponent-Process Theory of Motivation: II. Cigarette Addiction

    Science.gov (United States)

    Solomon, Richard L.; Corbit, John D.

    1973-01-01

    Methods suggested by opponent-process theory of acquired motivation in helping smokers to quit the habit include use of antagonistic drugs, total cessation from tobacco, and decrease in intensity and frequency of tobacco use. (DS)

  8. New Analysis and Theory of Deployable Folded Structures, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — A recently developed mathematical folding theory has great value for deployable space structures and in situ manufacture of large beams, panels and cylinders. The...

  9. Markov traces and II1 factors in conformal field theory

    International Nuclear Information System (INIS)

    Boer, J. de; Goeree, J.

    1991-01-01

    Using the duality equations of Moore and Seiberg we define for every primary field in a Rational Conformal Field Theory a proper Markov trace and hence a knot invariant. Next we define two nested algebras and show, using results of Ocneanu, how the position of the smaller algebra in the larger one reproduces part of the duality data. A new method for constructing Rational Conformal Field Theories is proposed. (orig.)

  10. Alternative basis for the theory of complex spectra II

    International Nuclear Information System (INIS)

    Harter, W.G.; Patterson, C.W.

    1975-01-01

    The atomic angular factor calculation methods are simplified and extended to include a treatment of spin-orbit operators and multiple shell configurations (II'...) sup(n). A tableau formula is given for the matrix between slater states and states of definite total spin

  11. Introduction to modern theoretical physics. Volume II. Quantum theory and statistical physics

    International Nuclear Information System (INIS)

    Harris, E.G.

    1975-01-01

    The topics discussed include the history and principles, some solvable problems, and symmetry in quantum mechanics, interference phenomena, approximation methods, some applications of nonrelativistic quantum mechanics, relativistic wave equations, quantum theory of radiation, second quantization, elementary particles and their interactions, thermodynamics, equilibrium statistical mechanics and its applications, the kinetic theory of gases, and collective phenomena

  12. Two Ramond-Ramond corrections to type II supergravity via field-theory amplitude

    Energy Technology Data Exchange (ETDEWEB)

    Bakhtiarizadeh, Hamid R. [Sirjan University of Technology, Department of Physics, Sirjan (Iran, Islamic Republic of)

    2017-12-15

    Motivated by the standard form of the string-theory amplitude, we calculate the field-theory amplitude to complete the higher-derivative terms in type II supergravity theories in their conventional form. We derive explicitly the O(α{sup '3}) interactions for the RR (Ramond-Ramond) fields with graviton, B-field and dilaton in the low-energy effective action of type II superstrings. We check our results by comparison with previous work that has been done by the other methods, and we find exact agreement. (orig.)

  13. Quantum field theory on discrete space-time. II

    International Nuclear Information System (INIS)

    Yamamoto, H.

    1985-01-01

    A quantum field theory of bosons and fermions is formulated on discrete Lorentz space-time of four dimensions. The minimum intervals of space and time are assumed to have different values in this paper. As a result the difficulties encountered in the previous paper (complex energy, incompleteness of solutions, and inequivalence between phase representation and momentum representation) are removed. The problem in formulating a field theory of fermions is solved by introducing a new operator and considering a theorem of translation invariance. Any matrix element given by a Feynman diagram is calculated in this theory to give a finite value regardless of the kinds of particles concerned (massive and/or massless bosons and/or fermions)

  14. Abelian Chern endash Simons theory. II. A functional integral approach

    International Nuclear Information System (INIS)

    Manoliu, M.

    1998-01-01

    Following Witten, [Commun. Math. Phys. 21, 351 endash 399 (1989)] we approach the Abelian quantum Chern endash Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170 endash 206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization. copyright 1998 American Institute of Physics

  15. Current-drive theory II: the lower-hybrid wave

    International Nuclear Information System (INIS)

    Fisch, N.J.

    1986-01-01

    The theory of current-drive seeks to predict the efficiency with which an external power source can produce current in a plasma torus. The theory, which is now well supported by experimental data, becomes especially simple in the important limit of lower-hybrid or electron-cyclotron waves interacting with superthermal electrons. The solution of an equation adjoint to the linearized Fokker-Planck equation gives both the steady-state and ramp-up current-drive efficiencies. Other phenomena, such as rf-induced runaway rates, rf-induced radiation, etc., may be calculated by this method, and analytical solutions have been obtained in several limiting cases. 12 refs

  16. KINETIC THEORY OF PLASMA WAVES: Part II: Homogeneous Plasma

    NARCIS (Netherlands)

    Westerhof, E.

    2010-01-01

    The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves are discussed in the limit of the cold

  17. Kinetic theory of plasma waves: Part II homogeneous plasma

    NARCIS (Netherlands)

    Westerhof, E.

    2000-01-01

    The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves are discussed in the limit of the cold

  18. Kinetic theory of plasma waves - Part II: Homogeneous plasma

    NARCIS (Netherlands)

    Westerhof, E.

    2008-01-01

    The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves axe discussed in the limit of the cold

  19. Braid group, knot theory and statistical mechanics II

    CERN Document Server

    Yang Chen Ning

    1994-01-01

    The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors.

  20. Beyond heat baths II: framework for generalized thermodynamic resource theories

    Science.gov (United States)

    Yunger Halpern, Nicole

    2018-03-01

    Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories. Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family’s structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd’s engine and Landauer’s Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories’ potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.

  1. Some findings on prospect and refuge theory: II.

    Science.gov (United States)

    Stamps, Arthur E

    2008-08-01

    This article presents four new studies on the efficacy of predictions based on prospect and refuge theory and summarizes the results over eight studies. New data covered 49 participants and 36 environments. The eight studies included in the summary covered 144 participants and 80 widely diverse environments (Japanese Tatami rooms, Western rooms, porch, meadow, neighborhood commercial, shopping mall, vacation landscapes). Data were available for hypotheses about five factors: prospect, refuge, light, venue, and spatial transition. Efficacy was represented by correlations for the levels of the factors with responses of preference or comfort. Overall, venue was the most efficacious factor (r = .42, 95% CI = .14, .64). Efficacies for the other factors were very near zero. It is suggested that a considerable amount of additional formal inquiry be conducted before assuming the utility of prospect and refuge theory.

  2. Continuous and distributed systems II theory and applications

    CERN Document Server

    Zgurovsky, Mikhail

    2015-01-01

    As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine, and the USA. ...

  3. Grassmann phase space methods for fermions. II. Field theory

    Energy Technology Data Exchange (ETDEWEB)

    Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)

    2017-02-15

    In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

  4. Grassmann phase space methods for fermions. II. Field theory

    International Nuclear Information System (INIS)

    Dalton, B.J.; Jeffers, J.; Barnett, S.M.

    2017-01-01

    In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

  5. SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-09-01

    This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

  6. The effective field theory of nonsingular cosmology: II

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Yong; Li, Hai-Guang [University of Chinese Academy of Sciences, School of Physics, Beijing (China); Qiu, Taotao [Central China Normal University, Institute of Astrophysics, Wuhan (China); Piao, Yun-Song [University of Chinese Academy of Sciences, School of Physics, Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, P.O. Box 2735, Beijing (China)

    2017-06-15

    Based on the effective field theory (EFT) of cosmological perturbations, we explicitly clarify the pathology in nonsingular cubic Galileon models and show how to cure it in EFT with new insights into this issue. With the least set of EFT operators that are capable to avoid instabilities in nonsingular cosmologies, we construct a nonsingular model dubbed the Genesis-inflation model, in which a slowly expanding phase (namely, Genesis) with increasing energy density is followed by slow-roll inflation. The spectrum of the primordial perturbation may be simulated numerically, which shows itself a large-scale cutoff, as the large-scale anomalies in CMB might be a hint for. (orig.)

  7. Numerical methods for studying anharmonic oscillator approximations to the phi super 4 sub 2 quantum field theory

    Science.gov (United States)

    Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.

    1980-01-01

    This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.

  8. Screened Coulomb interactions in metallic alloys. II. Screening beyond the single-site and atomic-sphere approximations

    DEFF Research Database (Denmark)

    Ruban, Andrei; Simak, S.I.; Korzhavyi, P.A.

    2002-01-01

    -electron potential and energy. In the case of a random alloy such interactions can be accounted for only by lifting the atomic-sphere and single-site approximations, in order to include the polarization due to local environment effects. Nevertheless, a simple parametrization of the screened Coulomb interactions...... for the ordinary single-site methods, including the generalized perturbation method, is still possible. We obtained such a parametrization for bulk and surface NiPt alloys, which allows one to obtain quantitatively accurate effective interactions in this system....

  9. Light-front QCD. II. Two-component theory

    International Nuclear Information System (INIS)

    Zhang, W.; Harindranath, A.

    1993-01-01

    The light-front gauge A a + =0 is known to be a convenient gauge in practical QCD calculations for short-distance behavior, but there are persistent concerns about its use because of its ''singular'' nature. The study of nonperturbative field theory quantizing on a light-front plane for hadronic bound states requires one to gain a priori systematic control of such gauge singularities. In the second paper of this series we study the two-component old-fashioned perturbation theory and various severe infrared divergences occurring in old-fashioned light-front Hamiltonian calculations for QCD. We also analyze the ultraviolet divergences associated with a large transverse momentum and examine three currently used regulators: an explicit transverse cutoff, transverse dimensional regularization, and a global cutoff. We discuss possible difficulties caused by the light-front gauge singularity in the applications of light-front QCD to both old-fashioned perturbative calculations for short-distance physics and upcoming nonperturbative investigations for hadronic bound states

  10. Lorentz covariance of an extended object in the tree approximation. II. Nonspherical object in 3+1 dimensions

    International Nuclear Information System (INIS)

    Umezawa, M.

    1983-01-01

    This is the second in the series of the papers in which we investigate the Lorentz covariance of the extended object. In this paper we examine the covariance of the deformed object in 3+1 dimensions in the tree approximation. We construct the solution of the Euler equation, which is Lorentz covariant. In such a covariant solution, the variables associated with the rotational and the translational zero modes appear as classical quantum mechanical operators. Consequently the covariant solution has an intrinsic spin, in addition to the intrinsic quantum mechanical momenta. Then, at the end of this work we will show that such a covariant solution can be obtained also by quantizing a classical solution of the Euler equation, having extra variables signifying the center and the orientation of the deformed object. In the tree approximation, the energy--momentum and the relativistic angular momentum of the extended object psi become pure classical quantum mechanical operators, having been integrated over the space. Then it is proven that such four-momenta and angular momentum operators form a classical quantum mechanics presented in a relativistic manner. The center of mass of the extended object, often called collective coordinate, is shown to be made of these four-momentum and angular momentum

  11. The approximate Loebl-Komlós-Sós Conjecture II: The rough structure of LKS graphs

    Czech Academy of Sciences Publication Activity Database

    Hladký, Jan; Komlós, J.; Piguet, Diana; Simonovits, M.; Stein, M.; Szemerédi, E.

    2017-01-01

    Roč. 31, č. 2 (2017), s. 983-1016 ISSN 0895-4801 R&D Projects: GA MŠk(CZ) 1M0545 EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 ; RVO:67985807 Keywords : extremal graph theory * Loebl–Komlós–Sós conjecture * regularity lemma Subject RIV: BA - General Mathematics; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics; Pure mathematics (UIVT-O) Impact factor: 0.755, year: 2016 http://epubs.siam.org/doi/10.1137/140982854

  12. The approximate Loebl-Komlós-Sós Conjecture II: The rough structure of LKS graphs

    Czech Academy of Sciences Publication Activity Database

    Hladký, Jan; Komlós, J.; Piguet, Diana; Simonovits, M.; Stein, M.; Szemerédi, E.

    2017-01-01

    Roč. 31, č. 2 (2017), s. 983-1016 ISSN 0895-4801 R&D Projects: GA MŠk(CZ) 1M0545 EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 ; RVO:67985807 Keywords : extremal graph theory * Loebl–Komlós–Sós conjecture * regularity lemma Subject RIV: BA - General Mathematics ; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics ; Pure mathematics (UIVT-O) Impact factor: 0.755, year: 2016 http://epubs.siam.org/doi/10.1137/140982854

  13. Inhomogeneous electrochemiluminescence. II Markovian encounter theory of the phenomenon

    International Nuclear Information System (INIS)

    Gladkikh, V.; Burshtein, A.I.

    2005-01-01

    The free energy dependence of the electro-chemiluminescence quantum yield is specified, with the Markovian encounter theory accounting for the reversibility of triplet production competing with the irreversible recombination to the ground state. It is shown that diffusional ion recombination is highly inhomogeneous in space. It proceeds at either large positive ionization free energy (mainly to the triplet product) or at large negative free energy when recombination to the ground state dominates. On the contrary at medium free energies, the quasi-resonant generation of triplets is under kinetic control and therefore much more homogeneous. In this case, both recombination products are generated in comparable amounts. The multiple reversible ionization is shown to act as an independent quenching mechanism previously unknown. The role of the triplet quenching at the electrode is also specified. These effects reduce noticeably the luminescence quantum yield but only at larger triplet life times and in different free energy regions

  14. Theory of Moxon-Rae type detectors. II

    International Nuclear Information System (INIS)

    Malik, S.S.; Majkrzak, C.F.

    1975-01-01

    Theoretical development of the Moxon-Rae detector's detection mechanism has been extended to include photoelectric effect and pair production for (γ,e) processes in addition to the previously considered Compton scattering. Further the converters now include Al and Pb along with C that was treated in the earlier theory. Quantitative calculations of the electron production probability, fsup((1)) (E,t) and the electron transmission probability, fsup((2)) (E,t) have been made for C, Al and Pb converters for photon energy Esub(γ) up to 10 MeV. A comparison of the fsup((1)) (E,t) fsup((2)) (E,t) values with the recently published Monte Carlo calculations of the response of Moxon-Rae detectors indicates that the two sets of values agree rather well. Various parameters useful for similar calculations, employing other converters, are also included. (Auth.)

  15. Geometry of Kaluza-Klein theory. II. Field equations

    International Nuclear Information System (INIS)

    Maia, M.D.

    1985-01-01

    In the preceding paper a geometric formulation of Kaluza-Klein theory was presented with the basic assumption that the space-time is locally and isometrically embedded in the high-dimensional space which emerged at the big bang. In the present note the Gauss-Codazzi-Ricci equations which are the integrability equations for the embedding are interpreted as the dynamical equations for a low-energy observer. The second quadratic form which results from the embedding is interpreted as a fundamental spin-two massless field. The dynamics for an observer with high-energy probes is described as usual by the Einstein-Hilbert action defined in the high-dimensional space and dimensionally reduced by integration over the internal space. The behavior of fermion masses under different gravitational field strengths is implemented by use of the mass operator defined with the second-order Casimir operator of the embedding symmetry group

  16. Novel theory of the HD dipole moment. II. Computations

    International Nuclear Information System (INIS)

    Thorson, W.R.; Choi, J.H.; Knudson, S.K.

    1985-01-01

    In the preceding paper we derived a new theory of the dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, and DT) in which the electrical asymmetry appears directly in the electronic Hamiltonian (in an appropriate Born-Oppenheimer separation) and the dipole moment may be computed as a purely electronic property. In the present paper we describe variation-perturbation calculations and convergence studies on the dipole moment for HD, which is found to have the value 8.51 x 10 -4 debye at 1.40 a.u. Using the two alternative formulations of the electronic problem, we can provide a test of basis-set adequacy and convergence of the results, and such convergence studies are reported here. We have also computed vibration-rotation transition matrix elements and these are compared with experimental and other theoretical results

  17. Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

    Science.gov (United States)

    Hahne, G. E.

    1993-01-01

    The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

  18. A New Approach for the Approximations of Solutions to a Common Fixed Point Problem in Metric Fixed Point Theory

    Directory of Open Access Journals (Sweden)

    Ishak Altun

    2016-01-01

    Full Text Available We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings T,S:X→X, where X is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.

  19. On unified field theories, dynamical torsion and geometrical models: II

    International Nuclear Information System (INIS)

    Cirilo-Lombardo, D.J.

    2011-01-01

    We analyze in this letter the same space-time structure as that presented in our previous reference (Part. Nucl, Lett. 2010. V.7, No.5. P.299-307), but relaxing now the condition a priori of the existence of a potential for the torsion. We show through exact cosmological solutions from this model, where the geometry is Euclidean RxO 3 ∼ RxSU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: i) the torsion is not identified directly with the Yang-Mills type strength field, ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact leads to the identification between derivatives of the scale factor a with the components of the torsion in order to allow the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), and iii) of two possible structures of the torsion the 'tratorial' form (the only one studied here) forbid wormhole configurations, leading only to cosmological instanton space-time in eternal expansion

  20. Quantum field theory II introductions to quantum gravity, supersymmetry and string theory

    CERN Document Server

    Manoukian, Edouard B

    2016-01-01

    This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author in...

  1. Hydrogen atom with a Yukawa potential: Perturbation theory and continued-fractions--Pade approximants at large order

    International Nuclear Information System (INIS)

    Vrscay, E.R.

    1986-01-01

    A simple power-series method is developed to calculate to large order the Rayleigh-Schroedinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pade approximants to these series generally avoid the region of the positive real axis 0 < lambda < lambda(, where lambda( represents the coupling constant threshold. As a result, the Pade sums afford accurate approximations to E(lambda) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ''quasioscillatory,'' but non-Stieltjes, behavior. Accurate values of E(lambda) as well as lambda( for the 1s, 2s, and 2p levels are reported

  2. Statistical significance approximation in local trend analysis of high-throughput time-series data using the theory of Markov chains.

    Science.gov (United States)

    Xia, Li C; Ai, Dongmei; Cram, Jacob A; Liang, Xiaoyi; Fuhrman, Jed A; Sun, Fengzhu

    2015-09-21

    Local trend (i.e. shape) analysis of time series data reveals co-changing patterns in dynamics of biological systems. However, slow permutation procedures to evaluate the statistical significance of local trend scores have limited its applications to high-throughput time series data analysis, e.g., data from the next generation sequencing technology based studies. By extending the theories for the tail probability of the range of sum of Markovian random variables, we propose formulae for approximating the statistical significance of local trend scores. Using simulations and real data, we show that the approximate p-value is close to that obtained using a large number of permutations (starting at time points >20 with no delay and >30 with delay of at most three time steps) in that the non-zero decimals of the p-values obtained by the approximation and the permutations are mostly the same when the approximate p-value is less than 0.05. In addition, the approximate p-value is slightly larger than that based on permutations making hypothesis testing based on the approximate p-value conservative. The approximation enables efficient calculation of p-values for pairwise local trend analysis, making large scale all-versus-all comparisons possible. We also propose a hybrid approach by integrating the approximation and permutations to obtain accurate p-values for significantly associated pairs. We further demonstrate its use with the analysis of the Polymouth Marine Laboratory (PML) microbial community time series from high-throughput sequencing data and found interesting organism co-occurrence dynamic patterns. The software tool is integrated into the eLSA software package that now provides accelerated local trend and similarity analysis pipelines for time series data. The package is freely available from the eLSA website: http://bitbucket.org/charade/elsa.

  3. Introduction to Stopping Time in Stochastic Finance Theory. Part II

    Directory of Open Access Journals (Sweden)

    Jaeger Peter

    2017-12-01

    Full Text Available We start proceeding with the stopping time theory in discrete time with the help of the Mizar system [1], [4]. We prove, that the expression for two stopping times k1 and k2 not always implies a stopping time (k1 + k2 (see Theorem 6 in this paper. If you want to get a stopping time, you have to cut the function e.g. (k1 + k2 ⋂ T (see [2, p. 283 Remark 6.14]. Next we introduce the stopping time in continuous time. We are focused on the intervals [0, r] where r ∈ ℝ. We prove, that for I = [0, r] or I = [0,+∞[ the set {A ⋂ I : A ∈ Borel-Sets} is a σ-algebra of I (see Definition 6 in this paper, and more general given in [3, p.12 1.8e]. The interval I can be considered as a timeline from now to some point in the future. This set is necessary to define our next lemma. We prove the existence of the σ-algebra of the τ -past, where τ is a stopping time (see Definition 11 in this paper and [6, p.187, Definition 9.19]. If τ1 and τ2 are stopping times with τ1 is smaller or equal than τ2 we can prove, that the σ-algebra of the τ1-past is a subset of the σ-algebra of the τ2-past (see Theorem 9 in this paper and [6, p.187 Lemma 9.21]. Suppose, that you want to use Lemma 9.21 with some events, that never occur, see as a comparison the paper [5] and the example for ST(1={+∞} in the Summary. We don’t have the element +1 in our above-mentioned time intervals [0, r[ and [0,+1[. This is only possible if we construct a new σ-algebra on ℝ {−∞,+∞}. This construction is similar to the Borel-Sets and we call this σ-algebra extended Borel sets (see Definition 13 in this paper and [3, p. 21]. It can be proved, that {+∞} is an Element of extended Borel sets (see Theorem 21 in this paper. Now we use the interval [0,+∞] as a basis. We construct a σ-algebra on [0,+∞] similar to the book ([3, p. 12 18e], see Definition 18 in this paper, and call it extended Borel subsets. We prove for stopping times with this given σ-algebra, that

  4. Predicting critical temperatures of iron(II) spin crossover materials: Density functional theory plus U approach

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Yachao, E-mail: yczhang@nano.gznc.edu.cn [Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Normal College, Guiyang 550018, Guizhou (China)

    2014-12-07

    A first-principles study of critical temperatures (T{sub c}) of spin crossover (SCO) materials requires accurate description of the strongly correlated 3d electrons as well as much computational effort. This task is still a challenge for the widely used local density or generalized gradient approximations (LDA/GGA) and hybrid functionals. One remedy, termed density functional theory plus U (DFT+U) approach, introduces a Hubbard U term to deal with the localized electrons at marginal computational cost, while treats the delocalized electrons with LDA/GGA. Here, we employ the DFT+U approach to investigate the T{sub c} of a pair of iron(II) SCO molecular crystals (α and β phase), where identical constituent molecules are packed in different ways. We first calculate the adiabatic high spin-low spin energy splitting ΔE{sub HL} and molecular vibrational frequencies in both spin states, then obtain the temperature dependent enthalpy and entropy changes (ΔH and ΔS), and finally extract T{sub c} by exploiting the ΔH/T − T and ΔS − T relationships. The results are in agreement with experiment. Analysis of geometries and electronic structures shows that the local ligand field in the α phase is slightly weakened by the H-bondings involving the ligand atoms and the specific crystal packing style. We find that this effect is largely responsible for the difference in T{sub c} of the two phases. This study shows the applicability of the DFT+U approach for predicting T{sub c} of SCO materials, and provides a clear insight into the subtle influence of the crystal packing effects on SCO behavior.

  5. Approximate Cores of a General Class of Economies. Part II. Set-Up Costs and Firm Formation in Coalition Production Economies,

    Science.gov (United States)

    1982-02-01

    r AAI1Z 608 YALE UNIV NEW HAVEN CT C OWLES FOUNDATION FOR RESEARC --ETC F/G 513 APPROXIMATE CORES 6F A GENERAL CLASS OF ECONOMIES. PART It. SET--ETC(U...theoretic models of the economy in strategic form are institutional. Markets and firms and even money are assumed to exist. Cooperative game theory can be...groups. Alternatively we can define firms and firms- in-being, specify the manner of trade in the markets , define what is meant by entry and exit and

  6. 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.).

  7. Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

    Science.gov (United States)

    Bardhan, Jaydeep P

    2008-10-14

    The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement

  8. An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

    Science.gov (United States)

    Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.

    2009-12-01

    A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.

  9. A vehicle stability control strategy with adaptive neural network sliding mode theory based on system uncertainty approximation

    Science.gov (United States)

    Ji, Xuewu; He, Xiangkun; Lv, Chen; Liu, Yahui; Wu, Jian

    2018-06-01

    Modelling uncertainty, parameter variation and unknown external disturbance are the major concerns in the development of an advanced controller for vehicle stability at the limits of handling. Sliding mode control (SMC) method has proved to be robust against parameter variation and unknown external disturbance with satisfactory tracking performance. But modelling uncertainty, such as errors caused in model simplification, is inevitable in model-based controller design, resulting in lowered control quality. The adaptive radial basis function network (ARBFN) can effectively improve the control performance against large system uncertainty by learning to approximate arbitrary nonlinear functions and ensure the global asymptotic stability of the closed-loop system. In this paper, a novel vehicle dynamics stability control strategy is proposed using the adaptive radial basis function network sliding mode control (ARBFN-SMC) to learn system uncertainty and eliminate its adverse effects. This strategy adopts a hierarchical control structure which consists of reference model layer, yaw moment control layer, braking torque allocation layer and executive layer. Co-simulation using MATLAB/Simulink and AMESim is conducted on a verified 15-DOF nonlinear vehicle system model with the integrated-electro-hydraulic brake system (I-EHB) actuator in a Sine With Dwell manoeuvre. The simulation results show that ARBFN-SMC scheme exhibits superior stability and tracking performance in different running conditions compared with SMC scheme.

  10. 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...

  11. Primary damage in tungsten using the binary collision approximation, molecular dynamic simulations and the density functional theory

    International Nuclear Information System (INIS)

    De Backer, A; Sand, A; Ortiz, C J; Domain, C; Olsson, P; Berthod, E; Becquart, C S

    2016-01-01

    The damage produced by primary knock-on atoms (PKA) in W has been investigated from the threshold displacement energy (TDE) where it produces one self interstitial atom–vacancy pair to larger energies, up to 100 keV, where a large molten volume is formed. The TDE has been determined in different crystal directions using the Born–Oppenheimer density functional molecular dynamics (DFT-MD). A significant difference has been observed without and with the semi-core electrons. Classical MD has been used with two different empirical potentials characterized as ‘soft’ and ‘hard’ to obtain statistics on TDEs. Cascades of larger energy have been calculated, with these potentials, using a model that accounts for electronic losses (Sand et al 2013 Europhys. Lett. 103 46003). Two other sets of cascades have been produced using the binary collision approximation (BCA): a Monte Carlo BCA using SDTrimSP (Eckstein et al 2011 SDTrimSP: Version 5.00. Report IPP 12/8) (similar to SRIM www.srim.org) and MARLOWE (RSICC Home Page. (https://rsicc.ornl.gov/codes/psr/psr1/psr-137.html) (accessed May, 2014)). The comparison of these sets of cascades gave a recombination distance equal to 12 Å which is significantly larger from the one we reported in Hou et al (2010 J. Nucl. Mater. 403 89) because, here, we used bulk cascades rather than surface cascades which produce more defects (Stoller 2002 J. Nucl. Mater. 307 935, Nordlund et al 1999 Nature 398 49). Investigations on the defect clustering aspect showed that the difference between BCA and MD cascades is considerably reduced after the annealing of the cascade debris at 473 K using our Object Kinetic Monte Carlo model, LAKIMOCA (Domain et al 2004 J. Nucl. Mater. 335 121). (paper)

  12. SU-G-BRC-16: Theory and Clinical Implications of the Constant Dosimetric Leaf Gap (DLG) Approximation

    Energy Technology Data Exchange (ETDEWEB)

    Kumaraswamy, L; Xu, Z; Podgorsak, M [Roswell Park Cancer Institute, Buffalo, NY (United States); Bailey, D [Northside Hospital, Atlanta, GA (United States); Schmitt, J [RadAmerica, LLC--MedStar Health, Baltimore, MD (United States)

    2016-06-15

    Purpose: Commercial dose calculation algorithms incorporate a single DLG value for a given beam energy that is applied across an entire treatment field. However, the physical processes associated with beam generation and dose delivery suggest that the DLG is not constant. The aim of this study is to evaluate the variation of DLG among all leaf pairs, to quantify how this variation impacts delivered dose, and to establish a novel method to correct dose distributions calculated using the approximation of constant DLG. Methods: A 2D diode array was used to measure the DLG for all 60 leaf pairs at several points along each leaf pair travel direction. This approach was validated by comparison to DLG values measured at select points using a 0.6 cc ion chamber with the standard formalism. In-house software was developed to enable incorporation of position dependent DLG values into dose distribution optimization and calculation. The accuracy of beam delivery of both the corrected and uncorrected treatment plans was studied through gamma pass rate evaluation. A comparison of DVH statistics in corrected and uncorrected treatment plans was made. Results: The outer 20 MLC leaf pairs (1.0 cm width) have DLG values that are 0.32 mm (mean) to 0.65 mm (maximum) lower than the central leaf-pair. VMAT plans using a large number of 1 cm wide leaves were more accurately delivered (gamma pass rate increased by 5%) and dose coverage was higher (D100 increased by 3%) when the 2D DLG was modeled. Conclusion: Using a constant DLG value for a given beam energy will result in dose optimization, dose calculation and treatment delivery inaccuracies that become significant for treatment plans with high modulation complexity scores delivered with 1 cm wide leaves.

  13. On SYM theory and all order bulk singularity structures of BPS strings in type II theory

    Science.gov (United States)

    Hatefi, Ehsan

    2018-06-01

    The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential Cn-1 Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of t , s , (t + s + u)-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to , exploring all the entire correlation functions and all order α‧ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, and are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order α‧ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order α‧ contact terms of this S-matrix which carry momentum of RR in transverse directions.

  14. Towards a comprehensive theory for He II: I. A zero-temperature hybrid approach

    International Nuclear Information System (INIS)

    Ghassib, H.B.; Khudeir, A.M.

    1982-09-01

    A simple hybrid approach based on a gauge theory as well as a Hartree formalism, is presented for He II at zero temperature. Although this is intended to be merely a first step in an all-embracing theory, it already resolves quite neatly several old inconsistencies and corrects a few errors. As an illustration of its feasibility, a crude but instructive calculation is performed for the static structure factor of the system at low momentum transfers. A number of planned extensions and generalizations are outlined. (author)

  15. Applicability of the Electrodynamic Approximation in the Theory of Liquid-Metal, Induction MHD Converters; O primenimosti ehlektrodinamicheskogo priblizheniya v teorii zhidkometallicheskikh induktsionnykh mgd preobrazovatelej ehnergii

    Energy Technology Data Exchange (ETDEWEB)

    Lielpeter, Ja. Ja. [Institut Fiziki AN Latvijskoj SSSR Riga, SSSR (Latvia)

    1966-11-15

    The paper deals with the present status of theoretical work on this problem and describes the results of a number of new experiments designed, to clarify the theory of MHD phenomena. The possibilities of using the electrodynamic approximation are discussed. Induction MHD machines with constant channel cross-section in the working zone are considered. (author) [Russian] Daetsja harakteristika sostojanija teorii voprosa, opisyvajutsja rezul'taty nekotoryh novyh jeksperimentov, postavlennyh s cel'ju utochnenija teorii MGD javlenij i obsuzhdajutsja vozmozhnosti ispol'zovanija jelektrodinamicheskogo priblizhenija. Rassmatrivajutsja indukcionnye MGD mashiny s postojannym po dline secheniem kanala v rabochej zone. (author)

  16. VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

    International Nuclear Information System (INIS)

    Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

    1975-10-01

    The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level

  17. Tight-binding approximations to time-dependent density functional theory — A fast approach for the calculation of electronically excited states

    Energy Technology Data Exchange (ETDEWEB)

    Rüger, Robert, E-mail: rueger@scm.com [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Lenthe, Erik van [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Heine, Thomas [Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Visscher, Lucas [Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands)

    2016-05-14

    We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.

  18. Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme.

    Science.gov (United States)

    Li, Shaohong L; Truhlar, Donald G

    2015-07-14

    Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations and atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.

  19. 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

  20. 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)

  1. U.S. Department Of Energy's nuclear engineering education research: highlights of recent and current research-II. 1. Comparison of Angular Approximations for PWR Cell Calculations

    International Nuclear Information System (INIS)

    Smith, M.A.; Tsoulfanidis, N.; Lewis, E.E.; Palmiotti, G.

    2001-01-01

    Increasing computer power is allowing higher-order angular approximations to replace diffusion theory methods in whole core reactor physics computations. Spherical harmonic (P n ), simplified spherical harmonic (SP n ), and discrete ordinates (S n ) methods are capable of performing such calculations in three dimensions. Most advantages of such transport methods are gained by eliminating fuel assembly homogenization, thus allowing pin powers to be calculated directly. A further step, currently under investigation, is the elimination of spatial homogenization at the pin cell level as well. The fuel-moderator interfaces may be treated explicitly in P n , S n , or SP n calculations by applying triangular finite elements (FEM) to the spatial variables. Early results using a modified form of the VARIANT code, however, indicate that without pin cell homogenization, high-order angular approximations may be required to represent the lattice effects accurately within the whole-core calculations. To examine these lattice effects further, a modified form of VARIANT was created to use the spatial triangular finite element scheme. The program was set up to treat a single heterogeneous pin cell coupled with P n , SP n , or S n angular approximations. Additional modifications replaced the nodal interface approximations with exact reflected boundary conditions to increase the accuracy of the results. Several pressurized water reactor pin cells, taken from a previous benchmark specification, were examined. However, the results shown here focus only on the most severe case, i.e., a pin cell containing 8.7% mixed-oxide enriched fuel. The DRAGON collision probability code was used to collapse a 69-group cross-section library to a more manageable 7-group library that contained cross sections for the fuel-cladding mixture and for the water. Eigenvalue results are shown in Figs. 1 and 2 using the modified VARIANT code with P n , SP n , and S n angular approximations. A 7-group MCNP Monte

  2. Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

    Science.gov (United States)

    Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.

    2018-06-01

    The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.

  3. Convergence estimates in approximation theory

    CERN Document Server

    Gupta, Vijay

    2014-01-01

    The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.

  4. Excited state nuclear forces from the Tamm-Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework

    Science.gov (United States)

    Hutter, Jürg

    2003-03-01

    An efficient formulation of time-dependent linear response density functional theory for the use within the plane wave basis set framework is presented. The method avoids the transformation of the Kohn-Sham matrix into the canonical basis and references virtual orbitals only through a projection operator. Using a Lagrangian formulation nuclear derivatives of excited state energies within the Tamm-Dancoff approximation are derived. The algorithms were implemented into a pseudo potential/plane wave code and applied to the calculation of adiabatic excitation energies, optimized geometries and vibrational frequencies of three low lying states of formaldehyde. An overall good agreement with other time-dependent density functional calculations, multireference configuration interaction calculations and experimental data was found.

  5. 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.

  6. Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Sato, Shunsuke A. [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Taniguchi, Yasutaka [Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan); Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435 (Japan); Shinohara, Yasushi [Max Planck Institute of Microstructure Physics, 06120 Halle (Germany); Yabana, Kazuhiro [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan)

    2015-12-14

    We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.

  7. Speeding up spin-component-scaled third-order pertubation theory with the chain of spheres approximation: the COSX-SCS-MP3 method

    Science.gov (United States)

    Izsák, Róbert; Neese, Frank

    2013-07-01

    The 'chain of spheres' approximation, developed earlier for the efficient evaluation of the self-consistent field exchange term, is introduced here into the evaluation of the external exchange term of higher order correlation methods. Its performance is studied in the specific case of the spin-component-scaled third-order Møller--Plesset perturbation (SCS-MP3) theory. The results indicate that the approximation performs excellently in terms of both computer time and achievable accuracy. Significant speedups over a conventional method are obtained for larger systems and basis sets. Owing to this development, SCS-MP3 calculations on molecules of the size of penicillin (42 atoms) with a polarised triple-zeta basis set can be performed in ∼3 hours using 16 cores of an Intel Xeon E7-8837 processor with a 2.67 GHz clock speed, which represents a speedup by a factor of 8-9 compared to the previously most efficient algorithm. Thus, the increased accuracy offered by SCS-MP3 can now be explored for at least medium-sized molecules.

  8. Constraining top quark effective theory in the LHC Run II era

    Energy Technology Data Exchange (ETDEWEB)

    Buckley, Andy; Englert, Christoph; Ferrando, James; Miller, David J.; Moore, Liam; Russell, Michael; White, Chris D. [School of Physics and Astronomy, Scottish Universities Physics Alliance, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Collaboration: The TopFitter collaboration

    2016-04-04

    We perform an up-to-date global fit of top quark effective theory to experimental data from the Tevatron, and from LHC Runs I and II. Experimental data includes total cross-sections up to 13 TeV, as well as differential distributions, for both single top and pair production. We also include the top quark width, charge asymmetries, and polarisation information from top decay products. We present bounds on the coefficients of dimension six operators, and examine the interplay between inclusive and differential measurements, and Tevatron/LHC data. All results are currently in good agreement with the Standard Model.

  9. A temperature-dependent theory for HeII: Application to the liquid structure factor

    International Nuclear Information System (INIS)

    Chela-Flores, J.; Ghassib, H.B.

    1981-08-01

    A temperature-dependent theory is presented for HeII, which is based on both a gauge-theoretic formulation as well as a mean-field (Hartree) approach. A simple model calculation is then performed within this framework for the liquid structure factor of the system. In particular, explicit expressions are obtained for the low-momentum-transfer and low-temperature limits, which seem to conform with the available experimental data. Further, the curvature of the structure factor is predicted, under these circumstances, to be only mildly dependent on temperature. Throughout, we compare and contrast with other theoretical attempts, including Feynman's. (author)

  10. Towards a comprehensive theory for He II: A temperature-dependent field-theoretic approach

    International Nuclear Information System (INIS)

    Ghassib, H.B.; Chela-Flores, J.

    1983-07-01

    New experimental aspects of He II, as well as recent developments in particle physics, are invoked to construct the rudiments of a comprehensive theory in which temperature-dependent U(1) and SU(2) gauge fields are incorporated into a hierarchy of effective Lagrangians. It is conjectured that an SU(n) gauge-theoretic description of superfluidity may be obtained in the limit n→infinity. However, it is outlined how experiments can be understood in the zeroth, first and second order of the hierarchy. (author)

  11. Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation

    Energy Technology Data Exchange (ETDEWEB)

    List, Nanna Holmgaard, E-mail: nhl@sdu.dk; Jensen, Hans Jørgen Aagaard [Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark); Kauczor, Joanna; Norman, Patrick, E-mail: panor@ifm.liu.se [Department of Physics, Chemistry and Biology, Linköping University, Linköping SE 58183 (Sweden); Saue, Trond [Laboratoire de Chimie et Physique Quantiques, UMR 5626—CNRS/Université Toulouse III (Paul Sabatier), 118 route de Narbonne, F-31062 Toulouse Cedex (France)

    2015-06-28

    We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.

  12. Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation.

    Science.gov (United States)

    List, Nanna Holmgaard; Kauczor, Joanna; Saue, Trond; Jensen, Hans Jørgen Aagaard; Norman, Patrick

    2015-06-28

    We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.

  13. The Wertheim integral equation theory with the ideal chain approximation and a dimer equation of state: Generalization to mixtures of hard-sphere chain fluids

    International Nuclear Information System (INIS)

    Chang, J.; Sandler, S.I.

    1995-01-01

    We have extended the Wertheim integral equation theory to mixtures of hard spheres with two attraction sites in order to model homonuclear hard-sphere chain fluids, and then solved these equations with the polymer-Percus--Yevick closure and the ideal chain approximation to obtain the average intermolecular and overall radial distribution functions. We obtain explicit expressions for the contact values of these distribution functions and a set of one-dimensional integral equations from which the distribution functions can be calculated without iteration or numerical Fourier transformation. We compare the resulting predictions for the distribution functions with Monte Carlo simulation results we report here for five selected binary mixtures. It is found that the accuracy of the prediction of the structure is the best for dimer mixtures and declines with increasing chain length and chain-length asymmetry. For the equation of state, we have extended the dimer version of the thermodynamic perturbation theory to the hard-sphere chain mixture by introducing the dimer mixture as an intermediate reference system. The Helmholtz free energy of chain fluids is then expressed in terms of the free energy of the hard-sphere mixture and the contact values of the correlation functions of monomer and dimer mixtures. We compared with the simulation results, the resulting equation of state is found to be the most accurate among existing theories with a relative average error of 1.79% for 4-mer/8-mer mixtures, which is the worst case studied in this work. copyright 1995 American Institute of Physics

  14. Continuum theory of the mixed-state and surface Joule effects in type-II superconductors

    International Nuclear Information System (INIS)

    Hocquet, T.; Mathieu, P.; Simon, Y.

    1992-01-01

    A phenomenological theory of vortex motion, where the mixed state is regarded as a continuum, has been proposed by two of the authors in a short previous letter. Its outlines are recalled in this paper with further comments and arguments; in particular the basic equations and their implications are discussed at some length. This theory leads to a model of pinning, from which we argue that critical currents I c , in soft type-II samples of standard bulk homogeneity, should be governed essentially by surface defects. I c is interpreted as a physically well-defined part of the total transport current I, which is flowing over a small depth close to the surface. Thus, on the scale of an ordinary sample, this part of the transport current is superficial, the remaining part I-I c being uniformly distributed over the cross section. Coherently, an analysis of the dissipation in such samples predicts that the part VI c of the total Joule effect VI must arise as surface heat sources, while the Joule effect V(I-I c ), usually associated with the steady viscous flow of vortices, is uniformly distributed in the bulk. As a proof, we present a method, using second-sound acoustics, to detect and separate surface and volume heat sources. Experimental results give clear evidence of a surface Joule effect, and support the validity of our model of surface pinning in soft materials

  15. Higher derivatives in Type II and M-theory on Calabi-Yau threefolds

    Science.gov (United States)

    Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias

    2018-02-01

    The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kähler structure of the compact space and the form-field back-ground are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kähler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kähler modulus case is presented for both Type II theories and M-theory.

  16. Demonstration of a viable quantitative theory for interplanetary type II radio bursts

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, J. M., E-mail: jschmidt@physics.usyd.edu.au; Cairns, Iver H. [School of Physics, Physics Road, Building A28, University of Sydney, NSW 2006 (Australia)

    2016-03-25

    Between 29 November and 1 December 2013 the two widely separated spacecraft STEREO A and B observed a long lasting, intermittent, type II radio burst for the extended frequency range ≈ 4 MHz to 30 kHz, including an intensification when the shock wave of the associated coronal mass ejection (CME) reached STEREO A. We demonstrate for the first time our ability to quantitatively and accurately simulate the fundamental (F) and harmonic (H) emission of type II bursts from the higher corona (near 11 solar radii) to 1 AU. Our modeling requires the combination of data-driven three-dimensional magnetohydrodynamic simulations for the CME and plasma background, carried out with the BATS-R-US code, with an analytic quantitative kinetic model for both F and H radio emission, including the electron reflection at the shock, growth of Langmuir waves and radio waves, and the radiations propagation to an arbitrary observer. The intensities and frequencies of the observed radio emissions vary hugely by factors ≈ 10{sup 6} and ≈ 10{sup 3}, respectively; the theoretical predictions are impressively accurate, being typically in error by less than a factor of 10 and 20 %, for both STEREO A and B. We also obtain accurate predictions for the timing and characteristics of the shock and local radio onsets at STEREO A, the lack of such onsets at STEREO B, and the z-component of the magnetic field at STEREO A ahead of the shock, and in the sheath. Very strong support is provided by these multiple agreements for the theory, the efficacy of the BATS-R-US code, and the vision of using type IIs and associated data-theory iterations to predict whether a CME will impact Earth’s magnetosphere and drive space weather events.

  17. Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

    Energy Technology Data Exchange (ETDEWEB)

    Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C. [Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Hine, N. D. M. [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom); Haynes, P. D. [Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom)

    2015-11-28

    We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

  18. 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.)

  19. 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.)

  20. Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics

    International Nuclear Information System (INIS)

    Ge Hao; Qian Min; Qian Hong

    2012-01-01

    The mathematical theory of nonequilibrium steady state (NESS) has a natural application in open biochemical systems which have sustained source(s) and sink(s) in terms of a difference in their chemical potentials. After a brief introduction in Section , in Part II of this review, we present the widely studied biochemical enzyme kinetics, the workhorse of biochemical dynamic modeling, in terms of the theory of NESS (Section ). We then show that several phenomena in enzyme kinetics, including a newly discovered activation–inhibition switching (Section ) and the well-known non-Michaelis–Menten-cooperativity (Section ) and kinetic proofreading (Section ), are all consequences of the NESS of driven biochemical systems with associated cycle fluxes. Section is focused on nonlinear and nonequilibrium systems of biochemical reactions. We use the phosphorylation–dephosphorylation cycle (PdPC), one of the most important biochemical signaling networks, as an example (Section ). It starts with a brief introduction of the Delbrück–Gillespie process approach to mesoscopic biochemical kinetics (Sections ). We shall discuss the zeroth-order ultrasensitivity of PdPC in terms of a new concept — the temporal cooperativity (Sections ), as well as PdPC with feedback which leads to biochemical nonlinear bistability (Section ). Also, both are nonequilibrium phenomena. PdPC with a nonlinear feedback is kinetically isomorphic to a self-regulating gene expression network, hence the theory of NESS discussed here could have wide applications to many other biochemical systems.

  1. Non-renormalisation conditions in type II string theory and maximal supergravity

    International Nuclear Information System (INIS)

    Green, Michael B.; Russo, Jorge G.; Vanhove, Pierre

    2007-01-01

    This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D 2k R 4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h = k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d<4+6/h - the same bound as for N = 4 Yang-Mills

  2. Non-renormalisation conditions in type II string theory and maximal supergravity

    Science.gov (United States)

    Green, Michael B.; Russo, Jorge G.; Vanhove, Pierre

    2007-02-01

    This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D2kR4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h = k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d<4+6/h - the same bound as for N = 4 Yang-Mills.

  3. A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions

    Science.gov (United States)

    Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo

    2016-04-01

    The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both

  4. 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.

  5. Ab initio theory of superconductivity in a magnetic field. II. Numerical solution

    Science.gov (United States)

    Linscheid, A.; Sanna, A.; Gross, E. K. U.

    2015-07-01

    We numerically investigate the spin density functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding Paper I [A. Linscheid et al., Phys. Rev. B 92, 024505 (2015), 10.1103/PhysRevB.92.024505]. As a test system, we employ a free-electron gas featuring an exchange splitting, a phononic pairing field, and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen-Cooper-Schrieffer theory, and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasiparticle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many-body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band-structure theory. This superconducting G0W0 method vastly improves the predicted spectra.

  6. Cephalometric effects of the use of 10-hour Force Theory for Class II treatment

    Directory of Open Access Journals (Sweden)

    Marise de Castro Cabrera

    2012-12-01

    Full Text Available OBJECTIVE: This study aimed to evaluate the cephalometric effects promoted by the orthodontic treatment of Class II malocclusion patients with the use of the 10-Hour Force Theory, that consists in the use of fixed appliances with 8 hours a day using a cervical headgear appliance and 16 hours a day using Class II elastics, 8 hours on the first mandibular molar and 8 hours in the second mandibular molar. METHODS: Sample comprised 31 patients with mean initial age of 14.90 years, final mean age of 17.25 years and mean treatment time of 2.35 years. The lateral cephalograms in pre-treatment and post-treatment stages were evaluated. Evaluation of cephalometric changes between initial and final treatment phases was performed by paired t test. RESULTS: The cases treated with the 10-Hour Force Theory presented a slight restriction of anterior displacement of the maxilla, increase in the effective length of the mandible, significant improvement of the maxillomandibular relationship, significant increase in anterior lower face height, distal tipping of the maxillary premolar crowns, extrusion and distal tipping of the roots of maxillary molars, significant proclination and protrusion of mandibular incisors, significant extrusion and mesialization of mandibular molars, besides a significant correction of the molar relationship, overjet and overbite. CONCLUSION: The use of the 10-Hour Force Theory in treatment of Class II malocclusion provided satisfactory results.OBJETIVO: esse estudo objetivou avaliar os efeitos cefalométricos promovidos pelo tratamento ortodôntico de pacientes com má oclusão de Classe II com o uso da Teoria de Força das 10 Horas, que consiste no uso de aparelho ortodôntico fixo, 8 horas diárias de uso de aparelho extrabucal cervical e 16 horas de uso de elásticos de Classe II, sendo 8 horas com apoio no primeiro molar inferior e 8 horas com apoio no segundo molar inferior. MÉTODOS: a amostra consistiu de 31 pacientes, com idade m

  7. Approximate Likelihood

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

  8. Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation

    CERN Document Server

    Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-01-01

    We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.

  9. Surface hopping, transition state theory, and decoherence. II. Thermal rate constants and detailed balance

    Energy Technology Data Exchange (ETDEWEB)

    Jain, Amber; Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu [Department of Chemistry, University of Pennsylvania, 231 South 34th Street, Philadelphia, Pennsylvania 19104 (United States)

    2015-10-07

    We investigate a simple approach to compute a non-adiabatic thermal rate constant using the fewest switches surface hopping (FSSH) dynamics. We study the effects of both decoherence (using our augmented-FSSH (A-FSSH) algorithm) and forbidden hops over a large range of parameters, including high and low friction regimes, and weak and strong electronic coupling regimes. Furthermore, when possible, we benchmark our results against exact hierarchy equations of motion results, where we usually find a maximum error of roughly a factor of two (at reasonably large temperatures). In agreement with Hammes-Schiffer and Tully, we find that a merger of transition state theory and surface hopping can be both accurate and efficient when performed correctly. We further show that detailed balance is followed approximately by A-FSSH dynamics.

  10. Adaptive Core Simulation Employing Discrete Inverse Theory - Part II: Numerical Experiments

    International Nuclear Information System (INIS)

    Abdel-Khalik, Hany S.; Turinsky, Paul J.

    2005-01-01

    Use of adaptive simulation is intended to improve the fidelity and robustness of important core attribute predictions such as core power distribution, thermal margins, and core reactivity. Adaptive simulation utilizes a selected set of past and current reactor measurements of reactor observables, i.e., in-core instrumentation readings, to adapt the simulation in a meaningful way. The companion paper, ''Adaptive Core Simulation Employing Discrete Inverse Theory - Part I: Theory,'' describes in detail the theoretical background of the proposed adaptive techniques. This paper, Part II, demonstrates several computational experiments conducted to assess the fidelity and robustness of the proposed techniques. The intent is to check the ability of the adapted core simulator model to predict future core observables that are not included in the adaption or core observables that are recorded at core conditions that differ from those at which adaption is completed. Also, this paper demonstrates successful utilization of an efficient sensitivity analysis approach to calculate the sensitivity information required to perform the adaption for millions of input core parameters. Finally, this paper illustrates a useful application for adaptive simulation - reducing the inconsistencies between two different core simulator code systems, where the multitudes of input data to one code are adjusted to enhance the agreement between both codes for important core attributes, i.e., core reactivity and power distribution. Also demonstrated is the robustness of such an application

  11. 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.

  12. 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.

  13. 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...

  14. The efficiency of Flory approximation

    International Nuclear Information System (INIS)

    Obukhov, S.P.

    1984-01-01

    The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

  15. Prognostic interaction patterns in diabetes mellitus II: A random-matrix-theory relation

    Science.gov (United States)

    Rai, Aparna; Pawar, Amit Kumar; Jalan, Sarika

    2015-08-01

    We analyze protein-protein interactions in diabetes mellitus II and its normal counterpart under the combined framework of random matrix theory and network biology. This disease is the fifth-leading cause of death in high-income countries and an epidemic in developing countries, affecting around 8 % of the total adult population in the world. Treatment at the advanced stage is difficult and challenging, making early detection a high priority in the cure of the disease. Our investigation reveals specific structural patterns important for the occurrence of the disease. In addition to the structural parameters, the spectral properties reveal the top contributing nodes from localized eigenvectors, which turn out to be significant for the occurrence of the disease. Our analysis is time-efficient and cost-effective, bringing a new horizon in the field of medicine by highlighting major pathways involved in the disease. The analysis provides a direction for the development of novel drugs and therapies in curing the disease by targeting specific interaction patterns instead of a single protein.

  16. Spontaneous symmetry breaking of (1+1)-dimensional φ4 theory in light-front field theory. II

    International Nuclear Information System (INIS)

    Pinsky, S.S.; van de Sande, B.

    1994-01-01

    We discuss spontaneous symmetry breaking of (1+1)-dimensional φ 4 theory in light-front field theory using a Tamm-Dancoff truncation. We show that, even though light-front field theory has a simple vacuum state which is an eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum expectation value. This occurs because the zero mode of the field must satisfy an operator-valued constraint equation. In the context of (1+1)-dimensional φ 4 theory we present solutions to the constraint equation using a Tamm-Dancoff truncation to a finite number of particles and modes. We study the behavior of the zero mode as a function of coupling and Fock space truncation. The zero mode introduces new interactions into the Hamiltonian which breaks the Z 2 symmetry of the theory when the coupling is stronger than the critical coupling. We investigate the energy spectrum in the symmetric and broken phases, show that the theory does not break down in the vicinity of the critical coupling, and discuss the connection to perturbation theory. Finally, we study the spectrum of the field φ and show that, in the broken phase, the field is localized away from φ=0 as one would expect from equal-time calculations. We explicitly show that tunneling occurs

  17. 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

  18. Approximate estimation method of the degree of lanthanide tetr[ effect and application to the tetr[ effects in lanthanide ionic r[ii

    International Nuclear Information System (INIS)

    Minami, M.

    1998-01-01

    Fitting of qu[ratic curves to four defined subgroups of lanthanides shows that the tetr[ effects in Ln 3+ ionic r[ii with coordination number (CN) 6 are larger than those with CN 8. The features for the first tetr[ are peculiar compared with other three subgroups, with both CN. The observed facts can be explained in terms of configuration of 4f electron clouds and their interaction with ligands. (orig.)

  19. Proceedings of the international colloquium on modern quantum field theory II

    International Nuclear Information System (INIS)

    Das, S.R.; Mandal, G.; Mukhi, S.; Wadia, S.R.

    1995-01-01

    In the second International Colloquium on Modern Quantum Field Theory an attempt was made to cover a broad spectrum of topics in theoretical physics that included string theory, quantum gravity, statistical mechanics, condensed matter theory, complexity, lattice gauge theory and epistemological aspects of quantum mechanics. Papers relevant to INIS in the published proceedings are indexed separately

  20. The range of validity of the two-body approximation in models of terrestrial planet accumulation. II - Gravitational cross sections and runaway accretion

    Science.gov (United States)

    Wetherill, G. W.; Cox, L. P.

    1985-01-01

    The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact (V/V-sub-e). Impact rates as a function of this ratio are calculated to within about 20 percent by numerical integration of the equations of motion. It is found that when the ratio is greater than 0.4 the two-body approximation is a good one. Consequences of reducing the ratio to less than 0.02 are examined. Factors leading to an optimal size for growth of planetesimals from a swarm of given eccentricity and placing a limit on the extent of runaway accretion are derived.

  1. Theory of flux cutting and flux transport at the critical current of a type-II superconducting cylindrical wire

    International Nuclear Information System (INIS)

    Clem, John R.

    2011-01-01

    I introduce a critical-state theory incorporating both flux cutting and flux transport to calculate the magnetic-field and current-density distributions inside a type-II superconducting cylinder at its critical current in a longitudinal applied magnetic field. The theory is an extension of the elliptic critical-state model introduced by Romero-Salazar and Perez-Rodriguez. The vortex dynamics depend in detail on two nonlinear effective resistivities for flux cutting (ρ(parallel)) and flux flow (ρ(perpendicular)), and their ratio r = ρ(parallel)/ρ(perpendicular). When r c (φ) that makes the vortex arc unstable.

  2. open-quotes Neglect of diatomic differential overlapclose quotes in nonempirical quantum chemical orbital theories. I. On the justification of the neglect of diatomic differential overlap approximation

    International Nuclear Information System (INIS)

    Neymeyr, K.; Seelig, F.F.

    1995-01-01

    A short review of the different approaches to the justification of the Neglect of Diatomic Differential Overlap in the basis of symmetrically orthogonalized basis functions is given. Brown and Roby employed the binomial expansion for the approximation of the inverse square root of the overlap matrix. For some overlap matrices, this expansion does not converge. The always-convergent power series given by Chandler and Grader provides a worse second-order approximation in comparison with the second-order binomial expansion. 9 refs

  3. Quality of Life Theory II. Quality of Life as the Realization of Life Potential: A Biological Theory of Human Being

    Directory of Open Access Journals (Sweden)

    Soren Ventegodt

    2003-01-01

    Full Text Available This review presents one of the eight theories of the quality of life (QOL used for making the SEQOL (self-evaluation of quality of life questionnaire or the quality of life as realizing life potential. This theory is strongly inspired by Maslow and the review furthermore serves as an example on how to fulfill the demand for an overall theory of life (or philosophy of life, which we believe is necessary for global and generic quality-of-life research.Whereas traditional medical science has often been inspired by mechanical models in its attempts to understand human beings, this theory takes an explicitly biological starting point. The purpose is to take a close view of life as a unique entity, which mechanical models are unable to do. This means that things considered to be beyond the individual's purely biological nature, notably the quality of life, meaning in life, and aspirations in life, are included under this wider, biological treatise. Our interpretation of the nature of all living matter is intended as an alternative to medical mechanism, which dates back to the beginning of the 20th century. New ideas such as the notions of the human being as nestled in an evolutionary and ecological context, the spontaneous tendency of self-organizing systems for realization and concord, and the central role of consciousness in interpreting, planning, and expressing human reality are unavoidable today in attempts to scientifically understand all living matter, including human life.

  4. On the foundations of special theory of relativity - II. (The principle of covariance and a basic inertial frame)

    International Nuclear Information System (INIS)

    Gulati, S.P.; Gulati, S.

    1979-01-01

    An attempt has been made to replace the principle of relativity with the principle of covariance. This amounts to modification of the theory of relativity based on the two postulates (i) the principle of covariance and (ii) the light principle. Some of the fundamental results and the laws of relativistic mechanics, electromagnetodynamics and quantum mechanics are re-examined. The principle of invariance is questioned. (A.K.)

  5. A numerical assessment of rough surface scattering theories. I - Horizontal polarization. II - Vertical polarization

    Science.gov (United States)

    Rodriguez, Ernesto; Kim, Yunjin; Durden, Stephen L.

    1992-01-01

    A numerical evaluation is presented of the regime of validity for various rough surface scattering theories against numerical results obtained by employing the method of moments. The contribution of each theory is considered up to second order in the perturbation expansion for the surface current. Considering both vertical and horizontal polarizations, the unified perturbation method provides best results among all theories weighed.

  6. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

    Science.gov (United States)

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

    2006-07-10

    On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

  7. Adducts of nitrogenous ligands with rhodium(II) tetracarboxylates and tetraformamidinate: NMR spectroscopy and density functional theory calculations.

    Science.gov (United States)

    Cmoch, Piotr; Głaszczka, Rafał; Jaźwiński, Jarosław; Kamieński, Bohdan; Senkara, Elżbieta

    2014-03-01

    Complexation of tetrakis(μ2-N,N'-diphenylformamidinato-N,N')-di-rhodium(II) with ligands containing nitrile, isonitrile, amine, hydroxyl, sulfhydryl, isocyanate, and isothiocyanate functional groups has been studied in liquid and solid phases using (1)H, (13)C and (15)N NMR, (13)C and (15)N cross polarisation-magic angle spinning NMR, and absorption spectroscopy in the visible range. The complexation was monitored using various NMR physicochemical parameters, such as chemical shifts, longitudinal relaxation times T1 , and NOE enhancements. Rhodium(II) tetraformamidinate selectively bonded only unbranched amine (propan-1-amine), pentanenitrile, and (1-isocyanoethyl)benzene. No complexation occurred in the case of ligands having hydroxyl, sulfhydryl, isocyanate, and isothiocyanate functional groups, and more expanded amine molecules such as butan-2-amine and 1-azabicyclo[2.2.2]octane. Such features were opposite to those observed in rhodium(II) tetracarboxylates, forming adducts with all kind of ligands. Special attention was focused on the analysis of Δδ parameters, defined as a chemical shift difference between signal in adduct and corresponding signal in free ligand. In the case of (1)H NMR, Δδ values were either negative in adducts of rhodium(II) tetraformamidinate or positive in adducts of rhodium(II) tetracarboxylates. Experimental findings were supported by density functional theory molecular modelling and gauge independent atomic orbitals chemical shift calculations. The calculation of chemical shifts combined with scaling procedure allowed to reproduce qualitatively Δδ parameters. Copyright © 2013 John Wiley & Sons, Ltd.

  8. 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...

  9. Spin-adapted open-shell time-dependent density functional theory. II. Theory and pilot application.

    Science.gov (United States)

    Li, Zhendong; Liu, Wenjian; Zhang, Yong; Suo, Bingbing

    2011-04-07

    The excited states of open-shell systems calculated by unrestricted Kohn-Sham-based time-dependent density functional theory (U-TD-DFT) are often heavily spin-contaminated and hence meaningless. This is solved ultimately by the recently proposed spin-adapted time-dependent density functional theory (TD-DFT) (S-TD-DFT) [J. Chem. Phys. 133, 064106 (2010)]. Unlike the standard restricted open-shell Kohn-Sham-based TD-DFT (R-TD-DFT) which can only access the singlet-coupled single excitations, the S-TD-DFT can capture both the singlet- and triplet-coupled single excitations with the same computational effort as the U-TD-DFT. The performances of the three approaches (U-TD-DFT, R-TD-DFT, and S-TD-DFT) are compared for both the spin-conserving and spin-flip excitations of prototypical open-shell systems, the nitrogen (N(2)(+)) and naphthalene (C(10)H(8)(+)) cations. The results show that the S-TD-DFT gives rise to balanced descriptions of excited states of open-shell systems.

  10. Circumstances under which various approximate relativistic and nonrelativistic theories yield accurate Compton scattering doubly differential cross sections at high photon energy

    International Nuclear Information System (INIS)

    LaJohn, L A; Pratt, R H

    2009-01-01

    We discuss the increase in error with increasing nuclear charge Z in the use of the relativistic impulse approximation (RIA) for the calculation of Compton K-shell scattering doubly differential cross sections (DDCS). We also show that nonrelativistic (nr) expressions can be used to obtain accurate peak region DDCS at scattering angles less than about 35 0 even at incident photon energies ω i exceeding 1 MeV, if Z<30. This is possible because in the Compton peak region, as θ→0, a low momentum transfer limit is being approached.

  11. Cybernetically sound organizational structures II: Relating de Sitter's design theory to Beer's viable system model

    NARCIS (Netherlands)

    Achterbergh, J.M.I.M.; Vriens, D.J.

    2011-01-01

    - Purpose – The purpose of this paper is to show how the viable system model (VSM) and de Sitter's design theory can complement each other in the context of the diagnosis and design of viable organizations. - Design/methodology/approach – Key concepts from Beer's model and de Sitter's design theory

  12. Adler's theorem in finite massless QED and possible extensions to non-Abelian gauge theories. II

    International Nuclear Information System (INIS)

    Bernstein, J.

    1975-01-01

    The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (Auth.)

  13. Infinite dimensional gauge structure of Kaluza-Klein theories II: D>5

    International Nuclear Information System (INIS)

    Aulakh, C.S.; Sahdev, D.

    1985-12-01

    We carry out the dimensional reduction of the pure gravity sector of Kaluza Klein theories without making truncations of any sort. This generalizes our previous result for the 5-dimensional case to 4+d(>1) dimensions. The effective 4-dimensional action has the structure of an infinite dimensional gauge theory

  14. Exactly renormalizable model in quantum field theory. II. The physical-particle representation

    NARCIS (Netherlands)

    Ruijgrok, Th.W.

    1958-01-01

    For the simplified model of quantum field theory discussed in a previous paper it is shown how the physical particles can be properly described by means of the so-called asymptotically stationary (a.s.) states. It is possible by formulating the theory in terms of these a.s. states to express it

  15. Algebraically approximate and noisy realization of discrete-time systems and digital images

    CERN Document Server

    Hasegawa, Yasumichi

    2009-01-01

    This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relationships. It also deal with approximation and noise cancellation of two dimensional arrays. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory and digital images. This monograph is composed of two parts. Part I and Part II will deal with approximation and noise cancellation of dynamical systems or digital images respectively. From noiseless or noisy data, reduction will be

  16. The use and abuse of attachment theory in clinical practice with maltreated children, part II: treatment.

    Science.gov (United States)

    Allen, Brian

    2011-01-01

    Recent years have witnessed a growing debate about the role of attachment theory in the treatment of maltreated children. Many professional organizations have issued statements against physically restraining children as some attachment therapists promote; however, often lost in these debates is the fundamental issue of what attachment theory and research proposes as the appropriate form of treatment. Given that these attachment therapies are often directed toward maltreated children, it becomes critical for clinicians working with abused and neglected children to understand these issues and recognize unethical and dangerous treatments. This article provides a summary of the theoretical and empirical bases for the use of attachment theory in the treatment of maltreated school-age children, an examination of the ways questionable approaches to treatment have misinterpreted and misapplied attachment theory, and a conceptualization of attachment-based intervention grounded in current theory and research.

  17. Deliberate practice theory: perceived relevance, effort, and inherent enjoyment of music practice: study II.

    Science.gov (United States)

    Hyllegard, Randy; Bories, Tamara L

    2009-10-01

    This study, based on the theory of deliberate practice, examined the practice relevance, effort, and inherent enjoyment aspects of the theory. 25 college undergraduates practiced playing a melody on an electronic keyboard for three 20-min. practice sessions. Following each session, the perceived relevance of the practice for improving performance of the melody, the effort needed to learn the melody, and the inherent enjoyment of the practice were each rated on 10-point scales. Findings were consistent with theory and similar to previous studies also involving music practice and other tasks.

  18. Game theory: Parts I and II - with 88 solved exercises. An open access textbook

    OpenAIRE

    Bonanno, Giacomo

    2015-01-01

    This is a draft of the first half of an open access textbook on game theory. I hope to complete the entire book by the end of 2015. After teaching game theory (at both the undergraduate and graduate level) at the University of California, Davis for 25 years, I decided to organize all my teaching material in a textbook. There are many excellent textbooks in game theory and there is hardly any need for a new one. However, there are two distinguishing features of this textbook: (1) it is open ac...

  19. Constructive tensorial group field theory II: the {U(1)-T^4_4} model

    Science.gov (United States)

    Lahoche, Vincent

    2018-05-01

    In this paper, we continue our program of non-pertubative constructions of tensorial group field theories (TGFT). We prove analyticity and Borel summability in a suitable domain of the coupling constant of the simplest super-renormalizable TGFT which contains some ultraviolet divergencies, namely the color-symmetric quartic melonic rank-four model with Abelian gauge invariance, nicknamed . We use a multiscale loop vertex expansion. It is an extension of the loop vertex expansion (the basic constructive technique for non-local theories) which is required for theories that involve non-trivial renormalization.

  20. Diophantine approximation and Dirichlet series

    CERN Document Server

    Queffélec, Hervé

    2013-01-01

    This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

  1. 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.

  2. Analysis of metal-matrix composite structures. I - Micromechanics constitutive theory. II - Laminate analyses

    Science.gov (United States)

    Arenburg, R. T.; Reddy, J. N.

    1991-01-01

    The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.

  3. Adler's theorem in finite massless QED and possible extensions to non- Abelian gauge theories II

    CERN Document Server

    Bernstein, J

    1975-01-01

    For pt.I see ibid., vol.B95, p.461 (1975). The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger (1962) for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (7 refs).

  4. Partially massless higher-spin theory II: one-loop effective actions

    Energy Technology Data Exchange (ETDEWEB)

    Brust, Christopher [Perimeter Institute for Theoretical Physics,31 Caroline St. N, Waterloo, Ontario, N2L 2Y5 (Canada); Hinterbichler, Kurt [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH, 44106 (United States)

    2017-01-30

    We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D=7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D=4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D=4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.

  5. Partially massless higher-spin theory II: one-loop effective actions

    International Nuclear Information System (INIS)

    Brust, Christopher; Hinterbichler, Kurt

    2017-01-01

    We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D=7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D=4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D=4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.

  6. Approximate reasoning in physical systems

    International Nuclear Information System (INIS)

    Mutihac, R.

    1991-01-01

    The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

  7. 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

  8. Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions

    Energy Technology Data Exchange (ETDEWEB)

    Berkolaiko, G. [Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States); Kuipers, J. [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)

    2013-12-15

    Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, calculation of transport moments reduces to codifying classical correlations between scattering trajectories. These can be represented as ribbon graphs and we develop an algorithmic combinatorial method to generate all such graphs with a given genus. This provides an expansion of the linear transport moments for systems both with and without time reversal symmetry. The computational implementation is then able to progress several orders further than previous semiclassical formulae as well as those derived from an asymptotic expansion of random matrix results. The patterns observed also suggest a general form for the higher orders.

  9. Mode-coupling theory of self-diffusion in diblock copolymers. II. Model calculations and experimental comparisons

    International Nuclear Information System (INIS)

    Guenza, M.; Schweizer, K.S.

    1998-01-01

    The predictions of polymer-mode-coupling theory for self-diffusion in entangled structurally and interaction symmetric diblock copolymer fluids are illustrated by explicit numerical calculations. We find that retardation of translational motion emerges near and somewhat below the order endash disorder transition (ODT) in an approximately exponential and/or thermally activated manner. At fixed reduced temperature, suppression of diffusion is enhanced with increasing diblock molecular weight, compositional symmetry, and/or copolymer concentration. At very low temperatures, a new entropic-like regime of mobility suppression is predicted based on an isotropic supercooled liquid description of the copolymer structure. Preliminary generalization of the theory to treat diblock tracer diffusion is also presented. Quantitative applications to recent self and tracer diffusion measurements on compositionally symmetric polyolefin diblock materials have been carried out, and very good agreement between theory and experiment is found. Asymmetry in block local friction constants is predicted to significantly influence mobility suppression, with the largest effects occurring when the minority block is also the high friction species. New experiments to further test the predictions of the theory are suggested. copyright 1998 American Institute of Physics

  10. Optimizing the Structure of Tetracyanoplatinate (II): A Comparison of Relativistic Density Functional Theory Methods

    DEFF Research Database (Denmark)

    Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.

    2013-01-01

    is almost quantitatively reproduced in the ZORA and ECP calculations. In addition, the effect of the exchange-correlation functional and one-electron basis set was studied by employing the two generalized gradient approximation (GGA) functionals, BLYP and PBE, as well as their hybrid version B3LYP and PBE0...

  11. Plasma theory and simulation. Quarterly progress report I, II, January 1-June 30, 1984

    International Nuclear Information System (INIS)

    Birdsall, C.K.

    1984-01-01

    Our group uses theory and simulation as tools in order to increase the understanding of instabilities, heating, transport, and other phenomena in plasmas. We also work on the improvement of simulation both theoretically and practically. Research in plasma theory and simulation has centered on the following: (1) electron Bernstein wave investigations; (2) simulation of plasma-sheath region, including ion reflection; (3) single ended plasma device, general behavior dc or ac; (4) single ended plasma device, unstable states; (5) corrections to time-independent Q-machine equilibria; (6) multifluid derivation of the Alfven ion-cyclotron linear dispersion relation; and (7) potential barrier between hot and cool plasmas

  12. Quantum field theory II: quantum electrodynamics. A bridge between mathematicians and physicists

    International Nuclear Information System (INIS)

    Zeidler, Eberhard

    2009-01-01

    This is the second volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. This book seeks to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to discover interesting interrelationships between quite diverse mathematical topics. For students of physics fairly advanced mathematics, beyond that included in the usual curriculum in physics, is presented. The present volume concerns a detailed study of the mathematical and physical aspects of the quantum theory of light. (orig.)

  13. Quantum field theory II: quantum electrodynamics. A bridge between mathematicians and physicists

    Energy Technology Data Exchange (ETDEWEB)

    Zeidler, Eberhard [Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany)

    2009-07-01

    This is the second volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. This book seeks to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to discover interesting interrelationships between quite diverse mathematical topics. For students of physics fairly advanced mathematics, beyond that included in the usual curriculum in physics, is presented. The present volume concerns a detailed study of the mathematical and physical aspects of the quantum theory of light. (orig.)

  14. Handbook of Game Theory and Industrial Organization, Volume II: Applications. An Introduction

    OpenAIRE

    Corchon, Luis; Marini, Marco A.

    2017-01-01

    We introduce here the second volume of the Handbook of Game Theory and Industrial Organization, by L. C. Corchón and M. A. Marini (ed.), Edward Elgar, Cheltenam, UK and Northampton, MA, describing its main aim and its basic structure.

  15. Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment

    Science.gov (United States)

    Marcus, R. A.

    1964-01-01

    In its usual classical form activated complex theory assumes a particular expression for the kinetic energy of the reacting system -- one associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic energy expression.

  16. Impaired Theory of Mind and psychosocial functioning among pediatric patients with Type I versus Type II bipolar disorder.

    Science.gov (United States)

    Schenkel, Lindsay S; Chamberlain, Todd F; Towne, Terra L

    2014-03-30

    Deficits in Theory of Mind (ToM) have been documented among pediatric patients with Bipolar Disorder (BD). However, fewer studies have directly examined differences between type I and type II patients and whether or not ToM deficits are related to psychosocial difficulties. Therefore, the aim of this study was to compare type I versus type II pediatric bipolar patients and matched Healthy Controls (HC) on ToM and interpersonal functioning tasks. All participants completed the Revised Mind in the Eyes Task (MET), the Cognitive and Emotional Perspective Taking Task (CEPTT), and the Index of Peer Relations (IPR). Type I BD patients reported greater peer difficulties on the IPR compared to HC, and also performed more poorly on the MET and the cognitive condition of the CEPTT, but did not differ significantly on the emotional condition. There were no significant group differences between type II BD patients and HC. More impaired ToM performance was associated with poorer interpersonal functioning. Type I BD patients show deficits in the ability to understand another's mental state, irrespective of emotional valence. Deficits in understanding others' mental states could be an important treatment target for type I pediatric patients with BD. © 2013 Elsevier Ireland Ltd. All rights reserved.

  17. A density functional theory and quantum theory of atoms-in-molecules analysis of the stability of Ni(II) complexes of some amino alcohol ligands.

    Science.gov (United States)

    Varadwaj, Pradeep R; Cukrowski, Ignacy; Perry, Christopher B; Marques, Helder M

    2011-06-23

    The structure of the complexes of the type [Ni(L)(H(2)O)(2)](2+), where L is an amino alcohol ligand, L = N,N'-bis(2-hydroxyethyl)-ethane-1,2-diamine (BHEEN), N,N'-bis(2-hydroxycyclohexyl)-ethane-1,2-diamine (Cy(2)EN), and N,N'-bis(2-hydroxycyclopentyl)-ethane-1,2-diamine, (Cyp(2)EN) were investigated at the X3LYP/6-31+G(d,p) level of theory both in the gas phase and in solvent (CPCM model) to gain insight into factors that control the experimental log K(1) values. We find that (i) analyses based on Bader's quantum theory of atoms in molecules (QTAIM) are useful in providing significant insight into the nature of metal-ligand bonding and in clarifying the nature of weak "nonbonded" interactions in these complexes and (ii) the conventional explanation of complex stability in these sorts of complexes (based on considerations of bond lengths, bite angles and H-clashes) could be inadequate and indeed might be misleading. The strength of metal-ligand bonds follows the order Ni-N > Ni-OH ≥ Ni-OH(2); the bonds are predominantly ionic with some covalent character decreasing in the order Ni-N > Ni-OH > Ni-OH(2), with Ni-OH(2) being close to purely ionic. We predict that the cis complexes are preferred over the trans complexes because of (i) stronger bonding to the alcoholic O-donor atoms and (ii) more favorable intramolecular interactions, which appear to be important in determining the conformation of a metal-ligand complex. We show that (i) the flexibility of the ligand, which controls the Ni-OH bond length, and (ii) the ability of the ligand to donate electron density to the metal are likely to be important factors in determining values of log K(1). We find that the electron density at the ring critical point of the cyclopentyl moieties in Cyp(2)EN is much higher than that in the cyclohexyl moieties of Cy(2)EN and interpret this to mean that Cyp(2)EN is a poorer donor of electron density to a Lewis acid than Cy(2)EN.

  18. Dynamic composite elastic medium theory. Part II. Three-dimensional media

    International Nuclear Information System (INIS)

    Kaelin, B.; Johnson, L.R.

    1998-01-01

    Non-self-consistent and self-consistent methods of estimating velocity and attenuation of P waves and S waves at all frequencies for heterogeneous media with three-dimensional inclusions are formulated using the scattering functions of the individual inclusions. The methods are the generalization of methods for one-dimensional media presented in the first paper of this series. The specific case of spherical inclusions is calculated with the exact scattering function and compared with several low frequency approximations. The self-consistent estimates are consistent with Berryman close-quote s low frequency approximation. We present spectra and wave forms of materials with solid and liquid inclusions in a solid matrix. The results show that the exact scattering functions are required to adequately describe wave propagation at all frequencies. The analysis of liquid inclusions demonstrates that viscous damping may become important only if scattering attenuation due to spherical pores is small

  19. Approximate reasoning in decision analysis

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, M M; Sanchez, E

    1982-01-01

    The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.

  20. Partial differential equations II elements of the modern theory equations with constant coefficients

    CERN Document Server

    Shubin, M

    1994-01-01

    This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

  1. Women in numbers Europe II contributions to number theory and arithmetic geometry

    CERN Document Server

    Ozman, Ekin; Johnson-Leung, Jennifer; Newton, Rachel

    2018-01-01

    Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researche...

  2. Entanglement entropy in integrable field theories with line defects II. Non-topological defect

    Science.gov (United States)

    Jiang, Yunfeng

    2017-08-01

    This is the second part of two papers where we study the effect of integrable line defects on bipartite entanglement entropy in integrable field theories. In this paper, we consider non-topological line defects in Ising field theory. We derive an infinite series expression for the entanglement entropy and show that both the UV and IR limits of the bulk entanglement entropy are modified by the line defect. In the UV limit, we give an infinite series expression for the coefficient in front of the logarithmic divergence and the exact defect g-function. By tuning the defect to be purely transmissive and reflective, we recover correctly the entanglement entropy of the bulk and with integrable boundary respectively.

  3. Receiving efficiency of monostatic pulsed coherent lidars. I - Theory. II - Applications

    Science.gov (United States)

    Zhao, Yanzeng; Post, Madison J.; Hardesty, Michael

    1990-01-01

    Pulsed coherent radars' receiving efficiency, eta, is presently investigated as a function of range z on the basis of a theory which relates eta(z) to both the transmitted laser intensity and the point-source receiving efficiency; this efficiency is calculated by a backward method employing the back-propagated local oscillator (BPLO) approach. The theory is applied to the ideal case, in order to study system optimization when both the transmitted and the BPLO fields at the antenna are Gaussian. In the second part of this work, eta(z) is calculated for various conditions of the NOAA/ERL Wave Propagation Laboratory CO2 Doppler lidar; the sensitivity of eta(z) to transmitted laser beam quality, telescope focal setting, telescope power, scanner astigmatism, and system misalignment.

  4. The group theory of oxidation II: cosets of non-split groups

    International Nuclear Information System (INIS)

    Keurentjes, Arjan

    2003-01-01

    The oxidation program given in the first article of this series (see preceding article in this issue) is extended to cover oxidation of 3d sigma model theories on a coset G/H, with G non-compact (but not necessarily split), and H the maximal compact subgroup. We recover the matter content, the equations of motion and Bianchi identities from group lattice and Cartan involution. Satake diagrams provide an elegant tool for the computations, the maximal oxidation dimension, and group disintegration chains can be directly read off. We give a complete list of theories that can be recovered from oxidation of a 3-dimensional coset sigma model on G/H, where G is a simple non-compact group

  5. Electron paramagnetic resonance and density-functional theory studies of Cu(II)-bis(oxamato) complexes.

    Science.gov (United States)

    Bräuer, Björn; Weigend, Florian; Fittipaldi, Maria; Gatteschi, Dante; Reijerse, Edward J; Guerri, Annalisa; Ciattini, Samuele; Salvan, Georgeta; Rüffer, Tobias

    2008-08-04

    In this work we present the investigation of the influence of electronic and structural variations induced by varying the N,N'-bridge on the magnetic properties of Cu(II)- bis(oxamato) complexes. For this study the complexes [Cu(opba)] (2-) ( 1, opba = o-phenylene- bis(oxamato)), [Cu(nabo)] (2-) ( 2, nabo = 2,3-naphthalene- bis(oxamato)), [Cu(acbo)] (2-) ( 3, acbo = 2,3-anthrachinone- bis(oxamato)), [Cu(pba)] (2-) ( 4, pba = propylene- bis(oxamato)), [Cu(obbo)] (2-) ( 5, obbo = o-benzyl- bis(oxamato)), and [Cu(npbo)] (2-) ( 6, npbo = 1,8-naphthalene- bis(oxamato)), and the respective structurally isomorphic Ni(II) complexes ( 8- 13) have been prepared as ( (n)Bu 4N) (+) salts. The new complex ( (n)Bu 4N) 2[Cu(R-bnbo)].2H 2O ( 7, R-bnbo = (R)-1,1'-binaphthalene-2,2'- bis(oxamato)) was synthesized and is the first chiral complex in the series of Cu(II)-bis(oxamato) complexes. The molecular structure of 7 has been determined by single crystal X-ray analysis. The Cu(II) ions of the complexes 1- 7 are eta (4)(kappa (2) N, kappa (2) O) coordinated with a more or less distorted square planar geometry for 1- 6 and a distorted tetrahedral geometry for 7. Using pulsed Electron Nuclear Double Resonance on complex 6, detailed information about the relative orientation of the hyperfine ( A) and nuclear quadrupole tensors ( Q) of the coordinating nitrogens with respect to the g tensor were obtained. Electron Paramagnetic Resonance studies in the X, Q, and W-band at variable temperatures were carried out to extract g and A values of N ligands and Cu ion for 1- 7. The hyperfine values were interpreted in terms of spin population on the corresponding atoms. The obtained trends of the spin population for the monomeric building blocks were shown to correlate to the trends obtained in the dependence of the exchange interaction of the corresponding trinuclear complexes on their geometry.

  6. Galileo-invariant theory of low energy pion-nucleus scattering. II

    International Nuclear Information System (INIS)

    Mach, R.

    1983-01-01

    Two classes of Galileo-invariant optical models are constructed for pion elastic scattering by nuclei. The former, the two-body model, was obtained assuming that the pion-bound nucleon dynamics is determined by the pion-nucleon kinetic energy. In deriving the latter model, the (A+1)-body dynamics was taken into account. The technique of effective nucleon momenta maintains the nonlocal propagation of the pion-target nucleon subsystem through the nucleus in contrast with the standard static approximation. (author)

  7. Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom

    International Nuclear Information System (INIS)

    Oliveira, L.N.; Gross, E.K.U.; Kohn, W.

    1988-01-01

    The two density-functional methods of calculating excitation energies proposed in the preceding paper, combined with the recently formulated quasi-local-density approximation for the equiensemble exchange-correlation energy functional [W. Kohn, Phys. Rev. A 34, 737 (1986)], are applied to the He atom. Although the splittings between nearly degenerate levels with different angular momenta are badly overestimated, in both approaches the averages over angular momentum and spin of the experimental excitation energies measured from the ionization threshold are reproduced within a few percent. The computed self-consistent ensemble-averaged densities and the Kohn-Sham potentials associated with them are discussed

  8. Theory of superconductivity. II. Excited Cooper pairs. Why does sodium remain normal down to 0 K?

    International Nuclear Information System (INIS)

    Fujita, S.

    1992-01-01

    Based on a generalized BCS Hamiltonian in which the interaction strengths (V 11 , V 22 , V 12 ) among and between electron (12) and hole (2) Cooper pairs are differentiated, the thermodynamic properties of a type-I superconductor below the critical temperature T c are investigated. An expression for the ground-state energy, W - W 0 , relative to the unperturbed Block system is obtained. The usual BCS formulas are obtained in the limits: (all) V jl = V 0 , N 1 (0) = N 2 (0). Any excitations generated through the BCS interaction Hamiltonian containing V jl must involve Cooper pairs of antiparallel spins and nearly opposite momenta. The nonzero momentum or excited Cooper pairs below T c are shown to have an excitation energy band minimum lower than the quasi-electrons, which were regarded as the elementary excitations in the original BCS theory. The energy gap var-epsilon g (T) defined relative to excited and zero-momentum Copper pairs (when V jl > 0) decreases from var-epsilon g (0) to 0 as the temperature T is raised from 0 to T c . If electrons only are available as in a monovalent metal like sodium (V 12 = 0), the energy constant Δ 1 is finite but the energy gap vanishes identically for all T. In agreement with the BCS theory, the present theory predicts that a pure nonmagnetic metal in any dimensions should have a Cooper-pair ground state whose energy is lower than that of the Bloch ground state. Additionally it predicts that a monovalent metal should remain normal down to 0 K, and that there should be no strictly one-dimensional superconductor

  9. Modeling PSA Problems - II: A Cell-to-Cell Transport Theory Approach

    International Nuclear Information System (INIS)

    Labeau, P.E.; Izquierdo, J.M.

    2005-01-01

    In the first paper of this series, we presented an extension of the classical theory of dynamic reliability in which the actual occurrence of an event causing a change in the system dynamics is possibly delayed. The concept of stimulus activation, which triggers the realization of an event after a distributed time delay, was introduced. This gives a new understanding of competing events in the sequence delineation process.In the context of the level-2 probabilistic safety analysis (PSA), the information on stimulus activation mainly consists of regions of the process variables space where the activation can occur with a given probability. The evolution equations of the extended theory of probabilistic dynamics are therefore particularized to a transport process between discrete cells defined in phase-space on this basis. Doing so, an integrated and coherent approach to level-2 PSA problems is propounded. This amounts to including the stimulus concept and the associated stochastic delays discussed in the first paper in the frame of a cell-to-cell transport process.In addition, this discrete model provides a theoretical basis for the definition of appropriate numerical schemes for integrated level-2 PSA applications

  10. Categorial compositionality II: universal constructions and a general theory of (quasi-systematicity in human cognition.

    Directory of Open Access Journals (Sweden)

    Steven Phillips

    2011-08-01

    Full Text Available A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary collection. The classical account supposes: (1 syntactically compositional representations; and (2 processes that are sensitive to--compatible with--their structure. Classical compositionality, however, does not explain why these two components must be compatible; they are only compatible by the ad hoc assumption (convention of employing the same mode of (concatenative compositionality (e.g., prefix/postfix, where a relation symbol is always prepended/appended to the symbols for the related entities. Architectures employing mixed modes do not support systematicity. Recently, we proposed an alternative explanation without ad hoc assumptions, using category theory. Here, we extend our explanation to domains that are quasi-systematic (e.g., aspects of most languages, where the domain includes some but not all possible combinations of constituents. The central category-theoretic construct is an adjunction involving pullbacks, where the primary focus is on the relationship between processes modelled as functors, rather than the representations. A functor is a structure-preserving map (or construction, for our purposes. An adjunction guarantees that the only pairings of functors are the systematic ones. Thus, (quasi-systematicity is a necessary consequence of a categorial cognitive architecture whose basic processes are functors that participate in adjunctions.

  11. Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition.

    Science.gov (United States)

    Phillips, Steven; Wilson, William H

    2011-08-01

    A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of capacities, rather than some other, arbitrary collection. The classical account supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to--compatible with--their structure. Classical compositionality, however, does not explain why these two components must be compatible; they are only compatible by the ad hoc assumption (convention) of employing the same mode of (concatenative) compositionality (e.g., prefix/postfix, where a relation symbol is always prepended/appended to the symbols for the related entities). Architectures employing mixed modes do not support systematicity. Recently, we proposed an alternative explanation without ad hoc assumptions, using category theory. Here, we extend our explanation to domains that are quasi-systematic (e.g., aspects of most languages), where the domain includes some but not all possible combinations of constituents. The central category-theoretic construct is an adjunction involving pullbacks, where the primary focus is on the relationship between processes modelled as functors, rather than the representations. A functor is a structure-preserving map (or construction, for our purposes). An adjunction guarantees that the only pairings of functors are the systematic ones. Thus, (quasi-)systematicity is a necessary consequence of a categorial cognitive architecture whose basic processes are functors that participate in adjunctions.

  12. Approximate quantum Markov chains

    CERN Document Server

    Sutter, David

    2018-01-01

    This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...

  13. Stochastic theory of molecular collisions. II. Application to atom--vibrotor collisions

    International Nuclear Information System (INIS)

    Augustin, S.D.; Rabitz, H.

    1977-01-01

    In this work stochastic theory is applied to the treatment of atom--vibrotor collisions. This is an extension of a previous paper which described molecular collisions by a Pauli master equation or a Fokker--Planck equation. In this framework an energy conserving classical path model is explored, and methods for solving the equations numerically are discussed. The coefficients of the Fokker--Planck equation are shown to be expressible as simple functions of the interaction potential. Estimates of the computational labor are also discussed. Finally as a followup on the initial work, numerical solutions of the master equation for the collinear vibrational excitation problem of Secrest and Johnson are presented in an Appendix

  14. Usability of a theory of visual attention (TVA) for parameter-based measurement of attention II

    DEFF Research Database (Denmark)

    Bublak, Peter; Finke, Kathrin; Krummenacher, Joseph

    2005-01-01

    , and spatial distribution of attention. The procedure used was short enough to be applicable within a standard clinical setting. Two brain-damaged patients, selected based on lesion location and neuropsychological test profile, were compared to a control group of 22 healthy subjects. One patient with a right......Based on a 'Theory of Visual Attention' (TVA), whole and partial report of brief letter arrays is presented as a diagnostic tool to estimate four clinically significant attentional components: perceptual processing speed, visual working memory storage capacity, efficiency of top-down control...... inferior parietal lesion showed a pattern of non-spatially and spatially lateralized attention deficits that is typically found in neglect patients. Results from the second patient supported the decisive role of superior frontal brain structures for top-down control of visual attention. This double...

  15. Electrical conductivity of highly ionized dense hydrogen plasma. II. Comparison of experiment and theory

    Energy Technology Data Exchange (ETDEWEB)

    Guenther, K [Akademie der Wissenschaften der DDR, Berlin. Zentralinstitut fuer Elektronenphysik; Popovic, M M; Popovic, S S; Radtke, R

    1976-05-11

    The electrical conductivity of a non-ideal hydrogen plasma at p = 10 atm and T = 14,000-21,500 K is derived from electrical measurements and the radial temperature distribution of a pulsed wall-stabilized hydrogen arc using the theoretical temperature dependence of conductivity in an ideal binary collision plasma. From the comparison of theory and experiment, a suggestion to modify the cut-off parameter for charged particle potential from rsub(D) is derived, where rsub(D) is the Debye length. An estimate of Kaklyugin and Norman (Kaklyugin, A.S. and Norman, G.E., 1973 Teplofiz. vysok. temp., vol.11, 238-244) which takes into account both particle correlation and electron localisation in the environment of ions agrees very well with the experimental results over the whole temperature range.

  16. Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration

    International Nuclear Information System (INIS)

    Voelkel, A.H.

    1986-01-01

    Within the gauge quantum field theory of the Wightman--Garding type, the integration of representations of Lie algebras is investigated. By means of the covariance condition (substitution rules) for the basic fields, it is shown that a form skew-symmetric representation of a Lie algebra can be integrated to a form isometric and in general unbounded representation of the universal covering group of a corresponding Lie group provided the conditions (Nelson, Sternheimer, etc.), which are well known for the case of Hilbert or Banach representations, hold. If a form isometric representation leaves the subspace from which the physical Hilbert space is obtained via factorization and completion invariant, then the same is proved to be true for its differential. Conversely, a necessary and sufficient condition is derived for the transmission of the invariance of this subspace under a form skew-symmetric representation of a Lie algebra to its integral

  17. Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

    Science.gov (United States)

    Levnajić, Zoran; Mezić, Igor

    2015-05-01

    We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

  18. Nonlinear scattering from a plasma column. I - Theory. II Special cases

    Science.gov (United States)

    Crawford, F. W.; Harker, K. J.

    1983-01-01

    The scattered signal excited by nonlinear mixing of two plane waves normally incident on an infinitely long column of plasma is investigated. A general solution is obtained for the polarization in which the electric field vectors of the waves are perpendicular to the column axis and the column is assumed to be radically inhomogeneous. This general theory is then applied to the special cases of the inhomogeneous column in the long-wavelength limit, and the homogeneous column both for the general case and in the long-wavelength limit. It is determined that dipole and quadrupole components should predominate in the polar radiation pattern for the long-wavelength case. The special case of second harmonic generation due to a single incident wave is analyzed in detail. Nonlinear scattering coefficients are computed, and the corresponding polar radiation patterns are determined. The findings of this study are employed to evaluate the feasibility of observing nonlinear scattering from meteor trails.

  19. Gauge theories of partial compositeness: scenarios for Run-II of the LHC

    International Nuclear Information System (INIS)

    Ferretti, Gabriele

    2016-01-01

    We continue our investigation of gauge theories in which the Higgs boson arises as a pseudo-Nambu-Goldstone boson (pNGB) and top-partners arise as bound states of three hyperfermions. All models have additional pNGBs in their spectrum that should be accessible at LHC. We analyze the patterns of symmetry breaking and present all relevant couplings of the pNGBs with the gauge fields. We discuss how vacuum misalignment and a mass for the pNGBs is generated by a loop-induced potential. Finally, we paint a very broad, qualitative, picture of the kind of experimental signatures these models give rise to, setting the stage for further analysis.

  20. A new formulation of the theory of tachyons. Part II: Tachyon electrodynamics

    International Nuclear Information System (INIS)

    Dawe, R.L.; Hines, K.C.

    1991-06-01

    A new formulation of the theory of tachyons using the same two postulates as in Special Relativity is applied to electrodynamics. Use is made of a 'switching principle' to show how tachyons automatically obey the law of conservation of electric charge in any inertial reference frame, even though the observed electric charge is not any invariant for tachyons. Tachyonic transformations of electromagnetic fields E, B, D, H, P and M are rigorously derived from Maxwell's equations and are shown to be the same as for bradyonic transformations. Tachyonic transformations of current and charge densities and scalar and vector potentials are also derived and discussed. Further examples include calculations of the magnetic dipole moment of a tachyonic current loop and of the speed of light in a tachyonic dielectric. Constitutive equations for a tachyonic dielectric are also given. The Lagrangian and Hamiltonian for charged tachyons are discussed, as well as generic tachyonic transformations. 51 refs., 15 figs

  1. Towards a Thomistic Theory of Intentional (“Fictive” Individuals (II

    Directory of Open Access Journals (Sweden)

    Stanislav Sousedík

    2015-12-01

    Full Text Available Following Aristotle’s stimuli, the medieval scholastics produced the theory of beings of reason (= intentional beings, i.e. beings that can only exist as an object of our reason (and in no other way. It is remarkable that an important component was omitted by the scholastic scholars, namely the teaching of intentional (nowadays called “fictional” more frequently individuals, e.g. Sherlock Holmes, Hamlet, Hephaistos etc. This issue was dealt with later by A. Meinong, E. Mally, T. Parsons and E. N. Zalta. This contribution strives to propose an alternative theory founded on the scholastic, specifically Thomistic thought. The author distinguishes 1 individual description of intentional individual, 2 this individual itself, and 3 its “representative” existing sometimes in the real world. An intentional being, in this conception, has only the properties ascribed to it by its description and the property of individuality (and no other property. Nevertheless, an intentional individual bears these properties differently from the real individual. Therefore, the author distinguishes two kinds of predication, the real and the intentional one. In this context, other logical problems of intentional individuals are addressed. By the “representative” of an intentional individual (e.g. Sherlock Holmes the author means e.g. its image made by the reader of A. C. Doyle in his (reader’s fantasy, or a real picture (illustration in the Hound of Baskerville book, further the actor who plays the role of famous detective in the film adaption of the novel etc. The goal of the contribution is to show that if existence is the first-level predicate, it can be predicated informatively, for as such it is able to distinguish the individuals that exist really from those that do not.

  2. On the effective theory of type II string compactifications on nilmanifolds and coset spaces

    International Nuclear Information System (INIS)

    Caviezel, Claudio

    2009-01-01

    In this thesis we analyzed a large number of type IIA strict SU(3)-structure compactifications with fluxes and O6/D6-sources, as well as type IIB static SU(2)-structure compactifications with fluxes and O5/O7-sources. Restricting to structures and fluxes that are constant in the basis of left-invariant one-forms, these models are tractable enough to allow for an explicit derivation of the four-dimensional low-energy effective theory. The six-dimensional compact manifolds we studied in this thesis are nilmanifolds based on nilpotent Lie-algebras, and, on the other hand, coset spaces based on semisimple and U(1)-groups, which admit a left-invariant strict SU(3)- or static SU(2)-structure. In particular, from the set of 34 distinct nilmanifolds we identified two nilmanifolds, the torus and the Iwasawa manifold, that allow for an AdS 4 , N = 1 type IIA strict SU(3)-structure solution and one nilmanifold allowing for an AdS 4 , N = 1 type IIB static SU(2)-structure solution. From the set of all the possible six-dimensional coset spaces, we identified seven coset spaces suitable for strict SU(3)-structure compactifications, four of which also allow for a static SU(2)-structure compactification. For all these models, we calculated the four-dimensional low-energy effective theory using N = 1 supergravity techniques. In order to write down the most general four-dimensional effective action, we also studied how to classify the different disconnected ''bubbles'' in moduli space. (orig.)

  3. Lamb shift in muonic hydrogen-II. Analysis of the discrepancy of theory and experiment

    International Nuclear Information System (INIS)

    Jentschura, U.D.

    2011-01-01

    Research highlights: → Various theoretical explanation for the recently observed experimental-theoretical discrepancy in the muonic hydrogen Lamb shift are explored. → These include a dip in the proton form factor slope, nonperturbative vacuum polarization and millicharged virtual particles, as well as process-dependent screening corrections. → Screening corrections may need to be explored further. → The need for an alternative determination of the Rydberg constant is highlighted. - Abstract: Currently, both the g factor measurement of the muon as well as the Lamb shift 2S-2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both 'muonic' discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.

  4. A density functional theory study of the magnetic exchange coupling in dinuclear manganese(II) inverse crown structures.

    Science.gov (United States)

    Vélez, Ederley; Alberola, Antonio; Polo, Víctor

    2009-12-17

    The magnetic exchange coupling constants between two Mn(II) centers for a set of five inverse crown structures have been investigated by means of a methodology based on broken-symmetry unrestricted density functional theory. These novel and highly unstable compounds present superexchange interactions between two Mn centers, each one with S = 5/2 through anionic "guests" such as oxygen, benzene, or hydrides or through the cationic ring formed by amide ligands and alkali metals (Na, Li). Magnetic exchange couplings calculated at B3LYP/6-31G(d,p) level yield strong antiferromagnetic couplings for compounds linked via an oxygen atom or hydride and very small antiferromagnetic couplings for those linked via a benzene molecule, deprotonated in either 1,4- or 1,3- positions. Analysis of the magnetic orbitals and spin polarization maps provide an understanding of the exchange mechanism between the Mn centers. The dependence of J with respect to 10 different density functional theory potentials employed and the basis set has been analyzed.

  5. Analysis of Dynamic Fracture Compliance Based on Poroelastic Theory - Part II: Results of Numerical and Experimental Tests

    Science.gov (United States)

    Wang, Ding; Ding, Pin-bo; Ba, Jing

    2018-03-01

    In Part I, a dynamic fracture compliance model (DFCM) was derived based on the poroelastic theory. The normal compliance of fractures is frequency-dependent and closely associated with the connectivity of porous media. In this paper, we first compare the DFCM with previous fractured media theories in the literature in a full frequency range. Furthermore, experimental tests are performed on synthetic rock specimens, and the DFCM is compared with the experimental data in the ultrasonic frequency band. Synthetic rock specimens saturated with water have more realistic mineral compositions and pore structures relative to previous works in comparison with natural reservoir rocks. The fracture/pore geometrical and physical parameters can be controlled to replicate approximately those of natural rocks. P- and S-wave anisotropy characteristics with different fracture and pore properties are calculated and numerical results are compared with experimental data. Although the measurement frequency is relatively high, the results of DFCM are appropriate for explaining the experimental data. The characteristic frequency of fluid pressure equilibration calculated based on the specimen parameters is not substantially less than the measurement frequency. In the dynamic fracture model, the wave-induced fluid flow behavior is an important factor for the fracture-wave interaction process, which differs from the models at the high-frequency limits, for instance, Hudson's un-relaxed model.

  6. Making theory: I. Producing physics and physicists in postwar America. II. Post-inflation reheating in an expanding universe

    Science.gov (United States)

    Kaiser, David Isaac

    2000-11-01

    This dissertation examines the reinvention of theoretical physics in the United States through pedagogical means after World War II. Physics graduate student enrollments ballooned immediately after the war. The unprecedented enrollments forced questions of procedures and standards for graduate training as never before. At the same time, the crush of numbers spurred an increased bureaucratization and, at least some American physicists feared, a different system of values than what had prevailed during the quieter interwar period. Out of these new bureaucratic and pedagogical developments, theoretical physics became a recognized specialty within American physics, surrounded by new ideas about what theory was for and how students should be trained to do it. Two case studies focus on developments within theoretical physics after the war, using pedagogy as a lens through which to understand the links between practices and practitioners. Within nuclear and particle physics, as Part II discusses, young graduate students and postdoctoral fellows puzzled over how to calculate with, and how to interpret, the simple line-drawings introduced by Richard Feynman in 1948. The number of distinct pictorial forms, calculational roles, and attributed meanings for the simple stick-figures quickly multiplied: rather than commanding a single use or interpretation, the diagrams came to be used for a wide variety of distinct tasks. Some theorists clung to the diagrams even as they declared the original theoretical framework from which the diagrams had sprung to be ``sterile'' and ``dead.'' These young theorists drew the diagrams much the same way as Feynman had, yet read content into them which had no correlate in the older approaches. Part III uses pedagogy to make sense of a similar series of changes within the long-dormant field of gravitational physics. Einstein's gravitational field equations proved to be no more obvious or auto-interpreting than Feynman's diagrams had been

  7. Bipolar outflows as a repulsive gravitational phenomenon - Azimuthally Symmetric Theory of Gravitation (II)

    International Nuclear Information System (INIS)

    Nyambuya, Golden Gadzirayi

    2010-01-01

    This paper is part of a series on the Azimuthally Symmetric Theory of Gravitation (ASTG). This theory is built on Laplace-Poisson's well known equation and it has been shown that the ASTG is capable of explaining, from a purely classical physics standpoint, the precession of the perihelion of solar planets as a consequence of the azimuthal symmetry emerging from the spin of the Sun. This symmetry has and must have an influence on the emergent gravitational field. We show herein that the emergent equations from the ASTG, under some critical conditions determined by the spin, do possess repulsive gravitational fields in the polar regions of the gravitating body in question. This places the ASTG on an interesting pedestal to infer the origins of outflows as a repulsive gravitational phenomenon. Outflows are a ubiquitous phenomenon found in star forming systems and their true origin is a question yet to be settled. Given the current thinking on their origin, the direction that the present paper takes is nothing short of an asymptotic break from conventional wisdom; at the very least, it is a complete paradigm shift because gravitation is not at all associated with this process, but rather it is thought to be an all-attractive force that only tries to squash matter together onto a single point. Additionally, we show that the emergent Azimuthally Symmetric Gravitational Field from the ASTG strongly suggests a solution to the supposed Radiation Problem that is thought to be faced by massive stars in their process of formation. That is, at ∼ 8-10 M sun , radiation from the nascent star is expected to halt the accretion of matter. We show that in-falling material will fall onto the equatorial disk and from there, this material will be channeled onto the forming star via the equatorial plane, thus accretion of mass continues well past the value of ∼ 8-10 M sun , albeit via the disk. Along the equatorial plane, the net force (with the radiation force included) on any

  8. A theory of drug tolerance and dependence II: the mathematical model.

    Science.gov (United States)

    Peper, Abraham

    2004-08-21

    The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

  9. Occipital plagiocephaly: deformation or lambdoid synostosis ? II. a unifying theory regarding pathogenesis

    International Nuclear Information System (INIS)

    Dias, M.S.; Klein, D.M.

    1997-01-01

    Occipital plagiocephaly is characterized by both unilateral occipital flattening and ipsilateral frontal prominence with anterior deviation of the ipsilateral ear, yielding a characteristic parallelogram shape to the cranium. Radiographic changes in the lambdoid suture are often evident, but the lambdoid suture is usually patent over most or all of its length on skull X-rays and/or CT scans. Both lambdoid synostosis and deformational forces have been implicated as potentially causal in the pathogenesis of this deformity. We propose a unifying theory which incorporates a common pathogenesis for both deformational plagiocephaly and most cases of lambdoid ''synostosis''. According to this hypothesis, intrauterine and/or postnatal deformational forces are responsible for the primary calvarial deformation. These forces initially act in a reversible manner to produce the typical parallelogram-shaped skull deformity. How-ever, with continued deformation, more enduring secondary pathological changes may eventually occur in the lambdoid suture and basicranium which are more difficult to correct even if the offending deformational forces are subsequently removed or reversed. (authors)

  10. The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

    Science.gov (United States)

    Roper, Ian P E; Besley, Nicholas A

    2016-03-21

    The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

  11. Approximating Markov Chains: What and why

    International Nuclear Information System (INIS)

    Pincus, S.

    1996-01-01

    Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics

  12. 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)

  13. Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors

    Science.gov (United States)

    Alarcón, J. M.; Weiss, C.

    2018-05-01

    We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining chiral effective field theory (χ EFT ) and dispersion analysis. The spectral functions on the two-pion cut at t >4 Mπ2 are constructed using the elastic unitarity relation and an N /D representation. χ EFT is used to calculate the real functions J±1(t ) =f±1(t ) /Fπ(t ) (ratios of the complex π π →N N ¯ partial-wave amplitudes and the timelike pion FF), which are free of π π rescattering. Rescattering effects are included through the empirical timelike pion FF | Fπ(t) | 2 . The method allows us to compute the isovector EM spectral functions up to t ˜1 GeV2 with controlled accuracy (leading order, next-to-leading order, and partial next-to-next-to-leading order). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at t =0 (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives, which are not affected by higher-order chiral corrections and are obtained almost parameter-free in our approach, and explain their collective behavior. We estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-Q2 FF data is achieved up to ˜0.5 GeV2 for GE, and up to ˜0.2 GeV2 for GM. Our results can be used to guide the analysis of low-Q2 elastic scattering data and the extraction of the proton charge radius.

  14. GUTs and exceptional branes in F-theory - II. Experimental predictions

    International Nuclear Information System (INIS)

    Beasley, Chris; Heckman, Jonathan J.; Vafa, Cumrun

    2009-01-01

    We consider realizations of GUT models in F-theory. Adopting a bottom up approach, the assumption that the dynamics of the GUT model can in principle decouple from Planck scale physics leads to a surprisingly predictive framework. An internal U(1) hypercharge flux Higgses the GUT group directly to the MSSM or to a flipped GUT model, a mechanism unavailable in heterotic models. This new ingredient automatically addresses a number of puzzles present in traditional GUT models. The internal U(1) hyperflux allows us to solve the doublet-triplet splitting problem, and explains the qualitative features of the distorted GUT mass relations for lighter generations due to the Aharanov-Bohm effect. These models typically come with nearly exact global symmetries which prevent bare μ terms and also forbid dangerous baryon number violating operators. Strong curvature around our brane leads to a repulsion mechanism for Landau wave functions for neutral fields. This leads to large hierarchies of the form exp(-c/ε 2γ ) where c and γ are order one parameters and ε ∼ α GUT -1 M GUT /M pl . This effect can simultaneously generate a viably small μ term as well as an acceptable Dirac neutrino mass on the order of 0.5 x 10 -2±0.5 eV. In another scenario, we find a modified seesaw mechanism which predicts that the light neutrinos have masses in the expected range while the Majorana mass term for the heavy neutrinos is ∼ 3 x 10 12±1.5 GeV. Communicating supersymmetry breaking to the MSSM can be elegantly realized through gauge mediation. In one scenario, the same repulsion mechanism also leads to messenger masses which are naturally much lighter than the GUT scale.

  15. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

  16. Localized multi-scale energy and vorticity analysis. II. Finite-amplitude instability theory and validation

    Science.gov (United States)

    San Liang, X.; Robinson, Allan R.

    2007-12-01

    Reynolds stress framework. Using the techniques of marginalization and localization, this work sets up an example for the generalization of certain geophysical fluid dynamics theories for more generic purposes.

  17. The Life Mission Theory II. The Structure of the Life Purpose and the Ego

    Directory of Open Access Journals (Sweden)

    Soren Ventegodt

    2003-01-01

    Full Text Available Pursuing your life mission is often very difficult, and many frustrations are experienced along the way. Major failures to bring out our potential can cause us considerable emotional pain. When this pain is unbearable, we are induced to shift from one intention and talent to another that better allows us to adapt and survive. Thus, we become set on a course that brings out a secondary or tertiary talent instead of the primary talent. This talent displacement may be expressed as a loss of our true nature or true self. The new purpose in life now functions as the core of a new personality: the ego. The ego has a structure similar to that of the true self. It is anchored in a talent and it draws on subtalents. But the person who is centered in his or her ego is not as powerful or talented as the person he or she originally was, living the primary purpose of life. This is because the original personality (the true self or “higher self” is still there, active and alive, behind the ego. Symptoms, disorders, and diseases may be explained by the loss of energy, joy in life, and intuitive competence because of inner conflicts, which may be alleviated or cured in the salutogenetic process of Antonovsky that helps patients find their sense of coherence or their primary purpose in life. Many cases of reduced ability to function, physically as well as psychologically, socially or sexually, can also be explained and alleviated in this way. When a person discovers his true talent and begins to use it with dedication, privately as well as professionally, his life will flourish and he may overcome even serious disease and great adversity in life. The salutogenetic process can also be called personal development or “quality of life as medicine”. It is important to note that the plan for personal development laid out by this theory is a plan not for the elimination of the ego, but for its cultivation. An existentially sound person still has a mental ego of

  18. 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.

  19. Generalized approximate spin projection calculations of effective exchange integrals of the CaMn4O5 cluster in the S1 and S3 states of the oxygen evolving complex of photosystem II.

    Science.gov (United States)

    Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K

    2014-06-28

    Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.

  20. A Study of Tongue and Pulse Diagnosis in Traditional Korean Medicine for Stroke Patients Based on Quantification Theory Type II

    Directory of Open Access Journals (Sweden)

    Mi Mi Ko

    2013-01-01

    Full Text Available In traditional Korean medicine (TKM, pattern identification (PI diagnosis is important for treating diseases. The aim of this study was to comprehensively investigate the relationship between the PI type and tongue diagnosis or pulse diagnosis variables. The study included 1,879 stroke patients who were admitted to 12 oriental medical university hospitals from June 2006 through March 2009. The status of the pulse and tongue was examined in each patient. Additionally, to investigate relatively important indicators related to specialist PI, the quantification theory type II analysis was performed regarding the PI type. In the first axis quantification of the external criteria, the Qi-deficiency and the Yin-deficiency patterns were located in the negative direction, while the dampness-phlegm (DP and fire-heat patterns were located in the positive direction. The explanatory variable with the greatest impact on the assessment was a fine pulse. In the second axis quantification, the external criteria were divided into either the DP or non-DP patterns. The slippery pulse exhibited the greatest effect on the division. This study attempted to build a model using a statistical method to objectively quantify PI and various indicators that constitute the unique diagnosis system of TKM. These results should assist the development of future diagnostic standards in stroke PI.

  1. 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.

  2. 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...

  3. Simultaneous approximation in scales of Banach spaces

    International Nuclear Information System (INIS)

    Bramble, J.H.; Scott, R.

    1978-01-01

    The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

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

    Science.gov (United States)

    Martin, E. Dale

    1989-01-01

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

  5. Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations II: the effect of the transverse mode

    International Nuclear Information System (INIS)

    Tatekawa, Takayuki

    2014-01-01

    We study the initial conditions for cosmological N-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of N-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological N-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theory in previous paper. In this paper, we evaluates the effect of the transverse mode in the third-order Lagrangian perturbation theory for several statistical quantities such as power spectrum and non-Gaussianty. Then we clarified that the effect of the transverse mode in the third-order Lagrangian perturbation theory is quite small

  6. 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

  7. 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.

  8. 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...

  9. Approximate solutions to Mathieu's equation

    Science.gov (United States)

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  10. Quantum tunneling beyond semiclassical approximation

    International Nuclear Information System (INIS)

    Banerjee, Rabin; Majhi, Bibhas Ranjan

    2008-01-01

    Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

  11. INTOR cost approximation

    International Nuclear Information System (INIS)

    Knobloch, A.F.

    1980-01-01

    A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de

  12. Low Rank Approximation Algorithms, Implementation, Applications

    CERN Document Server

    Markovsky, Ivan

    2012-01-01

    Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

  13. 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.

  14. 6d N=(1,0) theories on S{sup 1}/T{sup 2} and class S theories: part II

    Energy Technology Data Exchange (ETDEWEB)

    Ohmori, Kantaro; Shimizu, Hiroyuki [Department of Physics, Faculty of Science, University of Tokyo,Bunkyo-ku, Tokyo 133-0022 (Japan); Tachikawa, Yuji [Department of Physics, Faculty of Science, University of Tokyo,Bunkyo-ku, Tokyo 133-0022 (Japan); Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan); Yonekura, Kazuya [Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)

    2015-12-21

    We study the T{sup 2} compactification of a class of 6d N=(1,0) theories that is Higgsable to N=(2,0) theories. We show that the resulting 4d N=2 theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet and another conformal gauge multiplet. Our analysis utilizes the 5d theories obtained by putting the same class of 6d theories on S{sup 1}. Our class includes, among others, the 6d theories describing multiple M5 branes on an ALE singularity, and we analyze them in detail. The resulting 4d theory has manifestly both the SL(2,ℤ) and the full flavor symmetry. We also discuss in detail the special cases of 6d theories where the infrared-free gauge multiplet is absent. In an appendix, we give a field-theoretical argument for an F-theoretic constraint that forbids a particular 6d anomaly-free matter content, as an application of our analysis.

  15. Evaluation of hydrogen bond networks in cellulose Iβ and II crystals using density functional theory and Car-Parrinello molecular dynamics.

    Science.gov (United States)

    Hayakawa, Daichi; Nishiyama, Yoshiharu; Mazeau, Karim; Ueda, Kazuyoshi

    2017-09-08

    Crystal models of cellulose Iβ and II, which contain various hydrogen bonding (HB) networks, were analyzed using density functional theory and Car-Parrinello molecular dynamics (CPMD) simulations. From the CPMD trajectories, the power spectra of the velocity correlation functions of hydroxyl groups involved in hydrogen bonds were calculated. For the Iβ allomorph, HB network A, which is dominant according to the neutron diffraction data, was stable, and the power spectrum represented the essential features of the experimental IR spectra. In contrast, network B, which is a minor structure, was unstable because its hydroxymethyl groups reoriented during the CPMD simulation, yielding a different crystal structure to that determined by experiments. For the II allomorph, a HB network A is proposed based on diffraction data, whereas molecular modeling identifies an alternative network B. Our simulations showed that the interaction energies of the cellulose II (B) model are slightly more favorable than model II(A). However, the evaluation of the free energy should be waited for the accurate determination from the energy point of view. For the IR calculation, cellulose II (B) model reproduces the spectra better than model II (A). Copyright © 2017 Elsevier Ltd. All rights reserved.

  16. 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

  17. A density functional theory study of the electronic properties of Os(II) and Os(III) complexes immobilized on Au(111)

    DEFF Research Database (Denmark)

    O'Boyle, N.M.; Albrecht, Tim; Murgida, D.H.

    2007-01-01

    We present a density functional theory (DFT) study of an osmium polypyridyl complex adsorbed on Au(111). The osmium polypyridyl complex [Os(bpy)(2)(P0P)Cl](n+) [bpy is 2,2'-bipyridine, P0P is 4,4'-bipyridine, n = 1 for osmium(II), and n = 2 for osmium(III)] is bound to the surface through the fre...

  18. Fifth International Conference on "Approximation and Optimization in the Caribbean"

    CERN Document Server

    Approximation, Optimization and Mathematical Economic

    2001-01-01

    The articles in this proceedings volume reflect the current trends in the theory of approximation, optimization and mathematical economics, and include numerous applications. The book will be of interest to researchers and graduate students involved in functional analysis, approximation theory, mathematical programming and optimization, game theory, mathematical finance and economics.

  19. Perturbation theory

    International Nuclear Information System (INIS)

    Bartlett, R.; Kirtman, B.; Davidson, E.R.

    1978-01-01

    After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references

  20. Superstring theory

    International Nuclear Information System (INIS)

    Schwarz, J.H.

    1985-01-01

    Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(eta) or Sp(2eta) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D=10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N=4, D=4 super Yang-Mills theory and SST II reduces to N=8, D=4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions

  1. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    Science.gov (United States)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-07-01

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of "statistical associating fluid theory" that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH2 and CH3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ˜2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ˜1% from simulation data while the theory reproduces the excess

  2. The generalized gradient approximation in solids and molecules

    International Nuclear Information System (INIS)

    Haas, P.

    2010-01-01

    Today, most methods are based on theoretical calculations of the electronic structure of molecules, surfaces and solids on density functional theory (DFT) and the resulting Kohn-Sham equations. Unfortunately, the exact analytical expression for the exchange-correlation functional is not known and has to be approximated. The reliability of such a Kohn-Sham calculation depends i) from the numerical accuracy and ii) from the used approximation for the exchange-correlation energy. To solve the Kohn-Sham equations, the WIEN2k code, which is one of the most accurate methods for solid-state calculations, is used. The search for better approximations for the exchange-correlation energy is an intense field of research in chemistry and physics. The main objectives of the dissertation is the development, implementation and testing of advanced exchange-correlation functionals and the analysis of existing functionals. The focus of this work are GGA - functionals. Such GGA functionals are still the most widely used functionals, in particular because they are easy to implement and require little computational effort. Several recent studies have shown that an improvement of the GGA should be possible. A detailed analysis of the results will allow us to understand why a particular GGA approximation for a class of elements (compounds) works better than for another. (Kancsar) [de

  3. 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

  4. 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.

  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. Approximation by Cylinder Surfaces

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1997-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  7. 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.

  8. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    International Nuclear Information System (INIS)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-01-01

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of “statistical associating fluid theory” that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH 2 and CH 3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory reproduces

  9. Minimal entropy approximation for cellular automata

    International Nuclear Information System (INIS)

    Fukś, Henryk

    2014-01-01

    We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

  10. 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.

  11. 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.

  12. Approximate Bayesian recursive estimation

    Czech Academy of Sciences Publication Activity Database

    Kárný, Miroslav

    2014-01-01

    Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

  13. 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...

  14. Optimization and approximation

    CERN Document Server

    Pedregal, Pablo

    2017-01-01

    This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

  15. Ausubel's Theory of Learning and its Application to Introductory Science Part II--Primary Science: An Ausubelian View.

    Science.gov (United States)

    McClelland, J. A. G.

    1982-01-01

    In part 1 (SE 532 193) an outline of Ausubel's learning theory was given. The application of the theory to elementary school science is addressed in this part, clarifying what elementary science means and indicating how it relates to what may be expected to be already known by elementary school children. (Author/JN)

  16. Inhomogeneous ordered states and translational nature of the gauge group in the Landau continuum theory: II. Applications of the general theory

    International Nuclear Information System (INIS)

    Braginsky, A. Ya.

    2007-01-01

    A group theory approach to description of phase transitions to an inhomogeneous ordered state, proposed in the preceding paper, is applied to two problems. First, a theory of the state of a liquid-crystalline smectic type-A phase under the action of uniaxial pressure is developed. Second, a model of strengthening in quasicrystals is constructed. According to the proposed approach, the so-called elastic dislocations always appear during the phase transitions in an inhomogeneous deformed state in addition to static dislocations, which are caused by peculiarities of the crystal growth or by other features in the prehistory of a sample. The density of static dislocations weakly depends on the external factors, whereas the density of elastic dislocations depends on the state. An analogy between the proposed theory of the inhomogeneous ordered state and the quantum-field theory of interaction between material fields is considered. On this basis, the phenomenological Ginzburg-Landau equation for the superconducting state is derived using the principle of locality of the transformation properties of the superconducting order parameter with respect to temporal translations

  17. 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.)

  18. 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.)

  19. Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

    Science.gov (United States)

    Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.

    1987-01-01

    The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

  20. The Influence of Injection Pockets on the Performance of Tilting-Pad Thrust Bearings: Part II – Comparison Between Theory and Experiment

    DEFF Research Database (Denmark)

    Heinrichson, Niels; Santos, Ilmar

    2006-01-01

    This is Part II of a two-part series of papers describing the effects of high pressure injection pockets on the operating conditions of tilting-pad thrust bearings. Measurements of the distribution of pressure and oil film thickness are presented for tilting-pad thrust bearing pads of approximately...... 100 cm2 surface area. Two pads are measured in a laboratory test-rig at loads of approximately 0.5, 1.5 and 4.0 MPa and velocities of up to 33 m/s. One pad has a plain surface. The other pad has a conical injection pocket at the pivot point and a leading edge taper. The measurements are compared...... to theoretical values obtained using a three dimensional thermo-elasto-hydrodynamic (TEHD) numerical model. At low and intermediate loads the theoretical pressure distribution corresponds well to the measured values for both pads although the influence of the pocket is slightly underestimated. At high loads...

  1. Mean-field approximation minimizes relative entropy

    International Nuclear Information System (INIS)

    Bilbro, G.L.; Snyder, W.E.; Mann, R.C.

    1991-01-01

    The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach

  2. Effective collision frequency method in the theory of the conductivity of Coulomb systems. II. Strong interion interaction and plasma structure

    International Nuclear Information System (INIS)

    Bobrov, V.B.; Triger, S.A.

    1994-01-01

    The effective collision frequency method developed earlier by the authors for Coulomb systems characterized by strong interion interaction is developed further. An explicit expression is obtained for the effective electron collision frequency on the basis of the exact diagram representation obtained in Part I and the use of the model of a one-component plasma as initial approximation. The description of plasma structure in the corresponding approximation is considered. 25 refs

  3. Cyclic approximation to stasis

    Directory of Open Access Journals (Sweden)

    Stewart D. Johnson

    2009-06-01

    Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.

  4. On the WKBJ approximation

    International Nuclear Information System (INIS)

    El Sawi, M.

    1983-07-01

    A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)

  5. The relaxation time approximation

    International Nuclear Information System (INIS)

    Gairola, R.P.; Indu, B.D.

    1991-01-01

    A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs

  6. 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.

  7. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  8. Adaptive Disturbance Tracking Theory with State Estimation and State Feedback for Region II Control of Large Wind Turbines

    Science.gov (United States)

    Balas, Mark J.; Thapa Magar, Kaman S.; Frost, Susan A.

    2013-01-01

    A theory called Adaptive Disturbance Tracking Control (ADTC) is introduced and used to track the Tip Speed Ratio (TSR) of 5 MW Horizontal Axis Wind Turbine (HAWT). Since ADTC theory requires wind speed information, a wind disturbance generator model is combined with lower order plant model to estimate the wind speed as well as partial states of the wind turbine. In this paper, we present a proof of stability and convergence of ADTC theory with lower order estimator and show that the state feedback can be adaptive.

  9. Transition operators in acoustic-wave diffraction theory. I - General theory. II - Short-wavelength behavior, dominant singularities of Zk0 and Zk0 exp -1

    Science.gov (United States)

    Hahne, G. E.

    1991-01-01

    A formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles is established. The time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green's function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface (delta-Omega) of an impenetrable obstacle. With k0 as the free-space wavenumber of the signal, a simplified expression is obtained for the k0-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on delta-Omega. All the nonelementary operators entering the expression for the T operator are formally simple rational algebraic functions of a certain invertible linear radiation impedance operator which maps any sufficiently well-behaved complex-valued function on delta-Omega into another such function on delta-Omega. In the subsequent study, the short-wavelength and the long-wavelength behavior of the radiation impedance operator and its inverse (the 'radiation admittance' operator) as two-point kernels on a smooth delta-Omega are studied for pairs of points that are close together.

  10. Approximate Bayesian computation.

    Directory of Open Access Journals (Sweden)

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  11. Impulse approximation in solid helium

    International Nuclear Information System (INIS)

    Glyde, H.R.

    1985-01-01

    The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium

  12. Strong-coupling approximations

    International Nuclear Information System (INIS)

    Abbott, R.B.

    1984-03-01

    Standard path-integral techniques such as instanton calculations give good answers for weak-coupling problems, but become unreliable for strong-coupling. Here we consider a method of replacing the original potential by a suitably chosen harmonic oscillator potential. Physically this is motivated by the fact that potential barriers below the level of the ground-state energy of a quantum-mechanical system have little effect. Numerically, results are good, both for quantum-mechanical problems and for massive phi 4 field theory in 1 + 1 dimensions. 9 references, 6 figures

  13. Conformally reduced WZNW theory, new extended chiral algebras and their associated Toda type integrable systems (II) an example

    International Nuclear Information System (INIS)

    Hou Boyu; Zhao Liu

    1993-01-01

    As an example and application of the method of the previous work, the authors construct explicitly the W algebra W[p q p] 2 ] by the use of the canonical formalism of the corresponding generalized Toda theory, namely the (p q p) 2 Toda theory. Then the authors discuss various special limits of W[p q p) 2 ] and point out the isomorphism between W[(p q p) 2 ] and W[(p q + p) 1

  14. Predictor feedback for delay systems implementations and approximations

    CERN Document Server

    Karafyllis, Iasson

    2017-01-01

    This monograph bridges the gap between the nonlinear predictor as a concept and as a practical tool, presenting a complete theory of the application of predictor feedback to time-invariant, uncertain systems with constant input delays and/or measurement delays. It supplies several methods for generating the necessary real-time solutions to the systems’ nonlinear differential equations, which the authors refer to as approximate predictors. Predictor feedback for linear time-invariant (LTI) systems is presented in Part I to provide a solid foundation on the necessary concepts, as LTI systems pose fewer technical difficulties than nonlinear systems. Part II extends all of the concepts to nonlinear time-invariant systems. Finally, Part III explores extensions of predictor feedback to systems described by integral delay equations and to discrete-time systems. The book’s core is the design of control and observer algorithms with which global stabilization, guaranteed in the previous literature with idealized (b...

  15. SAM revisited: uniform semiclassical approximation with absorption

    International Nuclear Information System (INIS)

    Hussein, M.S.; Pato, M.P.

    1986-01-01

    The uniform semiclassical approximation is modified to take into account strong absorption. The resulting theory, very similar to the one developed by Frahn and Gross is used to discuss heavy-ion elastic scattering at intermediate energies. The theory permits a reasonably unambiguos separation of refractive and diffractive effects. The systems 12 C+ 12 C and 12 C+ 16 O, which seem to exhibit a remnant of a nuclear rainbow at E=20 Mev/N, are analysed with theory which is built directly on a model for the S-matrix. Simple relations between the fit S-matrix and the underlying complex potential are derived. (Author) [pt

  16. The quasilocalized charge approximation

    International Nuclear Information System (INIS)

    Kalman, G J; Golden, K I; Donko, Z; Hartmann, P

    2005-01-01

    The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two

  17. Large hierarchies from approximate R symmetries

    International Nuclear Information System (INIS)

    Kappl, Rolf; Ratz, Michael; Vaudrevange, Patrick K.S.

    2008-12-01

    We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales. (orig.)

  18. Quasiclassical approximation for ultralocal scalar fields

    International Nuclear Information System (INIS)

    Francisco, G.

    1984-01-01

    It is shown how to obtain the quasiclassical evolution of a class of field theories called ultralocal fields. Coherent states that follow the 'classical' orbit as defined by Klauder's weak corespondence principle and restricted action principle is explicitly shown to approximate the quantum evolutions as (h/2π) → o. (Author) [pt

  19. Self-similar continued root approximants

    International Nuclear Information System (INIS)

    Gluzman, S.; Yukalov, V.I.

    2012-01-01

    A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

  20. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-05-01

    Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed 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 recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.

  1. Time-dependent observables in heavy ion collisions. Part II. In search of pressure isotropization in the φ 4 theory

    Science.gov (United States)

    Kovchegov, Yuri V.; Wu, Bin

    2018-03-01

    To understand the dynamics of thermalization in heavy ion collisions in the perturbative framework it is essential to first find corrections to the free-streaming classical gluon fields of the McLerran-Venugopalan model. The corrections that lead to deviations from free streaming (and that dominate at late proper time) would provide evidence for the onset of isotropization (and, possibly, thermalization) of the produced medium. To find such corrections we calculate the late-time two-point Green function and the energy-momentum tensor due to a single 2 → 2 scattering process involving two classical fields. To make the calculation tractable we employ the scalar φ 4 theory instead of QCD. We compare our exact diagrammatic results for these quantities to those in kinetic theory and find disagreement between the two. The disagreement is in the dependence on the proper time τ and, for the case of the two-point function, is also in the dependence on the space-time rapidity η: the exact diagrammatic calculation is, in fact, consistent with the free streaming scenario. Kinetic theory predicts a build-up of longitudinal pressure, which, however, is not observed in the exact calculation. We conclude that we find no evidence for the beginning of the transition from the free-streaming classical fields to the kinetic theory description of the produced matter after a single 2 → 2 rescattering.

  2. Student Assessment System. Domain Referenced Tests. Transportation/Automotive Mechanics. Volume II: Theory. Georgia Vocational Education Program Articulation.

    Science.gov (United States)

    Watkins, James F., Comp.

    These written domain referenced tests (DRTs) for the area of transportation/automotive mechanics test cognitive abilities or knowledge of theory. Introductory materials describe domain referenced testing and test development. Each multiple choice test includes a domain statement, describing the behavior and content of the domain, and a test item…

  3. Experimental and density functional theory (DFT) studies on the interactions of Ru(II) polypyridyl complexes with the RAN triplex poly(U)˙poly(A)*poly(U).

    Science.gov (United States)

    Zhang, Hong; Liu, Xuewen; He, Xiaojun; Liu, Ying; Tan, Lifeng

    2014-11-01

    There is renewed interest in investigating triple helices because these novel structures have been implicated as a possible means of controlling cellular processes by endogenous or exogenous mechanisms. Due to the Hoogsteen base pairing, triple helices are, however, thermodynamically less stable than the corresponding duplexes. The poor stability of triple helices limits their practical applications under physiological conditions. In contrast to DNA triple helices, small molecules stabilizing RNA triple helices at present are less well established. Furthermore, most of these studies are limited to organic compounds and, to a far lesser extent, to metal complexes. In this work, two Ru(II) complexes, [Ru(bpy)2(btip)](2+) (Ru1) and [Ru(phen)2(btip)](2+) (Ru2), have been synthesized and characterized. The binding properties of the two metal complexes with the triple RNA poly(U)˙poly(A)*poly(U) were studied by various biophysical and density functional theory methods. The main results obtained here suggest that the slight binding difference in Ru1 and Ru2 may be attributed to the planarity of the intercalative ligand and the LUMO level of Ru(II) complexes. This study further advances our knowledge on the triplex RNA-binding by metal complexes, particularly Ru(II) complexes.

  4. Investigation of the Performance of Foot and Eye Care in Patients with Type II Diabetes in Fasa: An Application of the Theory of Planned Behavior

    Directory of Open Access Journals (Sweden)

    Ali Khani Jeihooni

    2016-12-01

    Full Text Available Background and Objectives: Diabetic foot ulcers and eye problems are the most frequent complications of patients with diabetes and can be controlled with care. This study aimed at investigating the situation of foot and eye care in patients with type II diabetes based on the Theory of Planned Behavior of Fasa. Materials and Methods: In this cross-sectional study, simple randomized sampling was used to select 151 patients with type II diabetes, who had referred to Shariati Teaching Hospital diabetic clinic, during year 2016. Data were gathered using a questionnaire including demographic data and measure theory of planned behavior (attitude, subjective norm, perceived behavioral control, and intention and the care of feet and eyes. Next, the data were entered in the SPSS statistical software, version 20 and analyzed using independent t test and descriptive statistical methods. P values of < 0.05 were considered statistically significant. Results: The mean age of participants was 52.17±12.41 and the mean duration of diabetes was 76.62±4.9. Knowledge on the care of feet and eyes was low. Foot and eye care, subjective norm and people are going to be at a moderate level. Among knowledge, attitude, subjective norm, perceived behavioral control, and intention, there was a significant correlation with performance (P<0.05. Knowledge, attitudes, perceived behavioral control, subjective norms, and intention were predictors of foot care and eye performance in patients with type 2 diabetes. Overall, variables predicted 31.6% of the performance of foot care and 28.4% of eye care. Conclusions: According to this study, design and implementation of training programs theory centered on promoting foot care and eye performance is recommended for patients with diabetes.

  5. Theory of elastic thin shells solid and structural mechanics

    CERN Document Server

    Gol'Denveizer, A L; Dryden, H L

    1961-01-01

    Theory of Elastic Thin Shells discusses the mathematical foundations of shell theory and the approximate methods of solution. The present volume was originally published in Russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration. The book is organized into five parts. Part I presents the general formulation and equations of the theory of shells, which are based on the well-known hypothesis of the preservation of the normal element. Part II is

  6. Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

    International Nuclear Information System (INIS)

    Pratiwi, B N; Suparmi, A; Cari, C; Yunianto, M; Husein, A S

    2016-01-01

    We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number n_r causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions. (paper)

  7. Ginzburg-Landau-Gor close-quote kov theory of magnetic oscillations in a type-II two-dimensional superconductor

    International Nuclear Information System (INIS)

    Bruun, G.M.; Nicopoulos, V.N.; Johnson, N.F.

    1997-01-01

    We investigate de Haas endash van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor close-quote kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eighth order against an exact numerical solution of the corresponding Bogoliubov endash de Gennes equations. The perturbation theory is found to describe well the onset of superconductivity close to the transition point H c2 . Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA oscillations below H c2 . Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore, we have investigated the recently debated issue of the possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement. copyright 1997 The American Physical Society

  8. A constrained approximation for nuclear barrier penetration and fission

    International Nuclear Information System (INIS)

    Tang, H.H.K.; Negele, J.W.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

    1983-01-01

    An approximation to the time-dependent mean-field theory for barrier penetration by a nucleus is obtained in terms of constrained Hartree-Fock wave functions and a coherent velocity field. A discrete approximation to the continuum theory suitable for practical numerical calculations is presented and applied to three illustrative models. Potential application of the theory to the study of nuclear fission is discussed. (orig.)

  9. Formalism for testing theories of gravity using lensing by compact objects. II. Probing post-post-Newtonian metrics

    International Nuclear Information System (INIS)

    Keeton, Charles R.; Petters, A.O.

    2006-01-01

    We study gravitational lensing by compact objects in gravity theories that can be written in a post-post-Newtonian (PPN) framework: i.e., the metric is static and spherically symmetric, and can be written as a Taylor series in m /r, where m is the gravitational radius of the compact object. Working invariantly, we compute corrections to standard weak-deflection lensing observables at first and second order in the perturbation parameter ε=θ/θ E , where θ is the angular gravitational radius and θ E is the angular Einstein ring radius of the lens. We show that the first-order corrections to the total magnification and centroid position vanish universally for gravity theories that can be written in the PPN framework. This arises from some surprising, fundamental relations among the lensing observables in PPN gravity models. We derive these relations for the image positions, magnifications, and time delays. A deep consequence is that any violation of the universal relations would signal the need for a gravity model outside the PPN framework (provided that some basic assumptions hold). In practical terms, the relations will guide observational programs to test general relativity, modified gravity theories, and possibly the cosmic censorship conjecture. We use the new relations to identify lensing observables that are accessible to current or near-future technology, and to find combinations of observables that are most useful for probing the spacetime metric. We give explicit applications to the galactic black hole, microlensing, and the binary pulsar J0737-3039

  10. Magneto-structural correlations in a family of Fe(II)Re(IV)(CN)2 single-chain magnets: density functional theory and ab initio calculations.

    Science.gov (United States)

    Zhang, Yi-Quan; Luo, Cheng-Lin; Wu, Xin-Bao; Wang, Bing-Wu; Gao, Song

    2014-04-07

    Until now, the expressions of the anisotropic energy barriers Δξ and ΔA, using the uniaxial magnetic anisotropy D, the intrachain coupling strength J, and the high-spin ground state S for single-chain magnets (SCMs) in the intermediate region between the Ising and the Heisenberg limits, were unknown. To explore this relationship, we used density functional theory and ab initio methods to obtain expressions of Δξ and ΔA in terms of D, J, and S of six R4Fe(II)-Re(IV)Cl4(CN)2 (R = diethylformamide (1), dibutylformamide (2), dimethylformamide (3), dimethylbutyramide (4), dimethylpropionamide (5), and diethylacetamide (6)) SCMs in the intermediate region. The ΔA value for compounds 1-3 was very similar to the magnetic anisotropic energy of a single Fe(II), while the value of Δξ was predicted using the exchange interaction of Fe(II) with the neighboring Re(IV), which could be expressed as 2JSReSFe. Similar to compounds 1-3, the anisotropy energy barrier ΔA of compounds 4 and 5 was also equal to (Di - Ei)SFe(2), but the correlation energy Δξ was closely equal to 2JSReSFe(cos 98.4 - cos 180) due to the reversal of the spins on the opposite Fe(II). For compound 6, one unit cell of Re(IV)Fe(II) was regarded as a domain wall since it had two different Re(IV)-Fe(II) couplings. Thus, the Δξ of compound 6 was expressed as 4J″SRe1Fe1SRe2Fe2, where J″ was the coupling constant of the neighboring unit cells of Re1Fe1 and Re2Fe2, and ΔA was equal to the anisotropic energy barrier of one domain wall given by DRe1Fe1(S(2)Re1Fe1 - 1/4).

  11. Differential electron scattering cross sections for the 3 (2)S to 3 (2)P0 h, k transitions in Mg II - Comparison of experiment and theory

    Science.gov (United States)

    Williams, I. D.; Chutjian, A.; Msezane, A. Z.; Henry, R. J. W.

    1985-01-01

    Angular differential electron scattering cross sections are reported for the unresolved inelastic 3s (2)S to 3p (2)P0 h, k transitions in Mg II for the first time. Relative differential cross sections have been measured at 35 eV and 50 eV in the angular range of Theta between 6 and 17 deg using the newly developed electron energy loss technique in a crossed electron-ion beam geometry. Theoretical values have been calculated in a five-state close-coupling approximation in which 3s, 3p, 3d, 4s, and 4p states were included, and to which measurements were normalized at Theta = 12 deg.

  12. A full-field residual stress estimation scheme for fitness-for-service assessment of pipe girth welds: Part II – A shell theory based implementation

    International Nuclear Information System (INIS)

    Song, Shaopin; Dong, Pingsha; Pei, Xianjun

    2015-01-01

    With the two key controlling parameters identified and their effectiveness demonstrated in Part I of this study series for constructing a continuous residual stress profile at weld region, a classical shell theory based model is proposed in this paper (Part II) for describing through-thickness residual stress distributions of both axial and hoop components at any axial location beyond weld region. The shell theory based model is analytically constructed through an assembly of two parts: One represents weld region and the other represents the remaining component section away from weld. The final assembly of the two parts leads to a closed form solution to both axial and hoop residual stress components as a function of axial distance from weld toe position. The effectiveness of the full-field residual stress estimation scheme is demonstrated by comparing with a series of finite element modeling results over a broad range of pipe weld geometries and welding conditions. The present development should provide a consistent and effective means for estimating through-thickness residual stress profile as a continuous function of pipe geometry, welding heat input, as well as material characteristics. - Highlights: • A shell theory based two-part assembly model is developed for generalizing residual stress distributions. • A full-field estimation of through-thickness residual stress profiles can be achieved. • The proposed estimation scheme offers both consistency and mechanics basis in residual stress profile generation. • An estimation scheme for welding-induced plastic zone size is proposed and validated. • The shell theory based estimation scheme can also provide a reasonable estimate on distortion in radial direction

  13. Perturbation expansions generated by an approximate propagator

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example

  14. Congruence Approximations for Entrophy Endowed Hyperbolic Systems

    Science.gov (United States)

    Barth, Timothy J.; Saini, Subhash (Technical Monitor)

    1998-01-01

    Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

  15. Calculation of interfacial tensions with gradient theory. I. Pure and Pseudo-Pure Fluids. II. Binary Systems

    DEFF Research Database (Denmark)

    Zuo, You-Xiang; Stenby, Erling Halfdan

    1997-01-01

    .26% at low pressure, and that of naphtha reformate cuts was 3.6%. In addition, the gradient theory was used to predict interfacial tensions for binary systems in the near-critical region. The results show excellent agreement between the predicted and experimental IFTs at high and moderate levels, while....... A consistent procedure for the estimation of properties associated to lumped systems. Fluid Phase Equilibria, 87: 89-197] was used to lump a mixture into one pseudocomponent, and its IFTs were calculated by means of the method of pure fluids. On the basis of the SRK EOS, the overall AAD of mixtures was 3...

  16. Pawlak algebra and approximate structure on fuzzy lattice.

    Science.gov (United States)

    Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

    2014-01-01

    The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

  17. Bond-equilibrium theory of liquid Se-Te alloys. II. Effect of singly attached ring molecules

    Science.gov (United States)

    Cutler, Melvin; Bez, Wolfgang G.

    1981-06-01

    A statistical-mechanical theory for bond equilibrium of chain polymers containing threefold (3F) and onefold (1F) bond defects is extended to include the effects of free ring molecules and ring molecules attached to chains by a single 3F atom. Positively charged singly attached rings are shown to play a key role in bond equilibrium in liquid Sex Te1-x by permitting the formation of ion pairs in which both constituents are effectively chain terminators, thus decreasing the average polymer size. The theory is applied to explain the behavior of the paramagnetic susceptibility, χp, and electronic transport as affected by the Fermi energy EF. It is found that the increase in χp with the concentration of Te is primarily the result of the smaller energy for breaking Te bonds. In addition, attached rings play an important role in determining the effect of temperature on χp. At x<~0.5, the concentrations of both free and attached rings becomes small at high T because of the high concentration of bond defects.

  18. Classification of three-family grand unification in string theory. II. The SU(5) and SU(6) models

    International Nuclear Information System (INIS)

    Kakushadze, Z.; Tye, S.H.

    1997-01-01

    Requiring that supersymmetric SU(5) and SU(6) grand unifications in the heterotic string theory must have three chiral families, adjoint (or higher representation) Higgs fields in the grand unified gauge group, and a non-Abelian hidden sector, we construct such string models within the framework of free conformal field theory and asymmetric orbifolds. Within this framework, we construct all such string models via Z 6 asymmetric orbifolds that include a Z 3 outerautomorphism, the latter yielding a level-three current algebra for the grand unification gauge group SU(5) or SU(6). We then classify all such Z 6 asymmetric orbifolds that result in models with a non-Abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. This Higgs field is neutral under all other gauge symmetries. The list of hidden sectors for three-family SU(6) string models are SU(2), SU(3), and SU(2)circle-times SU(2). In addition to these, three-family SU(5) string models can also have an SU(4) hidden sector. Some of the models have an apparent anomalous U(1) gauge symmetry. copyright 1997 The American Physical Society

  19. Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II. The Deconfined phase

    CERN Document Server

    Caselle, Michele; Feo, Alessandra; Gliozzi, Ferdinando; Gursoy, Umut; Panero, Marco; Schafer, Andreas

    2012-01-01

    We present a non-perturbative study of the equation of state in the deconfined phase of Yang-Mills theories in D=2+1 dimensions. We introduce a holographic model, based on the improved holographic QCD model, from which we derive a non-trivial relation between the order of the deconfinement phase transition and the behavior of the trace of the energy-momentum tensor as a function of the temperature T. We compare the theoretical predictions of this holographic model with a new set of high-precision numerical results from lattice simulations of SU(N) theories with N=2, 3, 4, 5 and 6 colors. The latter reveal that, similarly to the D=3+1 case, the bulk equilibrium thermodynamic quantities (pressure, trace of the energy-momentum tensor, energy density and entropy density) exhibit nearly perfect proportionality to the number of gluons, and can be successfully compared with the holographic predictions in a broad range of temperatures. Finally, we also show that, again similarly to the D=3+1 case, the trace of the en...

  20. Calculation of exchange coupling constants in triply-bridged dinuclear Cu(II) compounds based on spin-flip constricted variational density functional theory.

    Science.gov (United States)

    Seidu, Issaka; Zhekova, Hristina R; Seth, Michael; Ziegler, Tom

    2012-03-08

    The performance of the second-order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) for the calculation of the exchange coupling constant (J) is assessed by application to a series of triply bridged Cu(II) dinuclear complexes. A comparison of the J values based on SF-CV(2)-DFT with those obtained by the broken symmetry (BS) DFT method and experiment is provided. It is demonstrated that our methodology constitutes a viable alternative to the BS-DFT method. The strong dependence of the calculated exchange coupling constants on the applied functionals is demonstrated. Both SF-CV(2)-DFT and BS-DFT affords the best agreement with experiment for hybrid functionals.

  1. Design and verification of controllers for longitudinal oscillations using optimal control theory and numerical simulation: Predictions for PEP-II

    International Nuclear Information System (INIS)

    Hindi, H.; Prabhakar, S.; Fox, J.; Teytelman, D.

    1997-12-01

    The authors present a technique for the design and verification of efficient bunch-by-bunch controllers for damping longitudinal multibunch instabilities. The controllers attempt to optimize the use of available feedback amplifier power--one of the most expensive components of a feedback system--and define the limits of closed loop system performance. The design technique alternates between analytic computation of single bunch optimal controllers and verification on a multibunch numerical simulator. The simulator identifies unstable coupled bunch modes and predicts their growth and damping rates. The results from the simulator are shown to be in reasonable agreement with analytical calculations based on the single bunch model. The technique is then used to evaluate the performance of a variety of controllers proposed for PEP-II

  2. Theory of extended stellar atmospheres. II. A grid of static spherical models for O stars and planetary nebula nuclei

    International Nuclear Information System (INIS)

    Kunasz, P.B.; Hummer, D.G.; Mihalas, D.

    1975-01-01

    Spherical static non-LTE model atmospheres are presented for stars with M/M/sub sun/=30 and 60 at various points on their evolutionary tracks, and for some nuclei of planetary nebulae at two points of a modified Harman-Seaton sequence. The method of Mihalas and Hummer was employed, which uses a parametrized radiation force multiplier to simulate the force of radiation arising from the entire line spectrum. However, in the present work the density structure computed in the LTE models was held fixed in the calculation of the corresponding non-LTE models; in addition, the opacity of an ''average light ion'' was taken into account. The temperatures for the non-LTE models are generally lower, at a given depth, than for the corresponding LTE models when T/sub eff/<45,000 K, while the situation is reversed at higher temperatures. The continuous energy distributions are generally flattened by extension. The Lyman jump is in emission for extended models of massive stars, but never for the models of nuclei of planetary nebulae (this is primarily a temperature effect). The Balmer jumps are always in absorption. The Lyman lines are in emission, and the Balmer lines in absorption; He ii lambda4686 comes into emission in the most extended models without hydrogen line pumping, showing that it is an indicator of atmospheric extension. Very severe limb darkening is found for extended models, which have apparent angular sized significantly smaller than expected from the geometrical size of the star. Extensive tables are given of monochromatic magnitudes, continuum jumps and gradients, Stomgren-system colors, monochromatic extensions, and the profiles and equivalent widths of the hydrogen lines for all models, and of the He ii lines for some of the 60 M/sub X/ models

  3. Mathematical theories of classical particle channeling in perfect crystals

    International Nuclear Information System (INIS)

    Dumas, H. Scott

    2005-01-01

    We present an overview of our work on rigorous mathematical theories of channeling for highly energetic positive particles moving in classical perfect crystal potentials. Developed over the last two decades, these theories include: (i) a comprehensive, highly mathematical theory based on Nekhoroshev's theorem which embraces both axial and planar channeling as well as certain non-channeling particle motions (ii) a theory of axial channeling for relativistic particles based on a single-phase averaging method for ordinary differential equations and (iii) a theory of planar channeling for relativistic particles based on a two-phase averaging method for ordinary differential equations. Here we touch briefly on (i) and (ii), then focus on (iii). Together these theories place Lindhard's continuum model approximations on a firm mathematical foundation, and should serve as the starting point for more refined mathematical treatments of channeling

  4. 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.

  5. 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.

  6. The Hartree-Fock seniority approximation

    International Nuclear Information System (INIS)

    Gomez, J.M.G.; Prieto, C.

    1986-01-01

    A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)

  7. GENOVA: a generalized perturbation theory program for various applications to CANDU core physics analysis (II) - a user's manual

    International Nuclear Information System (INIS)

    Kim, Do Heon; Choi, Hang Bok

    2001-03-01

    A user's guide for GENOVA, a GENeralized perturbation theory (GPT)-based Optimization and uncertainty analysis program for Canada deuterium uranium (CANDU) physics VAriables, was prepared. The program was developed under the framework of CANDU physics design and analysis code RFSP. The generalized perturbation method was implemented in GENOVA to estimate the zone controller unit (ZCU) level upon refueling operation and calculate various sensitivity coefficients for fuel management study and uncertainty analyses, respectively. This documentation contains descriptions and directions of four major modules of GENOVA such as ADJOINT, GADJINT, PERTURB, and PERTXS so that it can be used as a practical guide for GENOVA users. This documentation includes sample inputs for the ZCU level estimation and sensitivity coefficient calculation, which are the main application of GENOVA. The GENOVA can be used as a supplementary tool of the current CANDU physics design code for advanced CANDU core analysis and fuel development

  8. Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition.

    Science.gov (United States)

    Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco

    2013-10-24

    We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the random first order transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis and a further transition at higher pressures in which a glassy structure of microstates is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Microstates that are small excitations of an amorphous matrix-separated by low entropic or energetic barriers-thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.

  9. FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M., E-mail: fang.307@osu.edu, E-mail: blazek@berkeley.edu, E-mail: mcewen.24@osu.edu, E-mail: hirata.10@osu.edu [Center for Cosmology and AstroParticle Physics, Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus OH 43210 (United States)

    2017-02-01

    Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.

  10. Non-affine deformation in microstructure selection in solids II: Elastoplastic theory for the dynamics of solid state transformations

    Energy Technology Data Exchange (ETDEWEB)

    Paul, Arya; Bhattacharya, Jayee; Sengupta, Surajit [S N Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Calcutta 700 098 (India); Rao, Madan [Raman Research Institute, C V Raman Avenue, Bangalore 560 080 (India)

    2008-09-10

    We study the nucleation dynamics of a model solid state transformation and the criterion for microstructure selection. Using a molecular dynamics (MD) simulation, we had shown that the dynamics of the solid is accompanied by the creation of transient non-affine zones (NAZ), which evolve with the rapidly moving transformation front. Guided by our MD results, we formulate a dynamical continuum theory of solid state transformation, which couples the elastic strain to the non-affine deformation. We demonstrate that our elastoplastic description recovers all qualitative features of the MD simulation. We construct a dynamical phase diagram for microstructure selection, including regimes where martensite or ferrite obtains, in addition to making several testable predictions.

  11. 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.

  12. Case study II: application of the divalent cation bridging theory to improve biofloc properties and industrial activated sludge system performance-using alternatives to sodium-based chemicals.

    Science.gov (United States)

    Higgins, Matthew J; Sobeck, David C; Owens, Steven J; Szabo, Lynn M

    2004-01-01

    The objective of this study was to investigate the application of the divalent cation bridging theory (DCBT) as a tool in the chemical selection process at an activated sludge plant to improve settling, dewatering, and effluent quality. According to the DCBT, to achieve improvements, the goal of chemical selection should be to reduce the ratio of monovalent-to-divalent (M/D) cations. A study was conducted to determine the effect of using magnesium hydroxide [Mg(OH)2] as an alternative to sodium hydroxide (NaOH) at a full-scale industrial wastewater treatment plant. Floc properties and treatment plant performance were measured for approximately one year during two periods of NaOH addition and Mg(OH)2 addition. A cost analysis of plant operation during NaOH and Mg(OH)2 use was also performed. During NaOH addition, the M/D ratio was 48, while, during Mg(OH)2 addition, this ratio was reduced to an average of approximately 0.1. During the Mg(OH)2 addition period, the sludge volume index, effluent total suspended solids, and effluent chemical oxygen demand were reduced by approximately 63, 31, and 50%, respectively, compared to the NaOH addition period. The alum and polymer dose used for clarification was reduced by approximately 50 and 60%, respectively, during Mg(OH)2 addition. The dewatering properties of the activated sludge improved dewatering as measured by decreased capillary suction time and specific resistance to filtration (SRF), along with an increase in cake solids from the SRF test. This corresponded to a reduction in the volume of solids thickened by centrifuges at the treatment plant, which reduced the disposal costs of solids. Considering the costs for chemicals and solids disposal, the annual cost of using Mg(OH)2 was approximately 30,000 dollars to 115,000 dollars less than using NaOH, depending on the pricing of NaOH. The results of this study confirm that the DCBT is a useful tool for assessing chemical-addition strategies and their potential effect

  13. Semiclassical approximation in Batalin-Vilkovisky formalism

    International Nuclear Information System (INIS)

    Schwarz, A.

    1993-01-01

    The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q}=0), a P-structure (odd symplectic structure) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion. (orig.)

  14. Approximation by planar elastic curves

    DEFF Research Database (Denmark)

    Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

    2016-01-01

    We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

  15. Conference on Abstract Spaces and Approximation

    CERN Document Server

    Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation

    1969-01-01

    The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...

  16. Approximating the physical inner product of loop quantum cosmology

    International Nuclear Information System (INIS)

    Bahr, Benjamin; Thiemann, Thomas

    2007-01-01

    In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity

  17. The binary collision approximation: Background and introduction

    International Nuclear Information System (INIS)

    Robinson, M.T.

    1992-08-01

    The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented

  18. El padecimiento ante la enfermedad: Un enfoque desde la teoría de la representación social The experience of illness: An approximation from the theory of the social representation

    Directory of Open Access Journals (Sweden)

    César Hueso Montoro

    2006-03-01

    Full Text Available Los actuales modelos de gestión del cuidado proponen un acercamiento a los aspectos más subjetivos inherentes a la enfermedad, entendiendo esa subjetividad como un cúmulo de circunstancias históricas, sociales, culturales, etc, que condicionan la respuesta que la persona desarrolla ante la misma. Este artículo propone una reflexión sobre el fenómeno del padecimiento ante la enfermedad, articulando su argumento principal en torno a la teoría de las representaciones sociales de Moscovici. Los elementos que definen dicha teoría convierten al padecimiento en un fenómeno susceptible de ser abordado como una representación social, en tanto que constituye una fuente de significados individuales y colectivos que condicionan el modo en que un sujeto actúa y responde ante la enfermedad.Nowadays, the models of care management propose an approach to the most subjective aspects inherent in the illness, understanding this as an accumulation of cultural, social, historic circumstances, etc, which influence the answer that the person develops. This article proposes an analysis about the phenomenon of the experience of illness, articulating its main argument around the theory of the social representations of Moscovici. The elements of this theory convert the experience of illness in a susceptible phenomenon to be analyzed as a social representation, because constitutes a source of collective and individual meanings that influence the way in which the person acts and responds to illness.

  19. Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems

    International Nuclear Information System (INIS)

    Wu, Wei; Wang, Jin

    2014-01-01

    We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series

  20. An open-source framework for analyzing N-electron dynamics. II. Hybrid density functional theory/configuration interaction methodology.

    Science.gov (United States)

    Hermann, Gunter; Pohl, Vincent; Tremblay, Jean Christophe

    2017-10-30

    In this contribution, we extend our framework for analyzing and visualizing correlated many-electron dynamics to non-variational, highly scalable electronic structure method. Specifically, an explicitly time-dependent electronic wave packet is written as a linear combination of N-electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time-dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open-source Python program detCI@ORBKIT, which extends the capabilities of our recently published post-processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom-centered Gaussian-type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one-electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser-driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher-level method provided a judicious choice of functional is made. Broadband excitation of a medium-sized organic chromophore further demonstrates the scalability of the method. In addition, the time-dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  1. [New theory of holistic integrative physiology and medicine. II: New insight of the control and regulation of circulation].

    Science.gov (United States)

    Sun, Xing-guo

    2015-07-01

    The interpretation of control and regulation of circulatory parameters in traditional physiology has some limitations. Human being is an organic, circulatory control and regulation should involve all the systems. Based upon the theory of holistic integrative physiology and medicine, we approach to explain the circulatory control and regulation from its purpose. The main purpose of circulation is to maintain a stable metabolism of cells, i.e. transport oxygen (from lung) and nutrients (from gastrointestinal tract) to cells, and return carbon dioxide and metabolic products back for elimination. Based on this goal, all respiration and gastrointestinal digestion, absorption, urinary excretion, etc. are integrative together for regulation to maintain the supply-demand balance at any metabolic status of resting, exercise and sleep. So that, we can explain many existing problems and questions, for example: why and how the foramen ovale closed after birth; mechanism of Cheyne-Stokes respiration; blood flow redistribution during exercise; variabilities of systolic blood pressure, heart rate and autonomic tone. The circulatory control and regulation is the integration of all systems of the body.

  2. A Thermodynamic History of the Solar Constitution — II: The Theory of a Gaseous Sun and Jeans' Failed Liquid Alternative

    Directory of Open Access Journals (Sweden)

    Robitaille P.-M.

    2011-07-01

    Full Text Available In this work, the development of solar theory is followed from the concept that the Sun was an ethereal nuclear body with a partially condensed photosphere to the creation of a fully gaseous object. An overview will be presented of the liquid Sun. A powerful lineage has brought us the gaseous Sun and two of its main authors were the direct sci- entific descendants of Gustav Robert Kirchhoff: Franz Arthur Friedrich Schuster and Arthur Stanley Eddington. It will be discovered that the seminal ideas of Father Secchi and Herv ́ e Faye were not abandoned by astronomy until the beginning of 20th century. The central role of carbon in early solar physics will also be highlighted by revisit- ing George Johnstone Stoney. The evolution of the gaseous models will be outlined, along with the contributions of Johann Karl Friedrich Z ̈ ollner, James Clerk Maxwell, Jonathan Homer Lane, August Ritter, William Thomson, William Huggins, William Edward Wilson, George Francis FitzGerald, Jacob Robert Emden, Frank Washington Very, Karl Schwarzschild, and Edward Arthur Milne. Finally, with the aid of Edward Arthur Milne, the work of James Hopwood Jeans, the last modern advocate of a liquid Sun, will be rediscovered. Jeans was a staunch advocate of the condensed phase, but deprived of a proper building block, he would eventually abandon his non-gaseous stars. For his part, Subrahmanyan Chandrasekhar would spend nine years of his life studying homogeneous liquid masses. These were precisely the kind of objects which Jeans had considered for his liquid stars.

  3. Approximate equations at breaking for nearshore wave transformation coefficients

    Digital Repository Service at National Institute of Oceanography (India)

    Chandramohan, P.; Nayak, B.U.; SanilKumar, V.

    Based on small amplitude wave theory approximate equations are evaluated for determining the coefficients of shoaling, refraction, bottom friction, bottom percolation and viscous dissipation at breaking. The results obtainEd. by these equations...

  4. Linear approximation model network and its formation via ...

    Indian Academy of Sciences (India)

    niques, an alternative `linear approximation model' (LAM) network approach is .... network is LPV, existing LTI theory is difficult to apply (Kailath 1980). ..... Beck J V, Arnold K J 1977 Parameter estimation in engineering and science (New York: ...

  5. Scalable high-performance algorithm for the simulation of exciton-dynamics. Application to the light harvesting complex II in the presence of resonant vibrational modes

    DEFF Research Database (Denmark)

    Kreisbeck, Christoph; Kramer, Tobias; Aspuru-Guzik, Alán

    2014-01-01

    high-performance many-core platforms using the Open Compute Language (OpenCL). For the light-harvesting complex II (LHC II) found in spinach, the HEOM results deviate from predictions of approximate theories and clarify the time-scale of the transfer-process. We investigate the impact of resonantly...

  6. Human development II: We Need an Integrated Theory for Matter, Life and Consciousness to Understand Life and Healing

    Directory of Open Access Journals (Sweden)

    Sören Ventegodt

    2006-01-01

    Full Text Available For almost a decade, we have experimented with supporting the philosophical development of severely ill patients to induce recovery and spontaneous healing. Recently, we have observed a new pattern of extremely rapid, spontaneous healing that apparently can facilitate even the spontaneous remission of cancer and the spontaneous recovery of mental diseases like schizophrenia and borderline schizophrenia. Our working hypothesis is that the accelerated healing is a function of the patient’s brain-mind and body-mind coming closer together due to the development of what we call “deep” cosmology. To understand and describe what happens at a biological level, we have suggested naming the process adult human metamorphosis, a possibility that is opened by the human genome showing full generic equipment for metamorphosis. To understand the mechanistic details in the complicated interaction between consciousness and biology, we need an adequate theory for biological information. In a series of papers, we propose what we call “holistic biology for holistic medicine”. We suggest that a relatively simple model based on interacting wholenesses instead of isolated parts can shed a new light on a number of difficult issues that we need to explain and understand in biology and medicine in order to understand and use metamorphosis in the holistic medical clinic. We aim to give a holistic theoretical interpretation of biological phenomena at large, morphogenesis, evolution, immune system regulation (self-nonself discrimination, brain function, consciousness, and health in particular. We start at the most fundamental problem: what is biological information at the subcellular, cellular, and supracellular levels if we presume that it is the same phenomenon on all levels (using Occam's razor, and how can this be described scientifically? The problems we address are all connected to the information flow in the functioning, living organism: function of the brain

  7. Human development II: we need an integrated theory for matter, life and consciousness to understand life and healing.

    Science.gov (United States)

    Ventegodt, Søren; Hermansen, Tyge Dahl; Nielsen, Maj Lyck; Clausen, Birgitte; Merrick, Joav

    2006-07-06

    For almost a decade, we have experimented with supporting the philosophical development of severely ill patients to induce recovery and spontaneous healing. Recently, we have observed a new pattern of extremely rapid, spontaneous healing that apparently can facilitate even the spontaneous remission of cancer and the spontaneous recovery of mental diseases like schizophrenia and borderline schizophrenia. Our working hypothesis is that the accelerated healing is a function of the patient's brain-mind and body-mind coming closer together due to the development of what we call "deep" cosmology. To understand and describe what happens at a biological level, we have suggested naming the process adult human metamorphosis, a possibility that is opened by the human genome showing full generic equipment for metamorphosis. To understand the mechanistic details in the complicated interaction between consciousness and biology, we need an adequate theory for biological information. In a series of papers, we propose what we call "holistic biology for holistic medicine". We suggest that a relatively simple model based on interacting wholenesses instead of isolated parts can shed a new light on a number of difficult issues that we need to explain and understand in biology and medicine in order to understand and use metamorphosis in the holistic medical clinic. We aim to give a holistic theoretical interpretation of biological phenomena at large, morphogenesis, evolution, immune system regulation (self-nonself discrimination), brain function, consciousness, and health in particular. We start at the most fundamental problem: what is biological information at the subcellular, cellular, and supracellular levels if we presume that it is the same phenomenon on all levels (using Occam's razor), and how can this be described scientifically? The problems we address are all connected to the information flow in the functioning, living organism: function of the brain and consciousness, the

  8. 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.

  9. Spherical Approximation on Unit Sphere

    Directory of Open Access Journals (Sweden)

    Eman Samir Bhaya

    2018-01-01

    Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

  10. The high intensity approximation applied to multiphoton ionization

    International Nuclear Information System (INIS)

    Brandi, H.S.; Davidovich, L.; Zagury, N.

    1980-08-01

    It is shown that the most commonly used high intensity approximations as applied to ionization by strong electromagnetic fields are related. The applicability of the steepest descent method in these approximations, and the relation between them and first-order perturbation theory, are also discussed. (Author) [pt

  11. Gauge-invariant intense-field approximations to all orders

    International Nuclear Information System (INIS)

    Faisal, F H M

    2007-01-01

    We present a gauge-invariant formulation of the so-called strong-field KFR approximations in the 'velocity' and 'length' gauges and demonstrate their equivalence in all orders. The theory thus overcomes a longstanding discrepancy between the strong-field velocity and the length-gauge approximations for non-perturbative processes in intense laser fields. (fast track communication)

  12. 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.

  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. Relativistic-particle quantum mechanics (applications and approximations) II

    International Nuclear Information System (INIS)

    Coester, F.

    1981-01-01

    In this lecture I hope to show that relativistic-particle quantum mechanics with direct interactions is a useful tool for building models applicable to hadron systems at intermediate energies. To do this I will first describe a class of models designed to incorporate nucleon-nucleon interactions, pion production, absorption and scattering into a single dynamical framework without dressing the nucleons with pion clouds. The second major topic concerns electromagnetic interactions. In the previous lecture I specifically excluded long-rang forces and zero-mass particles. Since many of the experimental data in hadron physics involve electromagnetic interactions this limitation is a major defect which must be addressed

  15. 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.

  16. Parametrized post-Newtonian approximation and Rastall's gravitational field equations

    International Nuclear Information System (INIS)

    Smalley, L.L.

    1978-01-01

    The parametrized post-Newtonian (PPN) approximation is generalized to accomodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and angular-momentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories

  17. X-ray Diffraction and Density Functional Theory Provide Insight into Vanadate Binding to Homohexameric Bromoperoxidase II and the Mechanism of Bromide Oxidation.

    Science.gov (United States)

    Radlow, Madlen; Czjzek, Mirjam; Jeudy, Alexandra; Dabin, Jerome; Delage, Ludovic; Leblanc, Catherine; Hartung, Jens

    2018-05-18

    X-ray diffraction of native bromoperoxidase II (EC 1.11.1.18) from the brown alga Ascophyllum nodosum reveals at a resolution of 2.26 Å details of orthovanadate binding and homohexameric protein organization. Three dimers interwoven in contact regions and tightened by hydrogen-bond-clamped guanidinium stacks along with regularly aligned water molecules form the basic structure of the enyzme. Intra- and intermolecular disulfide bridges further stabilize the enzyme preventing altogether the protein from denaturing up to a temperature of 90 °C, as evident from dynamic light scattering and the on-gel ortho-dianisidine assay. Every monomer binds one equivalent of orthovanadate in a cavity formed from side chains of three histidines, two arginines, one lysine, serine, and tryptophan. Protein binding occurs primarily through hydrogen bridges and superimposed by Coulomb attraction according to thermochemical model on density functional level of theory (B3LYP/6-311++G**). The strongest attractor is the arginine side chain mimic N-methylguanidinium, enhancing in positive cooperative manner hydrogen bridges toward weaker acceptors, such as residues from lysine and serine. Activating hydrogen peroxide occurs in the thermochemical model by side-on binding in orthovanadium peroxoic acid, oxidizing bromide with virtually no activation energy to hydrogen bonded hypobromous acid.

  18. Risk theory

    CERN Document Server

    Schmidli, Hanspeter

    2017-01-01

    This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II. Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management.

  19. Approximate Implicitization Using Linear Algebra

    Directory of Open Access Journals (Sweden)

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  20. Rollout sampling approximate policy iteration

    NARCIS (Netherlands)

    Dimitrakakis, C.; Lagoudakis, M.G.

    2008-01-01

    Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a

  1. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  2. Framework for sequential approximate optimization

    NARCIS (Netherlands)

    Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.

    2004-01-01

    An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python

  3. Role of dust in H II regions

    International Nuclear Information System (INIS)

    Sarazin, C.L.

    1975-01-01

    The purpose of this dissertation is to determine quantitatively the effects of U.V. absorbing dust on H II regions, and compare these effects with observations. Many observations indicate that dust grains are present within H II regions. An analytic theory is presented which describes all three of the effects of dust in H II regions. Although this model is relatively crude, it is useful in determining the approximate size of the modifications due to dust. In order to explore this problem more carefully, detailed numerical models of H II regions with dust were constructed. The ionization and thermal structure of these model H II regions is discussed. The observational consequences of the presence of dust are explored; the optical line intensities, radio continuum and line fluxes, and infrared emission of model H II regions with dust are given. These numerical models are compared with observations of diffuse nebulae. The optical line ratios are compared to several nearby bright H II regions, and it is found that the dust models may explain several anomalies in their spectrum

  4. 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

  5. Approximate Controllability of Semilinear Neutral Stochastic Integrodifferential Inclusions with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Meili Li

    2015-01-01

    Full Text Available The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.

  6. 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

  7. Critical Assessment of Time-Dependent Density Functional Theory for Excited States of Open-Shell Systems: II. Doublet-Quartet Transitions.

    Science.gov (United States)

    Li, Zhendong; Liu, Wenjian

    2016-06-14

    Compared with closed-shell systems, open-shell systems place three additional challenges to time-dependent density functional theory (TD-DFT) for electronically excited states: (a) the spin-contamination problem is a serious issue; (b) the exchange-correlation (XC) kernel may be numerically instable; and (c) the single-determinant description of open-shell ground states readily becomes energetically instable. Confined to flip-up single excitations, the spin-contamination problem can largely be avoided by using the spin-flip TD-DFT (SF-TD-DFT) formalism, provided that a noncollinear XC kernel is employed. As for the numerical instabilities associated with such a kernel, only an ad hoc scheme has been proposed so far, viz., the ALDA0 kernel, which amounts to setting the divergent components (arising from density gradients and kinetic energy density) simply to zero. The ground-state instability problem can effectively be avoided by introducing the Tamm-Dancoff approximation (TDA) to TD-DFT. Therefore, on a general basis, the SF-TDA/ALDA0 Ansatz is so far the only promising means within the TD-DFT framework for flip-up single excitations of open-shell systems. To assess systematically the performance of SF-TDA/ALDA0, in total 61 low-lying quartet excited states of the benchmark set of 11 small radicals [J. Chem. Theory Comput. 2016, 12, 238] are investigated with various XC functionals. Taking the MRCISD+Q (multireference configuration interaction with singles and doubles plus the Davidson correction) results as benchmark, it is found that the mean absolute errors of SF-TDA/ALDA0 with the SAOP (statistical averaging of model orbital potentials), global hybrid, and range-separated hybrid functionals are in the range of 0.2-0.4 eV. This is in line not only with the typical accuracy of TD-DFT for singlet and triplet excited states of closed-shell systems but also with the gross accuracy of spin-adapted TD-DFT for spin-conserving excited states of open-shell systems.

  8. Rational-driver approximation in car-following theory

    Science.gov (United States)

    Lubashevsky, Ihor; Wagner, Peter; Mahnke, Reinhard

    2003-11-01

    The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional is constructed. This functional ranks the outcomes of different driving strategies, which applies to fairly general properties of the driver behavior. Assuming rational-driver behavior, the existence of the Nash equilibrium is proved. Rational driving is defined by supposing that a driver corrects continuously the car motion to follow the optimal path minimizing the cost functional. The corresponding car-following dynamics is described quite generally by a boundary value problem based on the obtained extremal equations. Linearization of these equations around the stationary state results in a generalization of the widely used optimal velocity model. Under certain conditions (the “dense traffic” limit) the rational car dynamics comprises two stages, fast and slow. During the fast stage a driver eliminates the velocity difference between the cars, the subsequent slow stage optimizes the headway. In the dense traffic limit an effective Hamiltonian description is constructed. This allows a more detailed nonlinear analysis. Finally, the differences between rational and bounded rational driver behavior are discussed. The latter, in particular, justifies some basic assumptions used recently by the authors to construct a car-following model lying beyond the frameworks of rationality.

  9. On the Stationarity of Multiple Autoregressive Approximants: Theory and Algorithms

    Science.gov (United States)

    1976-08-01

    a I (3.4) Hannan and Terrell (1972) consider problems of a similar nature. Efficient estimates A(1),... , A(p) , and i of A(1)... ,A(p) and...34Autoregressive model fitting for control, Ann . Inst. Statist. Math., 23, 163-180. Hannan, E. J. (1970), Multiple Time Series, New York, John Wiley...Hannan, E. J. and Terrell , R. D. (1972), "Time series regression with linear constraints, " International Economic Review, 13, 189-200. Masani, P

  10. A Complete Approximation Theory for Weighted Transition Systems

    DEFF Research Database (Denmark)

    Hansen, Mikkel; Larsen, Kim Guldstrand; Mardare, Radu Iulian

    2016-01-01

    We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates states that exhibit transitions to bisimulation classes...... the image-finiteness restriction, a fact that makes this development general and robust....

  11. 3rd International Conference on Applied Mathematics and Approximation Theory

    CERN Document Server

    Duman, Oktay

    2016-01-01

    This special volume is a collection of outstanding theoretical articles presented at the conference AMAT 2015, held in Ankara, Turkey from May 28-31, 2015, at TOBB University of Economics and Technology. The collection is suitable for a range of applications: from researchers and practitioners of applied and computational mathematics, to students in graduate-level seminars. Furthermore it will be a useful resource for all science libraries. This book includes 27 self-contained and expertly-refereed chapters that provide numerous insights into the latest developments at the intersection of applied and computational mathematics, engineering, and statistics.

  12. Euclidean scalar field theory in the bilocal approximation

    Science.gov (United States)

    Nagy, S.; Polonyi, J.; Steib, I.

    2018-04-01

    The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.

  13. Approximations to camera sensor noise

    Science.gov (United States)

    Jin, Xiaodan; Hirakawa, Keigo

    2013-02-01

    Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

  14. Rational approximations for tomographic reconstructions

    International Nuclear Information System (INIS)

    Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

    2013-01-01

    We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)

  15. 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....

  16. Optimizing the structure of Tetracyanoplatinate(II)

    DEFF Research Database (Denmark)

    Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.

    2013-01-01

    . For the C-N bond these trends are reversed and an order of magnitude smaller. With respect to the basis set dependence we observed that a triple zeta basis set with polarization functions gives in general sufficiently converged results, but while for the Pt-C bond it is advantageous to include extra diffuse......The geometry of tetracyanoplatinate(II) (TCP) has been optimized with density functional theory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non...... is almost quantitatively reproduced in the ZORA and ECP calculations. In addition, the effect of the exchange-correlation functional and one-electron basis set was studied by employing the two generalized gradient approximation (GGA) functionals, BLYP and PBE, as well as their hybrid version B3LYP and PBE0...

  17. Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

    International Nuclear Information System (INIS)

    Riplinger, Christoph; Pinski, Peter; Becker, Ute; Neese, Frank; Valeev, Edward F.

    2016-01-01

    Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate

  18. 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.

  19. 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

  20. 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