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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. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  3. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  4. 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

  5. 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.

  6. 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.

  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. 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.

  9. 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)

  10. 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

  11. 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.)

  12. 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

  13. 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

  14. 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. ...

  15. 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

  16. 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

  17. 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

  18. 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.)

  19. 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

  20. 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...

  1. 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

  2. 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...

  3. 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

  4. 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.

  5. 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.)

  6. 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.

  7. 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

  8. 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)

  9. 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)

  10. 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

  11. 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.

  12. 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...

  13. Vacancy-rearrangement theory in the first Magnus approximation

    International Nuclear Information System (INIS)

    Becker, R.L.

    1984-01-01

    In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub α/-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references

  14. 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.

  15. 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

  16. 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)

  17. 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

  18. 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)

  19. 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

  20. 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.

  1. 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

  2. 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.)

  3. 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.

  4. 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...

  5. 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)

  6. 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

  7. 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

  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. 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

  10. 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.

  11. 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.

  12. 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)

  13. 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

  14. 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....

  15. 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.

  16. 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.

  17. 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.

  18. 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...

  19. 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

  20. 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

  1. 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.

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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)

  7. 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.)

  8. 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

  9. 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

  10. 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

  11. 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.

  12. 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

  13. 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.

  14. 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

  15. 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.

  16. 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

  17. 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

  18. 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.

  19. 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.

  20. 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.)

  1. 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.

  2. 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

  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. 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

  6. 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...

  7. 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

  8. 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

  9. 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...

  10. 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.)

  11. 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

  12. 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.

  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. 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

  15. 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

  16. 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

  17. 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.)

  18. 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.

  19. 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)

  20. 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...

  1. 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

  2. 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.

  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. 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

  5. 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...

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. 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...

  11. 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.

  12. 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

  13. 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)

  14. 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; ...

  15. 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)

  16. 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.

  17. 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

  18. 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

  19. 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.

  20. 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.

  1. 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.

  2. 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.)

  3. 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)

  4. 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)

  5. 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

  6. 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…

  7. 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.

  8. 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.

  9. 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...

  10. 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.

  11. 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

  12. 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.

  13. 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

  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. 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

  16. 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

  17. 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

  18. 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.)

  19. 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)

  20. 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.)

  1. 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

  2. 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...

  3. 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)

  4. 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...

  5. 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.

  6. 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.

  7. 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.)

  8. 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

  9. 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.

  10. 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.

  11. 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

  12. Effect of Cu(II), Cd(II) and Zn(II) on Pb(II) biosorption by algae Gelidium-derived materials.

    Science.gov (United States)

    Vilar, Vítor J P; Botelho, Cidália M S; Boaventura, Rui A R

    2008-06-15

    Biosorption of Pb(II), Cu(II), Cd(II) and Zn(II) from binary metal solutions onto the algae Gelidium sesquipedale, an algal industrial waste and a waste-based composite material was investigated at pH 5.3, in a batch system. Binary Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II) solutions have been tested. For the same equilibrium concentrations of both metal ions (1 mmol l(-1)), approximately 66, 85 and 86% of the total uptake capacity of the biosorbents is taken by lead ions in the systems Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II), respectively. Two-metal results were fitted to a discrete and a continuous model, showing the inhibition of the primary metal biosorption by the co-cation. The model parameters suggest that Cd(II) and Zn(II) have the same decreasing effect on the Pb(II) uptake capacity. The uptake of Pb(II) was highly sensitive to the presence of Cu(II). From the discrete model it was possible to obtain the Langmuir affinity constant for Pb(II) biosorption. The presence of the co-cations decreases the apparent affinity of Pb(II). The experimental results were successfully fitted by the continuous model, at different pH values, for each biosorbent. The following sequence for the equilibrium affinity constants was found: Pb>Cu>Cd approximately Zn.

  13. 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)

  14. 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

  15. 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

  16. 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

  17. 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.

  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. 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

  1. 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.

  2. 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...

  3. Quasilinear theory without the random phase approximation

    International Nuclear Information System (INIS)

    Weibel, E.S.; Vaclavik, J.

    1980-08-01

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

  4. 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

  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. 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...

  7. 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...

  8. Resistive theory of bunch lengthening

    International Nuclear Information System (INIS)

    Month, M.; Messerschmid, E.

    1977-01-01

    A new theory of bunch lengthening in electron storage rings is proposed. The equilibrium bunch length is that length which stabilizes the bunch against the onset of ''fast'' resistive instability, caused by the combination of many high frequency resonators such as vacuum flanges. The heat dissipated in these impedance sources follows immediately from the bunch length. It is found that the anomalous bunch length is determined by a scaling parameter g = (hVcos phi/sub s/)/I. Data taken in SPEAR I and II, data in which g extends in value by more than three orders of magnitude, can be fit with an appropriate choice of high frequency, large width coupling impedance. The impedance functions for SPEAR I and II are taken to be the same, a reflection of the fact that the high frequency sources are chamber discontinuities rather than structures connected with the rf systems. A parameter search leads to an impedance characterized by a central frequency approximately 5 GHz, a width (FWHM) approximately 1.8 GHz and a peak impedance approximately 0.2 M OMEGA. The expected and observed higher mode resistance (i.e., heat dissipated) for SPEAR are compared and found to be in agreement. Predictions are given for PEP and PETRA

  9. Gauge theories as string theories: the first results

    International Nuclear Information System (INIS)

    Gorsky, Aleksandr S

    2005-01-01

    The gauge/string theory duality in curved space is discussed mainly using a non-Abelian conformal N = 4 supersymmetric gauge theory and the theory of a closed superstring in the AdS 5 x S 5 metric as an example. It is shown that in the supergravity approximation, string duality yields the characteristics of a strong-coupling gauge theory. For a special shape of the contour, a Wilson loop expression is derived in the classical superstring approximation. The role of the hidden integrability in lower-loop calculations in gauge theory and in different approximations of string theory is discussed. It is demonstrated that in the large quantum-number limit, gauge theory operators can be described in terms of the dual string picture. Examples of metrics providing the dual description of gauge theories with broken conformal symmetry are presented, and formulations of the vacuum structure of such theories in terms of gravity are discussed. (reviews of topical problems)

  10. Theory and experiments in general relativity and other metric theories of gravity

    International Nuclear Information System (INIS)

    Ciufolini, I.

    1984-01-01

    In Chapter I, after an introduction to theories of gravity alternative to general relativity, metric theories, and the post-Newtonian parameterized (PNN) formalism, a new class of metric theories of gravity is defined. As a result the post-Newtonian approximation of the new theories is not described by the PPN formalism. In fact under the weak field and slow motion hypothesis, the post-Newtonian expression of the metric tensor contains an infinite set of new terms and correspondingly an infinite set of new PPN parameters. Chapter II, III, and IV are devoted to new experiments to test general relativity and other metric theories of gravity. In particular, in chapter IV, it is shown that two general relativistics effects, the Lense-Thirring and De Sitter-Fokker precessions of the nodal lines of an Earth artificial satellite are today detectable using high altitude laser ranged artificial satellites such as Lageos. The orbit of this satellite is known with unprecedented accuracy. The author then describes a method of measuring these relativistic precessions using Lageos together with another high altitude laser ranged similar satellite with appropriately chosen orbital parameters

  11. 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.

  12. 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.)

  13. 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.)

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. On the mathematical treatment of the Born-Oppenheimer approximation

    International Nuclear Information System (INIS)

    Jecko, Thierry

    2014-01-01

    Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

  19. On the mathematical treatment of the Born-Oppenheimer approximation

    Energy Technology Data Exchange (ETDEWEB)

    Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

    2014-05-15

    Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

  20. 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

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

    International Nuclear Information System (INIS)

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

    1979-01-01

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

  2. 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

  3. 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.

  4. 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...

  5. 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.

  6. 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.)

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. 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

  12. 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.

  13. 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.

  14. 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.)

  15. Psychometric evaluation of the Overexcitability Questionnaire-Two applying Bayesian Structural Equation Modeling (BSEM and multiple-group BSEM-based alignment with approximate measurement invariance

    Directory of Open Access Journals (Sweden)

    Niki eDe Bondt

    2015-12-01

    Full Text Available The Overexcitability Questionnaire-Two (OEQ-II measures the degree and nature of overexcitability, which assists in determining the developmental potential of an individual according to Dabrowski’s Theory of Positive Disintegration. Previous validation studies using frequentist confirmatory factor analysis, which postulates exact parameter constraints, led to model rejection and a long series of model modifications. Bayesian structural equation modeling (BSEM allows the application of zero-mean, small-variance priors for cross-loadings, residual covariances, and differences in measurement parameters across groups, better reflecting substantive theory and leading to better model fit and less overestimation of factor correlations. Our BSEM analysis with a sample of 516 students in higher education yields positive results regarding the factorial validity of the OEQ-II. Likewise, applying BSEM-based alignment with approximate measurement invariance, the absence of non-invariant factor loadings and intercepts across gender is supportive of the psychometric quality of the OEQ-II. Compared to males, females scored significantly higher on emotional and sensual overexcitability, and significantly lower on psychomotor overexcitability.

  16. Basic conservation laws in the electromagnetic theory of cyclotron radiation: further analysis

    International Nuclear Information System (INIS)

    Lieu, R.; Leahy, D.A.

    1984-01-01

    The conflict of basic conservation laws in cyclotron radiation is considered in more general terms, taking into account relativistic effects of the electron. Also investigated are the effects due to the most important approximation in cyclotron theory, viz the omission of radiation back reaction. The conclusions are (i) the disagreement is of a magnitude considerably larger than any errors introduced by the approximation; (ii) the 'degree of conflict' attains its maximum in relativistic velocities, when the energy loss to radiation can approach the total energy of the electron. (author)

  17. 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.

  18. 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

  19. 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

  20. Sums over geometries and improvements on the mean field approximation

    International Nuclear Information System (INIS)

    Sacksteder, Vincent E. IV

    2007-01-01

    The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels

  1. 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.)

  2. 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.)

  3. Life Origination Hydrate Theory (LOH-Theory) and Mitosis and Replication Hydrate Theory (MRH-Theory): three-dimensional PC validation

    Science.gov (United States)

    Kadyshevich, E. A.; Dzyabchenko, A. V.; Ostrovskii, V. E.

    2014-04-01

    Size compatibility of the CH4-hydrate structure II and multi-component DNA fragments is confirmed by three-dimensional simulation; it is validation of the Life Origination Hydrate Theory (LOH-Theory).

  4. A finite element formulation for perturbation theory calculations

    International Nuclear Information System (INIS)

    Ozgener, B.; Kaluc, S.

    2004-01-01

    Full text: When the introduced change in the configuration of a nuclear system is neutronically not too significant, the use of the perturbation theory approximation ('the perturbation theory method' or PTM) is usually considered as an alternative to the recalculation of the effective multiplication factor (K eff ) of the modified system ('the diffusion theory method' or DTM) for the determination of the ensuing change in reactivity. In the DTM, the change in reactivity due to the introduced change can be calculated by the multigroup diffusion theory by performing two K eff determinations, one for the original and one for the modified system. The accuracy of this method is only limited by the approximations inherent in the multigroup diffusion theory and the numerical method employed for its solution. The error stemming from the numerical approximation can be nearly eliminated by utilizing a fine enough spatial mesh ad an 'exact' solution is nearly possible. Its basic disadvantage relative to the PTM is the necessity of a new K eff calculation for every change in the configuration no matter how small. On the other hand, if we use PTM, with an only one-time calculation of the flux and the adjoint flux of the original system, the change in reactivity due to any kind of perturbation can be approximately calculated using the changes in the cross section data in the perturbation theory reactivity formula. The accuracy of the PTM is restricted by the size and location of the induced change. In this work, our aim is to assess the accuracy of PTM relative to the DTM and determine criteria for the justification of its use. For all required solutions of the normal and adjoint multigroup diffusion equations, we choose the finite element method (FEM) as our numerical method and a 1-D cylindrical geometry model. The underlying theory is implemented in our FORTRAN program PERTURB. The validation of PERTURB is carried out via comparisons with analytical solutions for bare and

  5. 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)

  6. 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

  7. 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.

  8. 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

  9. 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)

  10. 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....

  11. 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).

  12. 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.)

  13. 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.

  14. 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.)

  15. Inclusion of Dispersion Effects in Density Functional Theory

    DEFF Research Database (Denmark)

    Møgelhøj, Andreas

    on fitting to high-level ab initio and experimental results. The fitting scheme, based on Baysian theory, focuses on the three aspects: a) model space, b) datasets, and c) model selection. The model space consists of a flexible expansion of the exchange enhancement factor in the generalized gradient......In this thesis, applications and development will be presented within the field of van der Waals interactions in density functional theory. The thesis is based on the three projects: i) van der Waals interactions effect on the structure of liquid water at ambient conditions, ii) development......-range van der Waals interactions is essential to describe the adsorption/desorption process and commonly used generalized gradient approximation functionals are seen to be incapable of this....

  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. 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

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

    International Nuclear Information System (INIS)

    Chatterjee, P.

    1980-01-01

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

  19. 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.

  20. 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.

  1. 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.)

  2. 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.

  3. 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.

  4. On the validity of the equivalent-photon approximation for virtual photon-photon collisions

    International Nuclear Information System (INIS)

    Carimalo, C.; Kessler, P.; Parisi, J.

    1979-05-01

    For virtual photon-photon collisions in electron storage rings, one derive the equivalent-photon approximation from a helicity treatment, and present it in two forms, involving respectively (i) polarized transverse photons ('transverse-photon approximation') and (ii) unpolarized ones ('Williams-Weizsaecker approximation'). One first postulates the conditions of validity of the approximation on the basis of analytic considerations, and then check them numerically in the case of the process e e → e e μ + μ - . For this check, we consider the completely differentiated cross section as far as approximation (i) is concerned; and in the case of approximation (ii), the cross section differentiated with respect to all variables except the azimuthal angles. The results are given in the form of Tables showing the lower and higher limit of the error involved in the approximation for a large variety of kinematic configurations (i. e., energy losses and scattering angles of both electrons). Those Tables are discussed in detail, and conclusions are drawn as to the applicability of the equivalent-photon approximation to future experiments to be performed with high-energy electron storage rings

  5. Gaussian and 1/N approximations in semiclassical cosmology

    International Nuclear Information System (INIS)

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

    1989-01-01

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

  6. 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.

  7. 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

  8. Importance of the local constraint in slave-boson theories

    International Nuclear Information System (INIS)

    Zhang, L.; Jain, J.K.; Emery, V.J.

    1993-01-01

    Slave bosons are commonly introduced in order to implement an infinite Hubbard U by means of a local constraint. The usual starting point for investigations within this scheme is a mean-field theory in which the constraint is taken to be global. This approximate treatment of the constraint is studied in the context of a two-band Hubbard model, and it is shown that (i) the ground state has a significant number of doubly occupied sites, despite the infinite on-site repulsion in the original model, and (ii) there is an unphysical tendency for pairing. However, it is found that if the local constraint is retained for the insulator at half filling, then mean-field theory gives the correct result that the double occupancy is zero

  9. Analysis of expansion phase experiments with improved approximation schemes

    International Nuclear Information System (INIS)

    Foit, J.J.

    1987-05-01

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

  10. 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...

  11. Energies and bounds from perturbative approximations to the Bloch-Horowitz effective Hamiltonian

    International Nuclear Information System (INIS)

    Darema-Rogers, F.; Vincent, C.M.

    1978-01-01

    Bloch-Horowitz perturbation theory is applied to the calculation of approximate energies and model-space eigenvectors, for the solvable large-matrix Hamiltonian H used by Pittel, Vincent, and Vergados. Two types of upper and lower bounds to the energies are discussed: moment-theory bounds, obtained by applying moment theory to the terms of perturbation theory, and norm bounds, derived from the expectation E-bar and variance sigma 2 of H with respect to an eigenvector approximated by nth order perturbation theory (n < or = 6). It is shown that lower bounds cannot be constructed unless some fourth-order quantity is known. The upper bounds are generally stricter than the lower bounds. All of the bounds apply even when back-door intruder states cause perturbation theory to diverge; but they lose their rigor and become ''quasibounds'' when there are physical intruders. The moment-theory and norm lower quasibounds always require estimation of a parameter. For the solvable Hamiltonians, it is shown that this can be done quite reliably, and that the resulting quasibounds are tight enough to have some practical utility. The energy-independent effective interaction V is constructed and its errors are displayed and discussed. Finally, a certain [1/2] pseudo-Pade approximant is empirically shown to give energies with a mean absolute error of less than 0.3 MeV in all cases

  12. Studies in quantum field theory

    International Nuclear Information System (INIS)

    Bender, C.M.; Mandula, J.E.; Shrauner, J.E.

    1982-01-01

    Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD

  13. 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

  14. 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)

  15. 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

  16. 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.

  17. 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.

  18. Kullback-Leibler divergence and the Pareto-Exponential approximation.

    Science.gov (United States)

    Weinberg, G V

    2016-01-01

    Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.

  19. An overview on polynomial approximation of NP-hard problems

    Directory of Open Access Journals (Sweden)

    Paschos Vangelis Th.

    2009-01-01

    Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

  20. 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

  1. 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

  2. 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

  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. Approximate Dynamic Programming Based on High Dimensional Model Representation

    Czech Academy of Sciences Publication Activity Database

    Pištěk, Miroslav

    2013-01-01

    Roč. 49, č. 5 (2013), s. 720-737 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP102/11/0437 Institutional support: RVO:67985556 Keywords : approximate dynamic programming * Bellman equation * approximate HDMR minimization * trust region problem Subject RIV: BC - Control Systems Theory Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/pistek-0399560.pdf

  5. 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.

  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. 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.)

  8. The complex variable boundary element method: Applications in determining approximative boundaries

    Science.gov (United States)

    Hromadka, T.V.

    1984-01-01

    The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

  9. 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.

  10. Determination of the spiral Galaxy structure parameters based on neutral hydrogen radiowave radiation in 21 cm line. 2. Nonlinear theory. 30 deg <= |l| <= 60 deg

    International Nuclear Information System (INIS)

    Berman, V.G.; Mishurov, Yu.N.

    1980-01-01

    Gas flow and its density distribution in the Galaxy spiral arm gravitational potential is calculated by means of the nonlinear theory. Line profile of H I emission in 21 cm based on the Galaxy spiral structure models proposed by Lin and Marochnik are constructed for the galactic coordinates 30 deg < or approximately |l| < or approximately 60 deg. It is shown that the conclusion about the possibility of agreement of the Marochnik model with observations made by means of the linear theory is confirmed in the nonlinear theory. In the Marochnik model distributions with R H II regions, CO-clouds, γ-radiation, supernova remnants and so on may also be understood connecting them with variation of gas compression in galactic shock with H radius

  11. 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

  12. Variational transition state theory

    International Nuclear Information System (INIS)

    Truhlar, D.G.

    1986-01-01

    This project is concerned with the development and applications of generalized transition state theory and multidimensional tunneling approximations to chemical reaction rates. They have developed and implemented several practical versions of variational transition state theory (VTST), namely canonical variational theory (CVT), improved canonical variational theory (ICVT), and microcanonical variational theory (μVT). They have also developed and implemented several accurate multidimensional semiclassical tunneling approximations, the most accurate of which are the small-curvature semiclassical adiabatic (SCSA), large-curvature version-3 (LC3), and least-action (LA) approximations. They have applied the methods to thermal rate constants, using transmission coefficients based on ground-state tunneling, and they have also presented and applied adiabatic and diabatic extensions to calculated rate constants for vibrationally excited reactants. Their general goal is to develop accurate methods for calculating chemical reaction rate constants that remain practical even for reasonably complicated molecules. The approximations mentioned above yield rate constants for systems whose potential energy surface is known or assumed. Thus a second, equally important aspect of their work is the determination or modeling, semi-empirically and/or from electronic structure calculations, of potential energy surfaces

  13. 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: ...

  14. A self consistent study of the phase transition in the scalar electroweak theory at finite temperature

    International Nuclear Information System (INIS)

    Kerres, U.; Mack, G.; Palma, G.

    1994-12-01

    We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two-step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations. (orig.)

  15. A self consistent study of the phase transition in the scalar electroweak theory at finite temperature

    International Nuclear Information System (INIS)

    Kerres, U.

    1995-01-01

    We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two-step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations. ((orig.))

  16. 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

  17. An evaluation of multigroup flux predictions in the EBR-II core

    International Nuclear Information System (INIS)

    Hill, R.N.; Fanning, T.H.; Finck, P.J.

    1991-01-01

    The unique physics characteristics of EBR-II which are difficult to model with conventional neutronic methodologies are identified; the high neutron leakage fraction and importance of neutron reflection cause errors when conventional calculational approximations are utilized. In this paper, various conventional and higher-order group constant evaluations and flux computation methods are compared for a simplified R-Z model of the EBR-II system. Although conventional methods do provide adequate predictions of the flux in the core region, significant mispredictions are observed in the reflector and radial blanket regions. Calculational comparisons indicate that a fine energy group structure is required for accurate predictions of the eigenvalue and flux distribution; greater detail is needed in the iron resonance scattering treatment. Calculational comparisons also indicate that transport theory with detailed anisotropic scattering treatment is required

  18. An evaluation of multigroup flux predictions in the EBR-II core

    Energy Technology Data Exchange (ETDEWEB)

    Hill, R.N.; Fanning, T.H.; Finck, P.J.

    1991-12-31

    The unique physics characteristics of EBR-II which are difficult to model with conventional neutronic methodologies are identified; the high neutron leakage fraction and importance of neutron reflection cause errors when conventional calculational approximations are utilized. In this paper, various conventional and higher-order group constant evaluations and flux computation methods are compared for a simplified R-Z model of the EBR-II system. Although conventional methods do provide adequate predictions of the flux in the core region, significant mispredictions are observed in the reflector and radial blanket regions. Calculational comparisons indicate that a fine energy group structure is required for accurate predictions of the eigenvalue and flux distribution; greater detail is needed in the iron resonance scattering treatment. Calculational comparisons also indicate that transport theory with detailed anisotropic scattering treatment is required.

  19. An evaluation of multigroup flux predictions in the EBR-II core

    Energy Technology Data Exchange (ETDEWEB)

    Hill, R.N.; Fanning, T.H.; Finck, P.J.

    1991-01-01

    The unique physics characteristics of EBR-II which are difficult to model with conventional neutronic methodologies are identified; the high neutron leakage fraction and importance of neutron reflection cause errors when conventional calculational approximations are utilized. In this paper, various conventional and higher-order group constant evaluations and flux computation methods are compared for a simplified R-Z model of the EBR-II system. Although conventional methods do provide adequate predictions of the flux in the core region, significant mispredictions are observed in the reflector and radial blanket regions. Calculational comparisons indicate that a fine energy group structure is required for accurate predictions of the eigenvalue and flux distribution; greater detail is needed in the iron resonance scattering treatment. Calculational comparisons also indicate that transport theory with detailed anisotropic scattering treatment is required.

  20. Approximate Waveforms for Extreme-Mass-Ratio Inspirals: The Chimera Scheme

    International Nuclear Information System (INIS)

    Sopuerta, Carlos F; Yunes, Nicolás

    2012-01-01

    We describe a new kludge scheme to model the dynamics of generic extreme-mass-ratio inspirals (EMRIs; stellar compact objects spiraling into a spinning supermassive black hole) and their gravitational-wave emission. The Chimera scheme is a hybrid method that combines tools from different approximation techniques in General Relativity: (i) A multipolar, post-Minkowskian expansion for the far-zone metric perturbation (the gravitational waveforms) and for the local prescription of the self-force; (ii) a post-Newtonian expansion for the computation of the multipole moments in terms of the trajectories; and (iii) a BH perturbation theory expansion when treating the trajectories as a sequence of self-adjusting Kerr geodesies. The EMRI trajectory is made out of Kerr geodesic fragments joined via the method of osculating elements as dictated by the multipolar post-Minkowskian radiation-reaction prescription. We implemented the proper coordinate mapping between Boyer-Lindquist coordinates, associated with the Kerr geodesies, and harmonic coordinates, associated with the multipolar post-Minkowskian decomposition. The Chimera scheme is thus a combination of approximations that can be used to model generic inspirals of systems with extreme to intermediate mass ratios, and hence, it can provide valuable information for future space-based gravitational-wave observatories, like LISA, and even for advanced ground detectors. The local character in time of our multipolar post-Minkowskian self-force makes this scheme amenable to study the possible appearance of transient resonances in generic inspirals.

  1. approximate controllability of a non-autonomous differential equation

    Indian Academy of Sciences (India)

    53

    for a non-autonomous functional differential equation using the theory of linear ... approximate controllability of various functional differential equations in abstract ...... the operator A(t) and into the requirement that x(t) ∈ D(A) for all t ≥ 0.

  2. Jacob's ladder of approximations to paraxial dynamic electron scattering

    OpenAIRE

    Lubk, A.; Rusz, Jan

    2015-01-01

    Dynamical scattering theory describes the dominant scattering process of beam electrons at targets in the transmission electron microscope (TEM). Hence, practically every quantitative TEM study has to consider its ramifications, typically by some approximate modeling. Here, we elaborate on a hierarchy within the various approximations focusing on the two principal approaches used in practice, Bloch wave and multislice. We reveal characteristic differences in the capability of these methods to...

  3. Neutrons moderation theory; Theorie du ralentissement des neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Vigier, J P

    1949-07-01

    This report gives a summarized presentation of the theory of fast neutrons diffusion and moderation in a given environment as elaborated by M. Langevin, E. Fermi, R. Marshak and others. This statistical theory is based on three assumptions: there is no inelastic diffusion, the elastic diffusion has a spherical symmetry with respect to the center of gravity of the neutron-nucleus system (s-scattering), and the effects of chemical bonds and thermal agitation of nuclei are neglected. The first chapter analyzes the Boltzmann equation of moderation, its first approximate solution (age-velocity equation) and its domain of validity, the extension of the age-velocity theory (general solution) and the boundary conditions, the upper order approximation (spherical harmonics method and Laplace transformation), the asymptotic solutions, and the theory of spatial momenta. The second chapter analyzes the energy distribution of delayed neutrons (stationary and non-stationary cases). (J.S.)

  4. From Mie to Fresnel through effective medium approximation with multipole contributions

    International Nuclear Information System (INIS)

    Malasi, Abhinav; Kalyanaraman, Ramki; Garcia, Hernando

    2014-01-01

    The Mie theory gives the exact solution to scattering from spherical particles while the Fresnel theory provides the solution to optical behavior of multilayer thin film structures. Often, the bridge between the two theories to explain the behavior of materials such as nanoparticles in a host dielectric matrix, is done by effective medium approximation (EMA) models which exclusively rely on the dipolar response of the scattering objects. Here, we present a way to capture multipole effects using EMA. The effective complex dielectric function of the composite is derived using the Clausius–Mossotti relation and the multipole coefficients of the approximate Mie theory. The optical density (OD) of the dielectric slab is then calculated using the Fresnel approach. We have applied the resulting equation to predict the particle size dependent dipole and quadrupole behavior for spherical Ag nanoparticles embedded in glass matrix. This dielectric function contains the relevant properties of EMA and at the same time predicts the multipole contributions present in the single particle Mie model. (papers)

  5. 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...

  6. 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

  7. 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.

  8. 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

  9. Approximately dual frames in Hilbert spaces and applications to Gabor frames

    OpenAIRE

    Christensen, Ole; Laugesen, Richard S.

    2011-01-01

    Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in...

  10. Controllability distributions and systems approximations: a geometric approach

    NARCIS (Netherlands)

    Ruiz, A.C.; Nijmeijer, Henk

    1992-01-01

    Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions

  11. Inference with minimal Gibbs free energy in information field theory

    International Nuclear Information System (INIS)

    Ensslin, Torsten A.; Weig, Cornelius

    2010-01-01

    Non-linear and non-Gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the Gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from Poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a Gaussian signal with unknown spectrum, and (iii) inference of a Poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how Gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-Gaussian posterior.

  12. Beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

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

  13. 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.

  14. 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

  15. 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)

  16. 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 ...

  17. Effective Summation and Interpolation of Series by Self-Similar Root Approximants

    Directory of Open Access Journals (Sweden)

    Simon Gluzman

    2015-06-01

    Full Text Available We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined.

  18. 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.

  19. Lagrangians for plasmas in drift-fluid approximation

    International Nuclear Information System (INIS)

    Pfirsch, D.; Correa-Restrepo, D.

    1996-10-01

    For drift waves and related instabilities conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multi-fluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee all the conservation laws to hold. (orig.)

  20. 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.)

  1. Perturbation methods and closure approximations in nonlinear systems

    International Nuclear Information System (INIS)

    Dubin, D.H.E.

    1984-01-01

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

  2. 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.

  3. Large N field theories, string theory and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Maldacena, J [Lyman Laboratory of Physics, Harvard University, Cambridge (United States)

    2002-05-15

    We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/ M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions. These lecture notes are based on the Review written by O. Aharony, S. Gubser, J. Maldacena, H. Ooguri and Y. Oz. (author)

  4. Balancing Exchange Mixing in Density-Functional Approximations for Iron Porphyrin.

    Science.gov (United States)

    Berryman, Victoria E J; Boyd, Russell J; Johnson, Erin R

    2015-07-14

    Predicting the correct ground-state multiplicity for iron(II) porphyrin, a high-spin quintet, remains a significant challenge for electronic-structure methods, including commonly employed density functionals. An even greater challenge for these methods is correctly predicting favorable binding of O2 to iron(II) porphyrin, due to the open-shell singlet character of the adduct. In this work, the performance of a modest set of contemporary density-functional approximations is assessed and the results interpreted using Bader delocalization indices. It is found that inclusion of greater proportions of Hartree-Fock exchange, in hybrid or range-separated hybrid functionals, has opposing effects; it improves the ability of the functional to identify the ground state but is detrimental to predicting favorable dioxygen binding. Because of the uncomplementary nature of these properties, accurate prediction of both the relative spin-state energies and the O2 binding enthalpy eludes conventional density-functional approximations.

  5. Yosida approximations of stochastic differential equations in infinite dimensions and applications

    CERN Document Server

    Govindan, T E

    2016-01-01

    This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussi...

  6. 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.

  7. 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

  8. 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.

  9. 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...

  10. Pade approximants for the Saxon-Woods potential

    International Nuclear Information System (INIS)

    Niculescu, V.I.R.; Catana, D.

    1995-01-01

    In the present work central Saxon-Woods (SW) potential and a uniform sphere Coulomb potential for protons are replaced with a Pade approximants. In this way expressions of the matrix elements of this potential form can be evaluated by the theory of complex functions. The methods assures satisfactory precision in a shorter computational time. (M.I.C) 1 fig., 2 tabs., 5 refs

  11. Does general relativity theory possess the classical newtonian limit

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.

    1980-01-01

    A detailed comparison of newtonian approximation of the Einstein theory and the Newton theory of gravity is made. A difference of principle between these two theories is clarified at the stage of obtaining integrals of motion. Exact eqautions of motion and Einstein equations shows the existence only zero integrals of motion as well as in the newtonian approximation. A conclusion is that GRT has no classical newtonian limit, since the integrals of motion in the Newton theory of gravity and in the newtonian approximation of the Einstein theory do not coincide [ru

  12. The Zeldovich approximation and wide-angle redshift-space distortions

    Science.gov (United States)

    Castorina, Emanuele; White, Martin

    2018-06-01

    The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum . In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

  13. Theory of deep inelastic neutron scattering: Hard-core perturbation theory

    International Nuclear Information System (INIS)

    Silver, R.N.

    1988-01-01

    Details are presented of a new many-body theory for deep inelastic neutron scattering (DINS) experiments to measure momentum distributions in quantum fluids and solids. The high-momentum and energy-transfer scattering law in helium is shown to be a convolution of the impulse approximation with a final-state broadening function which depends on the scattering phase shifts and the radial distribution function. The predicted broadening satisfies approximate Y scaling, is neither Lorentzian nor Gaussian, and obeys the f, ω 2 , and ω 3 sum rules. The derivation uses a combination of Liouville perturbation theory, projection superoperators, and semiclassical methods which I term ''hard-core perturbation theory.'' A review is presented of the predictions of prior theories for DINS experiments in relation to the present work. A subsequent paper will present massive numerical predictions and a discussion of DINS experiments on superfluid 4 He

  14. Approximate analysis of high-rise frames with flexible connections

    NARCIS (Netherlands)

    Hoenderkamp, J.C.D.; Snijder, H.H.

    2000-01-01

    An approximate hand method for estimating horizontal deflections in high-rise steel frames with flexible beam–column connections subjected to horizontal loading is presented. The method is developed from the continuous medium theory for coupled walls which is expressed in non-dimensional structural

  15. 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.

  16. Understanding operational risk capital approximations: First and second orders

    Directory of Open Access Journals (Sweden)

    Gareth W. Peters

    2013-07-01

    Full Text Available We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA. Our emphasis is to focuss on the important loss processes with regard to those that contribute most to capital, the so called “high consequence, low frequency" loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard; Expected Shortfall (ES and the Spectral Risk Measure. These then form the capital approximations. We then provide a few example case studies to illustrate the accuracy of these asymptotic captial approximations, the rate of the convergence of the assymptotic result as a function of the LDA frequency and severity model parameters, the sensitivity

  17. 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.

  18. Clinical and radiographic assessment of approximal carious lesions

    International Nuclear Information System (INIS)

    Espelid, I.; Tveit, A.B.

    1986-01-01

    The aim of the study was to compare the radiographic diagnosis of approximal carious lesions with visual observations of the approximal surfaces and within drilled Class II cavities (made into the pulp). Sound (n=28) and carious (n=123) approximal surfaces of extracted premolars and molars were radiographed. The radiographs were studied by seven observers to diagnose caries. Lesions without cavitation were most often classified as sound (61.3%). When lesions had cavities, the rate of detection increased to 89.1%. Sound surfaces were erroneously classified as carious in 15.7% of cases. Statistically, about 6 our of every 10 qualitative assessments of lesion depth on the basis of radiographs, correctly recorded lesions as being in enamel or extending into dentin. The interexaminer variation in radiographic caries diagnosis were mostly due to difference in diagnostic criteria, whereas differences in diagnostic capability were less important

  19. Perturbation theory and importance functions in integral transport formulations

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory

  20. A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

    Directory of Open Access Journals (Sweden)

    V. V. Zozulya

    2013-01-01

    Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

  1. A critical review on some aspects of the theory of fission

    International Nuclear Information System (INIS)

    Pauli, H.C.

    1981-01-01

    The lecture notes display briefly some of the facets which eventually will be part of a theory for the fission process. They cover some important aspects of our present understanding in a qualitative fashion and complement the existing review articles rather than replacing them. The notes include sections on (I) The Bohr-Wheeler Fission of a Drop, (II) The Strutinsky-Swiatecki Quantum Droplet, (III) The Question of Inertias of a Fluid in Motion, (IV) Some Selected Aspects of the Distributions of Mass and Kinetic Energy, and (V) Possible Relations Between the Phenomenological Models and Self-Consistent Field Approximations. (author)

  2. 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.)

  3. Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

    Science.gov (United States)

    Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

    2017-12-07

    We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

  4. Treatment of divergent expansions in scattering theory

    International Nuclear Information System (INIS)

    Gersten, A.; Malin, S.

    1978-01-01

    One of the biggest obstacles in applying quantum field theory to realistic scattering problems are the divergencies of pertubation expansions for large coupling constants and the divergencies of partial wave expansions for massless particles exchanges. There exist, however, methods of summation of the divergent expansions which can lead to significant application in physics. In this paper we treat the problem of summing such expansions using three methods: (i) a generalization of the Pade approximation to the multivariable case. The suggested definition is unique and preserves unitarity. (ii) The summation of divergent partial waves for arbitrary spins. (iii) A successful application of a series inversion to the 3 P 1 nucleon-nucleon phase shift up to 200 MeV. (orig./WL) [de

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

    Science.gov (United States)

    Kim, SungKun; Lee, Hunpyo

    2017-06-01

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

  6. Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO(4).

    Science.gov (United States)

    Asaumi, K

    1993-10-20

    A simplified approximate expression for the effective nonlinear coefficient of type-II second-harmonicgeneration in KTiOPO(4) was obtained by observing that the difference between the refractive indices n(x) and n(y) is 1 order of magnitude smaller than the difference between n(z) and n(y) (or n(x)). The agreement of this approximate equation with the true definition is good, with a maximum discrepancy of 4%.

  7. 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

  8. New origin for approximate symmetries from distant breaking in extra dimensions

    International Nuclear Information System (INIS)

    Arkani-Hamed, Nima

    1998-01-01

    The recently proposed theories with TeV-scale quantum gravity do not have the usual ultraviolet desert between approximately 10 3 -10 19 GeV where effective field theory ideas apply. Consequently, the success of the desert in explaining approximate symmetries is lost, and theories of flavor, neutrino masses, proton longevity or supersymmetry breaking, lose their usual habitat. In this paper we show that these ideas can find a new home in an infrared desert: the large space in the extra dimensions. The main idea is that symmetries are primordially exact on our brane, but are broken at O(1) on distant branes. This breaking is communicated to us in a distance-suppressed way by bulk messengers. We illustrate these ideas in a number of settings: (1) We construct theories for the fermion mass hierarchy which avoid problems with large flavor-changing neutral currents. (2) We re-iterate that proton stability can arise if baryon number is gauged in the bulk. (3) We study limits on light gauge fields and scalars in the bulk coming from rare decays, astrophysics and cosmology. (4) We remark that the same ideas can be used to explain small neutrino masses, as well as hierarchical supersymmetry breaking. (5) We construct a theory with bulk technicolor, avoiding the difficulties with extended technicolor. There are also a number of interesting experimental signals of these ideas: (1) Attractive or repulsive, isotope dependent sub-millimeter forces approximately 10 6 times gravitational strength, from the exchange of light bulk particles. (2) Novel Higgs decays to light generation fermions plus bulk scalars. (3) Collider production of bulk vector and scalar fields, leading to γ or jet+ missing energy signals as in the case of bulk graviton production, with comparable or larger rates

  9. Dynamic hysteresis of a uniaxial superparamagnet: Semi-adiabatic approximation

    International Nuclear Information System (INIS)

    Poperechny, I.S.; Raikher, Yu.L.; Stepanov, V.I.

    2014-01-01

    The semi-adiabatic theory of magnetic response of a uniaxial single-domain ferromagnetic particle is presented. The approach is developed in the context of the kinetic theory and allows for any orientation of the external field. Within this approximation, the dynamic magnetic hysteresis loops in an ac field are calculated. It is demonstrated that they very closely resemble those obtained by the full kinetic theory. The behavior of the effective coercive force is analyzed in detail, and for it a simple formula is proposed. This relation accounts not only for the temperature behavior of the coercive force, as the previous ones do, but also yields the dependence on the frequency and amplitude of the applied field

  10. Singularity Theory and its Applications

    CERN Document Server

    Stewart, Ian; Mond, David; Montaldi, James

    1991-01-01

    A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

  11. Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

    International Nuclear Information System (INIS)

    Rizzato, F.B.

    1985-01-01

    Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)

  12. Effective medium super-cell approximation for interacting disordered systems: an alternative real-space derivation of generalized dynamical cluster approximation

    International Nuclear Information System (INIS)

    Moradian, Rostam

    2006-01-01

    We develop a generalized real-space effective medium super-cell approximation (EMSCA) method to treat the electronic states of interacting disordered systems. This method is general and allows randomness both in the on-site energies and in the hopping integrals. For a non-interacting disordered system, in the special case of randomness in the on-site energies, this method is equivalent to the non-local coherent potential approximation (NLCPA) derived previously. Also, for an interacting system the EMSCA method leads to the real-space derivation of the generalized dynamical cluster approximation (DCA) for a general lattice structure. We found that the original DCA and the NLCPA are two simple cases of this technique, so the EMSCA is equivalent to the generalized DCA where there is included interaction and randomness in the on-site energies and in the hopping integrals. All of the equations of this formalism are derived by using the effective medium theory in real space

  13. A tale of three theories: Feyerabend and Popper on progress and the aim of science.

    Science.gov (United States)

    Tambolo, Luca

    2015-06-01

    In this paper, three theories of progress and the aim of science are discussed: (i) the theory of progress as increasing explanatory power, advocated by Popper in The logic of scientific discovery (1935/1959); (ii) the theory of progress as approximation to the truth, introduced by Popper in Conjectures and refutations (1963); (iii) the theory of progress as a steady increase of competing alternatives, which Feyerabend put forward in the essay "Reply to criticism. Comments on Smart, Sellars and Putnam" (1965) and defended as late as the last edition of Against method (1993). It is argued that, contrary to what Feyerabend scholars have predominantly assumed, Feyerabend's changing attitude towards falsificationism-which he often advocated at the beginning of his career, and vociferously attacked in the 1970s and 1980s-must be explained by taking into account not only Feyerabend's very peculiar view of the aim of science, but also Popper's changing account of progress. Copyright © 2015 Elsevier Ltd. All rights reserved.

  14. Kinetic theory of spectral line broadening in plasmas

    International Nuclear Information System (INIS)

    Hussey, T.W.

    1974-01-01

    A formal kinetic theory is used to cast the line shape function into a form that, while similar to the ''unified'' theories of Smith, Cooper, and Vidal and of Voslamber, does not introduce some of the usual approximations. The resulting line shape function explicitly includes the initial correlations between the atom and perturbers, and also demonstrates the natural separation of plasma mean field and collisional effects. The classical path and no-quenching approximations are discussed and ultimately employed; however, they are not required in the formal development. The weak coupling limit is considered as a systematic approximation to the formal results. It is shown tha different ways of applying this limit lead to different expressions for the memory operator, some of which correspond to existing theories. One approximation is considered which systematically incorporates the effects of electron correlations within the framework of a unified theory. In addition, a practical approximation suitable for a strongly interacting plasma is discussed

  15. 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

  16. Approximate method for treating dispersion in one-way quantum channels

    International Nuclear Information System (INIS)

    Stace, T. M.; Wiseman, H. M.

    2006-01-01

    Coupling the output of a source quantum system into a target quantum system is easily treated by cascaded systems theory if the intervening quantum channel is dispersionless. However, dispersion may be important in some transfer protocols, especially in solid-state systems. In this paper we show how to generalize cascaded systems theory to treat such dispersion, provided it is not too strong. We show that the technique also works for fermionic systems with a low flux, and can be extended to treat fermionic systems with large flux. To test our theory, we calculate the effect of dispersion on the fidelity of a simple protocol of quantum state transfer. We find good agreement with an approximate analytical theory that had been previously developed for this example

  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. 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.

  19. On the convergence of multigroup discrete-ordinates approximations

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  20. Atomic structure calculations using the relativistic random phase approximation

    International Nuclear Information System (INIS)

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

    1981-01-01

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

  1. Hamiltonian lattice field theory: Computer calculations using variational methods

    International Nuclear Information System (INIS)

    Zako, R.L.

    1991-01-01

    I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems

  2. Hamiltonian lattice field theory: Computer calculations using variational methods

    International Nuclear Information System (INIS)

    Zako, R.L.

    1991-01-01

    A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems

  3. Parallel magnetic resonance imaging as approximation in a reproducing kernel Hilbert space

    International Nuclear Information System (INIS)

    Athalye, Vivek; Lustig, Michael; Martin Uecker

    2015-01-01

    In magnetic resonance imaging data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. To understand and design k-space sampling patterns, a theoretical framework is needed to analyze how well arbitrary sampling patterns reconstruct unsampled k-space using receive coil information. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a reproducing kernel Hilbert space with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional image-domain g-factor noise analysis to both noise amplification and approximation errors in k-space. This is demonstrated with numerical examples. (paper)

  4. Fuzzy Approximate Model for Distributed Thermal Solar Collectors Control

    KAUST Repository

    Elmetennani, Shahrazed

    2014-07-01

    This paper deals with the problem of controlling concentrated solar collectors where the objective consists of making the outlet temperature of the collector tracking a desired reference. The performance of the novel approximate model based on fuzzy theory, which has been introduced by the authors in [1], is evaluated comparing to other methods in the literature. The proposed approximation is a low order state representation derived from the physical distributed model. It reproduces the temperature transfer dynamics through the collectors accurately and allows the simplification of the control design. Simulation results show interesting performance of the proposed controller.

  5. Improvement of Tone's method with two-term rational approximation

    International Nuclear Information System (INIS)

    Yamamoto, Akio; Endo, Tomohiro; Chiba, Go

    2011-01-01

    An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method. (author)

  6. 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.

  7. Quantum field theory of point particles and strings

    CERN Document Server

    Hatfield, Brian

    1992-01-01

    The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string.

  8. Finite-rank potential that reproduces the Pade approximant

    International Nuclear Information System (INIS)

    Tani, S.

    1979-01-01

    If a scattering potential is of a finite rank, say N, the exact solution of the problem can be obtained from the Born series, if the potential strength is within the radius of convergence; the exact solution can be obtained from the analytical continuation of the formal Born series outside the radius of convergence. Beyond the first 2N terms of the Born series, an individual term of the Born series depends on the first 2N terms, and the [N/N] Pade approximant and the exact solution agree with each other. The above-mentioned features of a finite-rank problem are relevant to scattering theory in general, because most scattering problems may be handled as an extension of the rank-N problem, in which the rank N tends to infinity. The foregoing aspects of scattering theory will be studied in depth in the present paper, and in so doing we proceed in the opposite direction. Namely, given a potential, we calculate the first 2N terms of the Born series for the K matrix and the first N terms of the Born series for the wave function. Using these data, a special rank-N potential is constructed in such a way that it reproduces the [N/N] Pade approximant of the K matrix of the original scattering problem. One great advantage of obtaining such a rank-N potential is that the wave function of the system may be approximated in the same spirit as done for the K matrix; hence, we can introduce a new approximation method for dealing with an off-shell T matrix. A part of the mathematical work is incomplete, but the physical aspects are thoroughly discussed

  9. Justification of Shallow-Water Theory

    Science.gov (United States)

    Ostapenko, V. V.

    2018-01-01

    The basic conservation laws of shallow-water theory are derived from multidimensional mass and momentum integral conservation laws describing the plane-parallel flow of an ideal incompressible fluid above the horizontal bottom. This conclusion is based on the concept of hydrostatic approximation, which generalizes the concept of long-wavelength approximation and is used for justifying the applicability of the shallow-water theory in the simulation of wave flows of fluid with hydraulic bores.

  10. 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

  11. Canonical perturbation theory in linearized general relativity theory

    International Nuclear Information System (INIS)

    Gonzales, R.; Pavlenko, Yu.G.

    1986-01-01

    Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field

  12. 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

  13. [Studies in quantum field theory

    International Nuclear Information System (INIS)

    1990-01-01

    During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity

  14. 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)

  15. 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

  16. Higher order saddlepoint approximations in the Vasicek portfolio credit loss model

    NARCIS (Netherlands)

    Huang, X.; Oosterlee, C.W.; van der Weide, J.A.M.

    2006-01-01

    This paper utilizes the saddlepoint approximation as an efficient tool to estimate the portfolio credit loss distribution in the Vasicek model. Value at Risk (VaR), the risk measure chosen in the Basel II Accord for the evaluation of capital requirement, can then be found by inverting the loss

  17. 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

  18. 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.

  19. Pairing renormalization and regularization within the local density approximation

    International Nuclear Information System (INIS)

    Borycki, P.J.; Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M.V.

    2006-01-01

    We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications

  20. An extreme Fe II emitter the narrow line quasar PHL 1092

    CERN Document Server

    Bergeron, J

    1980-01-01

    A search for Fe II emission in a sample of radio-quiet quasars has revealed the outstanding properties of PHL 1092. Intense Fe II lines dominate the entire spectrum, and the Fe II UV multiplets are nearly as strong as the optical ones. In contrast the extreme weakness of the Balmer and Mg II lines is striking. For the first time, Fe I lines are identified in an extra-galactic object. The lines are narrow, with a FWHM of 1300 km s/sup -1/. The presence of Fe II UV lines and Fe I lines from the ground state requires moderate column densities. However Fe/sup 0/ can exist only in a region completely shielded from the UV continuum. The weakness of Mg II and H beta relative to Fe II lines is best explained by their thermalization. The emitting region is of high electron density n/sub e/ approximately=10/sup 12/ cm/sup -3/, low temperature T approximately=10000K, and has an optical depth in the Fe II UV lines tau /sub UV/ approximately=10/sup 3/-10/sup 4/. It is speculated that for higher densities all the lines wou...

  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. Best approximation of the Dunkl Multiplier Operators Tk,ℓ,m

    Directory of Open Access Journals (Sweden)

    Fethi Soltani

    2015-03-01

    Full Text Available We study some class of Dunkl multiplier operators Tk,ℓ,m; and we give for them an application of the theory of reproducing kernels to the Tikhonov regularization,which gives the best approximation of the operators Tk,ℓ,m on a Hilbert spaces Hskℓ.

  3. 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.

  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. Variational method for field theories on the lattice and the spectrum of the phi4 theory in 1+1 dimensions

    International Nuclear Information System (INIS)

    Abad, J.; Esteve, J.G.; Pacheco, A.F.

    1985-01-01

    An approximation technique to construct the low-lying energy eigenstates of any bosonic field theory on the lattice is proposed. It is based on the SLAC blocking method, after performing a finite-spin approximation to the individual degrees of freedom of the problem. General expressions for any polynomial self-interacting theory are given. Numerical results for phi 2 and phi 4 theories in 1+1 dimensions are offered; they exhibit a fast convergence rate. The complete low-lying energy spectrum of the phi 4 theory in 1+1 dimensions is calculated

  6. Visualizing, Approximating, and Understanding Black-Hole Binaries

    Science.gov (United States)

    Nichols, David A.

    Numerical-relativity simulations of black-hole binaries and advancements in gravitational-wave detectors now make it possible to learn more about the collisions of compact astrophysical bodies. To be able to infer more about the dynamical behavior of these objects requires a fuller analysis of the connection between the dynamics of pairs of black holes and their emitted gravitational waves. The chapters of this thesis describe three approaches to learn more about the relationship between the dynamics of black-hole binaries and their gravitational waves: modeling momentum flow in binaries with the Landau-Lifshitz formalism, approximating binary dynamics near the time of merger with post-Newtonian and black-hole-perturbation theories, and visualizing spacetime curvature with tidal tendexes and frame-drag vortexes. In Chapters 2--4, my collaborators and I present a method to quantify the flow of momentum in black-hole binaries using the Landau-Lifshitz formalism. Chapter 2 reviews an intuitive version of the formalism in the first-post-Newtonian approximation that bears a strong resemblance to Maxwell's theory of electromagnetism. Chapter 3 applies this approximation to relate the simultaneous bobbing motion of rotating black holes in the superkick configuration---equal-mass black holes with their spins anti-aligned and in the orbital plane---to the flow of momentum in the spacetime, prior to the black holes' merger. Chapter 4 then uses the Landau-Lifshitz formalism to explain the dynamics of a head-on merger of spinning black holes, whose spins are anti-aligned and transverse to the infalling motion. Before they merge, the black holes move with a large, transverse, velocity, which we can explain using the post-Newtonian approximation; as the holes merge and form a single black hole, we can use the Landau-Lifshitz formalism without any approximations to connect the slowing of the final black hole to its absorbing momentum density during the merger. In Chapters 5

  7. Mean-field theory of nuclear structure and dynamics

    International Nuclear Information System (INIS)

    Negele, J.W.

    1982-01-01

    The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission

  8. An effective algorithm for approximating adaptive behavior in seasonal environments

    DEFF Research Database (Denmark)

    Sainmont, Julie; Andersen, Ken Haste; Thygesen, Uffe Høgsbro

    2015-01-01

    Behavior affects most aspects of ecological processes and rates, and yet modeling frameworks which efficiently predict and incorporate behavioral responses into ecosystem models remain elusive. Behavioral algorithms based on life-time optimization, adaptive dynamics or game theory are unsuited...... for large global models because of their high computational demand. We compare an easily integrated, computationally efficient behavioral algorithm known as Gilliam's rule against the solution from a life-history optimization. The approximation takes into account only the current conditions to optimize...... behavior; the so-called "myopic approximation", "short sighted", or "static optimization". We explore the performance of the myopic approximation with diel vertical migration (DVM) as an example of a daily routine, a behavior with seasonal dependence that trades off predation risk with foraging...

  9. Gravitational effects in field gravitation theory

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Vlasov, A.A.

    1979-01-01

    The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows one to describe the whole set of experimental facts. The comparison of post-Newtonian parameters in FGT with those in the Einstein's theory makes it clear that these two; theories are undistinguishable from the viewpoint of any experiments, realized with post-Newtonian accuracy. Gravitational field of an island type source with spherically symmetrical distribution of matter and unstationary homogeneous model of Universe, which allows to describe the effect of cosmological red shift, are considered

  10. Uncertainty estimation with a small number of measurements, part II: a redefinition of uncertainty and an estimator method

    Science.gov (United States)

    Huang, Hening

    2018-01-01

    This paper is the second (Part II) in a series of two papers (Part I and Part II). Part I has quantitatively discussed the fundamental limitations of the t-interval method for uncertainty estimation with a small number of measurements. This paper (Part II) reveals that the t-interval is an ‘exact’ answer to a wrong question; it is actually misused in uncertainty estimation. This paper proposes a redefinition of uncertainty, based on the classical theory of errors and the theory of point estimation, and a modification of the conventional approach to estimating measurement uncertainty. It also presents an asymptotic procedure for estimating the z-interval. The proposed modification is to replace the t-based uncertainty with an uncertainty estimator (mean- or median-unbiased). The uncertainty estimator method is an approximate answer to the right question to uncertainty estimation. The modified approach provides realistic estimates of uncertainty, regardless of whether the population standard deviation is known or unknown, or if the sample size is small or large. As an application example of the modified approach, this paper presents a resolution to the Du-Yang paradox (i.e. Paradox 2), one of the three paradoxes caused by the misuse of the t-interval in uncertainty estimation.

  11. Approximate analysis of rigid plate loading on elastic multi-layered systems

    CSIR Research Space (South Africa)

    Maina, JW

    2008-07-01

    Full Text Available , this distribution was approximated using uniformly distributed multiple loads and analysis performed using Games. Results have shown good agreement with the theory for the case of a semi-infinite medium. Furthermore, extension of this method to multilayered system...

  12. Calculating properties with the coherent-potential approximation

    International Nuclear Information System (INIS)

    Faulkner, J.S.; Stocks, G.M.

    1980-01-01

    It is demonstrated that the expression that has hitherto been used for calculating the Bloch spectral-density function A/sup B/(E,k) in the Korringa-Kohn-Rostoker coherent-potential-approximation theory of alloys leads to manifestly unphysical results. No manipulation of the expression can eliminate this behavior. We develop an averaged Green's-function formulation and from it derive a new expression for A/sup B/(E,k) which does not contain unphysical features. The earlier expression for A/sup B/(E,k) was suggested as plausible on the basis that it is a spectral decomposition of the Lloyd formula. Expressions for many other properties of alloys have been obtained by manipulations of the Lloyd formula, and it is now clear that all such expressions must be considered suspect. It is shown by numerical and algebraic comparisons that some of the expressions obtained in this way are equivalent to the ones obtained from a Green's function, while others are not. In addition to studying these questions, the averaged Green's-function formulation developed in this paper is shown to furnish an interesting new way to approach many problems in alloy theory. The method is described in such a way that the aspects of the formulation that arise from the single-site approximation can be distinguished from those that depend on a specific choice for the effective scatterer

  13. When is a theory a theory? A case example.

    Science.gov (United States)

    Alkin, Marvin C

    2017-08-01

    This discussion comments on the approximately 20years history of writings on the prescriptive theory called Empowerment Evaluation. To do so, involves examining how "Empowerment Evaluation Theory" has been defined at various points of time (particularly 1996 and now in 2015). Defining a theory is different from judging the success of a theory. This latter topic has been addressed elsewhere by Michael Scriven, Michael Patton, and Brad Cousins. I am initially guided by the work of Robin Miller (2010) who has written on the issue of how to judge the success of a theory. In doing so, she provided potential standards for judging the adequacy of theories. My task is not judging the adequacy or success of the Empowerment Evaluation prescriptive theory in practice, but determining how well the theory is delineated. That is, to what extent do the writings qualify as a prescriptive theory. Copyright © 2016 Elsevier Ltd. All rights reserved.

  14. 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.

  15. 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

  16. 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

  17. 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.

  18. Transport with Astra in TJ-II; Transporte con Astra en TJ-II

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-Bruna, D; Castejon, F; Fontdecaba, J M

    2004-07-01

    This report describes the adaptation of the numerical transport shell ASTRA for performing plasma calculations in the TJ-II stellarator device. Firstly, an approximation to the TJ-II geometry is made and a simple transport model is shared with two other codes in order to compare these codes (PROCTR, PRETOR-Stellarator) with ASTRA as calculation tool for TJ-II plasmas are provided: interpretative and predictive transport. The first consists in estimating the transport coefficients from real experimental data, thes being taken from three TJ-II discharges. The predictive facet is illustrated using a model that is able to includes self-consistently thedynamics of transport barriers. The report includes this model, written in the ASTRA programming language, to illustrate the use of ASTRA. (Author) 26 refs.

  19. 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.

  20. 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.

  1. Approximating tunneling rates in multi-dimensional field spaces

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-10-01

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

  2. The theory of quantum liquids

    CERN Document Server

    Nozières, Philippe

    1999-01-01

    Originally published as two separate volumes, The Theory of Quantum Liquids is a classic text that attempts to describe the qualitative and unifying aspects of an extremely broad and diversified field. Volume I deals with 'normal' Fremi liquids, such as 3He and electrons in metals. Volume II consists of a detailed treatment of Bose condensation and liquid 4He, including the development of a Bose liquid theory and a microscopic basis for the two-fluid model, and the description of the elementary excitations of liquid HeII.

  3. Hydrogen atom excitation in intense attosecond laser field: Gauge dependence of dipole approximation

    Energy Technology Data Exchange (ETDEWEB)

    Aldarmaa, Ch., E-mail: aldaraa2004@yahoo.com, E-mail: l-xemee@yahoo.com; Khenmedekh, L., E-mail: aldaraa2004@yahoo.com, E-mail: l-xemee@yahoo.com [Theoretical Physics and Simulation Group, School of Materials Technology, MUST (Mongolia); Lkhagva, O. [School of Physics and Electronics, NUM (Mongolia)

    2014-03-24

    It is assumed that, the atomic excitations probability can be calculated using first order perturbation theory and dipole approximations. The validity of the dipole approximations had been examined by comparing the results with the results obtained by exact calculations within the first order perturbation theory[2]. Figure 1 shows the time dependence of the transition probability in the dipole approximation. From these plots it is obvious that, the probabilities obtained in the length gauge are higher than that in the velocity gauge, in the interaction period (−τ/2approximation) calculations results. (Figure 2) Though the time evolution of the same transition probabilities are different for these cases, the final results are the same for all three cases, excluding the 6s-6p{sub 0} transition. For the later case, only the length gauge give a false results, but the velocity gauge give the same result as the exact one, for the final value of the transition probability.

  4. Correlation effects beyond coupled cluster singles and doubles approximation through Fock matrix dressing.

    Science.gov (United States)

    Maitra, Rahul; Nakajima, Takahito

    2017-11-28

    We present an accurate single reference coupled cluster theory in which the conventional Fock operator matrix is suitably dressed to simulate the effect of triple and higher excitations within a singles and doubles framework. The dressing thus invoked originates from a second-order perturbative approximation of a similarity transformed Hamiltonian and induces higher rank excitations through local renormalization of individual occupied and unoccupied orbital lines. Such a dressing is able to recover a significant amount of correlation effects beyond singles and doubles approximation, but only with an economic n 5 additional cost. Due to the inclusion of higher rank excitations via the Fock matrix dressing, this method is a natural improvement over conventional coupled cluster theory with singles and doubles approximation, and this method would be demonstrated via applications on some challenging systems. This highly promising scheme has a conceptually simple structure which is also easily generalizable to a multi-reference coupled cluster scheme for treating strong degeneracy. We shall demonstrate that this method is a natural lowest order perturbative approximation to the recently developed iterative n-body excitation inclusive coupled cluster singles and doubles scheme [R. Maitra et al., J. Chem. Phys. 147, 074103 (2017)].

  5. Microscopic Theory of Magnetic Detwinning in Iron-Based Superconductors with Large-Spin Rare Earths

    Directory of Open Access Journals (Sweden)

    Jannis Maiwald

    2018-01-01

    Full Text Available Detwinning of magnetic (nematic domains in Fe-based superconductors has so far only been obtained through mechanical straining, which considerably perturbs the ground state of these materials. The recently discovered nonmechanical detwinning in EuFe_{2}As_{2} by ultralow magnetic fields offers an entirely different, nonperturbing way to achieve the same goal. However, this way seemed risky due to the lack of a microscopic understanding of the magnetically driven detwinning. Specifically, the following issues remained unexplained: (i ultralow value of the first detwinning field of approximately 0.1 T, two orders of magnitude below that of BaFe_{2}As_{2}, and (ii reversal of the preferential domain orientation at approximately 1 T and restoration of the low-field orientation above 10–15 T. In this paper, we present, using published as well as newly measured data, a full theory that quantitatively explains all the observations. The key ingredient of this theory is a biquadratic coupling between Fe and Eu spins, analogous to the Fe-Fe biquadratic coupling that drives the nematic transition in this family of materials.

  6. Semigroup evolution in the Wigner-Weisskopf pole approximation with Markovian spectral coupling

    International Nuclear Information System (INIS)

    Shikerman, F.; Peer, A.; Horwitz, L. P.

    2011-01-01

    We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator W(z) are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations z α ≠z β , and since the orthogonality relation does not generally hold at different values of z, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the W(z) projectors regardless of the number of poles. Such a possibility occurs when W(z), and hence its eigenvectors, is independent of z, which corresponds to the Markovian limit of the coupling to the continuum spectrum.

  7. Semigroup evolution in the Wigner-Weisskopf pole approximation with Markovian spectral coupling

    Energy Technology Data Exchange (ETDEWEB)

    Shikerman, F.; Peer, A. [Physics department and BINA center for nano-technology, Bar Ilan University, Ramat Gan 52900 (Israel); Horwitz, L. P. [Physics department and BINA center for nano-technology, Bar Ilan University, Ramat Gan 52900 (Israel); School of Physics, Tel-Aviv University, Ramat-Aviv 69978 (Israel); Department of Physics, Ariel University Center of Samaria, Ariel 40700 (Israel)

    2011-07-15

    We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator W(z) are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations z{sub {alpha}}{ne}z{sub {beta}}, and since the orthogonality relation does not generally hold at different values of z, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the W(z) projectors regardless of the number of poles. Such a possibility occurs when W(z), and hence its eigenvectors, is independent of z, which corresponds to the Markovian limit of the coupling to the continuum spectrum.

  8. Weighted density approximation for bonding in molecules: ring and cage polymers

    CERN Document Server

    Sweatman, M B

    2003-01-01

    The focus of this work is the bonded contribution to the intrinsic Helmholtz free energy of molecules. A weighted density approximation (WDA) for this contribution is presented within the interaction site model (ISM) for ring and cage polymers. The resulting density functional theory (ISM/WDA) for these systems is no more complex than theories for a pure simple fluid, and much less complex than density functional approaches that treat the bonding functional exactly. The ISM/WDA bonding functional is much more accurate than either the ISM/HNC or ISM/PY bonding functionals, which are related to the reference interaction-site model (RISM)/HNC and RISM/PY integral equations respectively, for ideal ring polymers. This means that the ISM/WDA functional should generally be more accurate for most 'real' ring or cage polymer systems when any reasonable approximation for the 'excess' contribution to the intrinsic Helmholtz free energy is employed.

  9. Weighted density approximation for bonding in molecules: ring and cage polymers

    International Nuclear Information System (INIS)

    Sweatman, M B

    2003-01-01

    The focus of this work is the bonded contribution to the intrinsic Helmholtz free energy of molecules. A weighted density approximation (WDA) for this contribution is presented within the interaction site model (ISM) for ring and cage polymers. The resulting density functional theory (ISM/WDA) for these systems is no more complex than theories for a pure simple fluid, and much less complex than density functional approaches that treat the bonding functional exactly. The ISM/WDA bonding functional is much more accurate than either the ISM/HNC or ISM/PY bonding functionals, which are related to the reference interaction-site model (RISM)/HNC and RISM/PY integral equations respectively, for ideal ring polymers. This means that the ISM/WDA functional should generally be more accurate for most 'real' ring or cage polymer systems when any reasonable approximation for the 'excess' contribution to the intrinsic Helmholtz free energy is employed

  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. 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)

  12. Evaluating the response of complex systems to environmental threats: the Σ II method

    International Nuclear Information System (INIS)

    Corynen, G.C.

    1983-05-01

    The Σ II method was developed to model and compute the probabilistic performance of systems that operate in a threatening environment. Although we emphasize the vulnerability of complex systems to earthquakes and to electromagnetic threats such as EMP (electromagnetic pulse), the method applies in general to most large-scale systems or networks that are embedded in a potentially harmful environment. Other methods exist for obtaining system vulnerability, but their complexity increases exponentially as the size of systems is increased. The complexity of the Σ II method is polynomial, and accurate solutions are now possible for problems for which current methods require the use of rough statistical bounds, confidence statements, and other approximations. For super-large problems, where the costs of precise answers may be prohibitive, a desired accuracy can be specified, and the Σ II algorithms will halt when that accuracy has been reached. We summarize the results of a theoretical complexity analysis - which is reported elsewhere - and validate the theory with computer experiments conducted both on worst-case academic problems and on more reasonable problems occurring in practice. Finally, we compare our method with the exact methods of Abraham and Nakazawa, and with current bounding methods, and we demonstrate the computational efficiency and accuracy of Σ II

  13. Approximate deconvolution models of turbulence analysis, phenomenology and numerical analysis

    CERN Document Server

    Layton, William J

    2012-01-01

    This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some advantages over more commonly used turbulence models – as well as some disadvantages. Our goal in this book is to provide a clear and complete mathematical development of ADMs, while pointing out the difficulties that remain. In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs.

  14. Discovery of functional and approximate functional dependencies in relational databases

    Directory of Open Access Journals (Sweden)

    Ronald S. King

    2003-01-01

    Full Text Available This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.

  15. 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.

  16. Traveling-cluster approximation for uncorrelated amorphous systems

    International Nuclear Information System (INIS)

    Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.

    1984-01-01

    We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results

  17. The finite section method and problems in frame theory

    DEFF Research Database (Denmark)

    Christensen, Ole; Strohmer, T.

    2005-01-01

    solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz......The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also...

  18. Topological fixed point theory of multivalued mappings

    CERN Document Server

    Górniewicz, Lech

    1999-01-01

    This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...

  19. Chemical potentials in gauge theories

    International Nuclear Information System (INIS)

    Actor, A.; Pennsylvania State Univ., Fogelsville

    1985-01-01

    One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter Asub(O)=const (Asub(μ) is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories. (orig.)

  20. 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.

  1. Unitary pole approximations and expansions in few-body systems

    International Nuclear Information System (INIS)

    Casel, A.; Haberzettl, H.; Sandhas, W.

    1982-01-01

    The unitary pole approximations or expansions of the two-body subsystem operators are well known, and particularly efficient and practical, methods to reduce the three-body problem to an effective two-body theory. In the present investigation we develop generalizations of these approximation techniques to the subsystem amplitudes of problems with higher particle numbers. They are based on the expansion of effective potentials which, in contrast to the genuine two-body interactions, are now energy dependent. Despite this feature our generalizations require only energy independent form factors, thus preserving one of the essential advantages of the genuine two-body approach. The application of these techniques to the four-body case is discussed in detail

  2. Monoenergetic approximation of a polyenergetic beam: a theoretical approach

    International Nuclear Information System (INIS)

    Robinson, D.M.; Scrimger, J.W.

    1991-01-01

    There exist numerous occasions in which it is desirable to approximate the polyenergetic beams employed in radiation therapy by a beam of photons of a single energy. In some instances, commonly used rules of thumb for the selection of an appropriate energy may be valid. A more accurate approximate energy, however, may be determined by an analysis which takes into account both the spectral qualities of the beam and the material through which it passes. The theoretical basis of this method of analysis is presented in this paper. Experimental agreement with theory for a range of materials and beam qualities is also presented and demonstrates the validity of the theoretical approach taken. (author)

  3. Dust in H II regions

    International Nuclear Information System (INIS)

    Isobe, S.

    1977-01-01

    Several pieces of evidence indicate that H II regions may contain dust: 1) the continuum light scattered by dust grains (O'Dell and Hubbard, 1965), 2) thermal radiation from dust grains at infrared wavelengths (Ney and Allen, 1969), 3) the abnormal helium abundance in some H II regions (Peimbert and Costero, 1969), etc. Although observations of the scattered continuum suggest that the H II region cores may be dust-free, dust grains and gas must be well mixed in view of the infrared observations. This difficulty may be solved by introducing globules with sizes approximately 0.001 pc. These globules and the molecular clouds adjacent to H II regions are the main sources supplying dust to H II regions. (Auth.)

  4. 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.)

  5. Approximation methods for efficient learning of Bayesian networks

    CERN Document Server

    Riggelsen, C

    2008-01-01

    This publication offers and investigates efficient Monte Carlo simulation methods in order to realize a Bayesian approach to approximate learning of Bayesian networks from both complete and incomplete data. For large amounts of incomplete data when Monte Carlo methods are inefficient, approximations are implemented, such that learning remains feasible, albeit non-Bayesian. The topics discussed are: basic concepts about probabilities, graph theory and conditional independence; Bayesian network learning from data; Monte Carlo simulation techniques; and, the concept of incomplete data. In order to provide a coherent treatment of matters, thereby helping the reader to gain a thorough understanding of the whole concept of learning Bayesian networks from (in)complete data, this publication combines in a clarifying way all the issues presented in the papers with previously unpublished work.

  6. EFFECTIVE ACTIONS FOR HETEROTIC STRING THEORY

    NARCIS (Netherlands)

    SUELMANN, H

    Heterotic String Theory is an attempt to construct a description of nature that is more satisfying than the Standard Model. A major problem is that it is very difficult to do explicit calculations in string theory. Therefore, it is useful to construct a 'normal' field theory that approximates HST.

  7. Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts.

    Science.gov (United States)

    Grzywacz, Piotr; Qin, Jian; Morse, David C

    2007-12-01

    Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, i.e., by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor S(-1)(k) predicted by a "one-loop" approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of an UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to S(-1)(k) is shown to be the sum of (i) a k -independent contribution that arises from a renormalization of the effective chi parameter, (ii) a k-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to k(2) that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a k-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.

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

    International Nuclear Information System (INIS)

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

    2014-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-12-07

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

  10. Approximately dual frames in Hilbert spaces and applications to Gabor frames

    DEFF Research Database (Denmark)

    Christensen, Ole; Laugesen, Richard S.

    2011-01-01

    constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in the duality conditions. To illustrate these results, we construct explicit approximate duals of Gabor...

  11. On the use of stochastic approximation Monte Carlo for Monte Carlo integration

    KAUST Repository

    Liang, Faming

    2009-01-01

    The stochastic approximation Monte Carlo (SAMC) algorithm has recently been proposed as a dynamic optimization algorithm in the literature. In this paper, we show in theory that the samples generated by SAMC can be used for Monte Carlo integration

  12. Study of the interaction between mercury (II) and bovine serum albumin by spectroscopic methods.

    Science.gov (United States)

    Chunmei, Dai; Cunwei, Ji; Huixiang, Lan; Yuze, Song; Wei, Yang; Dan, Zheng

    2014-03-01

    Mercury is a significant environmental pollutant that originates from industry. Mercury will bind with albumin and destroy biological functions in humans if it enters the blood. In this paper, the interaction between mercury (II) and bovine serum albumin (BSA) was investigated in vitro by fluorescence, UV-Vis absorption and circular dichroism (CD) under simulated physiological conditions. This study proves that the probable quenching mechanism of BSA by mercury (II) was mainly static quenching due to the formation of a mercury (II)-BSA complex. The quenching constant K(a) and the corresponding thermodynamic parameters (ΔH, ΔS and ΔG) at four different temperatures were calculated by a modified Stern-Volmer equation and the van't Hoff equation, respectively. The results revealed that the interaction between mercury (II) and BSA was mainly enthalpy-driven and that hydrogen bonding and van der Waals forces played a major role in the reaction. The obtained data for binding sites of n approximately equal to 1 indicated that there was a single class of binding site for the BSA with mercury (II). The value of the distance r (3.55 nm), determined by Föster's non-radioactive energy transfer theory, suggested that the energy transfer from BSA to mercury (II) occurred with a high probability. The conformational investigation from synchronous fluorescence, CD spectroscopy and three-dimensional fluorescence showed that the presence of mercury (II) resulted in micro-environmental and conformational changes of the BSA molecules, which may be responsible for the toxicity of mercury (II) in vivo. Copyright © 2014 Elsevier B.V. All rights reserved.

  13. Duality symmetries and the Type II string effective action

    International Nuclear Information System (INIS)

    Bergshoeff, E.

    1996-01-01

    We discuss the duality symmetries of Type II string effective actions in nine, ten and eleven dimensions. As a by-product we give a covariant action underlying the ten-dimensional Type IIB supergravity theory. We apply duality symmetries to construct dyonic Type II string solutions in six dimensions and their reformulation as solutions of the ten-dimensional Type IIB theory in ten dimensions. (orig.)

  14. A survey of hidden-variables theories

    CERN Document Server

    Belinfante, F J

    1973-01-01

    A Survey of Hidden-Variables Theories is a three-part book on the hidden-variable theories, referred in this book as """"theories of the first kind"""". Part I reviews the motives in developing different types of hidden-variables theories. The quest for determinism led to theories of the first kind; the quest for theories that look like causal theories when applied to spatially separated systems that interacted in the past led to theories of the second kind. Parts II and III further describe the theories of the first kind and second kind, respectively. This book is written to make the literat

  15. 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

  16. 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)

  17. 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

  18. Spin–Orbit TDDFT Electronic Structure of Diplatinum(II,II) Complexes

    Czech Academy of Sciences Publication Activity Database

    Záliš, Stanislav; Lam, Y.; Ch.; Gray, H. B.; Vlček, Antonín

    2015-01-01

    Roč. 54, č. 7 (2015), s. 3491-3500 ISSN 0020-1669 R&D Projects: GA MŠk LH13015 Institutional support: RVO:61388955 Keywords : BINUCLEAR PLATINUM(II) PHOTOCHEMISTRY * DENSITY-FUNCTIONAL THEORY * SPECTROSCOPIC PROPERTIES Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.820, year: 2015

  19. 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.

  20. 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.

  1. Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality

    CERN Document Server

    Saldi, Naci; Yüksel, Serdar

    2018-01-01

    In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...

  2. Symmetries of string, M- and F-theories

    NARCIS (Netherlands)

    Bergshoeff, Eric; Proeyen, Antoine Van

    2001-01-01

    The d = 10 type II string theories, d = 11 M-theory and d = 12 F-theory have the same symmetry group. It can be viewed either as a subgroup of a conformal group OSp(1|64) or as a contraction of OSp(1|32). The theories are related by different identifications of their symmetry operators as generators

  3. Approximate solution fuzzy pantograph equation by using homotopy perturbation method

    Science.gov (United States)

    Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.

    2017-09-01

    In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.

  4. Theoretical investigation of pressure-induced structural transitions in americium using GGA+U and hybrid density functional theory methods

    DEFF Research Database (Denmark)

    Verma, Ashok K.; Modak, P.; Sharma, Surinder M.

    2013-01-01

    First-principles calculations have been performed for americium (Am) metal using the generalized gradient approximation + orbital-dependent onsite Coulomb repulsion via Hubbard interaction (GGA+U) and hybrid density functional theory (HYB-DFT) methods to investigate various ground state properties......-I to Am-II transition. Good agreement was found between calculated and experimental equations of states for all phases, but the first three phases need larger U (α) parameters (where α represents the fraction of Hartree-Fock exchange energy replacing the DFT exchange energy) than the fourth phase in order...

  5. Unification of type-II strings and T duality.

    Science.gov (United States)

    Hohm, Olaf; Kwak, Seung Ki; Zwiebach, Barton

    2011-10-21

    We present a unified description of the low-energy limits of type-II string theories. This is achieved by a formulation that doubles the space-time coordinates in order to realize the T-duality group O(10,10) geometrically. The Ramond-Ramond fields are described by a spinor of O(10,10), which couples to the gravitational fields via the Spin(10,10) representative of the so-called generalized metric. This theory, which is supplemented by a T-duality covariant self-duality constraint, unifies the type-II theories in that each of them is obtained for a particular subspace of the doubled space. © 2011 American Physical Society

  6. 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.

  7. 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

  8. Final project report: TA-35 Los Alamos Power Reactor Experiment No. II (LAPRE II) decommissioning project

    International Nuclear Information System (INIS)

    Montoya, G.M.

    1993-02-01

    This final report addresses the decommissioning of the LAPRE II Reactor, safety enclosure, fuel reservoir tanks, emergency fuel recovery system, primary pump pit, secondary loop, associated piping, and the post-remediation activities. Post-remedial action measurements are also included. The cost of the project including, Phase I assessment and Phase II remediation was approximately $496K. The decommissioning operation produced 533 M 3 of mixed waste

  9. Collection of problems in transport theory

    International Nuclear Information System (INIS)

    Kaper, H.G.

    1975-01-01

    Problems presented are: (1) definition of transport operators; (2) relation between the integro-differential and integral form of the transport equation; (3) asymptotic behavior of the scalar density near curved boundaries and interfaces; (4) singularities at a corner; (5) regularity of the solution of the transport equation; (7) transport equations on a manifold; (8) numerical analysis; (9) cubature; (10) point spectrum of the transport operator; (11) convergence of the multigroup approximation; (12) convergence of discrete ordinates approximations; (13) the finite double-norm property; (14) convergence of discrete ordinates approximation. The presentation of the problems is intended to direct attention to gaps in the existing knowledge of transport theory and to stimulate research into new areas of transport theory

  10. Polygonal-path approximation on the path spaces of quantum mechanical systems: extended Feynman maps

    International Nuclear Information System (INIS)

    Exner, R.; Kolerov, G.I.

    1981-01-01

    Various types of polygonal-path approximations appearing in the functional-integration theory are discussed. The uniform approximation is applied to extend the definition of the Feynman maps from our previous paper and to prove consistency of this extension. Relations of the extended Fsub(-i)-map to the Wiener integral are given. In particular, the basic theorem about the sequential Wiener integral by Cameron is improved [ru

  11. 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.

  12. 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.

  13. Geometric transitions, flops and non-Kahler manifolds: II

    International Nuclear Information System (INIS)

    Becker, Melanie; Dasgupta, Keshav; Katz, Sheldon; Knauf, Anke; Tatar, Radu

    2006-01-01

    We continue our study of geometric transitions in type II and heterotic theories. In type IIB theory we discuss an F-theory setup which clarifies many of our earlier assumptions and allows us to study gravity duals of N=1 gauge theories with arbitrary global symmetry group G. We also point out the subtle differences between global and local metrics, and show that in many cases the global descriptions are far more complicated than discussed earlier. We determine the full global description in type I/heterotic theory. In type IIA, our analysis gives rise to a local non-Kahler metric whose global description involves a particular orientifold action with gauge fluxes localised on branes. We are also able to identify the three form fields that allow for a smooth flop in the M-theory lift. We briefly discuss the issues of generalized complex structures in type IIB theory and possible half-twisted models in the heterotic duals of our type II models. In a companion paper we will present details on the topological aspects of these models

  14. 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.

  15. Theory in Social Marketing

    DEFF Research Database (Denmark)

    Hastings, Gerard; Brown, Abraham; Anker, Thomas Boysen

    2010-01-01

    influence this positioning (Social Cognitive Theory and Social Norms) and; (iii) what offerings might encourage them to change their behaviour – or, those in a position to do so, to make the social context more conducive to change (Exchange Theory). Moreover, the chapter outlines how social marketers might......The chapter looks at three important theories which help social marketers to think more systematically about the key questions they need to address:  (i) how does the target group or population feel about a particular behaviour (Stages of Change Theory); (ii) what social and contextual factors...... benefit from a social epistemological approach....

  16. Homophobia in Marlowe’s Edward II Homophobia in Marlowe’s Edward II

    Directory of Open Access Journals (Sweden)

    Gelson Peres de Silva

    2008-04-01

    Full Text Available Drawing on queer theory, this essay demonstrates how homophobia motivates the plot of usurpation in Edward II, by Chistopher Marlowe (1564-1593, a play in which complex power relations can be verified. The main characters, King Edward II, Pierce of Gaveston, Mortimer Junior, Mortimer Senior and Queen Isabella, together with the nobles and the clerics, interact in a world of fierce political dispute. Power relations are at the core of the play and involve, on the one hand, the characters who envy and dispute Edward II’s royal power. On the other hand, the king suffers the effects of the power of his own homosexual drive and affective ties with Gaveston. Drawing on queer theory, this essay demonstrates how homophobia motivates the plot of usurpation in Edward II, by Chistopher Marlowe (1564-1593, a play in which complex power relations can be verified. The main characters, King Edward II, Pierce of Gaveston, Mortimer Junior, Mortimer Senior and Queen Isabella, together with the nobles and the clerics, interact in a world of fierce political dispute. Power relations are at the core of the play and involve, on the one hand, the characters who envy and dispute Edward II’s royal power. On the other hand, the king suffers the effects of the power of his own homosexual drive and affective ties with Gaveston.

  17. Analysis of carbon transport in the EBR-II and FFTF primary sodium systems

    International Nuclear Information System (INIS)

    Snyder, R.B.; Natesan, K.; Kassner, T.F.

    1976-01-01

    An analysis of the carburization-decarburization behavior of austenitic stainless steels in the primary heat-transport systems of the EBR-II and FFTF has been made that is based upon a kinetic model for the diffusion process and the surface area of steel in contact with flowing sodium at various temperatures in the two systems. The analysis was performed for operating conditions that result in sodium outlet temperatures of 474 and 566 0 C in the FFTF and 470 0 C in the EBR-II. If there was no external source of carbon to the system, i.e., other than the carbon initially present in the steel and the sodium, the dynamic-equilibrium carbon concentrations calculated for the FFTF primary sodium were approximately 0.025 and approximately 0.065 ppm for the 474 and 566 0 C outlet temperatures, respectively, and approximately 0.018 ppm for the EBR-II primary system. The analysis indicated that a carbon-source rate of approximately 250 g/y would be required to increase the carbon concentration of the EBR-II sodium to the measured range of approximately 0.16--0.19 ppm. An evaluation of possible carbon sources and the amount of carbonaceous material introduced into the reactor cover gas and sodium suggests that the magnitude of the calculated contamination rate is reasonable. For a 566 0 C outlet temperature, carbonaceous material would have to be introduced into the FFTF primary system at a rate approximately 4--6 times higher than in EBR-II to achieve the same carbon concentration in the sodium in the two systems. Since contamination rates of approximately 1500 g/y are unlikely, high-temperature fuel cladding in the FFTF should exhibit decarburization similar to that observed in laboratory loop systems, in contrast to the minimal compositional changes that result after exposure of Type 316 stainless steel to EBR-II sodium at temperatures between approximately 625 and 650 0 C

  18. Essentials of measure theory

    CERN Document Server

    Kubrusly, Carlos S

    2015-01-01

    Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces. The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. Th...

  19. Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

    Science.gov (United States)

    Wolpert, David H.

    2005-01-01

    A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

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

    International Nuclear Information System (INIS)

    Levit, S.

    1977-01-01

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

  1. Statistics II essentials

    CERN Document Server

    Milewski, Emil G

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Statistics II discusses sampling theory, statistical inference, independent and dependent variables, correlation theory, experimental design, count data, chi-square test, and time se

  2. Spectra theory for nuclei with closed shells (1962); Theorie des spectres des noyaux a couches completes (1962)

    Energy Technology Data Exchange (ETDEWEB)

    Gillet, V [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1962-07-01

    phenomenologie danns les resultats obtenus avec ces approximations on calcule un nombre maximum de faits experimentaux. Une recherche aux moindres carres portant sur quatorze niveaux de l'oxygene et du carbone determine la region d'accord optimum dans l'espace des parametres de l'interaction effective. Cette region est en partie une fonction des approximations numeriques utilisees. On espere qu'elle conservera une signification avec les ameliorations de la theorie. Elle est compatible avec certaines caracteristiques de la diffusion nucleon-nucleon libre. Cette recherche est en faveur de la seconde approximation qui seule conduit a une region d'accord optimum qui soit identique dans le carbone et l'oxygene. On obtient un accord general remarquablement bon avec les spectres connus de ces deux noyaux. Pour le calcium 40 on met en evidence l'importance de termes d'ordre superieur dans le calcul des etats collectifs 3{sup -} et 5{sup -}; par ailleurs seule l'approximation II permet d'expliquer ces niveaux. Des predictions sont faites avec les forces effectives ainsi obtenues. (auteur)

  3. Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients

    CERN Document Server

    Hutzenthaler, Martin

    2015-01-01

    Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation method

  4. Modelling of heating and evaporation of gasoline fuel droplets: A comparative analysis of approximations

    KAUST Repository

    Elwardani, Ahmed Elsaid

    2013-09-01

    Modelling of gasoline fuel droplet heating and evaporation processes is investigated using several approximations of this fuel. These are quasi-components used in the quasi-discrete model and the approximations of these quasi-components (Surrogate I (molar fractions: 83.0% n-C 6H14 + 15.6% n-C10H22 + 1.4% n-C14H30) and Surrogate II (molar fractions: 83.0% n-C7H16 + 15.6% n-C11H24 + 1.4% n-C15H32)). Also, we have used Surrogate A (molar fractions: 56% n-C7H16 + 28% iso-C8H 18 + 17% C7H8) and Surrogate B (molar fractions: 63% n-C7H16 + 20% iso-C8H 18 + 17% C7H8), originally introduced based on the closeness of the ignition delay of surrogates to that of gasoline fuel. The predictions of droplet radii and temperatures based on three quasi-components and their approximations (Surrogates I and II) are shown to be much more accurate than the predictions using Surrogates A and B. © 2013 Elsevier Ltd. All rights reserved.

  5. Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

    DEFF Research Database (Denmark)

    Nielsen, Søren R.K.; Sørensen, John Dalsgaard

    Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before...... passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response....... outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first...

  6. Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation

    International Nuclear Information System (INIS)

    Ye, Caier; Zhang, Weiguo

    2015-01-01

    Highlights: • Analyze the dynamical behavior of the planar dynamical system corresponding to the perturbed Klein–Gordon equation. • Present the relations between the properties of traveling wave solutions and the perturbation coefficient. • Obtain all explicit expressions of approximate damped oscillatory solutions. • Investigate error estimates between exact damped oscillatory solutions and the approximate solutions and give some numerical simulations. - Abstract: The influence of perturbation on traveling wave solutions of the perturbed Klein–Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis

  7. 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

  8. DFT: A Theory Full of Holes?

    Science.gov (United States)

    Pribram-Jones, Aurora; Gross, David A.; Burke, Kieron

    2015-04-01

    This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of approximations, and the tension between empirical and nonempirical approaches. Many ideas are illustrated on the exchange energy and hole. Features unique to this article include how approximations can be systematically derived in a nonempirical fashion and a survey of warm dense matter.

  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. International Conference on Semigroups, Algebras and Operator Theory

    CERN Document Server

    Meakin, John; Rajan, A

    2015-01-01

    This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will f...

  11. Analyzing the errors of DFT approximations for compressed water systems

    International Nuclear Information System (INIS)

    Alfè, D.; Bartók, A. P.; Csányi, G.; Gillan, M. J.

    2014-01-01

    We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm 3 where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE h ≃ 15 meV/monomer for the liquid and the

  12. New Pathways between Group Theory and Model Theory

    CERN Document Server

    Fuchs, László; Goldsmith, Brendan; Strüngmann, Lutz

    2017-01-01

    This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of th...

  13. 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

  14. 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

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

    International Nuclear Information System (INIS)

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

    1983-01-01

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

  16. Temperature dependent empirical pseudopotential theory for self-assembled quantum dots.

    Science.gov (United States)

    Wang, Jianping; Gong, Ming; Guo, Guang-Can; He, Lixin

    2012-11-28

    We develop a temperature dependent empirical pseudopotential theory to study the electronic and optical properties of self-assembled quantum dots (QDs) at finite temperature. The theory takes the effects of both lattice expansion and lattice vibration into account. We apply the theory to InAs/GaAs QDs. For the unstrained InAs/GaAs heterostructure, the conduction band offset increases whereas the valence band offset decreases with increasing temperature, and there is a type-I to type-II transition at approximately 135 K. Yet, for InAs/GaAs QDs, the holes are still localized in the QDs even at room temperature, because the large lattice mismatch between InAs and GaAs greatly enhances the valence band offset. The single-particle energy levels in the QDs show a strong temperature dependence due to the change of confinement potentials. Because of the changes of the band offsets, the electron wavefunctions confined in QDs increase by about 1-5%, whereas the hole wavefunctions decrease by about 30-40% when the temperature increases from 0 to 300 K. The calculated recombination energies of excitons, biexcitons and charged excitons show red shifts with increasing temperature which are in excellent agreement with available experimental data.

  17. 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

  18. Bilinear reduced order approximate model of parabolic distributed solar collectors

    KAUST Repository

    Elmetennani, Shahrazed

    2015-07-01

    This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the gaussian interpolation has been studied.

  19. Designing quantum information processing via structural physical approximation.

    Science.gov (United States)

    Bae, Joonwoo

    2017-10-01

    In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.

  20. 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

  1. Effective medium theories of inhomogeneous media from modern perspective

    International Nuclear Information System (INIS)

    Gubernatis, J.E.

    1977-01-01

    In the study of disordered alloys, theorists have stated the physics of the problem in terms of an integral equation and analyzed this equation by techniques developed in the quantum mechanical theory of scattering. The application of the scattering theory approach to the computation of the effective dielectric constant of a polycrystal is discussed. The problem is framed in the form of an integral equation. Several well-known intuitive approximations are recovered, and the connection of the approximations to perturbation theory is indicated

  2. K-theory, reality, and orientifolds

    International Nuclear Information System (INIS)

    Gukov, S.

    2000-01-01

    We use equivariant K-theory to classify charges of new (possibly non-supersymmetric) states localized on various orientifolds in type II string theory. We also comment on the stringy construction of new D-branes and demonstrate the discrete electric-magnetic duality in type I brane systems with p+q=7, as proposed by Witten. (orig.)

  3. Using Expectancy Theory to Explain Performance Appraisal ...

    African Journals Online (AJOL)

    pc

    2018-03-05

    Mar 5, 2018 ... appraisal conducting style, the relation between the performance appraisal system and task ... the article first explains the theory model which is based expectancy theory. II. ... which in return lead to rewards. According to [12],.

  4. Theory and design of broadband matching networks applied electricity and electronics

    CERN Document Server

    Chen, Wai-Kai

    1976-01-01

    Theory and Design of Broadband Matching Networks centers on the network theory and its applications to the design of broadband matching networks and amplifiers. Organized into five chapters, this book begins with a description of the foundation of network theory. Chapter 2 gives a fairly complete exposition of the scattering matrix associated with an n-port network. Chapter 3 considers the approximation problem along with a discussion of the approximating functions. Chapter 4 explains the Youla's theory of broadband matching by illustrating every phase of the theory with fully worked out examp

  5. Multigroup neutron transport equation in the diffusion and P{sub 1} approximation

    Energy Technology Data Exchange (ETDEWEB)

    Obradovic, D [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)

    1970-07-01

    Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P{sub 1} approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P{sub 1} approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)

  6. Applications exponential approximation by integer shifts of Gaussian functions

    Directory of Open Access Journals (Sweden)

    S. M. Sitnik

    2013-01-01

    Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.

  7. Research in particle theory

    International Nuclear Information System (INIS)

    Mansouri, F.; Suranyi, P; Wijewardhana, L.C.R.

    1991-10-01

    In the test particle approximation, the scattering amplitude for two-particle scattering in (2+1)-dimensional Chern-Simons-Witten gravity and supergravity was computed and compared to the corresponding metric solutions. The formalism was then extended to the exact gauge theoretic treatment of the two-particle scattering problem and compared to 't Hooft's results from the metric approach. We have studied dynamical symmetry breaking in 2+1 dimensional field theories. We have analyzed strong Extended Technicolor (ETC) models where the ETC coupling is close to a critical value. There are effective scalar fields in each of the theories. We have worked our how such scalar particles can be produced and how they decay. The φ 4 field theory was investigated in the Schrodinger representation. The critical behavior was extracted in an arbitrary number of dimensions in second order of a systematic truncation approximation. The correlation exponent agrees with known values within a few percent

  8. Eddington-inspired Born-Infeld gravity: nuclear physics constraints and the validity of the continuous fluid approximation

    Energy Technology Data Exchange (ETDEWEB)

    Avelino, P.P., E-mail: ppavelin@fc.up.pt [Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal)

    2012-11-01

    In this paper we investigate the classical non-relativistic limit of the Eddington-inspired Born-Infeld theory of gravity. We show that strong bounds on the value of the only additional parameter of the theory κ, with respect to general relativity, may be obtained by requiring that gravity plays a subdominant role compared to electromagnetic interactions inside atomic nuclei. We also discuss the validity of the continuous fluid approximation used in this and other astrophysical and cosmological studies. We argue that although the continuous fluid approximation is expected to be valid in the case of sufficiently smooth density distributions, its use should eventually be validated at a quantum level.

  9. Eddington-inspired Born-Infeld gravity: nuclear physics constraints and the validity of the continuous fluid approximation

    International Nuclear Information System (INIS)

    Avelino, P.P.

    2012-01-01

    In this paper we investigate the classical non-relativistic limit of the Eddington-inspired Born-Infeld theory of gravity. We show that strong bounds on the value of the only additional parameter of the theory κ, with respect to general relativity, may be obtained by requiring that gravity plays a subdominant role compared to electromagnetic interactions inside atomic nuclei. We also discuss the validity of the continuous fluid approximation used in this and other astrophysical and cosmological studies. We argue that although the continuous fluid approximation is expected to be valid in the case of sufficiently smooth density distributions, its use should eventually be validated at a quantum level

  10. Lectures on 2D gravity and 2D string theory

    International Nuclear Information System (INIS)

    Ginsparg, P.; Moore, G.

    1992-01-01

    This report the following topics: loops and states in conformal field theory; brief review of the Liouville theory; 2D Euclidean quantum gravity I: path integral approach; 2D Euclidean quantum gravity II: canonical approach; states in 2D string theory; matrix model technology I: method of orthogonal polynomials; matrix model technology II: loops on the lattice; matrix model technology III: free fermions from the lattice; loops and states in matrix model quantum gravity; loops and states in the C=1 matrix model; 6V model fermi sea dynamics and collective field theory; and string scattering in two spacetime dimensions

  11. A high resolution atlas of Mg II profiles

    Science.gov (United States)

    Ewald, R.; Nichols-Bohlin, Joy Y.; Kondo, Yoji

    1990-01-01

    An atlas of high dispersion Mg II profiles for standard stars of spectral types B0 through G9 is presented. The atlas contains plots of the Mg II profiles for approximately 65 stars and associated equivalent width measurements for both absorption and emission components, and the subordinate lines. The atlas is used to investigate systematic behavior of the Mg II profiles and correlation of the behavior with spectral classification.

  12. Calculus II For Dummies

    CERN Document Server

    Zegarelli, Mark

    2012-01-01

    An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit

  13. Immobilization of aqueous Hg(II) by mackinawite (FeS)

    International Nuclear Information System (INIS)

    Liu Jianrong; Valsaraj, Kalliat T.; Devai, Istvan; DeLaune, R.D.

    2008-01-01

    As one of the major constituents of acid volatile sulfide (AVS) in anoxic sediments, mackinawite (FeS) is known for its ability to scavenge trace metals. The interaction between aqueous Hg(II) (added as HgCl 2 ) and synthetic FeS was studied via batch sorption experiments conducted under anaerobic conditions. Due to the release of H + during formation of hydrolyzed Hg(II) species which is more reactive than Hg 2+ in surface adsorption, the equilibrium pH decreased with the increase in Hg(II)/FeS molar ratio. Counteracting the loss of FeS solids at lower pH, the maximum capacity for FeS to remove aqueous Hg(II) was approximately 0.75 mol Hg(II) (mol FeS) -1 . The comparison of X-ray power diffraction (XRPD) patterns of synthetic FeS sorbent before and after sorption showed that the major products formed from the interaction between FeS and the aqueous Hg(II) were metacinnabar, cinnabar, and mercury iron sulfides. With the addition of FeS at 0.4 g L -1 to a 1 mM Hg(II) solution with an initial pH of 5.6, Fe 2+ release was approximately 0.77 mol Fe 2+ per mol Hg(II) removed, suggesting that 77% of Hg(II) was removed via precipitation reaction under these conditions, with 23% of Hg(II) removed by adsorption. Aeration does not cause significant release of Hg(II) into the water phase

  14. Grand unified theories

    International Nuclear Information System (INIS)

    Langacker, P.

    1981-01-01

    In this talk I discuss the present status of these theories and of their observational and experimental implications. In section II, I briefly review the standard SU 3 sup(c) x SU 2 x U 1 model of the strong and electroweak interactions. Although phenomenologically successful, the standard model leaves many questions unanswered. Some of these questions are addressed by grand unified theories, which are defined and discussed in Section III. The Georgi-Glashow SU 5 model is described, as are theories based on larger groups such as SO 10 , E 6 , or SO 16 . It is emphasized that there are many possible grand unified theories and that it is an experimental problem not only to test the basic ideas but to discriminate between models. (orig./HSI)

  15. Theory of multiphoton ionization of atoms

    International Nuclear Information System (INIS)

    Szoeke, A.

    1986-03-01

    A non-perturbative approach to the theory of multiphoton ionization is reviewed. Adiabatic Floquet theory is its first approximation. It explains qualitatively the energy and angular distribution of photoelectrons. In many-electron atoms it predicts collective and inner shell excitation. 14 refs

  16. Light-scattering theory of diffraction.

    Science.gov (United States)

    Guo, Wei

    2010-03-01

    Since diffraction is a scattering process in principle, light propagation through one aperture in a screen is discussed in the light-scattering theory. Through specific calculation, the expression of the electric field observed at an observation point is obtained and is used not only to explain why Kirchhoff's diffraction theory is a good approximation when the screen is both opaque and sufficiently thin but also to demonstrate that the mathematical and physical problems faced by Kirchhoff's theory are avoided in the light-scattering theory.

  17. Rotating gravity currents. Part 1. Energy loss theory

    Science.gov (United States)

    Martin, J. R.; Lane-Serff, G. F.

    2005-01-01

    A comprehensive energy loss theory for gravity currents in rotating rectangular channels is presented. The model is an extension of the non-rotating energy loss theory of Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) and the steady-state dissipationless theory of rotating gravity currents of Hacker (PhD thesis, 1996). The theory assumes the fluid is inviscid, there is no shear within the current, and the Boussinesq approximation is made. Dissipation is introduced using a simple method. A head loss term is introduced into the Bernoulli equation and it is assumed that the energy loss is uniform across the stream. Conservation of momentum, volume flux and potential vorticity between upstream and downstream locations is then considered. By allowing for energy dissipation, results are obtained for channels of arbitrary depth and width (relative to the current). The results match those from earlier workers in the two limits of (i) zero rotation (but including dissipation) and (ii) zero dissipation (but including rotation). Three types of flow are identified as the effect of rotation increases, characterized in terms of the location of the outcropping interface between the gravity current and the ambient fluid on the channel boundaries. The parameters for transitions between these cases are quantified, as is the detailed behaviour of the flow in all cases. In particular, the speed of the current can be predicted for any given channel depth and width. As the channel depth increases, the predicted Froude number tends to surd 2, as for non-rotating flows.

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

    International Nuclear Information System (INIS)

    Lentzen, M.

    2014-01-01

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

  19. A foundation for the statistical dynamical theory of diffraction

    International Nuclear Information System (INIS)

    Kato, Norio

    1991-01-01

    The statistical dynamical theory is reformulated on a sounder basis. The starting wave equation is free from the so-called Takagi-Taupin (T-T) approximation. Functional calculus, an operational technique and the concept of the Green function are used as mathematical tools. Integro-differential equations are derived for the coherent (averaged) wave field and the energy flow vector of the incoherent intensity field. The formulae are exact except for assuming a model in which the fluctuation of the lattice phase is a set of Gaussian random variables defined in three-dimensional space. The general framework of the previous theory is justified within the T-T approximation. In general, however, new terms must be added and some terms have to be revised by introducing a Green function matrix. The theory may be used as a starting point when any approximate theory is developed for practical purposes. (orig.)

  20. Adaptive Sliding Mode Control of MEMS Gyroscope Based on Neural Network Approximation

    Directory of Open Access Journals (Sweden)

    Yuzheng Yang

    2014-01-01

    Full Text Available An adaptive sliding controller using radial basis function (RBF network to approximate the unknown system dynamics microelectromechanical systems (MEMS gyroscope sensor is proposed. Neural controller is proposed to approximate the unknown system model and sliding controller is employed to eliminate the approximation error and attenuate the model uncertainties and external disturbances. Online neural network (NN weight tuning algorithms, including correction terms, are designed based on Lyapunov stability theory, which can guarantee bounded tracking errors as well as bounded NN weights. The tracking error bound can be made arbitrarily small by increasing a certain feedback gain. Numerical simulation for a MEMS angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive neural control scheme and demonstrate the satisfactory tracking performance and robustness.

  1. Comparison of the GHSSmooth and the Rayleigh-Rice surface scatter theories

    Science.gov (United States)

    Harvey, James E.; Pfisterer, Richard N.

    2016-09-01

    The scalar-based GHSSmooth surface scatter theory results in an expression for the BRDF in terms of the surface PSD that is very similar to that provided by the rigorous Rayleigh-Rice (RR) vector perturbation theory. However it contains correction factors for two extreme situations not shared by the RR theory: (i) large incident or scattered angles that result in some portion of the scattered radiance distribution falling outside of the unit circle in direction cosine space, and (ii) the situation where the relevant rms surface roughness, σrel, is less than the total intrinsic rms roughness of the scattering surface. Also, the RR obliquity factor has been discovered to be an approximation of the more general GHSSmooth obliquity factor due to a little-known (or long-forgotten) implicit assumption in the RR theory that the surface autocovariance length is longer than the wavelength of the scattered radiation. This assumption allowed retaining only quadratic terms and lower in the series expansion for the cosine function, and results in reducing the validity of RR predictions for scattering angles greater than 60°. This inaccurate obliquity factor in the RR theory is also the cause of a complementary unrealistic "hook" at the high spatial frequency end of the predicted surface PSD when performing the inverse scattering problem. Furthermore, if we empirically substitute the polarization reflectance, Q, from the RR expression for the scalar reflectance, R, in the GHSSmooth expression, it inherits all of the polarization capabilities of the rigorous RR vector perturbation theory.

  2. 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...

  3. 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

  4. Microscopic theory of dynamical subspace for large amplitude collective motion

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

    1986-01-01

    A full quantum theory appropriate for describing large amplitude collective motion is proposed by exploiting the basic idea of the semi-classical theory so far developed within the time-depedent Hartree-Fock theory. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation specific for the collective subspace where the large amplitude collective motion is replicated as precisely as possible. As an extension of the semi-classical theory where the concept of an approximate integral surface played an important role, the collective subspace is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

  5. Density functional theory

    International Nuclear Information System (INIS)

    Das, M.P.

    1984-07-01

    The state of the art of the density functional formalism (DFT) is reviewed. The theory is quantum statistical in nature; its simplest version is the well-known Thomas-Fermi theory. The DFT is a powerful formalism in which one can treat the effect of interactions in inhomogeneous systems. After some introductory material, the DFT is outlined from the two basic theorems, and various generalizations of the theorems appropriate to several physical situations are pointed out. Next, various approximations to the density functionals are presented and some practical schemes, discussed; the approximations include an electron gas of almost constant density and an electron gas of slowly varying density. Then applications of DFT in various diverse areas of physics (atomic systems, plasmas, liquids, nuclear matter) are mentioned, and its strengths and weaknesses are pointed out. In conclusion, more recent developments of DFT are indicated

  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. Symmmetric double-well potential with Saxon-Woods tail and Pade approximations

    International Nuclear Information System (INIS)

    Niculescu, V.I.R.; Catana, D.

    1995-01-01

    In the present work we introduce a symmetric double-well potential with Woods-Saxon tail. The Woods-Saxon parts are replaced by Pade approximation.In this way the matrix elements of this potential form can be evaluated by the theory of complex functions. This results in a shorter computational time. (author). 1 fig., 1 tab., 7 refs

  8. Renormalization group study of scalar field theories

    International Nuclear Information System (INIS)

    Hasenfratz, A.; Hasenfratz, P.

    1986-01-01

    An approximate RG equation is derived and studied in scalar quantum field theories in d dimensions. The approximation allows for an infinite number of different couplings in the potential, but excludes interactions containing derivatives. The resulting non-linear partial differential equation can be studied by simple means. Both the gaussian and the non-gaussian fixed points are described qualitatively correctly by the equation. The RG flows in d=4 and the problem of defining an ''effective'' field theory are discussed in detail. (orig.)

  9. A generalized nodal finite element formalism for discrete ordinates equations in slab geometry Part I: Theory in the continuous moment case

    International Nuclear Information System (INIS)

    Hennart, J.P.; Valle, E. del.

    1995-01-01

    A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs

  10. On finite quantum field theories

    International Nuclear Information System (INIS)

    Rajpoot, S.; Taylor, J.G.

    1984-01-01

    The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)

  11. Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation

    CERN Document Server

    Scheck, Florian

    2012-01-01

    The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...

  12. Vortex sheet approximation of boundary layers

    International Nuclear Information System (INIS)

    Chorin, A.J.

    1978-01-01

    a grid free method for approximating incomprssible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier voartex method. The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder- piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms

  13. Errors due to the cylindrical cell approximation in lattice calculations

    Energy Technology Data Exchange (ETDEWEB)

    Newmarch, D A [Reactor Development Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)

    1960-06-15

    It is shown that serious errors in fine structure calculations may arise through the use of the cylindrical cell approximation together with transport theory methods. The effect of this approximation is to overestimate the ratio of the flux in the moderator to the flux in the fuel. It is demonstrated that the use of the cylindrical cell approximation gives a flux in the moderator which is considerably higher than in the fuel, even when the cell dimensions in units of mean free path tend to zero; whereas, for the case of real cells (e.g. square or hexagonal), the flux ratio must tend to unity. It is also shown that, for cylindrical cells of any size, the ratio of the flux in the moderator to flux in the fuel tends to infinity as the total neutron cross section in the moderator tends to zero; whereas the ratio remains finite for real cells. (author)

  14. Amorphous gauge glass theory

    International Nuclear Information System (INIS)

    Nielsen, H.B.; Bennett, D.L.

    1987-08-01

    Assuming that a lattice gauge theory describes a fundamental attribute of Nature, it should be pointed out that such a theory in the form of a gauge glass is a weaker assumption than a regular lattice model in as much as it is not constrained by the imposition of translational invariance; translational invariance is, however, recovered approximately in the long wavelength or continuum limit. (orig./WL)

  15. 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

  16. Les princi peseneraux tie toute theorie globale del' ecorceter restre

    Directory of Open Access Journals (Sweden)

    M. MATSCHINSKI

    1964-06-01

    Full Text Available Theories considering the local phenomena on/in the earth's crust — formation of a mountain chain, eruption of a volcano, accumulation of sediments, a.s.o. —, and theories considering the earth's crust as a whole on the way of studying the successions of states of this crust. 1. Cyclic successions (" cycles " and non-closed successions. 2. Exemples of cyclis successions (figures 1-A, 2-A, 3-A, 4-A, their graphic represesentations (figures 1-B, 2-B, 3-B, -t-B.3. Manifest existence of the cycles during the geologic history of the earth and absolute necessity of getting these cycles as a corollary of every theory of earth's crust. Practical impossibility of obtaining these consequences from the existing theories, and the causes of this impossibility.4. Three kinds of the mechanic theories in general and of the mechanic theories of earth's crust particulary: A. The exact continuous theories;B. The continuous theories which consider in first approximation the earth's crust a whole, and C. The theories considering the earth's crust as a whole in the full sense of these words. Examples. Astonishing fact that the theories of earth's crust of the kind C are non-existent till today. Hence the purpose of this article: the establishment of the general principles ofthese theories (— of the kind C. 5. Choice and definition of the quantities caracterising the states of the earth's crust. Definitive table of these quantities.6. Hypotheses necessary to build the system of differential equations of our problem. Simplifications which can be introduced. Pinal system of fundamental equations [2], Some remarks to resolving of [2], 7. Solutions [3] and [4] of the fundamental equations. Remarkable coincidence of these forms with the existing geological cycles.8. Different kinds of solutions [3] and [4]: I. Exactly periodic; II. Nearly periodic, and III. Aperiodic. Their geological meaning. On the choice of the constants in the fundamental equations [2].9. Some

  17. Data-Driven Model Reduction and Transfer Operator Approximation

    Science.gov (United States)

    Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank

    2018-06-01

    In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.

  18. First plasmas in the TJ-II flexible Heliac

    NARCIS (Netherlands)

    Alejaldre, C.; Alonso, J.; Almoguera, L.; Ascasibar, E.; Baciero, A.; Balbin, R.; Blaumoser, M.; Botija, J.; Branas, B.; De La Cal, E.; Cappa, A.; Carrasco, R.; Castejon, F.; Cepero, J. R.; Cremy, C.; Doncel, J.; Dulya, C.; Estrada, T.; Fernandez, A.; Frances, M.; Fuentes, C.; Garcia, A.; Garcia-Cortes, I.; Guasp, J.; Herranz, J.; Hidalgo, C.; Jimenez, J. A.; Kirpitchev, I.; Krivenski, V.; Labrador, I.; Lapayese, F.; Likin, K.; Liniers, M.; Lopez-Fraguas, A.; Lopez-Sanchez, A.; de la Luna, E.; Martin, R.; Martinez, A.; Medrano, M.; Mendez, P.; McCarthy, K.; Medina, F.; van Milligen, B.; Ochando, M.; Pacios, L.; Pastor, I.; Pedrosa, M. A.; de la Pena, A.; Portas, A.; Qin, J.; Rodriguez-Rodrigo, L.; Salas, A.; Sanchez, E.; Sanchez, J.; Tabares, F.; Tafalla, D.; Tribaldos, V.; Vaga, J.; Zurro, B.; Akulina, D.; Fadyanin, O. I.; Grebenshchicov, S.; Kharchev, N.; Meshcheryakov, A.; Barth, R.; van Dijk, G.; van der Meiden, H.; Petrov, S.

    1999-01-01

    The first experimental campaign of the TJ-II stellarator has been conducted using electron cyclotron resonance heating (f = 53.2 GHz, P-ECRH approximate to 250 kW) with a pulse length of Delta t approximate to (80-200) ms. The flexibility of the device has been used to study five different

  19. On Kaluza-Klein theory

    International Nuclear Information System (INIS)

    Salam, A.; Strathdee, J.

    1981-10-01

    Assuming the compactification of 4+K-dimensional spacetime implied in Kaluza-Klein type theories, we consider the case in which the internal manifold is a quotient space, G/H. We develop normal mode expansions on the internal manifold and show that the conventional gravitational plus Yang-Mills theory (realizing local G symmetry) is obtained in the leading approximation. The higher terms in the expansions give rise to field theories of massive particles. In particular, for the original Kaluza-Klein 4+1-dimensional theory, the higher excitations describe massive, charged, purely spin-2 particles. These belong to infinite dimensional representations of an 0(1,2). (author)

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

    Science.gov (United States)

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

    2018-03-01

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

  1. 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

  2. Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

    International Nuclear Information System (INIS)

    Wood, H.G. III; Morton, J.B.

    1980-01-01

    A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary layer type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman layer solutions. The results are presented in a form amenable to numerical calculations. Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall

  3. Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

    International Nuclear Information System (INIS)

    Wood, H.G.

    1980-01-01

    A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary-layer-type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman-layer solutions. The results are presented in a form amenable to numerical calculations. Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall. (author)

  4. Summability calculus a comprehensive theory of fractional finite sums

    CERN Document Server

    Alabdulmohsin, Ibrahim M

    2018-01-01

    This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergr...

  5. 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.

  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. Final project report, TA-35 Los Alamos Power Reactor Experiment No. II (LAPRE II) decommissioning project

    International Nuclear Information System (INIS)

    Montoya, G.M.

    1992-01-01

    This final report addresses the decommissioning of the LAPRE II Reactor, safety enclosure, fuel reservoir tanks, emergency fuel recovery system, primary pump pit, secondary loop, associated piping, and the post-remediation activities. Post-remedial action measurements are also included. The cost of the project, including Phase I assessment and Phase II remediation was approximately $496K. The decommissioning operation produced 533 m 3 of low-level solid radioactive waste and 5 m 3 of mixed waste

  8. 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...

  9. Gaussian processes and constructive scalar field theory

    International Nuclear Information System (INIS)

    Benfatto, G.; Nicolo, F.

    1981-01-01

    The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)

  10. Macrocyclic receptor showing extremely high Sr(II)/Ca(II) and Pb(II)/Ca(II) selectivities with potential application in chelation treatment of metal intoxication.

    Science.gov (United States)

    Ferreirós-Martínez, Raquel; Esteban-Gómez, David; Tóth, Éva; de Blas, Andrés; Platas-Iglesias, Carlos; Rodríguez-Blas, Teresa

    2011-04-18

    Herein we report a detailed investigation of the complexation properties of the macrocyclic decadentate receptor N,N'-Bis[(6-carboxy-2-pyridil)methyl]-4,13-diaza-18-crown-6 (H(2)bp18c6) toward different divalent metal ions [Zn(II), Cd(II), Pb(II), Sr(II), and Ca(II)] in aqueous solution. We have found that this ligand is especially suited for the complexation of large metal ions such as Sr(II) and Pb(II), which results in very high Pb(II)/Ca(II) and Pb(II)/Zn(II) selectivities (in fact, higher than those found for ligands widely used for the treatment of lead poisoning such as ethylenediaminetetraacetic acid (edta)), as well as in the highest Sr(II)/Ca(II) selectivity reported so far. These results have been rationalized on the basis of the structure of the complexes. X-ray crystal diffraction, (1)H and (13)C NMR spectroscopy, as well as theoretical calculations at the density functional theory (B3LYP) level have been performed. Our results indicate that for large metal ions such as Pb(II) and Sr(II) the most stable conformation is Δ(δλδ)(δλδ), while for Ca(II) our calculations predict the Δ(λδλ)(λδλ) form being the most stable one. The selectivity that bp18c6(2-) shows for Sr(II) over Ca(II) can be attributed to a better fit between the large Sr(II) ions and the relatively large crown fragment of the ligand. The X-ray crystal structure of the Pb(II) complex shows that the Δ(δλδ)(δλδ) conformation observed in solution is also maintained in the solid state. The Pb(II) ion is endocyclically coordinated, being directly bound to the 10 donor atoms of the ligand. The bond distances to the donor atoms of the pendant arms (2.55-2.60 Å) are substantially shorter than those between the metal ion and the donor atoms of the crown moiety (2.92-3.04 Å). This is a typical situation observed for the so-called hemidirected compounds, in which the Pb(II) lone pair is stereochemically active. The X-ray structures of the Zn(II) and Cd(II) complexes show that

  11. Approximating chiral quark models with linear σ-models

    International Nuclear Information System (INIS)

    Broniowski, Wojciech; Golli, Bojan

    2003-01-01

    We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear σ-model contains, at the lowest level of the gradient-expanded meson action, an additional term of the form ((1)/(2))A(σ∂ μ σ+π∂ μ π) 2 . We investigate the dynamical consequences of this term and its relevance to the phenomenology of the soliton models of the nucleon. It is found that the inclusion of the new term allows for a more efficient approximation of the underlying quark theory, especially in those cases where dynamics allows for a large deviation of the chiral fields from the chiral circle, such as in quark models with non-local regulators. This is of practical importance, since the σ-models with valence quarks only are technically much easier to treat and simpler to solve than the quark models with the full-fledged Dirac sea

  12. About Applications of the Fixed Point Theory

    Directory of Open Access Journals (Sweden)

    Bucur Amelia

    2017-06-01

    Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

  13. Lattice gauge theories

    International Nuclear Information System (INIS)

    Creutz, M.

    1983-04-01

    In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed

  14. Supergravity duals of matrix string theory

    International Nuclear Information System (INIS)

    Morales, Jose F.; Samtleben, Henning

    2002-01-01

    We study holographic duals of type II and heterotic matrix string theories described by warped AdS 3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS 3 xS 7 . The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the N=(8,8), N=(8,0) orbifold superconformal field theories to which type IIB/heterotic matrix strings flow in the infrared. In particular, we associate the dimension (h,h-bar) (32,32) twisted operator which brings the matrix string theories out from the conformal point (R; 8 ) N /S N with the dilaton profile in the supergravity background. The familiar dictionary between masses and 'scaling' dimensions of field and operators are modified by the presence of non-trivial warp factors and running dilatons. These modifications are worked out for the general case of domain wall/QFT correspondences between supergravities on warped AdS d+1 xS q geometries and super Yang-Mills theories with 16 supercharges. (author)

  15. Analytical theory of noncollinear amorphous metallic magnetism

    International Nuclear Information System (INIS)

    Kakehashi, Y.; Uchida, T.

    2001-01-01

    Analytical theory of noncollinear magnetism in amorphous metals is proposed on the basis of the Gaussian model for the distribution of the interatomic distance and the saddle-point approximation. The theory removes the numerical difficulty in the previous theory based on the Monte-Carlo sampling method, and reasonably describes the magnetic properties of amorphous transition metals

  16. Methods and Algorithms for Approximating the Gamma Function and Related Functions. A survey. Part I: Asymptotic Series

    Directory of Open Access Journals (Sweden)

    Cristinel Mortici

    2015-01-01

    Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.

  17. Inorganic anion-dependent assembly of zero-, one-, two- and three-dimensional Cu(II)/Ag(I) complexes under the guidance of the HSAB theory: Synthesis, structure, and magnetic property

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Yaru; Xing, Zhiyan [School of Science, North University of China, Taiyuan, Shanxi 030051 (China); Zhang, Xiao [MIIT Key Laboratory of Critical Materials Technology for New Energy Conversion and Storage, School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150080 (China); Key Laboratory of Functional Inorganic Material Chemistry, Ministry of Education, School of Chemistry and Materials Science, Heilongjiang University, Harbin 150080 PR China (China); Liang, Guorui [School of Science, North University of China, Taiyuan, Shanxi 030051 (China)

    2017-02-15

    To systematically explore the influence of inorganic anions on building coordination complexes, five novel complexes based on 1-(benzotriazole-1-methyl)−2-propylimidazole (bpmi), [Cu(bpmi){sub 2}(Ac){sub 2}]·H{sub 2}O (1), [Cu(bpmi){sub 2}(H{sub 2}O){sub 2}]·2NO{sub 3}·2H{sub 2}O (2), [Cu(bpmi)(N{sub 3}){sub 2}] (3), [Ag(bpmi)(NO{sub 3})] (4) and [Cu{sub 3}(bpmi){sub 2}(SCN){sub 4}(DMF)] (5) (Ac{sup −}=CH{sub 3}COO{sup −}, DMF=N,N-Dimethylformamide) are synthesized through rationally introducing Cu(II) salts and Ag(I) salt with different inorganic anions. X-ray single-crystal analyses reveal that these complexes show interesting structural features from mononuclear (1), one-dimensional (2 and 3), two-dimensional (4) to three-dimensional (5) under the influence of inorganic anions with different basicities. The structural variation can be explained by the hard-soft-acid-base (HSAB) theory. Magnetic susceptibility measurement indicates that complex 3 exhibits an antiferromagnetic coupling between adjacent Cu(II) ions. - Graphical abstract: Five new Cu(II)/Ag(I) complexes show interesting structural features from mononuclear, one-dimension, two-dimension to three-dimension under the influence of inorganic anions. The structural variation can be explained by the HSAB theory. - Highlights: • Five inorganic anion-dependent complexes are synthesized. • Structural variation can be explained by the hard-soft-acid-base (HSAB) theory. • The magnetic property of complex has been studied.

  18. Nonadiabatic charged spherical evolution in the postquasistatic approximation

    International Nuclear Information System (INIS)

    Rosales, L.; Barreto, W.; Peralta, C.; Rodriguez-Mueller, B.

    2010-01-01

    We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of dissipative and electrically charged distributions in general relativity. The numerical implementation of our approach leads to a solver which is globally second-order convergent. We evolve nonadiabatic distributions assuming an equation of state that accounts for the anisotropy induced by the electric charge. Dissipation is described by streaming-out or diffusion approximations. We match the interior solution, in noncomoving coordinates, with the Vaidya-Reissner-Nordstroem exterior solution. Two models are considered: (i) a Schwarzschild-like shell in the diffusion limit; and (ii) a Schwarzschild-like interior in the free-streaming limit. These toy models tell us something about the nature of the dissipative and electrically charged collapse. Diffusion stabilizes the gravitational collapse producing a spherical shell whose contraction is halted in a short characteristic hydrodynamic time. The streaming-out radiation provides a more efficient mechanism for emission of energy, redistributing the electric charge on the whole sphere, while the distribution collapses indefinitely with a longer hydrodynamic time scale.

  19. Unrenormalizable theories can be predictive

    CERN Document Server

    Kubo, J

    2003-01-01

    Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of a maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enables us to make unique predictions in the infrared regime in terms of a finite number of independent parameters. Therefore, this method might provide a way for calculating quantum corrections in a low-energy effective theory of quantum gravity. (orig.)

  20. $\\pi$ $\\pi$ theories

    CERN Document Server

    Basdevant, J L

    1972-01-01

    Reviews the structure of pion pion theories, in particular Roskies' sum rules, Martin's inequalities, Roy's relations, Roy's equations, Atkinsons Program, the Chew-Mandelstam equations, the Bootstrap phenomenological analyses, current algebra input, FESR bootstrap Lovelace Veneziano model and the Pade approximation. (63 refs).