WorldWideScience

Sample records for quadratic anharmonic constants

  1. Decay constants for pulsed monoenergetic neutron systems with quadratically anisotropic scattering

    International Nuclear Information System (INIS)

    Sjoestrand, N.G.

    1977-06-01

    The eigenvalues of the time-dependent transport equation for monoenergetic neutrons have been studied numerically for various combinations of linearly and quadratically anisotropic scattering assuming a space dependence of e β . The results, presented in the form of tables and graphs, show that quadratic anisotropy leads to a more complicated eigenvalue spectrum. However, no drastic changes occur in comparison to purely linear anistropy.(author)

  2. Anharmonic phonons and the isotope effect in superconductivity

    International Nuclear Information System (INIS)

    Crespi, V.H.; Cohen, M.L.; Penn, D.R.

    1991-01-01

    Anharmonic interionic potentials are examined in an Einstein model to study the unusual isotope-effect exponents for the high-T c oxides. The mass dependences of the electron-phonon coupling constant λ and the average phonon frequency √ left-angle ω 2 right-angle are computed from weighted sums over the oscillator levels. The isotope-effect exponent is depressed below 1/2 by either a double-well potential or a potential with positive quadratic and quartic parts. Numerical solutions of Schroedinger's equation for double-well potentials produce λ's in the range 1.5--4 for a material with a vanishing isotope-effect parameter α. However, low phonon frequencies limit T c to roughly 15 K. A negative quartic perturbation to a harmonic well can increase α above 1/2. In the extreme-strong-coupling limit, α is 1/2, regardless of anharmonicity

  3. Nonadiabatic anharmonic electron transfer

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, P. P. [Molecular Physics Research, 6547 Kristina Ursula Court, Falls Church, Virginia 22044 (United States)

    2013-03-28

    The effect of an inner sphere, local mode vibration on an electron transfer is modeled using the nonadiabatic transition probability (rate) expression together with both the anharmonic Morse and the harmonic oscillator potential. For an anharmonic inner sphere mode, a variational analysis uses harmonic oscillator basis functions to overcome the difficulties evaluating Morse-model Franck-Condon overlap factors. Individual matrix elements are computed with the use of new, fast, robust, and flexible recurrence relations. The analysis therefore readily addresses changes in frequency and/or displacement of oscillator minimums in the different electron transfer states. Direct summation of the individual Boltzmann weighted Franck-Condon contributions avoids the limitations inherent in the use of the familiar high-temperature, Gaussian form of the rate constant. The effect of harmonic versus anharmonic inner sphere modes on the electron transfer is readily seen, especially in the exoergic, inverted region. The behavior of the transition probability can also be displayed as a surface for all temperatures and values of the driving force/exoergicity {Delta}=-{Delta}G. The temperature insensitivity of the transfer rate is clearly seen when the exoergicity equals the collective reorganization energy ({Delta}={Lambda}{sub s}) along a maximum ln (w) vs. {Delta} ridge of the surface. The surface also reveals additional regions for {Delta} where ln (w) appears to be insensitive to temperature, or effectively activationless, for some kinds of inner sphere contributions.

  4. Kinks in systems with cubic and quartic anharmonicity

    International Nuclear Information System (INIS)

    Kashcheev, V.N.

    1988-01-01

    For a classical system of interacting particles with on-site cubic or quartic anharmonicity explicit analytic solutions of the d'Alembert equation are obtained in the form of kinks in the presence of dissipation (viscous or Rayleigh) and a constant force. These kinks will be asymptotically stable in the case of quartic anharmonicity and unstable in the case cubic anharmonicity

  5. Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion.

    Science.gov (United States)

    Soudackov, Alexander V; Hammes-Schiffer, Sharon

    2015-11-21

    Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton

  6. Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

    International Nuclear Information System (INIS)

    Soudackov, Alexander V.; Hammes-Schiffer, Sharon

    2015-01-01

    Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton

  7. Derivation of the cut-off length from the quantum quadratic enhancement of a mass in vacuum energy constant Lambda

    Science.gov (United States)

    Fukushima, Kimichika; Sato, Hikaru

    2018-04-01

    Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted self-energies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cut-off scheme. One of the cut-off formalisms is the field theory in terms of the step-function-type basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cut-off length. Based on the effectiveness of the continuum theory with the cut-off length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical self-energies are reduced to logarithmic forms by quantum corrections). The cut-off length is then determined to reproduce today's tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy.

  8. An Adaptive, Multi-Rate Linear Quadratic Regulator for a Shipboard MVDC Distribution System with Constant Power Loads

    Science.gov (United States)

    2017-09-01

    investigation into the factors which most strongly influence ROA size would be instructive. The genetic algorithm could be modified to assess ROA size and an...DISTRIBUTION SYSTEM WITH CONSTANT POWER LOADS 5. FUNDING NUMBERS REL95 REK4K 6. AUTHOR(S) Adam J. Mills 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS...ES) Naval Postgraduate School Monterey, CA 93943-5000 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING /MONITORING AGENCY NAME(S) AND

  9. Experimental determination of the anisotropy function for the Model 200 103Pd 'light seed' and derivation of the anisotropy constant based upon the linear quadratic model

    International Nuclear Information System (INIS)

    Yue Ning; Nath, Ravinder

    2002-01-01

    Since the publication of the AAPM Task Group 43 report in 1995, Model 200 103 Pd seed, which has been widely used in prostate seed implants and other brachytherapy procedures, has undergone some changes in its internal geometry resulting from the manufacturer's transition from lower specific activity reactor-produced 103 Pd ('heavy seeds') to higher specific activity accelerator-produced radioactive material ('light seeds'). Based on previously reported theoretical calculations and measurements, the dose rate constants and the radial dose functions of the two types of seeds are nearly the same and have already been reported. In this work, the anisotropy function of the 'light seed' was experimentally measured and an averaging method for the determination of the anisotropy constant from distance-dependent values of anisotropy factors is presented based upon the continuous low dose rate irradiation linear quadratic model for cell killing. The anisotropy function of Model 200 103 Pd 'light seeds' was measured in a Solid Water trade mark sign phantom using 1x1x1 mm micro LiF TLD chips at radial distances of 1, 2, 3, 4, 5, and 6 cm and at angles from 0 to 90 deg. with respect to the longitudinal axis of the seeds. At a radial distance of 1 cm, the measured anisotropy function of the 103 Pd 'light seed' is considerably lower than that of the 103 Pd 'heavy seed' reported in the TG 43 report. Our measured values at all radial distances are in excellent agreement with the results of a Monte Carlo simulation reported by Weaver, except for points along and near the seed longitudinal axis. The anisotropy constant of the 103 Pd 'light seed' was calculated using the linear quadratic biological model for cell killing in 30 clinical implants. For the model 200 ''light seed,'' it has a value of 0.865. However, our biological model calculations lead us to conclude that if the anisotropy factors of an interstitial brachytherapy seed vary significantly over radial distances anisotropy

  10. Anharmonic oscillator and Bogoliubov transformation

    International Nuclear Information System (INIS)

    Pattnayak, G.C.; Torasia, S.; Rath, B.

    1990-01-01

    The anharmonic oscillator occupies a cornerstone in many problems in physics. It was observed that none of the authors have tested Bogoliubov transformation to study anharmonic oscillator. The groundstate energy of the anharmonic oscillator is studied using Bogoliubov transformation and the results presented. (author)

  11. Quadratic Damping

    Science.gov (United States)

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  12. Separable quadratic stochastic operators

    International Nuclear Information System (INIS)

    Rozikov, U.A.; Nazir, S.

    2009-04-01

    We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

  13. Influence of anharmonic effects on the structural-mechanical and thermophysical properties of filled polymer systems

    International Nuclear Information System (INIS)

    Bordyuk, N.A.; Nikitchuk, V.I.; Voloshin, O.M.

    1995-01-01

    The force constants of anharmonicity, the total energy, and the force of interaction between structural elements of PVC systems are determined from the values of the quasielastic constants of filled polymer systems

  14. Anharmonicity in nuclear wobbling motion

    International Nuclear Information System (INIS)

    Oi, M.

    2007-01-01

    An unexpected strong anharmonicity was observed in the wobbling spectrum in 163 Lu. In an attempt to understand what causes the deviation from the original wobbling model by Bohr and Mottelson, an analysis is presented using several different approaches, such as exact diagonalization, a semiclassical model to deal with anharmonic wobbling motion, and a microscopic method based on the self-consistent cranking calculation

  15. Quadratic algebras

    CERN Document Server

    Polishchuk, Alexander

    2005-01-01

    Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

  16. Nonlinear (Anharmonic Casimir Oscillator

    Directory of Open Access Journals (Sweden)

    Habibollah Razmi

    2011-01-01

    Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.

  17. Microscopic approach to nuclear anharmonicities

    International Nuclear Information System (INIS)

    Matsuo, Masayuki; Shimizu, Yoshifumi; Matsuyanagi, Kenichi

    1985-01-01

    Present status of microscopic study of nuclear anharmonicity phenomena is reviewed from the viewpoint of the time-dependent Hartree-Bogoliubov approach. Both classical- and quantum-mechanical aspects of this approach are discussed. The Bohr-Mottelson-type collective Hamiltonian for anharmonic gamma vibrations is microscopically derived by means of the self-consistent-collective-coordinate method, and applied to the problem of two-phonon states of 168 Er. (orig.)

  18. Pressure dependence of the elastic constants and vibrational anharmonicity of Pd sub 3 sub 9 Ni sub 1 sub 0 Cu sub 3 sub 0 P sub 2 sub 1 bulk metallic glass

    CERN Document Server

    Wang Li; Sun, L L; Wang, W H; Wang, W K

    2003-01-01

    The pressure dependence of the acoustic velocities of a Pd sub 3 sub 9 Ni sub 1 sub 0 Cu sub 3 sub 0 P sub 2 sub 1 bulk metallic glass have been investigated up to 0.5 GPa at room temperature with the pulse echo overlap method. Two independent second-order elastic coefficients C sub 1 sub 1 and C sub 4 sub 4 and their pressure derivatives are yielded. The vibrational anharmonicity is shown by calculating both the acoustic mode Grueneisen parameters in the long-wavelength limit and the thermal Grueneisen parameter, and this result is compared with that for the Pd sub 4 sub 0 Ni sub 4 sub 0 P sub 2 sub 0 bulk glass.

  19. First-Principles Lattice Dynamics Method for Strongly Anharmonic Crystals

    Science.gov (United States)

    Tadano, Terumasa; Tsuneyuki, Shinji

    2018-04-01

    We review our recent development of a first-principles lattice dynamics method that can treat anharmonic effects nonperturbatively. The method is based on the self-consistent phonon theory, and temperature-dependent phonon frequencies can be calculated efficiently by incorporating recent numerical techniques to estimate anharmonic force constants. The validity of our approach is demonstrated through applications to cubic strontium titanate, where overall good agreement with experimental data is obtained for phonon frequencies and lattice thermal conductivity. We also show the feasibility of highly accurate calculations based on a hybrid exchange-correlation functional within the present framework. Our method provides a new way of studying lattice dynamics in severely anharmonic materials where the standard harmonic approximation and the perturbative approach break down.

  20. Detecting anharmonicity at a glance

    International Nuclear Information System (INIS)

    Giliberti, M; Stellato, M; Barbieri, S; Cavinato, M; Rigon, E; Tamborini, M

    2014-01-01

    Harmonic motion is generally presented in such a way that most of the students believe that the small oscillations of a body are all harmonic. Since the situation is not actually so simple, and since the comprehension of harmonic motion is essential in many physical contexts, we present here some suggestions, addressed to undergraduate students and pre-service teachers, that allow one to find out at a glance the anharmonicity of a motion. Starting from a didactically motivated definition of harmonic motion, and stressing the importance of the interplay between mathematics and experiments, we give a four-point criterion for anharmonicity together with some emblematic examples. The role of linear damping is also analysed in relation to the gradual changing of harmonicity into anharmonicity when the ratio between the damping coefficient and the zero-friction angular frequency increases. (paper)

  1. Crystal anharmonicity in Li(H,D) and Na(H,D) systems

    International Nuclear Information System (INIS)

    Islam, A.K.M.A.; Haque, E.; Azad, A.S.

    1993-05-01

    The reliability of our recently developed potential model is tested by extending the study to various anharmonic properties, e.g., third order elastic constants, fourth order elastic constants, Grueneisen parameters, and the pressure derivatives of second order elastic constants of hydrides and deuterides of lithium and sodium. A comparison of the calculated properties with the available experimental results and other theoretical estimates shows the validity and reliability of the derived potential in the study of crystal anharmonicities also. (author). 43 refs, 2 figs, 4 tabs

  2. First-principles study of anharmonic phonon effects in tetrahedral semiconductors via an external electric field

    Energy Technology Data Exchange (ETDEWEB)

    Dabiri, Zohreh, E-mail: z.dabiri@stu.yazd.ac.ir [Physics Department, Yazd University, P.O. Box 89195-741, Yazd (Iran, Islamic Republic of); Kazempour, Ali [Department of Physics, Payame Noor University, P.O. BOX 119395-3697, Tehran (Iran, Islamic Republic of); Nano Structured Coatings Institute of Yazd Payame Noor University, P.O. Code 89431-74559, Yazd (Iran, Islamic Republic of); Sadeghzadeh, Mohammad Ali [Physics Department, Yazd University, P.O. Box 89195-741, Yazd (Iran, Islamic Republic of)

    2016-11-15

    The strength of phonon anharmonicity is investigated in the framework of the Density Functional Perturbation Theory via an applied constant electric field. In contrast to routine approaches, we have employed the electric field as an effective probe to quest after the quasi-harmonic and anharmonic effects. Two typical tetrahedral semiconductors (diamond and silicon) have been selected to test the efficiency of this approach. In this scheme the applied field is responsible for establishing the perturbation and also inducing the anharmonicity in systems. The induced polarization is a result of changing the electronic density while ions are located at their ground state coordinates or at a specified strain. Employing this method, physical quantities of the semiconductors are calculated in presence of the electron–phonon interaction directly and, phonon–phonon interaction, indirectly. The present approach, which is in good agreement with previous theoretical and experimental studies, can be introduced as a benchmark to simply investigate the anharmonicity and pertinent consequences in materials.

  3. Study of thermophysical and anharmonic properties of fluorite compounds

    International Nuclear Information System (INIS)

    Singh, R.K.; Pandey, N.K.

    1983-01-01

    An extensive study is made of thermophysical and anharmonic properties of fluorite compounds using an interionic potential, which consists of a long-range Coulomb and three-body interactions and the short-range overlap repulsion and van der Waals attraction. The agreement achieved between experimental and theoretical results on third-order elastic constants and pressure derivatives of second order elastic constants are generally better than those obtained by others. This potential succeeds in predicting various thermophysical properties, like compressibility and its pressure and temperature derivatives, thermal expansion and Grueneisen parameters of seven crystals of fluorite structure. (author)

  4. Optimal Quadratic Programming Algorithms

    CERN Document Server

    Dostal, Zdenek

    2009-01-01

    Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers

  5. Self-Replicating Quadratics

    Science.gov (United States)

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  6. Linear-quadratic control and quadratic differential forms for multidimensional behaviors

    NARCIS (Netherlands)

    Napp, D.; Trentelman, H.L.

    2011-01-01

    This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

  7. Orientational anharmonicity of interatomic interaction in cubic monocrystals

    International Nuclear Information System (INIS)

    Belomestnykh, Vladimir N.; Tesleva, Elena P.

    2010-01-01

    Anharmonicity of interatomic interaction from a position of physical acoustics under the standard conditions is investigated. It is shown that the measure of anharmonicity of interatomic interaction (Grilneisen parameter) is explicitly expressed through velocities of sound. Calculation results of orientation anharmonicity are shown on the example of 116 cubic monocrystals with different lattice structural type and type of chemical bond. Two types of anharmonicity interatomic interaction anisotropy are determined. Keywords: acoustics, orientational anharmonicity, Gruneisen parameter, velocity of sound

  8. Kinematic anharmonicity of internal rotation of molecules

    International Nuclear Information System (INIS)

    Bataev, V.A.; Pupyshev, V.I.; Godunov, I.A.

    2017-01-01

    The methods of analysis the strongly coupled vibrations are proposed for a number of molecules of aromatic and heterocyclic carbonyl (and some others) compounds. The qualitative principles are formulated for molecular systems with a significant kinematic anharmonicity.

  9. Gravitation and quadratic forms

    International Nuclear Information System (INIS)

    Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

    2017-01-01

    The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

  10. Gravitation and quadratic forms

    Energy Technology Data Exchange (ETDEWEB)

    Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

    2017-03-31

    The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

  11. Nuclear catalysis mediated by localized anharmonic vibrations

    OpenAIRE

    Dubinko, Vladimir

    2015-01-01

    In many-body nonlinear systems with sufficient anharmonicity, a special kind of lattice vibrations, namely, Localized Anharmonic Vibrations (LAVs) can be excited either thermally or by external triggering, in which the amplitude of atomic oscillations greatly exceeds that of harmonic oscillations (phonons) that determine the system temperature. Coherency and persistence of LAVs may have drastic effect on quantum tunneling due to correlation effects discovered by Schrodinger and Robertson in 1...

  12. Hydrogen atom in a uniform electromagnetic field as an anharmonic oscillator

    International Nuclear Information System (INIS)

    Kibler, M.; Negadi, T.

    1984-01-01

    This work establishes, by means of the Kustaanheimo-Stiefel transformation, a connection between two branches of theoretical physics which are, in present times, the object of numerous studies: the quantum mechanics of anharmonic oscillators and of the hydrogen atom in a (strong) homogeneous and constant electromagnetic field

  13. Stochastic many-body perturbation theory for anharmonic molecular vibrations

    Energy Technology Data Exchange (ETDEWEB)

    Hermes, Matthew R. [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)

    2014-08-28

    A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

  14. Quantum theory of anharmonic oscillators

    International Nuclear Information System (INIS)

    Yamazaki, K.; Kyoto Univ.

    1983-01-01

    This in investigation of an anharmonic oscillator characterized by the potential ωsub(o) 2 /2 g 2 + lambda'q 4 . By using the equations of motion and the relations obtained by evaluating where O is an arbitrary operator, H is our total Hamiltonian and |i> and |j> are exact eigenstates of H, we derive an exact recurrence formula. This formula allows us to express tau-functions with a higher power of the variables through tau-functions with a lower power of the variables and energy eigenvalues. In this way we derive several exact relations, which are, in a sense, generalizations of the virial theorem and sum rules. These exact relations are the central equations of this paper. On the basis of these exact relations we propose our 'nearest neighbour level' (N.N.L.) approximation, which seems to provide a good approximation scheme. We can also use our exact relations to test the validity of various approximation methods, and as an example, we discuss the 'New-Tamm-Dancoff' (N.T.D)-type of approximation in detail. (Author)

  15. Comparison of Degrees of Potential-Energy-Surface Anharmonicity for Complexes and Clusters with Hydrogen Bonds

    Science.gov (United States)

    Kozlovskaya, E. N.; Doroshenko, I. Yu.; Pogorelov, V. E.; Vaskivskyi, Ye. V.; Pitsevich, G. A.

    2018-01-01

    Previously calculated multidimensional potential-energy surfaces of the MeOH monomer and dimer, water dimer, malonaldehyde, formic acid dimer, free pyridine-N-oxide/trichloroacetic acid complex, and protonated water dimer were analyzed. The corresponding harmonic potential-energy surfaces near the global minima were constructed for series of clusters and complexes with hydrogen bonds of different strengths based on the behavior of the calculated multidimensional potential-energy surfaces. This enabled the introduction of an obvious anharmonicity parameter for the calculated potential-energy surfaces. The anharmonicity parameter was analyzed as functions of the size of the analyzed area near the energy minimum, the number of points over which energies were compared, and the dimensionality of the solved vibrational problem. Anharmonicity parameters for potential-energy surfaces in complexes with strong, medium, and weak H-bonds were calculated under identical conditions. The obtained anharmonicity parameters were compared with the corresponding diagonal anharmonicity constants for stretching vibrations of the bridging protons and the lengths of the hydrogen bridges.

  16. Faithfully quadratic rings

    CERN Document Server

    Dickmann, M

    2015-01-01

    In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

  17. ANCA: Anharmonic Conformational Analysis of Biomolecular Simulations.

    Science.gov (United States)

    Parvatikar, Akash; Vacaliuc, Gabriel S; Ramanathan, Arvind; Chennubhotla, S Chakra

    2018-05-08

    Anharmonicity in time-dependent conformational fluctuations is noted to be a key feature of functional dynamics of biomolecules. Although anharmonic events are rare, long-timescale (μs-ms and beyond) simulations facilitate probing of such events. We have previously developed quasi-anharmonic analysis to resolve higher-order spatial correlations and characterize anharmonicity in biomolecular simulations. In this article, we have extended this toolbox to resolve higher-order temporal correlations and built a scalable Python package called anharmonic conformational analysis (ANCA). ANCA has modules to: 1) measure anharmonicity in the form of higher-order statistics and its variation as a function of time, 2) output a storyboard representation of the simulations to identify key anharmonic conformational events, and 3) identify putative anharmonic conformational substates and visualization of transitions between these substates. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  18. Rescuing Quadratic Inflation

    CERN Document Server

    Ellis, John; Sueiro, Maria

    2014-01-01

    Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

  19. Confinement-induced resonances in anharmonic waveguides

    Energy Technology Data Exchange (ETDEWEB)

    Peng Shiguo [Department of Physics, Tsinghua University, Beijing 100084 (China); Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia); Hu Hui; Liu Xiaji; Drummond, Peter D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)

    2011-10-15

    We develop the theory of anharmonic confinement-induced resonances (ACIRs). These are caused by anharmonic excitation of the transverse motion of the center of mass (c.m.) of two bound atoms in a waveguide. As the transverse confinement becomes anisotropic, we find that the c.m. resonant solutions split for a quasi-one-dimensional (1D) system, in agreement with recent experiments. This is not found in harmonic confinement theories. A new resonance appears for repulsive couplings (a{sub 3D}>0) for a quasi-two-dimensional (2D) system, which is also not seen with harmonic confinement. After inclusion of anharmonic energy corrections within perturbation theory, we find that these ACIRs agree extremely well with anomalous 1D and 2D confinement-induced resonance positions observed in recent experiments. Multiple even- and odd-order transverse ACIRs are identified in experimental data, including up to N=4 transverse c.m. quantum numbers.

  20. Theory of a quantum anharmonic oscillator

    International Nuclear Information System (INIS)

    Carusotto, S.

    1988-01-01

    The time evolution of a quantum single-quartic anharmonic oscillator is considered. The study is carried on in operational form by use of the raising and lowering operators of the oscillator. The equation of motion is solved by application of a new integration method based on iteration techniques, and the rigorous solutions that describe the time development of the displacement and momentum operators of the oscillator are obtained. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals. Finally, the results are employed to describe the time evolution of a quasiclassical anharmonic oscillator

  1. Scattering of Neutrons by an Anharmonic Crystal

    Energy Technology Data Exchange (ETDEWEB)

    Hoegberg, T; Bohlin, L; Ebbsjoe, I

    1967-04-15

    Numerical calculations have been performed for the anharmonic effects in neutron scattering. The phonon frequency widths and shifts have been calculated as a function of neutron frequency at different wave numbers and temperatures for a potential with central symmetry and for a face-centered cubic lattice.

  2. Heat transport in an anharmonic crystal

    Science.gov (United States)

    Acharya, Shiladitya; Mukherjee, Krishnendu

    2018-04-01

    We study transport of heat in an ordered, anharmonic crystal in the form of slab geometry in three dimensions. Apart from attaching baths of Langevin type to two extreme surfaces, we also attach baths of same type to the intermediate surfaces of the slab. Since the crystal is uninsulated, it exchanges energy with the intermediate heat baths. We find that both Fourier’s law of heat conduction and the Newton’s law of cooling hold to leading order in anharmonic coupling. The leading behavior of the temperature profile is exponentially falling from high to low temperature surface of the slab. As the anharmonicity increases, profiles fall more below the harmonic one in the log plot. In the thermodynamic limit thermal conductivity remains independent of the environment temperature and its leading order anharmonic contribution is linearly proportional to the temperature change between the two extreme surfaces of the slab. A fast crossover from one-dimensional (1D) to three-dimensional (3D) behavior of the thermal conductivity is observed in the system.

  3. Anharmonic vibrational spectroscopic investigation of malonaldehyde

    International Nuclear Information System (INIS)

    Alparone, A.; Millefiori, S.

    2003-01-01

    Anharmonic IR spectra of H-bonded and non-H-bonded conformers of malonaldehyde (MA) and its isotopomers MA-D 6 D 8 and MA-D 7 D 9 have been computed by the Vibrational-Self-Consistent-Field (VSCF) and the correlation-corrected-VSCF (CC-VSCF) techniques using ab initio MP2/6-31G*(+p) potential energies. The agreement between the experimental and calculated frequencies is significantly improved to within 2-3%. Anharmonic contributions are substantial especially for νOH of the H-bonded form, by reducing the harmonic value by more than 500 cm -1 . The effect is less important in the non-H-bonded form. The νOH stretching mode is strongly coupled with the ν 3 mode (essentially νCH 7 ) and with the in-plane and out-of-plane OH bending deformations. H-bond formation and deuteration batochromically shift νOH by an amount which is influenced by the anharmonic terms, the major contribution arising from coupling between modes. The comparison with the νOH mode of some other H-bonded systems suggests that anharmonic correction follows H-bonding strength

  4. Proof of Nishida's Conjecture on Anharmonic Lattices

    Science.gov (United States)

    Rink, Bob

    2006-02-01

    We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem, discrete symmetry considerations and an algebraic trick that considerably simplifies earlier results.

  5. Comparative study of quantum anharmonic potentials

    International Nuclear Information System (INIS)

    Amore, Paolo; Aranda, Alfredo; De Pace, Arturo; Lopez, Jorge A.

    2004-01-01

    We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with high precision, comparing the results with other techniques available in the literature

  6. Anharmonic, dimensionality and size effects in phonon transport

    Science.gov (United States)

    Thomas, Iorwerth O.; Srivastava, G. P.

    2017-12-01

    We have developed and employed a numerically efficient semi- ab initio theory, based on density-functional and relaxation-time schemes, to examine anharmonic, dimensionality and size effects in phonon transport in three- and two-dimensional solids of different crystal symmetries. Our method uses third- and fourth-order terms in crystal Hamiltonian expressed in terms of a temperature-dependent Grüneisen’s constant. All input to numerical calculations are generated from phonon calculations based on the density-functional perturbation theory. It is found that four-phonon processes make important and measurable contribution to lattice thermal resistivity above the Debye temperature. From our numerical results for bulk Si, bulk Ge, bulk MoS2 and monolayer MoS2 we find that the sample length dependence of phonon conductivity is significantly stronger in low-dimensional solids.

  7. On Convex Quadratic Approximation

    NARCIS (Netherlands)

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

    2000-01-01

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

  8. Aspects of Quadratic Gravity

    CERN Document Server

    Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

    2016-01-01

    We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

  9. A Quadratic Spring Equation

    Science.gov (United States)

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  10. On wave-packet dynamics in a decaying quadratic potential

    DEFF Research Database (Denmark)

    Møller, Klaus Braagaard; Henriksen, Niels Engholm

    1997-01-01

    We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....

  11. Anharmonic Vibrational Spectroscopy on Metal Transition Complexes

    Science.gov (United States)

    Latouche, Camille; Bloino, Julien; Barone, Vincenzo

    2014-06-01

    Advances in hardware performance and the availability of efficient and reliable computational models have made possible the application of computational spectroscopy to ever larger molecular systems. The systematic interpretation of experimental data and the full characterization of complex molecules can then be facilitated. Focusing on vibrational spectroscopy, several approaches have been proposed to simulate spectra beyond the double harmonic approximation, so that more details become available. However, a routine use of such tools requires the preliminary definition of a valid protocol with the most appropriate combination of electronic structure and nuclear calculation models. Several benchmark of anharmonic calculations frequency have been realized on organic molecules. Nevertheless, benchmarks of organometallics or inorganic metal complexes at this level are strongly lacking despite the interest of these systems due to their strong emission and vibrational properties. Herein we report the benchmark study realized with anharmonic calculations on simple metal complexes, along with some pilot applications on systems of direct technological or biological interest.

  12. Quantum anharmonic oscillator: The airy function approach

    Energy Technology Data Exchange (ETDEWEB)

    Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia); University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); AlFaify, S. [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia)

    2014-05-15

    New and simple numerical method is being reported to solve anharmonic oscillator problems. The method is setup to approach the real potential V(x) of the anharmonic oscillator system as a piecewise linear potential u(x) and to solve the Schrödinger equation of the system using the Airy function. Then, solutions continuity conditions lead to the energy quantification condition, and consequently, the energy eigenvalues. For testing purpose, the method was applied on the sextic and octic oscillators systems. The proposed method is found to be realistic, computationally simple, and having high degrees of accuracy. In addition, it can be applied to any form of potential. The results obtained by the proposed method were seen closely agreeing with results reached by other complicated methods.

  13. Hidden conic quadratic representation of some nonconvex quadratic optimization problems

    NARCIS (Netherlands)

    Ben-Tal, A.; den Hertog, D.

    The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

  14. Binary classification posed as a quadratically constrained quadratic ...

    Indian Academy of Sciences (India)

    Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

  15. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  16. Isotropy of quadratic forms

    Indian Academy of Sciences (India)

    V. Suresh University Of Hyderabad Hyderabad

    2008-10-31

    Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...

  17. Quadratic spatial soliton interactions

    Science.gov (United States)

    Jankovic, Ladislav

    Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

  18. Distance matrices and quadratic embedding of graphs

    Directory of Open Access Journals (Sweden)

    Nobuaki Obata

    2018-04-01

    Full Text Available A connected graph is said to be of QE class if it admits  a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.

  19. The effects of static quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent harmonic frequency: Perturbative analysis and numerical calculations

    International Nuclear Information System (INIS)

    Sarkar, P.; Bhattacharyya, S.P.

    1995-01-01

    The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab

  20. Equidistance of the complex two-dimensional anharmonic oscillator spectrum: the exact solution

    International Nuclear Information System (INIS)

    Cannata, F; Ioffe, M V; Nishnianidze, D N

    2012-01-01

    We study a class of quantum two-dimensional models with complex potentials of a specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to the conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must also include the corresponding associated functions. In the specific case of anharmonic second plus fourth-order interaction, expressions for the wavefunctions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wavefunctions is given. (paper)

  1. Quadratic soliton self-reflection at a quadratically nonlinear interface

    Science.gov (United States)

    Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

    2003-11-01

    The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

  2. Superconductivity mediated by anharmonic phonons: application to β-pyrochlore oxides

    Science.gov (United States)

    Hattori, Kazumasa; Tsunetsugu, Hirokazu

    2010-03-01

    We investigate three dimensional anharmonic phonons under tetrahedral symmetry and superconductivity mediated by these phonons. Three dimensional anharmonic phonon spectra are calculated directly by solving Schr"odinger equation and the superconducting transition temperature is determined by using the theory of strong coupling superconductivity assuming an isotropic gap function. With increasing the third order anharmonicity b of the tetrahedral potential, we find a crossover in the energy spectrum to a quantum tunneling regime. We obtain strongly enhanced transition temperatures around the crossover point. The first order transition observed in KOs2O6 is discussed in terms of the first excited state energy δ, and the coupling constant λ in the strong coupling theory of superconductivity. Our results suggest that the decrease of λ and increase of δ below the first order transition temperature. We point out that the change in the oscillation amplitude and characterizes this isomorphic transition. The chemical trends of the superconducting transition temperature, λ, and δ in the β-pyrochlore compounds are also discussed.

  3. Quadratic brackets from symplectic forms

    International Nuclear Information System (INIS)

    Alekseev, Anton Yu.; Todorov, Ivan T.

    1994-01-01

    We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

  4. Students' Understanding of Quadratic Equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  5. Anharmonic potential in the oscillator representation

    International Nuclear Information System (INIS)

    Dineykhan, M.; Efimov, G.V.

    1994-01-01

    In the non relativistic and relativized Schroedinger equation the Wick ordering method called the oscillator representation is proposed to calculate the energy spectrum for a wide class of potentials allowing the existence of a bound state. The oscillator representation method gives a unique regular way to describe and calculate the energy levels of ground as well as orbital and radial excitation states for a wide class of potentials. The results of the zeroth approximation oscillator representation are in good agreement with the exact values for the anharmonic potentials. The oscillator representation method was applied to the relativized Schroedinger equation too. The perturbation series converges fairly fast, i.e., the highest perturbation corrections over the interaction Hamiltonian are small enough. 29 refs.; 4 tabs. (author)

  6. Low-temperature anharmonicity in cesium chloride (CsCl)

    Energy Technology Data Exchange (ETDEWEB)

    Sist, Mattia; Faerch Fischer, Karl Frederik; Brummerstedt Iversen, Bo [Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus University (Denmark); Kasai, Hidetaka [Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus University (Denmark); Faculty of Pure and Applied Sciences, TIMS and CiRfSE, University of Tsukuba (Japan)

    2017-03-20

    Anharmonic lattice vibrations govern heat transfer in materials, and anharmonicity is commonly assumed to be dominant at high temperature. The textbook cubic ionic defect-free crystal CsCl is shown to have an unexplained low thermal conductivity at room temperature (ca. 1 W/(m K)), which increases to around 13 W/(m K) at 25 K. Through high-resolution X-ray diffraction it is unexpectedly shown that the Cs atomic displacement parameter becomes anharmonic at 20 K. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)

  7. Properties of one-dimensional anharmonic lattice solitons

    Science.gov (United States)

    Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed

    2000-12-01

    The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.

  8. A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

    International Nuclear Information System (INIS)

    Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan

    2007-01-01

    In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported

  9. Time evolution of gibbs states for an anharmonic lattice

    Energy Technology Data Exchange (ETDEWEB)

    Marchioro, C; Pellegrinotti, A; Suhov, Y [Camerino Univ. (Italy). Istituto di Matematica; Pulvirenti, M [L' Aquila Univ. (Italy). Istituto di Matematica; Rome Univ. (Italy). Istituto di Matematica)

    1979-01-01

    In this paper we study the time evolution of a regular class of states of an infinite classical system of anharmonic oscillators. The conditional probabilities are investigated and an explicit form for these is given.

  10. Dynamic of cold-atom tips in anharmonic potentials

    Science.gov (United States)

    Menold, Tobias; Federsel, Peter; Rogulj, Carola; Hölscher, Hendrik; Fortágh, József

    2016-01-01

    Background: Understanding the dynamics of ultracold quantum gases in an anharmonic potential is essential for applications in the new field of cold-atom scanning probe microscopy. Therein, cold atomic ensembles are used as sensitive probe tips to investigate nanostructured surfaces and surface-near potentials, which typically cause anharmonic tip motion. Results: Besides a theoretical description of this anharmonic tip motion, we introduce a novel method for detecting the cold-atom tip dynamics in situ and real time. In agreement with theory, the first measurements show that particle interactions and anharmonic motion have a significant impact on the tip dynamics. Conclusion: Our findings will be crucial for the realization of high-sensitivity force spectroscopy with cold-atom tips and could possibly allow for the development of advanced spectroscopic techniques such as Q-control. PMID:28144505

  11. Time evolution of gibbs states for an anharmonic lattice

    International Nuclear Information System (INIS)

    Marchioro, C.; Pellegrinotti, A.; Suhov, Y.; Pulvirenti, M.; Rome Univ.

    1979-01-01

    In this paper we study the time evolution of a regular class of states of an infinite classical system of anharmonic oscillators. The conditional probabilities are investigated and an explicit form for these is given. (orig.) [de

  12. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

  13. Projectile Motion with Quadratic Damping in a Constant ...

    Indian Academy of Sciences (India)

    IAS Admin

    finds its applications in various sports [1–5]. The prob- ... The time of flight and the maximum height attained are .... the equation is 0.80942s which gives the time of flight. ..... Service Science and Management, Vol.3, pp.98–105, 2010. [17].

  14. Effects of hypersonic field and anharmonic interactions on channelling radiation

    International Nuclear Information System (INIS)

    George, Juby; Pathak, Anand P; Goteti, L N S Prakash; Nagamani, G

    2007-01-01

    The effects of a hypersonic field on positron channelling radiation are considered. Anharmonic effects of the transverse potential induced by these longitudinal fields are incorporated and the wavefunction of the planar channelled positron is found by the solution of Dirac equation under the resonant influence of hypersound. An expression for the resonant frequency is estimated. The transition probabilities and the intensity of the channelling radiation are also calculated. It is found that the anharmonic effects change the spectral distributions considerably

  15. Ground state energy values and moments of the anharmonic oscillator

    International Nuclear Information System (INIS)

    Seetharaman, M.; Raghavan, Sekhar; Subba Rao, G.

    1981-01-01

    It is shown that a very satisfactory estimate of the energy values (for all values of the anharmonicity) and moments of the ground state of the quartic anharmonic oscillator can be obtained in the variational method, by considering trial wavefunctions which have the correct asymptotic properties. The results derived with a single variational parameter are a considerable improvement over the recent results of C.A. Ginsburg and E.W. Montroll (1978). (author)

  16. Improved models of dense anharmonic lattices

    Energy Technology Data Exchange (ETDEWEB)

    Rosenau, P., E-mail: rosenau@post.tau.ac.il; Zilburg, A.

    2017-01-15

    We present two improved quasi-continuous models of dense, strictly anharmonic chains. The direct expansion which includes the leading effect due to lattice dispersion, results in a Boussinesq-type PDE with a compacton as its basic solitary mode. Without increasing its complexity we improve the model by including additional terms in the expanded interparticle potential with the resulting compacton having a milder singularity at its edges. A particular care is applied to the Hertz potential due to its non-analyticity. Since, however, the PDEs of both the basic and the improved model are ill posed, they are unsuitable for a study of chains dynamics. Using the bond length as a state variable we manipulate its dispersion and derive a well posed fourth order PDE. - Highlights: • An improved PDE model of a Newtonian lattice renders compacton solutions. • Compactons are classical solutions of the improved model and hence amenable to standard analysis. • An alternative well posed model enables to study head on interactions of lattices' solitary waves. • Well posed modeling of Hertz potential.

  17. Quadratic programming with fuzzy parameters: A membership function approach

    International Nuclear Information System (INIS)

    Liu, S.-T.

    2009-01-01

    Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

  18. Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

    International Nuclear Information System (INIS)

    Sjoestrand, N.G.

    1981-01-01

    Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

  19. Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

    Science.gov (United States)

    Mansoori Kermani, Maryam; Dehestani, Maryam

    2018-06-01

    We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

  20. Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

    Science.gov (United States)

    Mansoori Kermani, Maryam; Dehestani, Maryam

    2018-03-01

    We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

  1. New robust chaotic system with exponential quadratic term

    International Nuclear Information System (INIS)

    Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

    2008-01-01

    This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

  2. Stability in quadratic torsion theories

    Energy Technology Data Exchange (ETDEWEB)

    Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

    2017-11-15

    We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

  3. Stability in quadratic torsion theories

    International Nuclear Information System (INIS)

    Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

    2017-01-01

    We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

  4. Anharmonic effects in the quantum cluster equilibrium method

    Science.gov (United States)

    von Domaros, Michael; Perlt, Eva

    2017-03-01

    The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

  5. Quantum versus semiclassical description of selftrapping: anharmonic effects

    International Nuclear Information System (INIS)

    Raghavan, S.; Bishop, A.R.; Kenkre, V.M.

    1998-09-01

    Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum mechanical analysis of a two-site system, where the oscillator is described by a tunably anharmonic potential, with a square well with infinite walls and the harmonic potential as its extreme limits, and wherein the interaction is nonlinear in the oscillator displacement. We find that even highly anharmonic polarons behave similar to their harmonic counterparts in that selftrapping is preserved for long times in the limit of strong coupling, and that the polaronic tunneling time scale depends exponentially on the polaron binding energy. Further, in agreement with earlier results related to harmonic polarons, the semiclassical approximation agrees with the full quantum result in the massive oscillator limit of small oscillator frequency and strong quasiparticle-oscillator coupling. (author)

  6. The anharmonic phonon decay rate in group-III nitrides

    International Nuclear Information System (INIS)

    Srivastava, G P

    2009-01-01

    Measured lifetimes of hot phonons in group-III nitrides have been explained theoretically by considering three-phonon anharmonic interaction processes. The basic ingredients of the theory include full phonon dispersion relations obtained from the application of an adiabatic bond charge model and crystal anharmonic potential within the isotropic elastic continuum model. The role of various decay routes, such as Klemens, Ridley, Vallee-Bogani and Barman-Srivastava channels, in determining the lifetimes of the Raman active zone-centre longitudinal optical (LO) modes in BN (zincblende structure) and A 1 (LO) modes in AlN, GaN and InN (wurtzite structure) has been quantified.

  7. Exact solutions and ladder operators for a new anharmonic oscillator

    International Nuclear Information System (INIS)

    Dong Shihai; Sun Guohua; Lozada-Cassou, M.

    2005-01-01

    In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrodinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r->ir

  8. Quadratic prediction of factor scores

    NARCIS (Netherlands)

    Wansbeek, T

    1999-01-01

    Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

  9. On quadratic variation of martingales

    Indian Academy of Sciences (India)

    On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

  10. Impurity solitons with quadratic nonlinearities

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

    1998-01-01

    We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

  11. Quadratic divergences and dimensional regularisation

    International Nuclear Information System (INIS)

    Jack, I.; Jones, D.R.T.

    1990-01-01

    We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)

  12. Phase space eigenfunctions of multidimensional quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Dodonov, V.V.; Man'ko, V.I.

    1986-01-01

    We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

  13. Investigating vibrational anharmonic couplings in cyanide-bridged transition metal mixed valence complexes using two-dimensional infrared spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Slenkamp, Karla M.; Lynch, Michael S.; Van Kuiken, Benjamin E.; Brookes, Jennifer F.; Bannan, Caitlin C.; Daifuku, Stephanie L.; Khalil, Munira, E-mail: mkhalil@chem.washington.edu [Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195 (United States)

    2014-02-28

    Using polarization-selective two-dimensional infrared (2D IR) spectroscopy, we measure anharmonic couplings and angles between the transition dipole moments of the four cyanide stretching (ν{sub CN}) vibrations found in [(NH{sub 3}){sub 5}Ru{sup III}NCFe{sup II}(CN){sub 5}]{sup −} (FeRu) dissolved in D{sub 2}O and formamide and [(NC){sub 5}Fe{sup II}CNPt{sup IV}(NH{sub 3}){sub 4}NCFe{sup II}(CN){sub 5}]{sup 4−} (FePtFe) dissolved in D{sub 2}O. These cyanide-bridged transition metal complexes serve as model systems for studying the role of high frequency vibrational modes in ultrafast photoinduced charge transfer reactions. Here, we focus on the spectroscopy of the ν{sub CN} modes in the electronic ground state. The FTIR spectra of the ν{sub CN} modes of the bimetallic and trimetallic systems are strikingly different in terms of frequencies, amplitudes, and lineshapes. The experimental 2D IR spectra of FeRu and FePtFe and their fits reveal a set of weakly coupled anharmonic ν{sub CN} modes. The vibrational mode anharmonicities of the individual ν{sub CN} modes range from 14 to 28 cm{sup −1}. The mixed-mode anharmonicities range from 2 to 14 cm{sup −1}. In general, the bridging ν{sub CN} mode is most weakly coupled to the radial ν{sub CN} mode, which involves the terminal CN ligands. Measurement of the relative transition dipole moments of the four ν{sub CN} modes reveal that the FeRu molecule is almost linear in solution when dissolved in formamide, but it assumes a bent geometry when dissolved in D{sub 2}O. The ν{sub CN} modes are modelled as bilinearly coupled anharmonic oscillators with an average coupling constant of 6 cm{sup −1}. This study elucidates the role of the solvent in modulating the molecular geometry and the anharmonic vibrational couplings between the ν{sub CN} modes in cyanide-bridged transition metal mixed valence complexes.

  14. Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x = Ax2α + Bx2

    Directory of Open Access Journals (Sweden)

    N. Al Sdran

    2016-06-01

    Full Text Available The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x = Ax2α + Bx2, (A>0, B<0, with (α = 2 for quadratic, (α =3 for sextic and (α =4 for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x by a piecewise-linear potential v(x, while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

  15. Charged black holes in quadratic gravity

    International Nuclear Information System (INIS)

    Matyjasek, Jerzy; Tryniecki, Dariusz

    2004-01-01

    Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by r + =|e|. Similarly to the classical Reissner-Nordstroem solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed

  16. Thermal behaviour of the Debye-Waller factor and the specific heat of anharmonic crystals

    International Nuclear Information System (INIS)

    Lima, R.A.T. de; Tsallis, C.

    1979-08-01

    The influence of the cubic and quartic crystalline anharmonicity on the classical and quantum thermal behaviour of the specific heat, Debye temperaturetheta, Debye-Waller factor W, crystalline expansion and phonon spectrum is studied, within the framework of the Variational Method in Statistical Mechanics. The sistems, mainly focalized are the single oscillator, the mono-atomic linear chain and simple cubic crystal. The trial Hamiltonian is an harmonic one, therefore the various anharmonic influences are mainly absorbed into the renormalization of theta(T). Several differences between the classical and quantum results are exhibited. Satisfactory qualitative agreement with experience was obtained in the low-temperature regime, in particular in what concerns the existence of a minimum in theta(T) which has been observed in Cu, Al, Ag, Au and Pb. For the intermediate-temperature regime the customary linear behaviour of W(T) (hence theta(T) almost constant) is reobtained. Finally in the high-temperature regime, the present treatment leads to a √T - dependence for the W-factor, which implies in the wrong curvature with respect to experimental data. A possible explanation of this disagreement might be related to the melting phenomenon, which is not covered by the present theory. (Author) [pt

  17. Quadratic third-order tensor optimization problem with quadratic constraints

    Directory of Open Access Journals (Sweden)

    Lixing Yang

    2014-05-01

    Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

  18. Variational random phase approximation for the anharmonic oscillator

    International Nuclear Information System (INIS)

    Dukelsky, J.; Schuck, P.

    1990-04-01

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

  19. Spherical anharmonic oscillator in self-similar approximation

    International Nuclear Information System (INIS)

    Yukalova, E.P.; Yukalov, V.I.

    1992-01-01

    The method of self-similar approximation is applied here for calculating the eigenvalues of the three-dimensional spherical anharmonic oscillator. The advantage of this method is in its simplicity and high accuracy. The comparison with other known analytical methods proves that this method is more simple and accurate. 25 refs

  20. Harmonic and Anharmonic Behaviour of a Simple Oscillator

    Science.gov (United States)

    O'Shea, Michael J.

    2009-01-01

    We consider a simple oscillator that exhibits harmonic and anharmonic regimes and analyse its behaviour over the complete range of possible amplitudes. The oscillator consists of a mass "m" fixed at the midpoint of a horizontal rope. For zero initial rope tension and small amplitude the period of oscillation, tau, varies as tau is approximately…

  1. Exact solutions to quadratic gravity

    Czech Academy of Sciences Publication Activity Database

    Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

    2017-01-01

    Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

  2. On Quadratic Variation of Martingales

    Indian Academy of Sciences (India)

    where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...

  3. Exact solutions to quadratic gravity

    Czech Academy of Sciences Publication Activity Database

    Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

    2017-01-01

    Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

  4. Orthogonality preserving infinite dimensional quadratic stochastic operators

    International Nuclear Information System (INIS)

    Akın, Hasan; Mukhamedov, Farrukh

    2015-01-01

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators

  5. Extending the Scope of Robust Quadratic Optimization

    NARCIS (Netherlands)

    Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

    In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

  6. Design of Linear-Quadratic-Regulator for a CSTR process

    Science.gov (United States)

    Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

    2017-11-01

    This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

  7. Investigation of the vibration spectrum of SbSI crystals in harmonic and in anharmonic approximations

    International Nuclear Information System (INIS)

    Audzijonis, A.; Zigas, L.; Vinokurova, I.V.; Farberovic, O.V.; Zaltauskas, R.; Cijauskas, E.; Pauliukas, A.; Kvedaravicius, A.

    2006-01-01

    The force constants of SbSI crystal have been calculated by the pseudo-potential method. The frequencies and normal coordinates of SbSI vibration modes along the c (z) direction have been determined in harmonic approximation. The potential energies of SbSI normal modes dependence on normal coordinates along the c (z) direction V(z) have been determined in anharmonic approximation, taking into account the interaction between the phonons. It has been found, that in the range of 30-120 cm -1 , the vibrational spectrum is determined by a V(z) double-well normal mode, but in the range of 120-350 cm -1 , it is determined by a V(z) single-well normal mode

  8. Anharmonic vibrational modes of chemisorbed H on the Rh(001) surface

    International Nuclear Information System (INIS)

    Hamann, D.R.; Feibelman, P.J.

    1988-01-01

    The potential for H atoms in the vicinity of the fourfold hollow chemisorption site on the Rh(001) surface at monolayer coverage is calculated using local-density-functional theory, and the linear-augmented-plane-wave method. The potential is found to contain important anharmonic components, one that couples parallel and perpendicular motion, and another producing azimuthal anisotropy. Variational solutions are found for the ground and low-lying excited states of H and D in this potential. The fundamental asymmetric- and symmetric-stretch H vibrational excitations are found to have energies of 67 and 92 meV. The latter agrees with recent experimental results, and higher-lying experimental modes are interpreted as mixed excitations. Comparisons are made with spring-constant models, calculated potentials for H on Ni and Pd(001), and theories of Bloch states for H on Ni

  9. Coherent states for quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  10. Quadratic Variation by Markov Chains

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Horel, Guillaume

    We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...

  11. Factorization method of quadratic template

    Science.gov (United States)

    Kotyrba, Martin

    2017-07-01

    Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

  12. Optimal control linear quadratic methods

    CERN Document Server

    Anderson, Brian D O

    2007-01-01

    This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

  13. Dirac bound states of anharmonic oscillator in external fields

    International Nuclear Information System (INIS)

    Hamzavi, Majid; Ikhdair, Sameer M.; Falaye, Babatunde J.

    2014-01-01

    We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method. -- Highlights: • Effect of the external fields on the energy levels of Dirac particle with the anharmonic oscillator is investigated. • The solutions are discussed in view of spin and pseudospin symmetries limits. • The energy levels and wave function are presented by the Nikiforov–Uvarov method

  14. Anharmonic phonons and magnons in BiFeO3

    Energy Technology Data Exchange (ETDEWEB)

    Delaire, Olivier A [ORNL; Ma, Jie [ORNL; Stone, Matthew B [ORNL; Huq, Ashfia [ORNL; Gout, Delphine J [ORNL; Brown, Craig [National Institute of Standards and Technology (NIST); Wang, Kefeng [Nanjing National Laboratory of Microstructures, Nanjing University, Nanjing; Ren, Zhifeng [Boston College, Chestnut Hill

    2012-01-01

    The phonon density of states (DOS) and magnetic excitation spectrum of polycrystalline BiFeO3 were measured for temperatures 200 < T < 750K , using inelastic neutron scattering (INS). Our results indicate that the magnetic spectrum of BiFeO3 closely resembles that of similar Fe perovskites, such as LaFeO3, despite the cycloid modulation in BiFeO3. We do not find any evidence for a spin gap. A strong T-dependence of the phonon DOS was found, with a marked broadening of the whole spectrum, providing evidence of strong anharmonicity. This anharmonicity is corroborated by large amplitude motions of Bi and O ions observed with neutron diffraction. These results highlight the importance of spin-phonon coupling in this material.

  15. Instantons and Borel resummability for the perturbed supersymmetric anharmonic oscillator

    International Nuclear Information System (INIS)

    Verbaarschot, J.J.M.; West, P.

    1991-01-01

    In this paper we give an analytical derivation of the large-order behavior of the perturbation series for both the ground state and the excited states of the supersymmetric anharmonic oscillator and of the anharmonic oscillator obtained from the supersymmetric case by varying the strength of the fermion coupling. The results which are obtained with the help of instanton calculus coincide with those obtained numerically in previous work. The large-order perturbation series of the ground state vanishes in the supersymmetric case, whereas away from the supersymmetric point the perturbation series diverges factorially. The perturbation series of the excited states diverges factorially both at the supersymmetric point and away from this point

  16. Finite-element time evolution operator for the anharmonic oscillator

    Science.gov (United States)

    Milton, Kimball A.

    1995-01-01

    The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

  17. Computer Program for Inelastic Neutron Scattering by an Anharmonic Crystal

    International Nuclear Information System (INIS)

    Bohlin, L.; Ebbsjoe, I.; Hoegberg, T.

    1969-02-01

    A description is given of the program SAW (Shift and Width), which calculates the energy-dependent shift and width of the intensity peaks obtained for thermal neutrons scattered inelastically by an anharmonic crystal. The program has been coded in FORTRAN IV and may be applied to every solid with a monatomic face-centered cubic lattice where the intermolecular interactions can be described by a centro-symmetrical potential. Interactions beyond third neighbours are neglected

  18. Computer Program for Inelastic Neutron Scattering by an Anharmonic Crystal

    Energy Technology Data Exchange (ETDEWEB)

    Bohlin, L; Ebbsjoe, I; Hoegberg, T

    1969-02-15

    A description is given of the program SAW (Shift and Width), which calculates the energy-dependent shift and width of the intensity peaks obtained for thermal neutrons scattered inelastically by an anharmonic crystal. The program has been coded in FORTRAN IV and may be applied to every solid with a monatomic face-centered cubic lattice where the intermolecular interactions can be described by a centro-symmetrical potential. Interactions beyond third neighbours are neglected.

  19. Jacobian elliptic wave solutions in an anharmonic molecular crystal model

    International Nuclear Information System (INIS)

    Teh, C.G.R.; Lee, B.S.; Koo, W.K.

    1997-07-01

    Explicit Jacobian elliptic wave solutions are found in the anharmonic molecular crystal model for both the continuum limit and discrete modes. This class of wave solutions include the famous pulse-like and kink-like solitary modes. We would also like to report on the existence of some highly discrete staggered solitary wave modes not found in the continuum limit. (author). 9 refs, 1 fig

  20. Quadratic reactivity fuel cycle model

    International Nuclear Information System (INIS)

    Lewins, J.D.

    1985-01-01

    For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

  1. Quantum versus semiclassical description of self-trapping: Anharmonic effects

    International Nuclear Information System (INIS)

    Raghavan, S.; Bishop, A.R.; Kenkre, V.M.

    1999-01-01

    Self-trapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum-mechanical analysis of a two-site system, where the oscillator is described by a tunably anharmonic potential, with a square well with infinite walls and the harmonic potential as its extreme limits, and wherein the interaction is nonlinear in the oscillator displacement. We find that even highly anharmonic polarons behave similar to their harmonic counterparts in that self-trapping is preserved for long times in the limit of strong coupling, and that the polaronic tunneling time scale depends exponentially on the polaron binding energy. Further, in agreement, with earlier results related to harmonic polarons, the semiclassical approximation agrees with the full quantum result in the massive oscillator limit of small oscillator frequency and strong quasiparticle-oscillator coupling. copyright 1999 The American Physical Society

  2. Fragility, anharmonicity and anelasticity of silver borate glasses

    International Nuclear Information System (INIS)

    Carini, Giovanni; Carini, Giuseppe; D'Angelo, Giovanna; Tripodo, Gaspare; Bartolotta, Antonio; Marco, Gaetano Di

    2006-01-01

    The fragility and the anharmonicity of (Ag 2 O) x (B 2 O 3 ) 1-x borate glasses have been quantified by measuring the change in the specific heat capacity at the glass transition temperature T g and the room-temperature thermodynamic Grueneisen parameter. Increasing the silver oxide content above X = 0.10 leads to an increase of both the parameters, showing that a growing fragility of a glass-forming liquid is predictive of an increasing overall anharmonicity of its glassy state. The attenuation and velocity of ultrasonic waves of frequencies in the range of 10-70 MHz have also been measured in silver borate glasses as a function of temperature between 1.5 and 300 K. The experimental data reveal anelastic behaviours which are governed by (i) quantum-mechanical tunnelling below 20 K (ii) thermally activated relaxations between 20 and 200 K and (iii) vibrational anharmonicity at even higher temperatures. Evaluation of tunnelling (C) and relaxation (C * ) strengths shows that C is independent of the structural changes affecting the borate network with increasing metal oxide content and is at least one order of magnitude smaller than C * . The latter observation implies that only a small fraction of the locally mobile defects are subjected to tunnelling motions

  3. On the buckling of magnetothermoviscoelastic plate and an associated quadratic operator bundle

    International Nuclear Information System (INIS)

    El-Sayed, M.A.

    1987-10-01

    The paper is devoted to the application of the theory of quadratic self-adjoint operator bundles to investigate the problem of oscillations and stability of an isotropic homogeneous, thermoviscoelastic ferromagnetic plate of arbitrary shape, small constant thickness and infinite electric conductivity, placed in a transverse uniform constant magnetic field and clamped along its whole boundary. 14 refs

  4. The construction of partner potential from the general potential anharmonic in D-dimensional Schrodinger system

    Science.gov (United States)

    Suparmi; Cari, C.; Wea, K. N.; Wahyulianti

    2018-03-01

    The Schrodinger equation is the fundamental equation in quantum physics. The characteristic of the particle in physics potential field can be explained by using the Schrodinger equation. In this study, the solution of 4 dimensional Schrodinger equation for the anharmonic potential and the anharmonic partner potential have done. The method that used to solve the Schrodinger equation was the ansatz wave method, while to construction the partner potential was the supersymmetric method. The construction of partner potential used to explain the experiment result that cannot be explained by the original potential. The eigenvalue for anharmonic potential and the anharmonic partner potential have the same characteristic. Every increase of quantum orbital number the eigenvalue getting smaller. This result corresponds to Bohrn’s atomic theory that the eigenvalue is inversely proportional to the atomic shell. But the eigenvalue for the anharmonic partner potential higher than the eigenvalue for the anharmonic original potential.

  5. Dynamical invariants for variable quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Suslov, Sergei K

    2010-01-01

    We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

  6. Quadratically convergent MCSCF scheme using Fock operators

    International Nuclear Information System (INIS)

    Das, G.

    1981-01-01

    A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

  7. Geometrical and Graphical Solutions of Quadratic Equations.

    Science.gov (United States)

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  8. Multiobjective Optimization Involving Quadratic Functions

    Directory of Open Access Journals (Sweden)

    Oscar Brito Augusto

    2014-01-01

    Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

  9. Quadratic Lagrangians and Legendre transformation

    International Nuclear Information System (INIS)

    Magnano, G.

    1988-01-01

    In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor

  10. An efficient and accurate framework for calculating lattice thermal conductivity of solids: AFLOW—AAPL Automatic Anharmonic Phonon Library

    Science.gov (United States)

    Plata, Jose J.; Nath, Pinku; Usanmaz, Demet; Carrete, Jesús; Toher, Cormac; de Jong, Maarten; Asta, Mark; Fornari, Marco; Nardelli, Marco Buongiorno; Curtarolo, Stefano

    2017-10-01

    One of the most accurate approaches for calculating lattice thermal conductivity, , is solving the Boltzmann transport equation starting from third-order anharmonic force constants. In addition to the underlying approximations of ab-initio parameterization, two main challenges are associated with this path: high computational costs and lack of automation in the frameworks using this methodology, which affect the discovery rate of novel materials with ad-hoc properties. Here, the Automatic Anharmonic Phonon Library (AAPL) is presented. It efficiently computes interatomic force constants by making effective use of crystal symmetry analysis, it solves the Boltzmann transport equation to obtain , and allows a fully integrated operation with minimum user intervention, a rational addition to the current high-throughput accelerated materials development framework AFLOW. An "experiment vs. theory" study of the approach is shown, comparing accuracy and speed with respect to other available packages, and for materials characterized by strong electron localization and correlation. Combining AAPL with the pseudo-hybrid functional ACBN0 is possible to improve accuracy without increasing computational requirements.

  11. Nuclear constants

    International Nuclear Information System (INIS)

    Foos, J.

    1999-01-01

    This paper is written in two tables. The first one describes the different particles (bosons and fermions). The second one gives the isotopes nuclear constants of the different elements, for Z = 1 to 56. (A.L.B.)

  12. Nuclear constants

    International Nuclear Information System (INIS)

    Foos, J.

    2000-01-01

    This paper is written in two tables. The first one describes the different particles (bosons and fermions). The second one gives the isotopes nuclear constants of the different elements, for Z = 56 to 68. (A.L.B.)

  13. Nuclear constants

    International Nuclear Information System (INIS)

    Foos, J.

    1998-01-01

    This paper is made of two tables. The first table describes the different particles (bosons and fermions) while the second one gives the nuclear constants of isotopes from the different elements with Z = 1 to 25. (J.S.)

  14. Nuclear constants

    International Nuclear Information System (INIS)

    Foos, J.

    1999-01-01

    This paper is written in two tables. The first one describes the different particles (bosons and fermions). The second one gives the isotopes nuclear constants of the different elements, for Z = 56 to 68. (A.L.B.)

  15. Novel interpolative perturbation theory for quantum anharmonic oscillators in one and three dimensions and the ground state of a lattice model of the phi4 field theory

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1977-01-01

    A new method for approximating the eigenfunctions and eigenvalues of anharmonic oscillators. An attempt was made to develop an analytic method which provides simple formulae for all values of the parameters as the W.K.B. approximation and perturbation theory do for certain limiting case, and which has the convergence properties associated with the computer methods. The procedure is based upon combining knowledge of the asymptotic behavior of the wave function for large and small values of the coordinate(s) to obtain approximations valid for all values of coordinate(s) and all strengths of the anharmonicity. A systematic procedure for improving these approximations is developed. Finally the groundstate of a lattice model of the phi 4 field theory which consists of an infinite number of coupled anharmonic oscillators. A first order calculation yields a covariant expression for the groundstate eigenvalue with the physical mass, m, given by a characteristic polynomial which involves the bare mass, μ, the lattice spacing, l, and the coupling constant, lambda. For l > 0, μ can be adjusted (a mass renormalization) 0 < m < infinity. As l → 0 lambda (l) (a charge renormalization) is adjusted so that lambda/sup 1/3//l → eta, a constant, as l → 0. Then eta can be chosen so that m can take any experimental value

  16. Quadratic independence of coordinate functions of certain ...

    Indian Academy of Sciences (India)

    ... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

  17. Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

    African Journals Online (AJOL)

    Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

  18. An example in linear quadratic optimal control

    NARCIS (Netherlands)

    Weiss, George; Zwart, Heiko J.

    1998-01-01

    We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

  19. Quadratic Boost A-Source Impedance Network

    DEFF Research Database (Denmark)

    Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

    2016-01-01

    A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

  20. Phonon density of states and anharmonicity of UO2

    Science.gov (United States)

    Pang, Judy W. L.; Chernatynskiy, Aleksandr; Larson, Bennett C.; Buyers, William J. L.; Abernathy, Douglas L.; McClellan, Kenneth J.; Phillpot, Simon R.

    2014-03-01

    Phonon density of states (PDOS) measurements have been performed on polycrystalline UO2 at 295 and 1200 K using time-of-flight inelastic neutron scattering to investigate the impact of anharmonicity on the vibrational spectra and to benchmark ab initio PDOS simulations performed on this strongly correlated Mott insulator. Time-of-flight PDOS measurements include anharmonic linewidth broadening, inherently, and the factor of ˜7 enhancement of the oxygen spectrum relative to the uranium component by the increased neutron sensitivity to the oxygen-dominated optical phonon modes. The first-principles simulations of quasiharmonic PDOS spectra were neutron weighted and anharmonicity was introduced in an approximate way by convolution with wave-vector-weighted averages over our previously measured phonon linewidths for UO2, which are provided in numerical form. Comparisons between the PDOS measurements and the simulations show reasonable agreement overall, but they also reveal important areas of disagreement for both high and low temperatures. The discrepancies stem largely from a ˜10 meV compression in the overall bandwidth (energy range) of the oxygen-dominated optical phonons in the simulations. A similar linewidth-convoluted comparison performed with the PDOS spectrum of Dolling et al. obtained by shell-model fitting to their historical phonon dispersion measurements shows excellent agreement with the time-of-flight PDOS measurements reported here. In contrast, we show by comparisons of spectra in linewidth-convoluted form that recent first-principles simulations for UO2 fail to account for the PDOS spectrum determined from the measurements of Dolling et al. These results demonstrate PDOS measurements to be stringent tests for ab inito simulations of phonon physics in UO2 and they indicate further the need for advances in theory to address the lattice dynamics of UO2.

  1. Anharmonicity and hydrogen bonding in electrooptic sucrose crystal

    Science.gov (United States)

    Szostak, M. M.; Giermańska, J.

    1990-03-01

    The polarized absorption spectra of the sucrose crystal in the 5300 - 7300 cm -1 region have been measured. The assignments of all the eight OH stretching overtones are proposed and their mechanical anharmonicities are estimated. The discrepancies from the oriented gas model (OGM) in the observed relative band intensities, especially of the -CH vibrations, are assumed to be connected with vibronic couplings enhanced by the helical arrangement of molecules joined by hydrogen bondings. It seems that this kind of interactions might be important for the second harmonic generation (SHG) by the sucrose crystal.

  2. Quadratic Hedging of Basis Risk

    Directory of Open Access Journals (Sweden)

    Hardy Hulley

    2015-02-01

    Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.

  3. Are fundamental constants really constant

    International Nuclear Information System (INIS)

    Norman, E.B.

    1986-01-01

    Reasons for suspecting that fundamental constants might change with time are reviewed. Possible consequences of such variations are examined. The present status of experimental tests of these ideas is discussed

  4. Remarks on the choice of trial hamiltonians for the quantum statistical treatment of anharmonic systems

    International Nuclear Information System (INIS)

    Tsallis, C.; Valle, J.W.F.

    1979-01-01

    The use of the Variational Method to discuss Quantum Statistical Mechanics of anharmonic systems requires, in order to be able to obtain the correct classical limit, the allowance for renormalization of every operator whose definition depends on the harmonic coefficients. The point is exhibited for a single anharmonic oscillator. In this particular case there is no need for mass renormalization. (Author) [pt

  5. Phonon anharmonicity and Gruneisen parameters of alpha-plutonium

    International Nuclear Information System (INIS)

    Filanovich, A.N.; Povzner, A.A.

    2015-01-01

    A self-consistent thermodynamic model of alpha-phase of plutonium is constructed. The calculations of thermal and elastic properties of α-Pu, carried out within this model, demonstrate that anomalously strong temperature dependence of the bulk modulus and unusually high value of the coefficient of thermal expansion of α-Pu are caused by its strong lattice anharmonicity. The isothermal and isobaric Gruneisen parameters of α-Pu and δ-Pu Pu_0_._9_6Ga_0_._0_4 are calculated. It is shown that wide spread of the values of Gruneisen parameter of α-Pu, obtained previously from different experimental data, is explained by the dependence of Gruneisen parameter of α-Pu on temperature. - Highlights: • A self-consistent thermodynamic model of alpha-plutonium is developed. • Thermal and elastic properties of alpha-plutonium are calculated. • The reason of spread in the values of Gruneisen parameter of alpha-Pu is established. • Different types of phonon anharmonicity in alpha-Pu and delta-Pu are revealed.

  6. linear-quadratic-linear model

    Directory of Open Access Journals (Sweden)

    Tanwiwat Jaikuna

    2017-02-01

    Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

  7. Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x) = Ax{sup 2α} + Bx{sup 2}

    Energy Technology Data Exchange (ETDEWEB)

    Al Sdran, N. [King Khalid University, Faculty of Science, Physics Department P.O. Box 9004 Abha (Saudi Arabia); Najran University, Faculty of Sciences and Arts, Najran (Saudi Arabia); Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department P.O. Box 9004 Abha (Saudi Arabia); Thermal Process Laboratory Research and Technologies Centre of Energy, BP 95, 2050 Hammam-lif (Tunisia)

    2016-06-15

    The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x) = Ax{sup 2α} + Bx{sup 2}, (A>0, B<0), with (α = 2) for quadratic, (α =3) for sextic and (α =4) for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x) by a piecewise-linear potential v(x), while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

  8. Designing Camera Networks by Convex Quadratic Programming

    KAUST Repository

    Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

    2015-01-01

    be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

  9. Schur Stability Regions for Complex Quadratic Polynomials

    Science.gov (United States)

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  10. Quadratic Functionals with General Boundary Conditions

    International Nuclear Information System (INIS)

    Dosla, Z.; Dosly, O.

    1997-01-01

    The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions

  11. Linear quadratic optimization for positive LTI system

    Science.gov (United States)

    Muhafzan, Yenti, Syafrida Wirma; Zulakmal

    2017-05-01

    Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

  12. Radiotherapy treatment planning linear-quadratic radiobiology

    CERN Document Server

    Chapman, J Donald

    2015-01-01

    Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

  13. Solitons in quadratic nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2001-01-01

    We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

  14. Resolving the Origins of Crystalline Anharmonicity Using Terahertz Time-Domain Spectroscopy and ab Initio Simulations.

    Science.gov (United States)

    Ruggiero, Michael T; Zeitler, J Axel

    2016-11-17

    Anharmonicity has been shown to be an important piece of the fundamental framework that dictates numerous observable phenomena. In particular, anharmonicity is the driving force of vibrational relaxation processes, mechanisms that are integral to the proper function of numerous chemical processes. However, elucidating its origins has proven difficult due to experimental and theoretical challenges, specifically related to separating the anharmonic contributions from other unrelated effects. While no one technique is particularly suited for providing a complete picture of anharmonicity, by combining multiple complementary methods such a characterization can be made. In this study the role of individual atomic interactions on the anharmonic properties of crystalline purine, the building block of many DNA and RNA nucleobases, is studied by experimental terahertz time-domain spectroscopy and first-principles density functional theory (DFT) and ab initio molecular dynamics simulations (AIMD). In particular, the detailed vibrational information provided by the DFT calculations is used to interpret the atomic origins of anharmonic-related effects as determined by the AIMD calculations, which are in good agreement with the experimental data. The results highlight that anharmonicity is especially pronounced in the intermolecular interactions, particularly along the amine hydrogen bond coordinate, and yields valuable insight into what is similarly observed complex biosystems and crystalline solids.

  15. DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

    Science.gov (United States)

    Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

    2016-10-01

    This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

  16. Terahertz generation via laser coupling to anharmonic carbon nanotube array

    Science.gov (United States)

    Sharma, Soni; Vijay, A.

    2018-02-01

    A scheme of terahertz radiation generation employing a matrix of anharmonic carbon nanotubes (CNTs) embedded in silica is proposed. The matrix is irradiated by two collinear laser beams that induce large excursions on CNT electrons and exert a nonlinear force at the beat frequency ω = ω1-ω2. The force derives a nonlinear current producing THz radiation. The THz field is resonantly enhanced at the plasmon resource, ω = ω p ( 1 + β ) / √{ 2 } , where ωp is the plasma frequency and β is a characteristic parameter. Collisions are a limiting factor, suppressing the plasmon resonance. For typical values of plasma parameters, we obtain power conversion efficiency of the order of 10-6.

  17. A quantum anharmonic oscillator model for the stock market

    Science.gov (United States)

    Gao, Tingting; Chen, Yu

    2017-02-01

    A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.

  18. Approximation methods for the partition functions of anharmonic systems

    International Nuclear Information System (INIS)

    Lew, P.; Ishida, T.

    1979-07-01

    The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations

  19. Anharmonic effective pair potentials of gold under high pressure and high temperature

    CERN Document Server

    Okube, M; Ohtaka, O; Fukui, H; Katayama, Y; Utsumi, W

    2002-01-01

    In order to examine the effect of pressure on the anharmonicity of Au, extended x-ray absorption fine-structure spectra near the Au L sub 3 edge were measured in the temperature range from 300 to 1100 K under pressures up to 14 GPa using large-volume high-pressure devices and synchrotron radiation. The anharmonic effective pair potentials of Au, V (u) = au sup 2 + bu sup 3 , at 0.1 MPa, 6 and 14 GPa have been calculated. The pressure dependence of the thermal expansion coefficients has also been evaluated. The reliability of the anharmonic correction proposed on the basis of the Anderson scale has been discussed.

  20. Ab initio calculations of anharmonic vibrational circular dichroism intensities of trans-2,3-dideuteriooxirane

    DEFF Research Database (Denmark)

    Bak, KL; Bludsky, O.; Jorgensen, P

    1995-01-01

    A priori theory is derived for anharmonic calculations of vibrational circular dichroism (VCD). The anharmonic VCD expression is gauge origin independent and reduce to the magnetic field perturbation theory expression in the double-harmonic approximation. The theory has been implemented using...... for the atomic axial tensors and using second-order Moller-Plesset theory for the atomic polar tensors and the force fields, The changes of the vibrational rotatory strengths from anharmonicities are small, and do not explain the previously observed large discrepancies between the double-harmonic results...

  1. Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2006-01-01

    This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

  2. Fluctuations and Anharmonicity in Lead Iodide Perovskites from Molecular Dynamics Supercell Simulationss

    KAUST Repository

    Carignano, Marcelo André s; Aravindh, S. Assa; Roqan, Iman S.; Even, Jacky; Katan, Claudine

    2017-01-01

    cations as the temperature is decreased from 450 K. The reverse transformation from tetragonal to cubic is also monitored through the large distribution of the octahedral tilting angles accompanied by an increase in the anharmonicity of the iodine atoms

  3. A New Quasi-Exactly Solvable Problem and Its Connection with an Anharmonic Oscillator

    International Nuclear Information System (INIS)

    Yang Dabao; Zhang Fulin; Chen Jingling

    2010-01-01

    The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KS transformation. (general)

  4. Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals

    Energy Technology Data Exchange (ETDEWEB)

    Jasper, Ahren W. [Chemical Sciences and Engineering; Gruey, Zackery B. [Chemical Sciences and Engineering; Harding, Lawrence B. [Chemical Sciences and Engineering; Georgievskii, Yuri [Chemical Sciences and Engineering; Klippenstein, Stephen J. [Chemical Sciences and Engineering; Wagner, Albert F. [Chemical Sciences and Engineering

    2018-02-03

    Monte Carlo phase space integration (MCPSI) is used to compute full dimensional and fully anharmonic, but classical, rovibrational partition functions for 22 small- and medium-sized molecules and radicals. Several of the species considered here feature multiple minima and low-frequency nonlocal motions, and efficiently sampling these systems is facilitated using curvilinear (stretch, bend, and torsion) coordinates. The curvilinear coordinate MCPSI method is demonstrated to be applicable to the treatment of fluxional species with complex rovibrational structures and as many as 21 fully coupled rovibrational degrees of freedom. Trends in the computed anharmonicity corrections are discussed. For many systems, rovibrational anharmonicities at elevated temperatures are shown to vary consistently with the number of degrees of freedom and with temperature once rovibrational coupling and torsional anharmonicity are accounted for. Larger corrections are found for systems with complex vibrational structures, such as systems with multiple large-amplitude modes and/or multiple minima.

  5. Equivalence of classical spins and Hartree-Fock-Bogoliubov approximation of the Fermionic Anharmonic Oscillator

    International Nuclear Information System (INIS)

    Thomaz, M.T.; Toledo Piza, A.F.R. de

    1994-01-01

    We show that the Hartree-Fock-Bogoliubov (alias Gaussian) approximation of the initial condition problem of the Fermionic Anharmonic Oscillator i equivalent to a bosonic Hamiltonian system of two classical spin. (author)

  6. Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress

    OpenAIRE

    Monserrat, Bartomeu; Drummond, N. D.; Needs, R. J.

    2013-01-01

    A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at finite temperatures. The low-energy portion of the Born-Oppenheimer energy surface is mapped and used to calculate the total vibrational energy including anharmonic effects, electron-phonon coupling, and the vibrational contribution to the stress tensor. W...

  7. Accurate Anharmonic Zero-Point Energies for Some Combustion-Related Species from Diffusion Monte Carlo.

    Science.gov (United States)

    Harding, Lawrence B; Georgievskii, Yuri; Klippenstein, Stephen J

    2017-06-08

    Full-dimensional analytic potential energy surfaces based on CCSD(T)/cc-pVTZ calculations have been determined for 48 small combustion-related molecules. The analytic surfaces have been used in Diffusion Monte Carlo calculations of the anharmonic zero-point energies. The resulting anharmonicity corrections are compared to vibrational perturbation theory results based both on the same level of electronic structure theory and on lower-level electronic structure methods (B3LYP and MP2).

  8. E x circle epsilon Jahn-Teller anharmonic coupling for an octahedral system

    CERN Document Server

    Avram, N M; Kibler, M R

    2001-01-01

    The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian are derived.

  9. Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space

    International Nuclear Information System (INIS)

    Daszkiewicz, Marcin; Walczyk, Cezary J.

    2008-01-01

    The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces

  10. Guises and disguises of quadratic divergences

    Energy Technology Data Exchange (ETDEWEB)

    Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  11. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  12. Nonlinear dynamics of quadratically cubic systems

    International Nuclear Information System (INIS)

    Rudenko, O V

    2013-01-01

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

  13. PSQP: Puzzle Solving by Quadratic Programming.

    Science.gov (United States)

    Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

    2017-02-01

    In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  14. Cascaded Quadratic Soliton Compression in Waveguide Structures

    DEFF Research Database (Denmark)

    Guo, Hairun

    between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

  15. On orthogonality preserving quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  16. Bound constrained quadratic programming via piecewise

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.

    1999-01-01

    of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...

  17. On orthogonality preserving quadratic stochastic operators

    International Nuclear Information System (INIS)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-01-01

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too

  18. Eigenfunctions of quadratic hamiltonians in Wigner representation

    International Nuclear Information System (INIS)

    Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

    1984-01-01

    Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

  19. Bizarre behavior of heat capacity in crystals due to interplay between two types of anharmonicities.

    Science.gov (United States)

    Yurchenko, Stanislav O; Komarov, Kirill A; Kryuchkov, Nikita P; Zaytsev, Kirill I; Brazhkin, Vadim V

    2018-04-07

    The heat capacity of classical crystals is determined by the Dulong-Petit value C V ≃ D (where D is the spatial dimension) for softly interacting particles and has the gas-like value C V ≃ D/2 in the hard-sphere limit, while deviations are governed by the effects of anharmonicity. Soft- and hard-sphere interactions, which are associated with the enthalpy and entropy of crystals, are specifically anharmonic owing to violation of a linear relation between particle displacements and corresponding restoring forces. Here, we show that the interplay between these two types of anharmonicities unexpectedly induces two possible types of heat capacity anomalies. We studied thermodynamics, pair correlations, and collective excitations in 2D and 3D crystals of particles with a limited range of soft repulsions to prove the effect of interplay between the enthalpy and entropy types of anharmonicities. The observed anomalies are triggered by the density of the crystal, changing the interaction regime in the zero-temperature limit, and can provide about 10% excess of the heat capacity above the Dulong-Petit value. Our results facilitate understanding effects of complex anharmonicity in molecular and complex crystals and demonstrate the possibility of new effects due to the interplay between different types of anharmonicities.

  20. Quadratic mass relations in topological bootstrap theory

    International Nuclear Information System (INIS)

    Jones, C.E.; Uschersohn, J.

    1980-01-01

    From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed

  1. STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY

    Directory of Open Access Journals (Sweden)

    Damián Fernández

    2014-12-01

    Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.

  2. The Quadratic Selective Travelling Salesman Problem

    DEFF Research Database (Denmark)

    Thomadsen, Tommy; Stidsen, Thomas K.

    2003-01-01

    A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

  3. orthogonal and scaling transformations of quadratic functions

    African Journals Online (AJOL)

    Preferred Customer

    functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.

  4. Fundamental quadratic variational principle underlying general relativity

    International Nuclear Information System (INIS)

    Atkins, W.K.

    1983-01-01

    The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed

  5. Investigating Students' Mathematical Difficulties with Quadratic Equations

    Science.gov (United States)

    O'Connor, Bronwyn Reid; Norton, Stephen

    2016-01-01

    This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

  6. Commuting quantum traces for quadratic algebras

    International Nuclear Information System (INIS)

    Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve

    2005-01-01

    Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians

  7. Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

    Energy Technology Data Exchange (ETDEWEB)

    Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

    2015-02-15

    This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.

  8. Anharmonicity Rise the Thermal Conductivity in Amorphous Silicon

    Science.gov (United States)

    Lv, Wei; Henry, Asegun

    We recently proposed a new method called Direct Green-Kubo Modal Analysis (GKMA) method, which has been shown to calculate the thermal conductivity (TC) of several amorphous materials accurately. A-F method has been widely used for amorphous materials. However, researchers have found out that it failed on several different materials. The missing component of A-F method is the harmonic approximation and considering only the interactions of modes with similar frequencies, which neglect interactions of modes with large frequency difference. On the contrary, GKMA method, which is based on molecular dynamics, intrinsically includes all types of phonon interactions. In GKMA method, each mode's TC comes from both mode self-correlations (autocorrelations) and mode-mode correlations (crosscorrelations). We have demonstrated that the GKMA predicted TC of a-Si from Tersoff potential is in excellent agreement with one of experimental results. In this work, we will present the GKMA applications on a-Si using multiple potentials and gives us more insight of the effect of anharmonicity on the TC of amorphous silicon. This research was supported Intel grant AGMT DTD 1-15-13 and computational resources by NSF supported XSEDE resources under allocations DMR130105 and TG- PHY130049.

  9. Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

    Directory of Open Access Journals (Sweden)

    Xue-Gang Zhou

    2014-01-01

    Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

  10. Vibrational spectroscopy of the G...C base pair: Experiment, harmonic and anharmonic calculations, and the nature of the anharmonic couplings

    Czech Academy of Sciences Publication Activity Database

    Brauer, B.; Gerber, R. B.; Kabeláč, Martin; Hobza, Pavel; Bakker, J. M.; Abo-Riziq, A.; Vries de, M. S.

    2005-01-01

    Roč. 109, - (2005), s. 6974-6984 ISSN 1089-5639 Grant - others:NSF(US) CHE-0244341 Institutional research plan: CEZ:AV0Z40550506 Keywords : nucleic acids bases * vibrational spectrum * frequencies anharmonicity Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.898, year: 2005

  11. Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

    Science.gov (United States)

    Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal

    2017-03-01

    Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

  12. Graviton fluctuations erase the cosmological constant

    Science.gov (United States)

    Wetterich, C.

    2017-10-01

    Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity, with effective Planck mass proportional to the scalar field, we find that the potential increases asymptotically at most quadratically with the scalar field. The solutions of the derived cosmological equations lead to an asymptotically vanishing cosmological "constant" in the infinite future, providing for dynamical dark energy in the present cosmological epoch. Beyond a solution of the cosmological constant problem, our simplified computation also entails a sizeable positive graviton-induced anomalous dimension for the quartic Higgs coupling in the ultraviolet regime, substantiating the successful prediction of the Higgs boson mass within the asymptotic safety scenario for quantum gravity.

  13. Geometric Approaches to Quadratic Equations from Other Times and Places.

    Science.gov (United States)

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  14. HIGH-RESOLUTION IR ABSORPTION SPECTROSCOPY OF POLYCYCLIC AROMATIC HYDROCARBONS: THE REALM OF ANHARMONICITY

    Energy Technology Data Exchange (ETDEWEB)

    Maltseva, Elena; Buma, Wybren Jan [University of Amsterdam, Science Park 904, 1098 XH Amsterdam (Netherlands); Petrignani, Annemieke; Candian, Alessandra; Mackie, Cameron J.; Tielens, Alexander G. G. M. [Leiden Observatory, Niels Bohrweg 2, 2333 CA Leiden (Netherlands); Huang, Xinchuan; Lee, Timothy J. [SETI Institute, 189 Bernardo Avenue, Suite 100, Mountain View, CA 94043 (United States); Oomens, Jos, E-mail: w.j.buma@uva.nl, E-mail: petrignani@strw.leidenuniv.nl [Radboud University, Toernooiveld 7, 6525 ED Nijmegen (Netherlands)

    2015-11-20

    We report on an experimental and theoretical investigation of the importance of anharmonicity in the 3-μm CH stretching region of polycyclic aromatic hydrocarbon (PAH) molecules. We present mass-resolved, high-resolution spectra of the gas-phase cold (∼4 K) linear PAH molecules naphthalene, anthracene, and tetracene. The measured IR spectra show a surprisingly high number of strong vibrational bands. For naphthalene, the observed bands are well separated and limited by the rotational contour, revealing the band symmetries. Comparisons are made to the harmonic and anharmonic approaches of the widely used Gaussian software. We also present calculated spectra of these acenes using the computational program SPECTRO, providing anharmonic predictions with a Fermi-resonance treatment that utilizes intensity redistribution. We demonstrate that the anharmonicity of the investigated acenes is strong, dominated by Fermi resonances between the fundamental and double combination modes, with triple combination bands as possible candidates to resolve remaining discrepancies. The anharmonic spectra as calculated with SPECTRO lead to predictions of the main bands that fall within 0.5% of the experimental frequencies. The implications for the aromatic infrared bands, specifically the 3-μm band, are discussed.

  15. High-Resolution IR Absorption Spectroscopy of Polycyclic Aromatic Hydrocarbons: The Realm of Anharmonicity

    Science.gov (United States)

    Maltseva, Elena; Petrignani, Annemieke; Candian, Alessandra; Mackie, Cameron J.; Huang, Xinchuan; Lee, Timothy J.; Tielens, Alexander G. G. M.; Oomens, Jos; Buma, Wybren Jan

    2016-01-01

    We report on an experimental and theoretical investigation of the importance of anharmonicity in the 3 micrometers CH stretching region of Polycyclic Aromatic Hydrocarbon (PAH) molecules. We present mass-resolved, high-resolution spectra of the gas-phase cold ((is) approximately 4K) linear PAH molecules naphthalene, anthracene, and tetracene. The measured IR spectra show a surprisingly high number of strong vibrational bands. For naphthalene, the observed bands are well separated and limited by the rotational contour, revealing the band symmetries. Comparisons are made to the harmonic and anharmonic approaches of the widely used Gaussian software. We also present calculated spectra of these acenes using the computational program SPECTRO, providing anharmonic predictions enhanced with a Fermi-resonance treatment that utilizes intensity redistribution. We demonstrate that the anharmonicity of the investigated acenes is strong, dominated by Fermi resonances between the fundamental and double combination modes, with triple combination bands as possible candidates to resolve remaining discrepancies. The anharmonic spectra as calculated with SPECTRO lead to predictions of the main modes that fall within 0.5% of the experimental frequencies. The implications for the Aromatic Infrared Bands, specifically the 3-m band are discussed.

  16. Coherent states of systems with quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

    2015-06-15

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  17. Coherent states of systems with quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

    2015-01-01

    Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

  18. On quadratic residue codes and hyperelliptic curves

    Directory of Open Access Journals (Sweden)

    David Joyner

    2008-01-01

    Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

  19. Quaternion orders, quadratic forms, and Shimura curves

    CERN Document Server

    Alsina, Montserrat

    2004-01-01

    Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

  20. Quadratic hamiltonians and relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

    1981-01-01

    For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

  1. Lambda-lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, O.; Schultz, U.P.

    2004-01-01

    -lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

  2. Quadratic Interpolation and Linear Lifting Design

    Directory of Open Access Journals (Sweden)

    Joel Solé

    2007-03-01

    Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

  3. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  4. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2003-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  5. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  6. Temporal quadratic expansion nodal Green's function method

    International Nuclear Information System (INIS)

    Liu Cong; Jing Xingqing; Xu Xiaolin

    2000-01-01

    A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

  7. Walking solitons in quadratic nonlinear media

    OpenAIRE

    Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru

    1996-01-01

    We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed

  8. Quadratic Term Structure Models in Discrete Time

    OpenAIRE

    Marco Realdon

    2006-01-01

    This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

  9. Least Squares Problems with Absolute Quadratic Constraints

    Directory of Open Access Journals (Sweden)

    R. Schöne

    2012-01-01

    Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.

  10. Stochastic Linear Quadratic Optimal Control Problems

    International Nuclear Information System (INIS)

    Chen, S.; Yong, J.

    2001-01-01

    This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well

  11. Electrical and mechanical anharmonicities from NIR-VCD spectra of compounds exhibiting axial and planar chirality: the cases of (S)-2,3-pentadiene and methyl-d(3) (R)- and (S)-[2.2]paracyclophane-4-carboxylate.

    Science.gov (United States)

    Abbate, Sergio; Longhi, Giovanna; Gangemi, Fabrizio; Gangemi, Roberto; Superchi, Stefano; Caporusso, Anna Maria; Ruzziconi, Renzo

    2011-10-01

    The IR and Near infrared (NIR) vibrational circular dichroism (VCD) spectra of molecules endowed with noncentral chirality have been investigated. Data for fundamental, first, and second overtone regions of (S)-2,3-pentadiene, exhibiting axial chirality, and methyl-d(3) (R)- and (S)-[2.2]paracyclophane-4-carboxylate, exhibiting planar chirality have been measured and analyzed. The analysis of NIR and IR VCD spectra was based on the local-mode model and the use of density functional theory (DFT), providing mechanical and electrical anharmonic terms for all CH-bonds. The comparison of experimental and calculated spectra is satisfactory and allows one to monitor fine details in the asymmetric charge distribution in the molecules: these details consist in the harmonic frequencies, in the principal anharmonicity constants, in both the atomic polar and axial tensors and in their first and second derivatives with respect to the CH-stretching coordinates. Copyright © 2011 Wiley-Liss, Inc.

  12. Quadratic tracer dynamical models tobacco growth

    International Nuclear Information System (INIS)

    Qiang Jiyi; Hua Cuncai; Wang Shaohua

    2011-01-01

    In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

  13. A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

    1999-01-01

    The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

  14. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    Science.gov (United States)

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  15. High pressure behavior of complex phosphate K2Ce[PO4]2: Grüneisen parameter and anharmonicity properties

    Science.gov (United States)

    Mishra, Karuna Kara; Bevara, Samatha; Ravindran, T. R.; Patwe, S. J.; Gupta, Mayanak K.; Mittal, Ranjan; Krishnan, R. Venkata; Achary, S. N.; Tyagi, A. K.

    2018-02-01

    Herein we reported structural stability, vibrational and thermal properties of K2Ce[PO4]2, a relatively underexplored complex phosphate of tetravalent Ce4+ from in situ high-pressure Raman spectroscopic investigations up to 28 GPa using a diamond anvil cell. The studies identified the soft phonons that lead to a reversible phase transformation above 8 GPa, and a phase coexistence of ambient (PI) and high pressure (PII) phases in a wider pressure region 6-11 GPa. From a visual representation of the computed eigen vector displacements, the Ag soft mode at 82 cm-1 is assigned as a lattice mode of K+ cation. Pressure-induced positional disorder is apparent from the substantial broadening of internal modes and the disappearance of low frequency lattice and external modes in phase PII above 18 GPa. Isothermal mode Grüneisen parameters γi of the various phonon modes are calculated and compared for several modes. Using these values, thermal properties such as average Grüneisen parameter, and thermal expansion coefficient are estimated as 0.47, and 2.5 × 10-6 K-1, respectively. The specific heat value was estimated from all optical modes obtained from DFT calculations as 314 J-mol-1 K-1. Our earlier reported temperature dependence of phonon frequencies is used to decouple the "true anharmonic" (explicit contribution at constant volume) and "quasi harmonic" (implicit contribution brought out by volume change) contributions from the total anharmonicity. In addition to the 81 cm-1 Ag lattice mode, several other lattice and external modes of PO43- ions are found to be strongly anharmonic.

  16. Exchange–correlation errors at harmonic and anharmonic orders ...

    Indian Academy of Sciences (India)

    Unknown

    coefficient of linear expansion α as a function of tem- perature, obtained by differentiating our results for the lattice constant as a function of temperature. It is seen from the figure that the LDA underestimates not only the static lattice constant (as mentioned above), but also the coefficient of thermal expansion at all ...

  17. Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions.

    Science.gov (United States)

    Danecek, Petr; Kapitán, Josef; Baumruk, Vladimír; Bednárová, Lucie; Kopecký, Vladimír; Bour, Petr

    2007-06-14

    The difference spectroscopy of the Raman optical activity (ROA) provides extended information about molecular structure. However, interpretation of the spectra is based on complex and often inaccurate simulations. Previously, the authors attempted to make the calculations more robust by including the solvent and exploring the role of molecular flexibility for alanine and proline zwitterions. In the current study, they analyze the IR, Raman, and ROA spectra of these molecules with the emphasis on the force field modeling. Vibrational harmonic frequencies obtained with 25 ab initio methods are compared to experimental band positions. The role of anharmonic terms in the potential and intensity tensors is also systematically explored using the vibrational self-consistent field, vibrational configuration interaction (VCI), and degeneracy-corrected perturbation calculations. The harmonic approach appeared satisfactory for most of the lower-wavelength (200-1800 cm(-1)) vibrations. Modern generalized gradient approximation and hybrid density functionals, such as the common B3LYP method, provided a very good statistical agreement with the experiment. Although the inclusion of the anharmonic corrections still did not lead to complete agreement between the simulations and the experiment, occasional enhancements were achieved across the entire region of wave numbers. Not only the transitional frequencies of the C-H stretching modes were significantly improved but also Raman and ROA spectral profiles including N-H and C-H lower-frequency bending modes were more realistic after application of the VCI correction. A limited Boltzmann averaging for the lowest-frequency modes that could not be included directly in the anharmonic calculus provided a realistic inhomogeneous band broadening. The anharmonic parts of the intensity tensors (second dipole and polarizability derivatives) were found less important for the entire spectral profiles than the force field anharmonicities (third

  18. Neutron scattering by anharmonic crystals and the effect of sublattice displacements

    International Nuclear Information System (INIS)

    Viswanathan, K.S.; Phillip, Jacob

    1979-01-01

    A theory has been described for the scattering of neutrons by anharmonic crystals, for which terms of the type Vsup(3) (k 1 j 1 ;-k 1 j 1 ;aj) which contribute to the sublattice displacements are not neglected. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. (author)

  19. Quadratic stochastic operators: Results and open problems

    International Nuclear Information System (INIS)

    Ganikhodzhaev, R.N.; Rozikov, U.A.

    2009-03-01

    The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)

  20. Sequential Quadratic Programming Algorithms for Optimization

    Science.gov (United States)

    1989-08-01

    quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the

  1. On a quadratic inverse eigenvalue problem

    International Nuclear Information System (INIS)

    Cai, Yunfeng; Xu, Shufang

    2009-01-01

    This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

  2. Quadratic forms for Feynman-Kac semigroups

    International Nuclear Information System (INIS)

    Hibey, Joseph L.; Charalambous, Charalambos D.

    2006-01-01

    Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

  3. Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2004-01-01

    A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

  4. Rotational states of Bose gases with attractive interactions in anharmonic traps

    International Nuclear Information System (INIS)

    Lundh, Emil; Collin, Anssi; Suominen, Kalle-Antti

    2004-01-01

    A rotated and harmonically trapped Bose gas with attractive interactions is expected to either remain stationary or escape from the trap. Here we report that, on the contrary, in an anharmonic trapping potential the Bose gas with attractive interactions responds to external rotation very differently, namely, through center-of-mass motion or by formation of vortices

  5. Scattering of acoustic waves from a surface in the presence of an anharmonic interface

    DEFF Research Database (Denmark)

    Kulak, A.; Lodziana, Zbigniew; Srokowski, T.

    2002-01-01

    Energy transfer coefficient (analogue of LDOS) and aperiodicity index are defined to characterise the nonlinear response and the surface resonances in a thin layer separated from the underlying bulk crystal by an anharmonic interface. Regions of periodic, aperiodic and intermittent motion of the ...

  6. Internal oscillation frequencies and anharmonic effects for the double sine-Gordon kink

    DEFF Research Database (Denmark)

    Salerno, M.; Samuelsen, Mogens Rugholm

    1989-01-01

    A simple derivation of the small oscillation frequency around 4π-kink solutions of the double sine-Gordon equation is presented. Small corrections to these frequencies due to anharmonic effects are also numerically and analytically investigated. The analysis is based on energetic considerations...

  7. Anharmonicities of coupled β and γ vibrations discussed in a simple model

    International Nuclear Information System (INIS)

    Piepenbring, R.; Silvestre-Brac, B.; Szymanski, Z.

    1984-01-01

    The multiphonon method based on β and γ phonons is tested in a simple model allowing an exact solution for a many body fermion system where pairing and quadrupole forces are acting. The properties exhibiting the anharmonicities of the lowest-lying vibrational states of positive parity are nicely reproduced by this method. (orig.)

  8. Anharmonicities of coupled β and γ vibrations discussed in a simple model

    International Nuclear Information System (INIS)

    Piepenbring, R.; Silvestre-Brac, B.; Szymanski, Z.

    1983-11-01

    The multiphonon method based on β and γ phonons is tested in a simple model allowing an exact solution for a many body fermion system where pairing and quadrupole forces are acting. The properties exhibiting the anharmonicities of the lowest-lying vibrational states of positive parity are nicely reproduced by this method

  9. Infrared and Raman Spectra of and Isotopomers: A DFT-PT2 Anharmonic Study

    Directory of Open Access Journals (Sweden)

    Andrea Alparone

    2013-01-01

    Full Text Available IR and Raman spectra of selenophene and of its perdeuterated isotopomer have been obtained in gas phase through density-functional theory (DFT computations. Vibrational wavenumbers have been calculated using harmonic and anharmonic second-order perturbation theory (PT2 procedures with the B3LYP method and the 6-311 basis set. Anharmonic overtones have been determined by means of the PT2 method. The introduction of anharmonic terms decreases the harmonic wavenumbers, giving a significantly better agreement with the experimental data. The most significant anharmonic effects occur for the C–H and C–D stretching modes, the observed H/D isotopic wavenumber redshifts being satisfactorily reproduced by the PT2 computations within 6–20 cm−1 (1–3%. In the spectral region between 500 cm−1 and 1500 cm−1, the IR spectra are dominated by the out-of-plane C–H (C–D bending transition, whereas the Raman spectra are mainly characterized by a strong peak mainly attributed to the C=C + C–C bonds stretching vibration with the contribution of the in-plane C–H (C–D bending deformation. The current results confirm that the PT2 approach combined with the B3LYP/6-311 level of calculation is a satisfactory choice for predicting vibrational spectra of cyclic molecules.

  10. Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

    International Nuclear Information System (INIS)

    Rezende, J.

    1983-01-01

    We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)

  11. Anharmonic solution of Schrödinger time-independent equation

    Indian Academy of Sciences (India)

    243–261. Anharmonic solution of Schrödinger time-independent equation. MOHAMMED ASHRAFUL ISLAM1,2,∗ and JAMAL NAZRUL ISLAM1. 1Research Centre for Mathematical and Physical Sciences, University of Chittagong, Chittagong,. Bangladesh. 2Department of Mathematics, University of Chittagong, Chittagong, ...

  12. Anharmonic thermal vibrations of be metal found in the MEM nuclear density map

    International Nuclear Information System (INIS)

    Takata, Masaki; Sakata, Makoto; Larsen, F.K.; Kumazawa, Shintaro; Iversen, B.B.

    1993-01-01

    A direct observation of the thermal vibrations of Be metal was performed by the Maximum Entropy Method (MEM) using neutron single crystal data. In the previous study, the existence of the small but significant cubic anharmonicity of Be has been found by the conventional least squares refinement of the observed structure factors [Larsen, Lehmann and Merisalo (1980) Acta Cryst. A36, 159-163]. In the present study, the same data were used for the MEM analysis which are comprised of 48 reflections up to sinθ/λ = 1.41A -1 in order to obtain the high resolution nuclear density of Be without using any thermal vibrational model. It was directly visible in the MEM map that not only the cubic terms but also quartic anharmonicities exist in the thermal vibrations of Be nuclei. In order to evaluate thermal parameters of Be including anharmonic terms quantitatively, the least squares refinement of the effective one-particle potential (OPP) parameters up to quartic term was carried out by using the MEM nuclear densities around atomic sites as the data set to be fitted. It was found that the present treatment has a great advantage to decide the most appropriate model of OPP by visually comparing the model with MEM density map. As a result of the least squares refinement, the anharmonic thermal parameters are obtained as α 33 = -0.340(5)[eV/A 3 ], α 40 = 0, β 20 = 9.89(1)[eV/A 4 ] and γ 00 = 0. No other anharmonic term was significant. (author)

  13. Quadratic residues and non-residues selected topics

    CERN Document Server

    Wright, Steve

    2016-01-01

    This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

  14. Exact cancellation of quadratic divergences in top condensation models

    International Nuclear Information System (INIS)

    Blumhofer, A.

    1995-01-01

    We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

  15. Internal molecular dynamics of LaI3. I. Potential energy function of vibrational modes in harmonic and anharmonic approximations

    International Nuclear Information System (INIS)

    Giricheva, N.I.; Girichev, G.V.; Smorodin, S.V.

    2007-01-01

    Scanning of potential energy surface in the LaI 3 molecule along normal coordinates are realized using the B3LYP/SDD,SDD method. The most anharmonicity is shown to have a potential function of non-planar oscillation ν 2 (A 2 ''). Effect of anharmonicity on the value of mean-square oscillation amplitudes and oscillation spectrum of the molecule is established. It is noted that the account of anharmonicity of potential functions leads to decreasing mean-square oscillation amplitudes [ru

  16. Universal relation between spectroscopic constants

    Indian Academy of Sciences (India)

    , viz., ∆ 2 2re has been obtained for the ... G depends on anharmonicityωexe, (ii) ∆ is governed by the dissociation energy,De and (iii) the nature of the outer ..... solid state edited by P O Löwdin (Academic Press, New York, 1996) p. 231. [12] K P ...

  17. Agreement of quadratic and CRE models in predicting the late effects of continuous low dose-rate radiotherapy; and reply

    International Nuclear Information System (INIS)

    O'Donoghue, J.A.

    1986-01-01

    These letters discuss the problems associated with the fact that the normal tissue isoeffect formulae based on the Ellis equation (1969) do not correctly account for the late-occurring effects of fractionated radiotherapy, and with the extension of the linear quadratic model to include continuous low dose-rate radiotherapy with constant or decaying sources by R.G. Dale (1985). J.A. O'Donoghue points out that the 'late effects' and CRE curves correspond closely, whilst the 'acute effects; and CRE curves are in obvious disagreement. For continuous low-dose-rate radiotherapy, the CRE and late effects quadratic model are in agreement. Useful bibliography. (U.K.)

  18. Low-rank quadratic semidefinite programming

    KAUST Repository

    Yuan, Ganzhao

    2013-04-01

    Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

  19. Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

    International Nuclear Information System (INIS)

    Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

    2005-01-01

    The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

  20. Gain scheduled linear quadratic control for quadcopter

    Science.gov (United States)

    Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

    2017-12-01

    This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

  1. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...

  2. Low-rank quadratic semidefinite programming

    KAUST Repository

    Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng

    2013-01-01

    Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

  3. A ''quadratized'' augmented plane wave method

    International Nuclear Information System (INIS)

    Smrcka, L.

    1982-02-01

    The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)

  4. Quadratic gravity in first order formalism

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)

    2017-10-01

    We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.

  5. Large-scale sequential quadratic programming algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  6. Constant physics and characteristics of fundamental constant

    International Nuclear Information System (INIS)

    Tarrach, R.

    1998-01-01

    We present some evidence which supports a surprising physical interpretation of the fundamental constants. First, we relate two of them through the renormalization group. This leaves as many fundamental constants as base units. Second, we introduce and a dimensional system of units without fundamental constants. Third, and most important, we find, while interpreting the units of the a dimensional system, that is all cases accessible to experimentation the fundamental constants indicate either discretization at small values or boundedness at large values of the corresponding physical quantity. (Author) 12 refs

  7. Breakdown of the Arrhenius Law in Describing Vacancy Formation Energies: The Importance of Local Anharmonicity Revealed by Ab initio Thermodynamics

    Directory of Open Access Journals (Sweden)

    A. Glensk

    2014-02-01

    Full Text Available We study the temperature dependence of the Gibbs energy of vacancy formation in Al and Cu from T=0  K up to the melting temperature, fully taking into account anharmonic contributions. Our results show that the formation entropy of vacancies is not constant as often assumed but increases almost linearly with temperature. The resulting highly nonlinear temperature dependence in the Gibbs formation energy naturally explains the differences between positron annihilation spectroscopy and differential dilatometry data and shows that nonlinear thermal corrections are crucial to extrapolate high-temperature experimental data to T=0  K. Employing these corrections—rather than the linear Arrhenius extrapolation that is commonly assumed in analyzing experimental data—revised formation enthalpies are obtained that differ up to 20% from the previously accepted ones. Using the revised experimental formation enthalpies, we show that a large part of the discrepancies between DFT-GGA and unrevised experimental vacancy formation energies disappears. The substantial shift between previously accepted and the newly revised T=0  K formation enthalpies also has severe consequences in benchmarking ab initio methods against experiments, e.g., in deriving corrections that go beyond commonly used LDA and GGA exchange-correlation functionals such as the AM05 functional.

  8. The Boltzmann constant from a snifter

    International Nuclear Information System (INIS)

    Tyukodi, B; Sárközi, Zs; Néda, Z; Tunyagi, A; Györke, E

    2012-01-01

    Evaporation of a small glass of ethylic alcohol is studied both experimentally and through an elementary thermal physics approach. For a cylindrical beaker and no air flow in the room, a simple quadratic relation is found between the evaporation time and the mass of evaporated liquid. This problem and the obtained results offer excellent possibilities for simple student experiments and for testing basic principles of thermal physics. As an example, we use the obtained results for estimating the value of the Boltzmann constant from evaporation experiments. (paper)

  9. Non-chaotic behaviour for a class of quadratic jerk equations

    International Nuclear Information System (INIS)

    Malasoma, J.-M.

    2009-01-01

    It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

  10. Quadratic interaction effect on the dark energy density in the universe

    International Nuclear Information System (INIS)

    Deveci, Derya G; Aydiner, Ekrem

    2017-01-01

    In this study, we deal with the holographic model of interacting dark components of dark energy and dark matter quadratic case of the equation of state parameter (EoS). The effective equations of states for the interacting holographic energy density are derived and the results are analyzed and compared with the solution of the linear form in the literature. The result of our work shows that the value of interaction term between dark components affects the fixed points at far future in the DE-dominated universe in the case of quadratic EoS parameter; it is a different result from the linear case in the theoretical results in the literature, and as the Quintom scenario the equations of state had coincidence at the cosmological constant boundary of –1 from above to below. (paper)

  11. Orthogonal and Scaling Transformations of Quadratic Functions with ...

    African Journals Online (AJOL)

    In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

  12. Quadratic Twists of Rigid Calabi–Yau Threefolds Over

    DEFF Research Database (Denmark)

    Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

    2013-01-01

    of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

  13. Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

    Directory of Open Access Journals (Sweden)

    Park Choonkil

    2011-01-01

    Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

  14. A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

    NARCIS (Netherlands)

    de Klerk, E.; Pasechnik, D.V.

    2005-01-01

    The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

  15. Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

    Science.gov (United States)

    Vaiyavutjamai, Pongchawee; Clements, M. A.

    2006-01-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

  16. Analysis of Students' Error in Learning of Quadratic Equations

    Science.gov (United States)

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  17. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    Science.gov (United States)

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  18. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    Science.gov (United States)

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  19. Visualising the Roots of Quadratic Equations with Complex Coefficients

    Science.gov (United States)

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  20. Inflation with a constant rate of roll

    International Nuclear Information System (INIS)

    Motohashi, Hayato; Starobinsky, Alexei A.; Yokoyama, Jun'ichi

    2015-01-01

    We consider an inflationary scenario where the rate of inflaton roll defined by ·· φ/H φ-dot remains constant. The rate of roll is small for slow-roll inflation, while a generic rate of roll leads to the interesting case of 'constant-roll' inflation. We find a general exact solution for the inflaton potential required for such inflaton behaviour. In this model, due to non-slow evolution of background, the would-be decaying mode of linear scalar (curvature) perturbations may not be neglected. It can even grow for some values of the model parameter, while the other mode always remains constant. However, this always occurs for unstable solutions which are not attractors for the given potential. The most interesting particular cases of constant-roll inflation remaining viable with the most recent observational data are quadratic hilltop inflation (with cutoff) and natural inflation (with an additional negative cosmological constant). In these cases even-order slow-roll parameters approach non-negligible constants while the odd ones are asymptotically vanishing in the quasi-de Sitter regime

  1. Cosmological Hubble constant and nuclear Hubble constant

    International Nuclear Information System (INIS)

    Horbuniev, Amelia; Besliu, Calin; Jipa, Alexandru

    2005-01-01

    The evolution of the Universe after the Big Bang and the evolution of the dense and highly excited nuclear matter formed by relativistic nuclear collisions are investigated and compared. Values of the Hubble constants for cosmological and nuclear processes are obtained. For nucleus-nucleus collisions at high energies the nuclear Hubble constant is obtained in the frame of different models involving the hydrodynamic flow of the nuclear matter. Significant difference in the values of the two Hubble constant - cosmological and nuclear - is observed

  2. Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

    International Nuclear Information System (INIS)

    Zhao Yunbin

    2010-01-01

    While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.

  3. Energy eigenvalues and squeezing properties of general systems of coupled quantum anharmonic oscillators

    International Nuclear Information System (INIS)

    Chung, N. N.; Chew, L. Y.

    2007-01-01

    We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems

  4. Two-step approach to the dynamics of coupled anharmonic oscillators

    International Nuclear Information System (INIS)

    Chung, N. N.; Chew, L. Y.

    2009-01-01

    We have further extended the two-step approach developed by Chung and Chew [N. N. Chung and L. Y. Chew, Phys. Rev. A 76, 032113 (2007)] to the solution of the quantum dynamics of general systems of N-coupled anharmonic oscillators. The idea is to employ an optimized basis set to represent the dynamical quantum states of these oscillator systems. The set is generated via the action of the optimized Bogoliubov transformed bosonic operators on the optimal squeezed vacuum product state. The procedure requires (i) applying the two-step approach to the eigendecomposition of the time evolution operator and (ii) transforming the representation of the initial state from the original to the optimal bases. We have applied the formalism to examine the dynamics of squeezing and entanglement of several anharmonic oscillator systems.

  5. Raman scattering study of the anharmonic effects in CeO2-y nanocrystals

    Science.gov (United States)

    Popović, Z. V.; Dohčević-Mitrović, Z.; Cros, A.; Cantarero, A.

    2007-12-01

    We have studied the temperature dependence of the F2g Raman mode phonon frequency and broadening in CeO2-y nanocrystals. The phonon softening and phonon linewidth are calculated using a model which takes into account the three-and four-phonon anharmonic processes. A detailed comparison of the experimental data with theoretical calculations revealed the predominance of four-phonon anharmonic processes in the temperature dependence of the phonon energy and broadening of the nanocrystals. On the other hand, three-phonon processes dominate the temperature behavior of phonons in polycrystalline samples. The anti-Stokes/Stokes peak intensity ratio was also investigated and found to be smaller for nanosized CeO2 powders than in the bulk counterpart.

  6. Raman scattering study of the anharmonic effects in CeO2-y nanocrystals

    International Nuclear Information System (INIS)

    Popovic, Z V; Dohcevic-Mitrovic, Z; Cros, A; Cantarero, A

    2007-01-01

    We have studied the temperature dependence of the F 2g Raman mode phonon frequency and broadening in CeO 2-y nanocrystals. The phonon softening and phonon linewidth are calculated using a model which takes into account the three-and four-phonon anharmonic processes. A detailed comparison of the experimental data with theoretical calculations revealed the predominance of four-phonon anharmonic processes in the temperature dependence of the phonon energy and broadening of the nanocrystals. On the other hand, three-phonon processes dominate the temperature behavior of phonons in polycrystalline samples. The anti-Stokes/Stokes peak intensity ratio was also investigated and found to be smaller for nanosized CeO 2 powders than in the bulk counterpart

  7. Raman scattering study of the anharmonic effects in CeO{sub 2-y} nanocrystals

    Energy Technology Data Exchange (ETDEWEB)

    Popovic, Z V [Center for Solid State Physics and New Materials, Institute of Physics, Pregrevica 118, 11080 Belgrade (Serbia); Dohcevic-Mitrovic, Z [Center for Solid State Physics and New Materials, Institute of Physics, Pregrevica 118, 11080 Belgrade (Serbia); Cros, A [Materials Science Institute, University of Valencia, P O Box 22085, E-46071, Valencia (Spain); Cantarero, A [Materials Science Institute, University of Valencia, P O Box 22085, E-46071, Valencia (Spain)

    2007-12-12

    We have studied the temperature dependence of the F{sub 2g} Raman mode phonon frequency and broadening in CeO{sub 2-y} nanocrystals. The phonon softening and phonon linewidth are calculated using a model which takes into account the three-and four-phonon anharmonic processes. A detailed comparison of the experimental data with theoretical calculations revealed the predominance of four-phonon anharmonic processes in the temperature dependence of the phonon energy and broadening of the nanocrystals. On the other hand, three-phonon processes dominate the temperature behavior of phonons in polycrystalline samples. The anti-Stokes/Stokes peak intensity ratio was also investigated and found to be smaller for nanosized CeO{sub 2} powders than in the bulk counterpart.

  8. Mellin-Barnes regularization, Borel summation and the Bender-Wu asymptotics for the anharmonic oscillator

    International Nuclear Information System (INIS)

    Kowalenko, V.; Rawlinson, A.A.

    1998-01-01

    We introduce the numerical technique of Mellin-Barnes regularization, which can be used to evaluate both convergent and divergent series. The technique is shown to be numerically equivalent to the corresponding results obtained by Borel summation. Both techniques are then applied to the Bender-Wu formula, which represents an asymptotic expansion for the energy levels of the anharmonic oscillator. We find that this formula is unable to give accurate values for the ground state energy, particularly when the coupling is greater than 0.1. As a consequence, the inability of the Bender-Wu formula to yield exact values for the energy level of the anharmonic oscillator cannot be attributed to its asymptotic nature. (authors)

  9. AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

    International Nuclear Information System (INIS)

    2005-01-01

    Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

  10. Are ghost surfaces quadratic-flux-minimizing?

    International Nuclear Information System (INIS)

    Hudson, S.R.; Dewar, R.L.

    2009-01-01

    Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.

  11. Securing Digital Audio using Complex Quadratic Map

    Science.gov (United States)

    Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi

    2018-03-01

    In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.

  12. Designing Camera Networks by Convex Quadratic Programming

    KAUST Repository

    Ghanem, Bernard

    2015-05-04

    ​In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport). ​

  13. Two new types of solvability of the one-dimensional anharmonic oscillators

    International Nuclear Information System (INIS)

    Znojil, M.

    1989-01-01

    In the Schroedinger picture, we propose a new modification of the so-called Hill-determinant technique. It is shown to guarantee a proper matching of the two underlying power series Ψ(x) at x=0. In the Heisenberg picture, an evolution of the same one-dimensional polynomially anharmonic oscillator is considered. A modified Peano-Baker method is applied and shown to define the explicit solutions by recurrences. 11 refs

  14. Large time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics

    OpenAIRE

    Jochmann, Frank

    2005-01-01

    The anharmonic oscillator model describing the propagation of electromagnetic waves in an exterior domain containing a nonlinear dielectric medium is investigated. The system under consideration consists of a generally nonlinear second order differential equation for the dielectrical polarization coupled with Maxwell's equations for the electromagnetic field. Local decay of the electromagnetic field for t to infinity in the charge free case is shown for a large class of potentials. (This pape...

  15. Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions

    Czech Academy of Sciences Publication Activity Database

    Daněček, Petr; Kapitán, Josef; Baumruk, V.; Bednárová, Lucie; Kopecký, V.; Bouř, Petr

    2007-01-01

    Roč. 126, č. 22 (2007), s. 224513-1 ISSN 0021-9606 R&D Projects: GA ČR GA203/06/0420; GA ČR GA202/07/0732; GA AV ČR IAA400550702 Institutional research plan: CEZ:AV0Z40550506 Keywords : IR * Raman * ROA spectra * Anharmonic effects Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.044, year: 2007

  16. Perturbative treatment of anharmonic vibrational effects on bond distances: an extended Langevin dynamics method.

    Science.gov (United States)

    Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin

    2014-03-05

    In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant. Copyright © 2013 Wiley Periodicals, Inc.

  17. Raman spectra of long chain hydrocarbons: anharmonic calculations, experiment and implications for imaging of biomembranes.

    Science.gov (United States)

    Šebek, Jiří; Pele, Liat; Potma, Eric O; Gerber, R Benny

    2011-07-28

    First-principles anharmonic vibrational calculations are carried out for the Raman spectrum of the C-H stretching bands in dodecane, and for the C-D bands in the deuterated molecule. The calculations use the Vibrational Self-Consistent Field (VSCF) algorithm. The results are compared with liquid-state experiments, after smoothing the isolated-molecule sharp-line computed spectra. Very good agreement between the computed and experimental results is found for the two systems. The combined theoretical and experimental results provide insights into the spectrum, elucidating the roles of symmetric and asymmetric CH(3) and CH(2) hydrogenic stretches. This is expected to be very useful for the interpretation of spectra of long-chain hydrocarbons. The results show that anharmonic effects on the spectrum are large. On the other hand, vibrational degeneracy effects seem to be rather modest at the resolution of the experiments. The degeneracy effects may have more pronounced manifestations in higher-resolution experiments. The results show that first-principles anharmonic vibrational calculations for hydrocarbons are feasible, in good agreement with experiment, opening the way for applications to many similar systems. The results may be useful for the analysis of CARS imaging of lipids, for which dodecane is a representative molecule. It is suggested that first-principles vibrational calculations may be useful also for CARS imaging of other systems. This journal is © the Owner Societies 2011

  18. Generalized theory of spin fluctuations in itinerant electron magnets: Crucial role of spin anharmonicity

    International Nuclear Information System (INIS)

    Solontsov, A.

    2015-01-01

    The paper critically overviews the recent developments of the theory of spatially dispersive spin fluctuations (SF) in itinerant electron magnetism with particular emphasis on spin-fluctuation coupling or spin anharmonicity. It is argued that the conventional self-consistent renormalized (SCR) theory of spin fluctuations is usually used aside of the range of its applicability actually defined by the constraint of weak spin anharmonicity based on the random phase approximation (RPA) arguments. An essential step in understanding SF in itinerant magnets beyond RPA-like arguments was made recently within the soft-mode theory of SF accounting for strong spin anharmonicity caused by zero-point SF. In the present paper we generalize it to apply for a wider range of temperatures and regimes of SF and show it to lead to qualitatively new results caused by zero-point effects. - Highlights: • We review the spin-fluctuation theory of itinerant electron magnets with account of zero-point effects. • We generalize the existing theory to account for different regimes of spin fluctuations. • We show that zero-point spin fluctuations play a crucial role in both low- and high-temperature properties of metallic magnets. • We argue that a new scheme of calculation of ground state properties of magnets is needed including zero-point effects

  19. Anharmonic phonon-phonon scattering modeling of three-dimensional atomistic transport: An efficient quantum treatment

    Science.gov (United States)

    Lee, Y.; Bescond, M.; Logoteta, D.; Cavassilas, N.; Lannoo, M.; Luisier, M.

    2018-05-01

    We propose an efficient method to quantum mechanically treat anharmonic interactions in the atomistic nonequilibrium Green's function simulation of phonon transport. We demonstrate that the so-called lowest-order approximation, implemented through a rescaling technique and analytically continued by means of the Padé approximants, can be used to accurately model third-order anharmonic effects. Although the paper focuses on a specific self-energy, the method is applicable to a very wide class of physical interactions. We apply this approach to the simulation of anharmonic phonon transport in realistic Si and Ge nanowires with uniform or discontinuous cross sections. The effect of increasing the temperature above 300 K is also investigated. In all the considered cases, we are able to obtain a good agreement with the routinely adopted self-consistent Born approximation, at a remarkably lower computational cost. In the more complicated case of high temperatures (≫300 K), we find that the first-order Richardson extrapolation applied to the sequence of the Padé approximants N -1 /N results in a significant acceleration of the convergence.

  20. Anharmonic behavior and structural phase transition in Yb2O3

    Directory of Open Access Journals (Sweden)

    Sugandha Dogra Pandey

    2013-12-01

    Full Text Available The investigation of structural phase transition and anharmonic behavior of Yb2O3 has been carried out by high-pressure and temperature dependent Raman scattering studies respectively. In situ Raman studies under high pressure were carried out in a diamond anvil cell at room temperature which indicate a structural transition from cubic to hexagonal phase at and above 20.6 GPa. In the decompression cycle, Yb2O3 retained its high pressure phase. We have observed a Stark line in the Raman spectra at 337.5 cm−1 which arises from the electronic transition between 2F5/2 and 2F7/2 multiplates of Yb3+ (4f13 levels. These were followed by temperature dependent Raman studies in the range of 80–440 K, which show an unusual mode hardening with increasing temperature. The hardening of the most dominant mode (Tg + Ag was analyzed in light of the theory of anharmonic phonon-phonon interaction and thermal expansion of the lattice. Using the mode Grüneisen parameter obtained from high pressure Raman measurements; we have calculated total anharmonicity of the Tg + Ag mode from the temperature dependent Raman data.

  1. A revisit to quadratic programming with fuzzy parameters

    International Nuclear Information System (INIS)

    Liu, S.-T.

    2009-01-01

    Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

  2. FORMATION CONSTANTS AND THERMODYNAMIC ...

    African Journals Online (AJOL)

    KEY WORDS: Metal complexes, Schiff base ligand, Formation constant, DFT calculation ... best values for the formation constants of the proposed equilibrium model by .... to its positive charge distribution and the ligand deformation geometry.

  3. Renormalization of correlations in a quasiperiodically forced two-level system: quadratic irrationals

    International Nuclear Information System (INIS)

    Mestel, B D; Osbaldestin, A H

    2004-01-01

    Generalizing from the case of golden mean frequency to a wider class of quadratic irrationals, we extend our renormalization analysis of the self-similarity of correlation functions in a quasiperiodically forced two-level system. We give a description of all piecewise-constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case. We establish a criterion for periodic orbits to be globally bounded, and also calculate the asymptotic height of the main peaks in the correlation function

  4. Ion exchange equilibrium constants

    CERN Document Server

    Marcus, Y

    2013-01-01

    Ion Exchange Equilibrium Constants focuses on the test-compilation of equilibrium constants for ion exchange reactions. The book first underscores the scope of the compilation, equilibrium constants, symbols used, and arrangement of the table. The manuscript then presents the table of equilibrium constants, including polystyrene sulfonate cation exchanger, polyacrylate cation exchanger, polymethacrylate cation exchanger, polysterene phosphate cation exchanger, and zirconium phosphate cation exchanger. The text highlights zirconium oxide anion exchanger, zeolite type 13Y cation exchanger, and

  5. Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

    International Nuclear Information System (INIS)

    Scott, D.S.; Ward, R.C.

    1981-01-01

    Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

  6. Integrable Hamiltonian systems and interactions through quadratic constraints

    International Nuclear Information System (INIS)

    Pohlmeyer, K.

    1975-08-01

    Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

  7. A perturbative solution for gravitational waves in quadratic gravity

    International Nuclear Information System (INIS)

    Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

    2003-01-01

    We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

  8. Accurate nonlocal theory for cascaded quadratic soliton compression

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Moses, Jeffrey

    2007-01-01

    We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

  9. Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control

    OpenAIRE

    Härkegård, Ola

    2004-01-01

    When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...

  10. Quadratic measurement and conditional state preparation in an optomechanical system

    DEFF Research Database (Denmark)

    A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.

    2014-01-01

    We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....

  11. Scale-Invariant Rotating Black Holes in Quadratic Gravity

    Directory of Open Access Journals (Sweden)

    Guido Cognola

    2015-07-01

    Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

  12. A Trust-region-based Sequential Quadratic Programming Algorithm

    DEFF Research Database (Denmark)

    Henriksen, Lars Christian; Poulsen, Niels Kjølstad

    This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

  13. Staff turnover in hotels : exploring the quadratic and linear relationships.

    OpenAIRE

    Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

    2015-01-01

    The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

  14. The stability of quadratic-reciprocal functional equation

    Science.gov (United States)

    Song, Aimin; Song, Minwei

    2018-04-01

    A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

  15. Burgers' turbulence problem with linear or quadratic external potential

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

    2005-01-01

    We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

  16. On using the linear-quadratic model in daily clinical practice

    International Nuclear Information System (INIS)

    Yaes, R.J.; Patel, P.; Maruyama, Y.

    1991-01-01

    To facilitate its use in the clinic, Barendsen's formulation of the Linear-Quadratic (LQ) model is modified by expressing isoeffect doses in terms of the Standard Effective Dose, Ds, the isoeffective dose for the standard fractionation schedule of 2 Gy fractions given once per day, 5 days per week. For any arbitrary fractionation schedule, where total dose D is given in N fractions of size d in a total time T, the corresponding Standard Effective Dose, Ds, will be proportional to the total dose D and the proportionality constant will be called the Standard Relative Effectiveness, SRE, to distinguish it from Barendsen's Relative Effectiveness, RE. Thus, Ds = SRE.D. The constant SRE depends on the parameters of the fractionation schedule, and on the tumor or normal tissue being irradiated. For the simple LQ model with no time dependence, which is applicable to late reacting tissue, SRE = [(d + delta)/(2 + delta)], where d is the fraction size and delta = alpha/beta is the alpha/beta ratio for the tissue of interest, with both d and delta expressed in units of Gy. Application of this method to the Linear Quadratic model with a time dependence, the LQ + time model, and to low dose rate brachytherapy will be discussed. To clarify the method of calculation, and to demonstrate its simplicity, examples from the clinical literature will be used

  17. A study of anharmonic al and nonlinear behaviours of vibrations of atomic nuclei

    International Nuclear Information System (INIS)

    Volpe, M.C.

    1997-01-01

    Double Giant Resonances, vibrational states in which a Giant Resonance is excited on top of another Giant Resonance, have been in the last years the object of many theories and studies. Whereas the measured energies and widths of these states agree with a theoretical predictions, the measured excitation cross sections on the other hand are almost always larger than the calculated ones. The standard theoretical approaches are based both on a harmonic approximation for the collective motion on the nucleus and on its linear response to an external field. In this work the influence of anharmonicities and non-linearities in the external field on the excitation of Double Giant Resonances are studied. First, an oscillator model and an extension of the Lipkin-Meshkow-Glick model are used to study the effects of anharmonicities and non-linearities on the excitation probabilities. The results show that these terms can influence the excitation probability of the second excited state in a significant way. Secondly, these exactly soluble schematic models are used to study some of the approximations made in microscopic calculations based on boson expansion methods and also some aspects on the time-dependent mean field approach. Finally, a microscopic calculation of the Coulomb excitation cross sections of Double Giant Resonances is presented for several nuclei. It is found that, for 208 Pb, the inclusion of anharmonicities and non-linearities and the consideration of many states that play a role in the excitation process give a satisfactory agreement between calculated and observed cross sections. (author)

  18. Isotopic effects on phonon anharmonicity in layered van der Waals crystals: Isotopically pure hexagonal boron nitride

    Science.gov (United States)

    Cuscó, Ramon; Artús, Luis; Edgar, James H.; Liu, Song; Cassabois, Guillaume; Gil, Bernard

    2018-04-01

    Hexagonal boron nitride (h -BN) is a layered crystal that is attracting a great deal of attention as a promising material for nanophotonic applications. The strong optical anisotropy of this crystal is key to exploit polaritonic modes for manipulating light-matter interactions in 2D materials. h -BN has also great potential for solid-state neutron detection and neutron imaging devices, given the exceptionally high thermal neutron capture cross section of the boron-10 isotope. A good knowledge of phonons in layered crystals is essential for harnessing long-lived phonon-polariton modes for nanophotonic applications and may prove valuable for developing solid-state 10BN neutron detectors with improved device architectures and higher detection efficiencies. Although phonons in graphene and isoelectronic materials with a similar hexagonal layer structure have been studied, the effect of isotopic substitution on the phonons of such lamellar compounds has not been addressed yet. Here we present a Raman scattering study of the in-plane high-energy Raman active mode on isotopically enriched single-crystal h -BN. Phonon frequency and lifetime are measured in the 80-600-K temperature range for 10B-enriched, 11B-enriched, and natural composition high quality crystals. Their temperature dependence is explained in the light of perturbation theory calculations of the phonon self-energy. The effects of crystal anisotropy, isotopic disorder, and anharmonic phonon-decay channels are investigated in detail. The isotopic-induced changes in the phonon density of states are shown to enhance three-phonon anharmonic decay channels in 10B-enriched crystals, opening the possibility of isotope tuning of the anharmonic phonon decay processes.

  19. Pressure measurements of TO-phonon anharmonicity in isotopic ZnS

    Energy Technology Data Exchange (ETDEWEB)

    Tallman, R.E.; Weinstein, B.A. [SUNY at Buffalo, Department of Physics, Buffalo, NY 14260 (United States); Ritter, T.M. [Dept. of Chemistry and Physics, UNC Pembroke, NC 28372 (United States); Cantarero, A. [Dept. of Physics and Institute of Materials Science, University of Valencia (Spain); Serrano, J.; Lauck, R.; Cardona, M. [Max-Planck-Institut fuer Festkoerperforschung, 70569 Stuttgart (Germany)

    2004-03-01

    We have measured the dependence on pressure of the line-widths of the TO and LO Raman phonons of {beta}-ZnS. In order to enhance the phenomena observed, and to eliminate possible effects of isotopic disorder, we have measured a nearly isotopically pure crystal, {sup 68}Zn{sup 32}S. The strongly structured pressure effects observed are interpreted on the basis of anharmonic decay and the corresponding two-phonon density of states. (copyright 2004 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  20. Transformation of potential energy surfaces for estimating isotopic shifts in anharmonic vibrational frequency calculations

    Energy Technology Data Exchange (ETDEWEB)

    Meier, Patrick; Oschetzki, Dominik; Rauhut, Guntram, E-mail: rauhut@theochem.uni-stuttgart.de [Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, Robert [Clemens-Schöpf Institut für Organische Chemie and Biochemie, Technische Universität Darmstadt, Petersenstrasse 22, 64287 Darmstadt (Germany)

    2014-05-14

    A transformation of potential energy surfaces (PES) being represented by multi-mode expansions is introduced, which allows for the calculation of anharmonic vibrational spectra of any isotopologue from a single PES. This simplifies the analysis of infrared spectra due to significant CPU-time savings. An investigation of remaining deviations due to truncations and the so-called multi-level approximation is provided. The importance of vibrational-rotational couplings for small molecules is discussed in detail. In addition, an analysis is proposed, which provides information about the quality of the transformation prior to its execution. Benchmark calculations are provided for a set of small molecules.

  1. Vibrational spectra and thermal rectification in three-dimensional anharmonic lattices

    International Nuclear Information System (INIS)

    Lan Jinghua; Li Baowen

    2007-01-01

    We study thermal rectification in a three-dimensional model consisting of two segments of anharmonic lattices. One segment consists of layers of harmonic oscillator arrays coupled to a substrate potential, which is a three-dimensional Frenkel-Kontorova model, and the other segment is a three-dimensional Fermi-Pasta-Ulam model. We study the vibrational bands of the two lattices analytically and numerically, and find that, by choosing the system parameters properly, the rectification can be as high as a few thousands, which is high enough to be observed in experiment. Possible experiments in nanostructures are discussed

  2. Remarks on the boundary curve of a constant mean curvature topological disc

    DEFF Research Database (Denmark)

    Brander, David; Lopéz, Rafael

    2017-01-01

    We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the bo......We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature...

  3. Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

    Energy Technology Data Exchange (ETDEWEB)

    Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl

    2017-02-15

    A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

  4. Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

    International Nuclear Information System (INIS)

    Plyushchay, Mikhail S.

    2017-01-01

    A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

  5. The curious case of cuprous chloride: Giant thermal resistance and anharmonic quasiparticle spectra driven by dispersion nesting

    Science.gov (United States)

    Mukhopadhyay, Saikat; Bansal, Dipanshu; Delaire, Olivier; Perrodin, Didier; Bourret-Courchesne, Edith; Singh, David J.; Lindsay, Lucas

    2017-09-01

    Strongly anharmonic phonon properties of CuCl are investigated with inelastic neutron-scattering measurements and first-principles simulations. An unusual quasiparticle spectral peak emerges in the phonon density of states with increasing temperature, in both simulations and measurements, emanating from exceptionally strong coupling between conventional phonon modes. Associated with this strong anharmonicity, the lattice thermal conductivity of CuCl is extremely low and exhibits anomalous, nonmonotonic pressure dependence. We show how this behavior arises from the structure of the phonon dispersions augmenting the phase space available for anharmonic three-phonon scattering processes, and contrast this mechanism with common arguments based on negative Grüneisen parameters. These results demonstrate the importance of considering intrinsic phonon-dispersion structure toward understanding scattering processes and designing new ultralow thermal conductivity materials.

  6. First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds.

    Science.gov (United States)

    Errea, Ion; Calandra, Matteo; Mauri, Francesco

    2013-10-25

    Palladium hydrides display the largest isotope effect anomaly known in the literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion, and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being mainly responsible for the isotope anomaly.

  7. The Fine Structure Constant

    Indian Academy of Sciences (India)

    IAS Admin

    The article discusses the importance of the fine structure constant in quantum mechanics, along with the brief history of how it emerged. Al- though Sommerfelds idea of elliptical orbits has been replaced by wave mechanics, the fine struc- ture constant he introduced has remained as an important parameter in the field of ...

  8. Constant-work-space algorithms for geometric problems

    Directory of Open Access Journals (Sweden)

    Tetsuo Asano

    2011-07-01

    Full Text Available Constant-work-space algorithms may use only constantly many cells of storage in addition to their input, which is provided as a read-only array. We show how to construct several geometric structures efficiently in the constant-work-space model. Traditional algorithms process the input into a suitable data structure (like a doubly-connected edge list that allows efficient traversal of the structure at hand. In the constant-work-space setting, however, we cannot afford to do this. Instead, we provide operations that compute the desired features on the fly by accessing the input with no extra space. The whole geometric structure can be obtained by using these operations to enumerate all the features. Of course, we must pay for the space savings by slower running times. While the standard data structure allows us to implement traversal operations in constant time, our schemes typically take linear time to read the input data in each step.We begin with two simple problems: triangulating a planar point set and finding the trapezoidal decomposition of a simple polygon. In both cases adjacent features can be enumerated in linear time per step, resulting in total quadratic running time to output the whole structure. Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant work-space. As another application, we demonstrate how to enumerate the features of an Euclidean minimum spanning tree (EMST in quadratic time per step, so that the whole EMST can be found in cubic time using constant work-space.Finally, we describe how to compute a shortest geodesic path between two points in a simple polygon. Although the shortest path problem in general graphs is NL-complete (Jakoby and Tantau 2003, this constrained problem can be solved in quadratic time using only constant work-space.

  9. Comparison between linear quadratic and early time dose models

    International Nuclear Information System (INIS)

    Chougule, A.A.; Supe, S.J.

    1993-01-01

    During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

  10. Cosmological constants and variations

    International Nuclear Information System (INIS)

    Barrow, John D

    2005-01-01

    We review properties of theories for the variation of the gravitation and fine structure 'constants'. We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that is consistent with time-variation in the fine structure 'constant' since a redshift of 3.5. The behaviour of a simple class of varying alpha cosmologies is outlined in the light of all the observational constraints. We also discuss some of the consequences of varying 'constants' for oscillating universes and show by means of exact solutions that they appear to evolve monotonically in time even though the scale factor of the universe oscillates

  11. Fluctuations and Anharmonicity in Lead Iodide Perovskites from Molecular Dynamics Supercell Simulationss

    KAUST Repository

    Carignano, Marcelo Andrés

    2017-09-05

    We present a systematic study based on first principles molecular dynamics simulations of lead iodide perovskites with three different cations, including methylammonium (MA), formamidinium (FA) and cesium. Using the high temperature perovskite structure as a reference, we investigate the instabilities that develop as the material is cooled down to 370 K. All three perovskites display anharmonicity in the motion of the iodine atoms, with the stronger effect observed for the MAPbI$_3$ and CsPbI$_3$. At high temperature, this behavior can be traced back to the reduced effective size of the Cs$^+$ and MA$^+$ cations. MAPbI$_3$ undergoes a spontaneous phase transition within our simulation model driven by the dipolar interaction between neighboring MA cations as the temperature is decreased from 450 K. The reverse transformation from tetragonal to cubic is also monitored through the large distribution of the octahedral tilting angles accompanied by an increase in the anharmonicity of the iodine atoms motion. Both MA and FA hybrid perovskites show a strong coupling between the molecular orientations and the local lattice deformations, suggesting mixed order-disorder/displacive characters of the high temperature phase transitions.

  12. Non-Gaussian wave packet dynamics in anharmonic potential: Cumulant expansion treatment

    International Nuclear Information System (INIS)

    Toutounji, Mohamad

    2015-01-01

    This manuscript utilizes cumulant expansion as an alternative algebraic approach to evaluating integrals and solving a system of nonlinear differential equations for probing anharmonic dynamics in condensed phase systems using Morse oscillator. These integrals and differential equations become harder to solve as the anharmonicity of the system goes beyond that of Morse oscillator description. This algebraic approach becomes critically important in case of Morse oscillator as it tends to exhibit divergent dynamics and numerical uncertainties at low temperatures. The autocorrelation function is calculated algebraically and compared to the exact one for they match perfectly. It is also compared to the approximate autocorrelation function using the differential equations technique reported in Toutounji (2014) for weak and strong electron–phonon coupling cases. It is found that the present cumulant method is more efficient, and easier to use, than the exact expression. Deviation between the approximate autocorrelation function and the exact autocorrelation function starts to arise as the electron–phonon coupling strength increases. The autocorrelation function obtained using cumulants identically matches the exact autocorrelation function, thereby surpassing the approach presented in Toutounji (2014). The advantage of the present methodology is its applicability to various types of electron–phonon coupling cases. Additionally, the herein approach only uses algebraic techniques, thereby avoiding both the divergence integral and solving a set of linear first- and second-order partial differential equations as was done in previous work. Model calculations are presented to demonstrate the accuracy of the herein work

  13. The quadratic reciprocity law a collection of classical proofs

    CERN Document Server

    Baumgart, Oswald

    2015-01-01

    This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

  14. Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

    International Nuclear Information System (INIS)

    Marquette, Ian

    2011-01-01

    There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

  15. The bounds of feasible space on constrained nonconvex quadratic programming

    Science.gov (United States)

    Zhu, Jinghao

    2008-03-01

    This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

  16. The cosmological constant problem

    International Nuclear Information System (INIS)

    Dolgov, A.D.

    1989-05-01

    A review of the cosmological term problem is presented. Baby universe model and the compensating field model are discussed. The importance of more accurate data on the Hubble constant and the Universe age is stressed. 18 refs

  17. Large N saddle formulation of quadratic building block theories

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1980-01-01

    I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)

  18. Remarks on second-order quadratic systems in algebras

    Directory of Open Access Journals (Sweden)

    Art Sagle

    2017-10-01

    Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

  19. Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-01-01

    Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

  20. Quantum tomography and classical propagator for quadratic quantum systems

    International Nuclear Information System (INIS)

    Man'ko, O.V.

    1999-03-01

    The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)

  1. Subgroups of class groups of algebraic quadratic function fields

    International Nuclear Information System (INIS)

    Wang Kunpeng; Zhang Xianke

    2001-09-01

    Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)

  2. Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

    Science.gov (United States)

    Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

    2018-03-01

    A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

  3. Thermal expansion and temperature variation of elastic constants of Li(H,D) and Na(H,D) systems

    International Nuclear Information System (INIS)

    Islam, A.K.M.A.; Hoque, M.T.

    1994-11-01

    An analysis of thermal expansion of Li(H,D) systems up to melting temperature has been performed using the theory of anharmonic lattice. The study has for the first time been extended to Na(H,D) systems where very little or no data are available. The calculated lattice constants of Li(H,D) systems show quite good agreement with experiment. The success of the present calculation with Li(H,D) and room temperature lattice constant data for Na(H,D) given an indication of the reliability of the computed lattice constants and thermal expansion coefficients for Na(H,D) systems. The study also allows us to predict the hitherto unknown lattice constants of Na(H,D) crystal at 0K. The temperature dependence of elastic constants for Li(H,D) systems has also been evaluated. Comparison with measurements shows the reliability of the present calculations. (author). 45 refs, 4 figs

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

    Science.gov (United States)

    Mauri, Francesco

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

  5. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...

  6. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

    2016-01-01

    We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

  7. ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS

    Directory of Open Access Journals (Sweden)

    E. L. Shishkina

    2016-12-01

    Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.

  8. Feedback nash equilibria for linear quadratic descriptor differential games

    NARCIS (Netherlands)

    Engwerda, J.C.; Salmah, S.

    2012-01-01

    In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a

  9. Initial post dynamic buckling of a quadratic-cubic column ...

    African Journals Online (AJOL)

    In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...

  10. Quadratic algebras in the noncommutative integration method of wave equation

    International Nuclear Information System (INIS)

    Varaksin, O.L.

    1995-01-01

    The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras

  11. Propagator of a time-dependent unbound quadratic Hamiltonian system

    International Nuclear Information System (INIS)

    Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.

    1996-01-01

    The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct

  12. On Fredholm-Stieltjes quadratic integral equation with supremum

    International Nuclear Information System (INIS)

    Darwish, M.A.

    2007-08-01

    We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)

  13. Quadratic theory and feedback controllers for linear time delay systems

    International Nuclear Information System (INIS)

    Lee, E.B.

    1976-01-01

    Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)

  14. Pareto optimality in infinite horizon linear quadratic differential games

    NARCIS (Netherlands)

    Reddy, P.V.; Engwerda, J.C.

    2013-01-01

    In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal

  15. Special cases of the quadratic shortest path problem

    NARCIS (Netherlands)

    Sotirov, Renata; Hu, Hao

    2017-01-01

    The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP

  16. Quadratic Poisson brackets compatible with an algebra structure

    OpenAIRE

    Balinsky, A. A.; Burman, Yu.

    1994-01-01

    Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.

  17. On misclassication probabilities of linear and quadratic classiers ...

    African Journals Online (AJOL)

    We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...

  18. Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

    NARCIS (Netherlands)

    Engwerda, J.C.; Salmah, Y.

    2010-01-01

    In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a

  19. A Unified Approach to Teaching Quadratic and Cubic Equations.

    Science.gov (United States)

    Ward, A. J. B.

    2003-01-01

    Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

  20. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

    Science.gov (United States)

    Leyendekkers, J. V.; Shannon, A. G.

    2004-01-01

    An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

  1. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    Science.gov (United States)

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  2. Nonlocal description of X waves in quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole

    2006-01-01

    We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...

  3. Linear and quadratic in temperature resistivity from holography

    Energy Technology Data Exchange (ETDEWEB)

    Ge, Xian-Hui [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing, 100049 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Wu, Shang-Yu [Department of Electrophysics, National Chiao Tung University,Hsinchu 300 (China); Wu, Shao-Feng [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China)

    2016-11-22

    We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.

  4. Asymmetric Vibration of Polar Orthotropic Annular Circular Plates of Quadratically Varying Thickness with Same Boundary Conditions

    Directory of Open Access Journals (Sweden)

    N. Bhardwaj

    2008-01-01

    Full Text Available In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b Lateral vibration characteristics of F-Fplates is more sensitive towards parametric changes in material orthotropy and foundation stiffness than C-C and S-Splates; (c Effect of quadratical thickness variation on fundamental frequency is more significant in cases of C-C and S-S plates than that of F-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d Fundamental mode of vibration of C-C and S-Splates is axisymmetrical while that of F-Fplates is asymmetrical.

  5. Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

    Science.gov (United States)

    Kendal, W S

    2000-04-01

    To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

  6. Radiographic constant exposure technique

    DEFF Research Database (Denmark)

    Domanus, Joseph Czeslaw

    1985-01-01

    The constant exposure technique has been applied to assess various industrial radiographic systems. Different X-ray films and radiographic papers of two producers were compared. Special attention was given to fast film and paper used with fluorometallic screens. Radiographic image quality...... was tested by the use of ISO wire IQI's and ASTM penetrameters used on Al and Fe test plates. Relative speed and reduction of kilovoltage obtained with the constant exposure technique were calculated. The advantages of fast radiographic systems are pointed out...

  7. Temperature variation of higher-order elastic constants of MgO

    Indian Academy of Sciences (India)

    series of strains using Taylor's series expansion. The coefficients of quadratic, cu- ... as thermal expansion, specific heat at higher temperature, temperature variation of ultrasonic velocity and attenuation, .... such studies have an impression that linear variation of elastic constant is true. The experimental study shows that ...

  8. Anharmonic properties of Raman modes in double wall carbon nano tubes

    Energy Technology Data Exchange (ETDEWEB)

    Marquina, J. [Universidad de los Andes, Facultad de Ciencias, Centro de Estudios Avanzados en Optica, 5101 Merida (Venezuela, Bolivarian Republic of); Power, Ch.; Gonzalez, J. [Universidad de los Andes, Facultad de Ciencias, Centro de Estudios en Semiconductores, 5101 Merida (Venezuela, Bolivarian Republic of); Broto, J. M. [Universite de Toulouse, Laboratoire National des Champs Magnetiques Intenses, CNRS UPR 3228, 31400 Toulouse (France); Flahaut, E., E-mail: castella@ula.v [Universite Paul Sabatier, Laboratoire de Chimie des Materiaux Inorganiques, UMR CNRS 5085, 31062 Toulouse (France)

    2011-07-01

    The temperature dependence of the radial breathing modes (RB Ms) and the zone-center tangential optical phonons (G-bands) of double-walled carbon nano tubes has been investigated between 300 and 700 K using Raman scattering. As expected, with increasing temperature, the frequencies of the Raman peaks, including the RB Ms and G-bands downshift simultaneously. We show here that the temperature dependence of the RB Ms can be fitted by a simple linear dependence and different RB Ms have different frequency shifts. We observe a noticeable nonlinearity in the temperature dependence of the G-band associated with the outer semiconducting tube G+ext (s). The deviation from the linear trend is due to the contribution of the third-order anharmonic term in the lattice potential energy with a pure temperature effect. An estimated value of 1.5 for the Grueneisen parameter of the G+ext (s) band was found. (Author)

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

    International Nuclear Information System (INIS)

    Aouissat, Z.; Martin, C.

    2004-01-01

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

  10. Anharmonicity, mechanical instability, and thermodynamic properties of the Cr-Re σ-phase

    Energy Technology Data Exchange (ETDEWEB)

    Palumbo, Mauro, E-mail: mauro.palumbo@rub.de; Fries, Suzana G. [ICAMS, Ruhr University Bochum, Universität Str. 150, D-44801 Bochum (Germany); Pasturel, Alain [SIMAP, UMR CNRS-INPG-UJF 5266, BP 75, F-38402 Saint Martin d’Hères (France); Alfè, Dario [Department of Earth Sciences, Department of Physics and Astronomy, London Centre for Nanotechnology and Thomas Young Centre-UCL, University College London, Gower Street, London WC1E 6BT (United Kingdom)

    2014-04-14

    Using density-functional theory in combination with the direct force method and molecular dynamics we investigate the vibrational properties of a binary Cr-Re σ-phase. In the harmonic approximation, we have computed phonon dispersion curves and density of states, evidencing structural and chemical effects. We found that the σ-phase is mechanically unstable in some configurations, for example, when all crystallographic sites are occupied by Re atoms. By using a molecular-dynamics-based method, we have analysed the anharmonicity in the system and found negligible effects (∼0.5 kJ/mol) on the Helmholtz energy of the binary Cr-Re σ-phase up to 2000 K (∼0.8T{sub m}). Finally, we show that the vibrational contribution has significant consequences on the disordering of the σ-phase at high temperature.

  11. Frequency and Temperature Dependence of Anharmonic Phonon Relaxation Rate in Carbon Nanotubes

    International Nuclear Information System (INIS)

    Hepplestone, S P; Srivastava, G P

    2007-01-01

    The relaxation rate of phonon modes in the (10, 10) single wall carbon nanotube undergoing three-phonon interactions at various temperatures has been studied using both qualitative and quantitative approaches based upon Fermi's Golden Rule and a quasi-elastic continuum model for the anharmonic potential. For the quantitative calculations, dispersion relations for the phonon modes were obtained from analytic expressions developed by Zhang et al. The qualitative expressions were derived using simple linear phonon dispersions relations. We show that in the high temperature regime the relaxation rate varies linearly with temperature and with the square of the frequency. In the low temperature regime we show that the relaxation rate varies exponentially with the inverse of temperature. These results have some very interesting implifications for effects for mean free path and thermal conductivity calculations

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2004-02-01

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

  13. Two-qubit gate operations in superconducting circuits with strong coupling and weak anharmonicity

    International Nuclear Information System (INIS)

    Lü Xinyou; Ashhab, S; Cui Wei; Wu Rebing; Nori, Franco

    2012-01-01

    We theoretically study the implementation of two-qubit gates in a system of two coupled superconducting qubits. In particular, we analyze two-qubit gate operations under the condition that the coupling strength is comparable with or even larger than the anharmonicity of the qubits. By numerically solving the time-dependent Schrödinger equation under the assumption of negligible decoherence, we obtain the dependence of the two-qubit gate fidelity on the system parameters in the case of both direct and indirect qubit-qubit coupling. Our numerical results can be used to identify the ‘safe’ parameter regime for experimentally implementing two-qubit gates with high fidelity in these systems. (paper)

  14. Quantum effects in amplitude death of coupled anharmonic self-oscillators

    Science.gov (United States)

    Amitai, Ehud; Koppenhöfer, Martin; Lörch, Niels; Bruder, Christoph

    2018-05-01

    Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017), 10.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.

  15. Cylindrical Penning traps with dynamic orthogonalized anharmonicity compensation for precision experiments

    International Nuclear Information System (INIS)

    Fei Xiang; Snow, W.M.

    1999-01-01

    Harmonic potentials can be produced in cylindrical ion traps by means of dynamic orthogonalized anharmonicity compensation with use of two (or multiple) sets of compensation electrodes. One special example is for traps with multiple identical electrodes which are not only easy to construct and allow access to the center region of the trap for particle loading and releasing, laser beams, and microwaves, but also flexible in forming harmonic potential wells in many locations. The nested trap configuration and the side-by-side trap configuration are readily available in this special scheme. Analytical solutions for cylindrical traps with multiple sets of compensation potentials are presented. This work will be useful for studies involving Penning trap diagnostics, atomic and molecular interactions (including the production of antihydrogen atoms), accurate mass measurements of exotic particles, and precision measurements of the spin precession frequencies of trapped particles

  16. Cylindrical Penning traps with dynamic orthogonalized anharmonicity compensation for precision experiments

    CERN Document Server

    Fei Xiang

    1999-01-01

    Harmonic potentials can be produced in cylindrical ion traps by means of dynamic orthogonalized anharmonicity compensation with use of two (or multiple) sets of compensation electrodes. One special example is for traps with multiple identical electrodes which are not only easy to construct and allow access to the center region of the trap for particle loading and releasing, laser beams, and microwaves, but also flexible in forming harmonic potential wells in many locations. The nested trap configuration and the side-by-side trap configuration are readily available in this special scheme. Analytical solutions for cylindrical traps with multiple sets of compensation potentials are presented. This work will be useful for studies involving Penning trap diagnostics, atomic and molecular interactions (including the production of antihydrogen atoms), accurate mass measurements of exotic particles, and precision measurements of the spin precession frequencies of trapped particles.

  17. Numerical solutions of anharmonic vibration of BaO and SrO molecules

    Energy Technology Data Exchange (ETDEWEB)

    Pramudito, Sidikrubadi; Sanjaya, Nugraha Wanda [Theoretical Physics Division, Department of Physics, Bogor Agricultural University, Jalan Meranti Kampus IPB Dramaga Bogor 16680 (Indonesia); Sumaryada, Tony, E-mail: tsumaryada@ipb.ac.id [Theoretical Physics Division, Department of Physics, Bogor Agricultural University, Jalan Meranti Kampus IPB Dramaga Bogor 16680 (Indonesia); Computational Biophysics and Molecular Modeling Research Group (CBMoRG), Department of Physics, Bogor Agricultural University, Jalan Meranti Kampus IPB Dramaga Bogor 16680 (Indonesia)

    2016-03-11

    The Morse potential is a potential model that is used to describe the anharmonic behavior of molecular vibration between atoms. The BaO and SrO molecules, which are two almost similar diatomic molecules, were investigated in this research. Some of their properties like the value of the dissociation energy, the energy eigenvalues of each energy level, and the profile of the wavefunctions in their correspondence vibrational states were presented in this paper. Calculation of the energy eigenvalues and plotting the wave function’s profiles were performed using Numerov method combined with the shooting method. In general we concluded that the Morse potential solved with numerical methods could accurately produce the vibrational properties and the wavefunction behavior of BaO and SrO molecules from the ground state to the higher states close to the dissociation level.

  18. On the cosmical constant

    International Nuclear Information System (INIS)

    Chandra, R.

    1977-01-01

    On the grounds of the two correspondence limits, the Newtonian limit and the special theory limit of Einstein field equations, a modification of the cosmical constant has been proposed which gives realistic results in the case of a homogeneous universe. Also, according to this modification an explanation for the negative pressure in the steady-state model of the universe has been given. (author)

  19. Cosmological constant problem

    International Nuclear Information System (INIS)

    Weinberg, S.

    1989-01-01

    Cosmological constant problem is discussed. History of the problem is briefly considered. Five different approaches to solution of the problem are described: supersymmetry, supergravity, superstring; anthropic approach; mechamism of lagrangian alignment; modification of gravitation theory and quantum cosmology. It is noted that approach, based on quantum cosmology is the most promising one

  20. The Yamabe constant

    International Nuclear Information System (INIS)

    O Murchadha, N.

    1991-01-01

    The set of riemannian three-metrics with positive Yamabe constant defines the space of independent data for the gravitational field. The boundary of this set is investigated, and it is shown that metrics close to the boundary satisfy the positive-energy theorem. (Author) 18 refs

  1. Theoretical Kinetic Study of the Formic Acid Catalyzed Criegee Intermediate Isomerization: Multistructural Anharmonicity and Atmospheric Implications

    KAUST Repository

    Monge Palacios, Manuel

    2018-01-29

    We performed a theoretical study on the double hydrogen shift isomerization reaction of a six carbon atom Criegee intermediate (C6-CI), catalyzed by formic acid (HCOOH), to produce vinylhydroperoxide (VHP), C6-CI+HCOOH→VHP+HCOOH. This Criegee intermediate can serve as a surrogate for larger CIs derived from important volatile organic compounds like monoterpenes, whose reactivity is not well understood and are difficult to handle computationally. The reactant HCOOH exerts a pronounced catalytic effect on the studied reaction by lowering the barrier height, but the kinetic enhancement is hindered by the multistructural anharmonicity. First, the rigid ring-structure adopted by the saddle point to facilitate simultaneous transfer of two atoms does not allow formation of as many conformers as those formed by the reactant C6-CI. And second, the flexible carbon chain of C6-CI facilitates the formation of stabilizing intramolecular C–H···O hydrogen bonds; this stabilizing effect is less pronounced in the saddle point structure due to its tightness and steric effects. Thus, the contribution of the reactant C6-CI conformers to the multistructural partition function is larger than that of the saddle point conformers. The resulting low multistructural anharmonicity factor partially cancels out the catalytic effect of the carboxylic acid, yielding in a moderately large rate coefficient, k(298 K) = 4.9·10-13 cm3 molecule-1 s-1. We show that carboxylic acids may promote the conversion of stabilized Criegee intermediates into vinylhydroperoxides in the atmosphere, which generates OH radicals and leads to secondary organic aerosol, thereby affecting the oxidative capacity of the atmosphere and ultimately the climate.

  2. Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules.

    Science.gov (United States)

    Krasnoshchekov, Sergey V; Stepanov, Nikolay F

    2013-11-14

    In the theory of anharmonic vibrations of a polyatomic molecule, mixing the zero-order vibrational states due to cubic, quartic and higher-order terms in the potential energy expansion leads to the appearance of more-or-less isolated blocks of states (also called polyads), connected through multiple resonances. Such polyads of states can be characterized by a common secondary integer quantum number. This polyad quantum number is defined as a linear combination of the zero-order vibrational quantum numbers, attributed to normal modes, multiplied by non-negative integer polyad coefficients, which are subject to definition for any particular molecule. According to Kellman's method [J. Chem. Phys. 93, 6630 (1990)], the corresponding formalism can be conveniently described using vector algebra. In the present work, a systematic consideration of polyad quantum numbers is given in the framework of the canonical Van Vleck perturbation theory (CVPT) and its numerical-analytic operator implementation for reducing the Hamiltonian to the quasi-diagonal form, earlier developed by the authors. It is shown that CVPT provides a convenient method for the systematic identification of essential resonances and the definition of a polyad quantum number. The method presented is generally suitable for molecules of significant size and complexity, as illustrated by several examples of molecules up to six atoms. The polyad quantum number technique is very useful for assembling comprehensive basis sets for the matrix representation of the Hamiltonian after removal of all non-resonance terms by CVPT. In addition, the classification of anharmonic energy levels according to their polyad quantum numbers provides an additional means for the interpretation of observed vibrational spectra.

  3. X ray absorption fine structure of systems in the anharmonic limit

    Science.gov (United States)

    Mustredeleon, J.; Conradson, S. D.; Batistic, I.; Bishop, A. R.; Raistrick, I.; Jackson, W. E.; Brown, G. E.

    A new approach to the analysis of x-ray absorption fine structure (XAFS) data is presented. It is based on the use of radial distribution functions directly calculated from a single-particle ion Hamiltonian containing model potentials. The starting point of this approach is the statistical average of the XAFS for an atomic pair. This average can be computed using a radial distribution function (RDF), which can be expressed in terms of the eigenvalues and wavefunctions associated with the model potential. The pair potential describing the ionic motion is then expressed in terms of parameters that are determined by fitting this statistical average to the experimental XAFS spectrum. This approach allows the use of XAFS as a tool for mapping near-neighbor interatomic potentials, and allows the treatment of systems which exhibit strongly anharmonic potentials which can be treated by perturbative methods. Using this method we have analyzed the high temperature behavior of the oxygen contributions to the Fe K-edge XAFS in the ferrosilicate minerals andradite (Ca3Fe2Si3O12) and magnesiowustite (Mg(0.9)Fe(0.1)O). Using a temperature dependent anharmonic correction derived from these model compounds, we have found evidence for a local structural change in the Fe-O coordination environment upon melting of the geologically important mineral fayalite (Fe2SiO4). We have also employed this method to the study of the axial oxygen contributions to the polarized Cu K-edge XAFS on oriented samples of YBa2Cu3O7 and related compounds. From this study we find evidence for an axial oxygen-centered lattice distortion accompanying the superconducting phase transition and a correlation between this distortion and Tc. The relation of the observed lattice distortion to mechanisms of superconductivity is discussed.

  4. X-ray absorption fine structure of systems in the anharmonic limit

    International Nuclear Information System (INIS)

    Mustre de Leon, J.; Conradson, S.D.; Batistic, I.; Bishop, A.R.; Raistrick, I.; Jackson, W.E.; Brown, G.E.

    1991-01-01

    A new approach to the analysis of x-ray absorption fine structure (XAFS) data is presented. It is based on the use of radial distribution functions directly calculated from a single-particle ion hamiltonian containing model potentials. The starting point of this approach is the statistical average of the XAFS for an atomic pair. This average can be computed using a radial distribution function (RDF), which can be expressed in terms of the eigenvalues and wavefunctions associated with the model potential. The pair potential describing the ionic motion is then expressed in terms of parameters that are determined by fitting this statistical average to the experimental XAFS spectrum. This approach allow the use of XAFS as a tool for mapping near-neighbor interatomic potentials, and allows the treatment of systems which exhibit strongly anharmonic potentials which can be treated by perturbative methods. Using this method we have analyzed the high temperature behavior of the oxygen contributions to the Fe K-edge XAFS in the ferrosilicate minerals andradite (Ca 3 Fe 2 Si 3 O 12 ) and magnesiowustite (Mg 0.9 Fe 0.1 O). Using a temperature dependent anharmonic correction derived from these model compounds, we have found evidence for a local structural change in the Fe-O coordination environment upon melting of the geologically important mineral fayalite (Fe 2 SiO 4 ). We have also employed this method to the study of the axial oxygen contributions to the polarized Cu K-edge XAFS on oriented samples of YBa 2 Cu 3 O 7 and related compounds. From this study we find evidence for an axial oxygen-centered lattice distortion accompanying the superconducting phase transition and a correlation between this distortion and T c . The relation of the observed lattice distortion to mechanisms of superconductivity is discussed. 33 refs., 6 figs

  5. On the distribution of estimators of diffusion constants for Brownian motion

    International Nuclear Information System (INIS)

    Boyer, Denis; Dean, David S

    2011-01-01

    We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.

  6. Production in constant evolution

    International Nuclear Information System (INIS)

    Lozano, T.

    2009-01-01

    The Cofrentes Nuclear Power Plant now has 25 years of operation behind it: a quarter century adding value and demonstrating the reasons why it is one of the most important energy producing facilities in the Spanish power market. Particularly noteworthy is the enterprising spirit of the plant, which has strived to continuously improve with the large number of modernization projects that it has undertaken over the past 25 years. The plant has constantly evolved thanks to the amount of investments made to improve safety and reliability and the perseverance to stay technologically up to date. Efficiency, training and teamwork have been key to the success of the plant over these 25 years of constant change and progress. (Author)

  7. Is the sun constant

    International Nuclear Information System (INIS)

    Blake, J.B.; Dearborn, D.S.P.

    1979-01-01

    Small fluctuations in the solar constant can occur on timescales much shorter than the Kelvin time. Changes in the ability of convection to transmit energy through the superadiabatic and transition regions of the convection zone cause structure adjustments which can occur on a time scale of days. The bulk of the convection zone reacts to maintain hydrostatic equilibrium (though not thermal equilibrium) and causes a luminosity change. While small radius variations will occur, most of the change will be seen in temperature

  8. Stabilized power constant alimentation

    International Nuclear Information System (INIS)

    Roussel, L.

    1968-06-01

    The study and realization of a stabilized power alimentation variable from 5 to 100 watts are described. In order to realize a constant power drift of Lithium compensated diodes, we have searched a 1 per cent precision of regulation and a response time minus than 1 sec. Recent components like Hall multiplicator and integrated amplifiers give this possibility and it is easy to use permutable circuits. (author) [fr

  9. Feigenbaum constants in hadron collisions

    International Nuclear Information System (INIS)

    Batunin, A.V.

    1991-01-01

    The coincidence is found between the law n ch (s) growth in hadron collisions for symmetric rapidity intervals and the law of growth of the number of elements in limit 2 m -cycles for one-dimensional quadratic maps when a govering parameter is varied. Fractal structure of the corresponding attractor underlies intermittency phenomenon in the multiplicity distribution of particles. 12 refs.; 1 fig

  10. Universe of constant

    Science.gov (United States)

    Yongquan, Han

    2016-10-01

    The ideal gas state equation is not applicable to ordinary gas, it should be applied to the Electromagnetic ``gas'' that is applied to the radiation, the radiation should be the ultimate state of matter changes or initial state, the universe is filled with radiation. That is, the ideal gas equation of state is suitable for the Singular point and the universe. Maybe someone consider that, there is no vessel can accommodate radiation, it is because the Ordinary container is too small to accommodate, if the radius of your container is the distance that Light through an hour, would you still think it can't accommodates radiation? Modern scientific determinate that the radius of the universe now is about 1027 m, assuming that the universe is a sphere whose volume is approximately: V = 4.19 × 1081 cubic meters, the temperature radiation of the universe (cosmic microwave background radiation temperature of the universe, should be the closest the average temperature of the universe) T = 3.15k, radiation pressure P = 5 × 10-6 N / m 2, according to the law of ideal gas state equation, PV / T = constant = 6 × 1075, the value of this constant is the universe, The singular point should also equal to the constant Author: hanyongquan

  11. Connecting Fundamental Constants

    International Nuclear Information System (INIS)

    Di Mario, D.

    2008-01-01

    A model for a black hole electron is built from three basic constants only: h, c and G. The result is a description of the electron with its mass and charge. The nature of this black hole seems to fit the properties of the Planck particle and new relationships among basic constants are possible. The time dilation factor in a black hole associated with a variable gravitational field would appear to us as a charge; on the other hand the Planck time is acting as a time gap drastically limiting what we are able to measure and its dimension will appear in some quantities. This is why the Planck time is numerically very close to the gravitational/electric force ratio in an electron: its difference, disregarding a π√(2) factor, is only 0.2%. This is not a coincidence, it is always the same particle and the small difference is between a rotating and a non-rotating particle. The determination of its rotational speed yields accurate numbers for many quantities, including the fine structure constant and the electron magnetic moment

  12. The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

    International Nuclear Information System (INIS)

    Li, Chengzhi; Llibre, Jaume

    2009-01-01

    We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles

  13. Induced motion of domain walls in multiferroics with quadratic interaction

    Energy Technology Data Exchange (ETDEWEB)

    Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)

    2013-10-15

    We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.

  14. Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

    International Nuclear Information System (INIS)

    Aquilanti, V; Marinelli, D; Marzuoli, A

    2014-01-01

    Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed

  15. Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

    Science.gov (United States)

    Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

    2017-10-01

    We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

  16. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    Science.gov (United States)

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

  17. Linear Quadratic Controller with Fault Detection in Compact Disk Players

    DEFF Research Database (Denmark)

    Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.

    2001-01-01

    The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....

  18. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  19. Information sets as permutation cycles for quadratic residue codes

    Directory of Open Access Journals (Sweden)

    Richard A. Jenson

    1982-01-01

    Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1,   (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.

  20. On a linear-quadratic problem with Caputo derivative

    Directory of Open Access Journals (Sweden)

    Dariusz Idczak

    2016-01-01

    Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.

  1. Stationary walking solitons in bulk quadratic nonlinear media

    OpenAIRE

    Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís

    1997-01-01

    We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...

  2. Bifurcation in Z2-symmetry quadratic polynomial systems with delay

    International Nuclear Information System (INIS)

    Zhang Chunrui; Zheng Baodong

    2009-01-01

    Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.

  3. A Note on 5-bit Quadratic Permutations’ Classification

    OpenAIRE

    Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali

    2017-01-01

    Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...

  4. Integrable systems with quadratic nonlinearity in Fourier space

    International Nuclear Information System (INIS)

    Marikhin, V.G.

    2003-01-01

    The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

  5. General quadratic gauge theory: constraint structure, symmetries and physical functions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

    2005-06-17

    How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.

  6. Quadratic time dependent Hamiltonians and separation of variables

    International Nuclear Information System (INIS)

    Anzaldo-Meneses, A.

    2017-01-01

    Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.

  7. Design of reinforced areas of concrete column using quadratic polynomials

    Science.gov (United States)

    Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

    2017-11-01

    Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

  8. Fast, multiple optimizations of quadratic dose objective functions in IMRT

    International Nuclear Information System (INIS)

    Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M

    2006-01-01

    Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved

  9. Measurement of quadratic electrogyration effect in castor oil

    Science.gov (United States)

    Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

    2015-07-01

    This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

  10. The Hubble Constant

    Directory of Open Access Journals (Sweden)

    Neal Jackson

    2015-09-01

    Full Text Available I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individual astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of all-sky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, object-based measurements give H_0 values of around 72–74 km s^–1 Mpc^–1, with typical errors of 2–3 km s^–1 Mpc^–1. This is in mild discrepancy with CMB-based measurements, in particular those from the Planck satellite, which give values of 67–68 km s^–1 Mpc^–1 and typical errors of 1–2 km s^–1 Mpc^–1. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the object-based methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the all-sky methods.

  11. The inconstant solar constant

    International Nuclear Information System (INIS)

    Willson, R.C.; Hudson, H.

    1984-01-01

    The Active Cavity Radiometer Irradiance Monitor (ACRIM) of the Solar Maximum Mission satellite measures the radiant power emitted by the sun in the direction of the earth and has worked flawlessly since 1980. The main motivation for ACRIM's use to measure the solar constant is the determination of the extent to which this quantity's variations affect earth weather and climate. Data from the solar minimum of 1986-1987 is eagerly anticipated, with a view to the possible presence of a solar cycle variation in addition to that caused directly by sunspots

  12. The influence of anharmonic and solvent effects on the theoretical vibrational spectra of the guanine-cytosine base pairs in Watson-Crick and Hoogsteen configurations.

    Science.gov (United States)

    Bende, Attila; Muntean, Cristina M

    2014-03-01

    The theoretical IR and Raman spectra of the guanine-cytosine DNA base pairs in Watson-Crick and Hoogsteen configurations were computed using DFT method with M06-2X meta-hybrid GGA exchange-correlation functional, including the anharmonic corrections and solvent effects. The results for harmonic frequencies and their anharmonic corrections were compared with our previously calculated values obtained with the B3PW91 hybrid GGA functional. Significant differences were obtained for the anharmonic corrections calculated with the two different DFT functionals, especially for the stretching modes, while the corresponding harmonic frequencies did not differ considerable. For the Hoogtseen case the H⁺ vibration between the G-C base pair can be characterized as an asymmetric Duffing oscillator and therefore unrealistic anharmonic corrections for normal modes where this proton vibration is involved have been obtained. The spectral modification due to the anharmonic corrections, solvent effects and the influence of sugar-phosphate group for the Watson-Crick and Hoogsteen base pair configurations, respectively, were also discussed. For the Watson-Crick case also the influence of the stacking interaction on the theoretical IR and Raman spectra was analyzed. Including the anharmonic correction in our normal mode analysis is essential if one wants to obtain correct assignments of the theoretical frequency values as compared with the experimental spectra.

  13. Anharmonicity of lattice vibrations induced by charged nickel additions in A sup 2 B sup 6 semiconductors

    CERN Document Server

    Sokolov, V I; Shirokov, E A; Kislov, A N

    2002-01-01

    Paper presents the results of investigations into lattice vibrations induced by nickel impurities charged negatively as to the lattice in ZnSe:Ni, ZnO:Ni, ZnS:Ni, CdS:Ni semiconductors. To investigate into vibrations one applies a sensitive technique of field exciton-oscillation spectroscopy. One observes experimentally oscillating reiterations of the impurity exciton head line including the intensive peaks of combined repetitions up to the 8-th order. The experimental results are discussed on the basis of the model estimations of oscillations of a lattice with a charged impurity centre, as well as, on the ground of calculations for oscillations of monoatomic chain with high anharmonicity. Charged impurity centres are shown to induce new oscillations of lattice - impurity anharmonic modes

  14. Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

    Science.gov (United States)

    Lesmana, E.; Chaerani, D.; Khansa, H. N.

    2018-03-01

    Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

  15. Anharmonic correlated Debye model high-order expanded interatomic effective potential and Debye-Waller factors of bcc crystals

    Energy Technology Data Exchange (ETDEWEB)

    Van Hung, Nguyen, E-mail: hungnv@vnu.edu.vn [Department of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi (Viet Nam); Hue, Trinh Thi [Department of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi (Viet Nam); Khoa, Ha Dang [School of Engineering Physics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi (Viet Nam); Vuong, Dinh Quoc [Quang Ninh Education & Training Department, Nguyen Van Cu, Ha Long, Quang Ninh (Viet Nam)

    2016-12-15

    High-order expanded interatomic effective potential and Debye-Waller factors (DWFs) for local vibrational amplitudes in X-ray absorption fine structure (XAFS) of bcc crystals have been studied based on the anharmonic correlated Debye model. DWFs are presented in terms of cumulant expansion up to the fourth order and the many-body effects are taken into account in the present one-dimensional model based on the first shell near neighbor contribution approach used in the derivations of the anharmonic effective potential and XAFS cumulants where Morse potential is assumed to describe the single-pair atomic interaction. Analytical expressions for the dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS cumulants have been derived based on the many-body perturbation approach. Thermodynamic properties and anharmonic effects in XAFS of bcc crystals described by the obtained cumulants have been in detail discussed. The advantage and efficiency of the present theory are illustrated by good agreement of the numerical results for Mo, Fe and W with experiment.

  16. Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

    International Nuclear Information System (INIS)

    Lopez de la Cruz, J.; Gutierrez, M.A.

    2008-01-01

    This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed

  17. Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator

    International Nuclear Information System (INIS)

    Belendez, Augusto; Pascual, Carolina

    2007-01-01

    The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A

  18. Anharmonic Infrared Spectroscopy through the Fourier Transform of Time Correlation Function Formalism in ONETEP.

    Science.gov (United States)

    Vitale, Valerio; Dziedzic, Jacek; Dubois, Simon M-M; Fangohr, Hans; Skylaris, Chris-Kriton

    2015-07-14

    Density functional theory molecular dynamics (DFT-MD) provides an efficient framework for accurately computing several types of spectra. The major benefit of DFT-MD approaches lies in the ability to naturally take into account the effects of temperature and anharmonicity, without having to introduce any ad hoc or a posteriori corrections. Consequently, computational spectroscopy based on DFT-MD approaches plays a pivotal role in the understanding and assignment of experimental peaks and bands at finite temperature, particularly in the case of floppy molecules. Linear-scaling DFT methods can be used to study large and complex systems, such as peptides, DNA strands, amorphous solids, and molecules in solution. Here, we present the implementation of DFT-MD IR spectroscopy in the ONETEP linear-scaling code. In addition, two methods for partitioning the dipole moment within the ONETEP framework are presented. Dipole moment partitioning allows us to compute spectra of molecules in solution, which fully include the effects of the solvent, while at the same time removing the solvent contribution from the spectra.

  19. 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)

  20. Exploiting elastic anharmonicity in aluminum nitride matrix for phase-synchronous frequency reference generation

    Science.gov (United States)

    Ghatge, Mayur; Tabrizian, Roozbeh

    2018-03-01

    A matrix of aluminum-nitride (AlN) waveguides is acoustically engineered to realize electrically isolated phase-synchronous frequency references through nonlinear wave-mixing. AlN rectangular waveguides are cross-coupled through a periodically perforated plate that is engineered to have a wide acoustic bandgap around a desirable frequency ( f1≈509 MHz). While the coupling plate isolates the matrix from resonant vibrations of individual waveguide constituents at f1, it is transparent to the third-order harmonic waves (3f1) that are generated through nonlinear wave-mixing. Therefore, large-signal excitation of the f1 mode in a constituent waveguide generates acoustic waves at 3f1 with an efficiency defined by elastic anharmonicity of the AlN film. The phase-synchronous propagation of the third harmonic through the matrix is amplified by a high quality-factor resonance mode at f2≈1529 MHz, which is sufficiently close to 3f1 (f2 ≅ 3f1). Such an architecture enables realization of frequency-multiplied and phase-synchronous, yet electrically and spectrally isolated, references for multi-band/carrier and spread-spectrum wireless communication systems.

  1. Vacuum solutions of Bianchi cosmologies in quadratic gravity

    International Nuclear Information System (INIS)

    Deus, Juliano Alves de; Muller, Daniel

    2011-01-01

    Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

  2. Lipschitz stability of the K-quadratic functional equation | Chahbi ...

    African Journals Online (AJOL)

    Let N be the set of all positive integers, G an Abelian group with a metric d and E a normed space. For any f : G → E we define the k-quadratic difference of the function f by the formula Qk ƒ(x; y) := 2ƒ(x) + 2k2ƒ(y) - f(x + ky) - f(x - ky) for x; y ∈ G and k ∈ N. Under some assumptions about f and Qkƒ we prove that if Qkƒ is ...

  3. Uniform sparse bounds for discrete quadratic phase Hilbert transforms

    Science.gov (United States)

    Kesler, Robert; Arias, Darío Mena

    2017-09-01

    For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

  4. BRST operator for superconformal algebras with quadratic nonlinearity

    International Nuclear Information System (INIS)

    Khviengia, Z.; Sezgin, E.

    1993-07-01

    We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs

  5. Quadratic integrand double-hybrid made spin-component-scaled

    Energy Technology Data Exchange (ETDEWEB)

    Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Sancho-García, Juan C.; Pérez-Jiménez, Ángel J. [Departamento de Química Física, Universidad de Alicante, E-03080 Alicante (Spain); Adamo, Carlo [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris IRCP, F-75005 Paris (France); Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris (France)

    2016-03-28

    We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

  6. SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.

  7. On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations

    International Nuclear Information System (INIS)

    Sekine, Jun

    2006-01-01

    The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula

  8. Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

    Science.gov (United States)

    T. Sardari, Naser

    2018-03-01

    Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

  9. Abelian groups and quadratic residues in weak arithmetic

    Czech Academy of Sciences Publication Activity Database

    Jeřábek, Emil

    2010-01-01

    Roč. 56, č. 3 (2010), s. 262-278 ISSN 0942-5616 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * abelian group * Fermat's little theorem * quadratic reciprocity Subject RIV: BA - General Mathematics Impact factor: 0.361, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/malq.200910009/abstract;jsessionid=9F636FFACB84C025FD90C7E6880350DD.f03t03

  10. Analysis of electroperforated materials using the quadrat counts method

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, E; Garzon, C; Garcia-Garcia, J [Departament d' Enginyeria Electronica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); MartInez-Cisneros, C; Alonso, J, E-mail: enrique.miranda@uab.cat [Departament de Quimica AnalItica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain)

    2011-06-23

    The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.

  11. C1 Rational Quadratic Trigonometric Interpolation Spline for Data Visualization

    Directory of Open Access Journals (Sweden)

    Shengjun Liu

    2015-01-01

    Full Text Available A new C1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h3. Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

  12. Soliton interaction in quadratic and cubic bulk media

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær; Bang, Ole

    2000-01-01

    Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...

  13. Linear-quadratic model predictions for tumor control probability

    International Nuclear Information System (INIS)

    Yaes, R.J.

    1987-01-01

    Sigmoid dose-response curves for tumor control are calculated from the linear-quadratic model parameters α and Β, obtained from human epidermoid carcinoma cell lines, and are much steeper than the clinical dose-response curves for head and neck cancers. One possible explanation is the presence of small radiation-resistant clones arising from mutations in an initially homogeneous tumor. Using the mutation theory of Delbruck and Luria and of Goldie and Coldman, the authors discuss the implications of such radiation-resistant clones for clinical radiation therapy

  14. Sub-quadratic decoding of one-point hermitian codes

    DEFF Research Database (Denmark)

    Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter

    2015-01-01

    We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....

  15. Field equations for gravity quadratic in the curvature

    International Nuclear Information System (INIS)

    Rose, B.

    1992-01-01

    Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs

  16. Quadratic Hamiltonians on non-symmetric Poisson structures

    International Nuclear Information System (INIS)

    Arribas, M.; Blesa, F.; Elipe, A.

    2007-01-01

    Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases

  17. Potential constants and centrifugal distortion constants of octahedral hexafluoride molecules

    Energy Technology Data Exchange (ETDEWEB)

    Manivannan, G [Government Thirumagal Mill' s Coll., Gudiyattam, Tamil Nadu (India)

    1981-04-01

    The kinetic constants method outlined by Thirugnanasambandham (1964) based on Wilson's (1955) group theory has been adapted in evaluating the potential constants for SF/sub 6/, SeF/sub 6/, WF/sub 6/, IrF/sub 6/, UF/sub 6/, NpF/sub 6/, and PuF/sub 6/ using the experimentally observed vibrational frequency data. These constants are used to calculate the centrifugal distortion constants for the first time.

  18. Higgs inflation and the cosmological constant

    Energy Technology Data Exchange (ETDEWEB)

    Jegerlehner, Fred [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2014-02-15

    The Higgs not only induces the masses of all SM particles, the Higgs, given its special mass value, is the natural candidate for the inflaton and in fact is ruling the evolution of the early universe, by providing the necessary dark energy which remains the dominant energy density. SM running couplings not only allow us to extrapolate SM physics up to the Planck scale, but equally important they are triggering the Higgs mechanism. This is possible by the fact that the bare mass term in the Higgs potential changes sign at about μ{sub 0}≅1.40 x 10{sup 16} GeV and in the symmetric phase is enhanced by quadratic terms in the Planck mass. Such a huge Higgs mass term is able to play a key role in triggering inflation in the early universe. In this article we extend our previous investigation by working out the details of a Higgs inflation scenario. We show how different terms contributing to the Higgs Lagrangian are affecting inflation. Given the SM and its extrapolation to scales μ>μ{sub 0} we find a calculable cosmological constant V(0) which is weakly scale dependent and actually remains large during inflation. This is different to the Higgs fluctuation field dependent ΔV(φ), which decays exponentially during inflation, and actually would not provide a sufficient amount of inflation. The fluctuation field has a different effective mass which shifts the bare Higgs transition point to a lower value μ'{sub 0} ≅7.7 x 10{sup 14} GeV. The vacuum energy V(0) being proportional to M{sub Pl}{sup 4} has a coefficient which vanishes near the Higgs transition point, such that the bare and the renormalized cosmological constant match at this point. The role of the Higgs in reheating and baryogenesis is emphasized.

  19. Cyclic subgroups in class groups of real quadratic fields

    International Nuclear Information System (INIS)

    Washington, L.C.; Zhang Xianke.

    1994-01-01

    While examining the class numbers of the real quadratic field Q(√n 2 + 3n + 9), we observed that the class number is often a multiple of 3. There is a simple explanation for this, namely -27 = (2n + 3) 2 - 4(n 2 + 3n + 9), so the cubes of the prime ideals above 3 are principal. If the prime ideals themselves are non-principal then 3 must divide the class number. In the present paper, we study this idea from a couple different directions. In the first section we present a criterion that allows us to show that the ideal class group of a real quadratic field has a cyclic subgroup of a given order n. We then give several families of fields to which this criterion applies, hence in which the ideal class groups contain elements of order n. In the second section, we discuss the situation where there is only a potential element of order p (=an odd prime) in the class group, such as the situation described above. We present a modification of the Cohen-Lenstra heuristics for the probability that in this situation the class number is actually a multiple of p. We also extend this idea to predict how often the potential element of order p is actually non-trivial. Both of these predictions agree fairly well with the numerical data. (author). 14 refs, 2 tabs

  20. Universality of quadratic to linear magnetoresistance crossover in disordered conductors

    Science.gov (United States)

    Lara, Silvia; Ramakrishnan, Navneeth; Lai, Ying Tong; Adam, Shaffique

    Many experiments measuring Magnetoresistance (MR) showed unsaturating linear behavior at high magnetic fields and quadratic behavior at low fields. In the literature, two very different theoretical models have been used to explain this classical MR as a consequence of sample disorder. The phenomenological Random Resistor Network (RRN) model constructs a grid of four-terminal resistors each with a varying random resistance. The Effective Medium Theory (EMT) model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. In this theoretical work, we demonstrate numerically that both the RRN and EMT models belong to the same universality class, and that a single parameter (the ratio of the fluctuations in the carrier density to the average carrier density) completely determines both the magnitude of the MR and the B-field scale for the crossover from quadratic to linear MR. By considering several experimental data sets in the literature, ranging from thin films of InSb to graphene to Weyl semimetals like Na3Bi, we show that this disorder-induced mechanism for MR is in good agreement with the experiments, and that this comparison of MR with theory reveals information about the spatial carrier density inhomogeneity. This work was supported by the National Research Foundation of Singapore (NRF-NRFF2012-01).

  1. STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION

    Directory of Open Access Journals (Sweden)

    KOSOLAP A. I.

    2015-11-01

    Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.

  2. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    International Nuclear Information System (INIS)

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-01-01

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

  3. Electroweak vacuum stability and finite quadratic radiative corrections

    Energy Technology Data Exchange (ETDEWEB)

    Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)

    2015-07-15

    If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.

  4. Learning quadratic receptive fields from neural responses to natural stimuli.

    Science.gov (United States)

    Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

    2013-07-01

    Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

  5. On bent and semi-bent quadratic Boolean functions

    DEFF Research Database (Denmark)

    Charpin, P.; Pasalic, Enes; Tavernier, C.

    2005-01-01

    correlation and high nonlinearity. We say that such a sequence is generated by a semi-bent function. Some new families of such function, represented by f(x) = Sigma(i=1)(n-1/2) c(i)Tr(x(2t+1)), n odd and c(i) is an element of F-2, have recently (2002) been introduced by Khoo et al. We first generalize......The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross...... their results to even n. We further investigate the conditions on the choice of ci for explicit definitions of new infinite families having three and four trace terms. Also, a class of nonpermutation polynomials whose composition with a quadratic function yields again a quadratic semi-bent function is specified...

  6. Beyond the Hubble Constant

    Science.gov (United States)

    1995-08-01

    about the distances to galaxies and thereby about the expansion rate of the Universe. A simple way to determine the distance to a remote galaxy is by measuring its redshift, calculate its velocity from the redshift and divide this by the Hubble constant, H0. For instance, the measured redshift of the parent galaxy of SN 1995K (0.478) yields a velocity of 116,000 km/sec, somewhat more than one-third of the speed of light (300,000 km/sec). From the universal expansion rate, described by the Hubble constant (H0 = 20 km/sec per million lightyears as found by some studies), this velocity would indicate a distance to the supernova and its parent galaxy of about 5,800 million lightyears. The explosion of the supernova would thus have taken place 5,800 million years ago, i.e. about 1,000 million years before the solar system was formed. However, such a simple calculation works only for relatively ``nearby'' objects, perhaps out to some hundred million lightyears. When we look much further into space, we also look far back in time and it is not excluded that the universal expansion rate, i.e. the Hubble constant, may have been different at earlier epochs. This means that unless we know the change of the Hubble constant with time, we cannot determine reliable distances of distant galaxies from their measured redshifts and velocities. At the same time, knowledge about such change or lack of the same will provide unique information about the time elapsed since the Universe began to expand (the ``Big Bang''), that is, the age of the Universe and also its ultimate fate. The Deceleration Parameter q0 Cosmologists are therefore eager to determine not only the current expansion rate (i.e., the Hubble constant, H0) but also its possible change with time (known as the deceleration parameter, q0). Although a highly accurate value of H0 has still not become available, increasing attention is now given to the observational determination of the second parameter, cf. also the Appendix at the

  7. Association constants of telluronium salts

    International Nuclear Information System (INIS)

    Kovach, N.A.; Rivkin, B.B.; Sadekov, T.D.; Shvajka, O.P.

    1996-01-01

    Association constants in acetonitrile of triphenyl telluronium salts, which are dilute electrolytes, are determined through the conductometry method. Satisfactory correlation dependence of constants of interion association and threshold molar electroconductivity on the Litvinenko-Popov constants for depositing groups is identified. 6 refs

  8. Anisotropic constant-roll inflation

    Energy Technology Data Exchange (ETDEWEB)

    Ito, Asuka; Soda, Jiro [Kobe University, Department of Physics, Kobe (Japan)

    2018-01-15

    We study constant-roll inflation in the presence of a gauge field coupled to an inflaton. By imposing the constant anisotropy condition, we find new exact anisotropic constant-roll inflationary solutions which include anisotropic power-law inflation as a special case. We also numerically show that the new anisotropic solutions are attractors in the phase space. (orig.)

  9. Quintessence and the cosmological constant

    International Nuclear Information System (INIS)

    Doran, M.; Wetterich, C.

    2003-01-01

    Quintessence -- the energy density of a slowly evolving scalar field -- may constitute a dynamical form of the homogeneous dark energy in the universe. We review the basic idea in the light of the cosmological constant problem. Cosmological observations or a time variation of fundamental 'constants' can distinguish quintessence from a cosmological constant

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

    Science.gov (United States)

    Adams, Donat J; Passerone, Daniele

    2016-08-03

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

  11. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

    DEFF Research Database (Denmark)

    Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

    2016-01-01

    We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...

  12. Spectra-structure correlations in NIR region: Spectroscopic and anharmonic DFT study of n-hexanol, cyclohexanol and phenol

    Science.gov (United States)

    Beć, Krzysztof B.; Grabska, Justyna; Czarnecki, Mirosław A.

    2018-05-01

    We investigated near-infrared (7500-4000 cm-1) spectra of n-hexanol, cyclohexanol and phenol in CCl4 (0.2 M) by using anharmonic quantum calculations. These molecules represent three major kinds of alcohols; linear and cyclic aliphatic, and aromatic ones. Vibrational second-order perturbation theory (VPT2) was employed to calculate the first overtones and binary combination modes and to reproduce the experimental NIR spectra. The level of conformational flexibility of these three alcohols varies from one stable conformer of phenol through four conformers of cyclohexanol to few hundreds conformers in the case of n-hexanol. To take into account the most relevant conformational population of n-hexanol, a systematic conformational search was performed. Accurate reproduction of the experimental NIR spectra was achieved and detailed spectra-structure correlations were obtained for these three alcohols. VPT2 approach provides less reliable description of highly anharmonic modes, i.e. OH stretching. In the present work this limitation was manifested in erroneous results yielded by VPT2 for 2νOH mode of cyclohexanol. To study the anharmonicity of this mode we solved the corresponding time-independent Schrödinger equation based on a dense-grid probing of the relevant vibrational potential. These results allowed for significant improvement of the agreement between the calculated and experimental 2νOH band of cyclohexanol. Various important biomolecules include similar structural units to the systems investigated here. A detailed knowledge on spectral properties of these three types of alcohols is therefore essential for advancing our understanding of NIR spectroscopy of biomolecules.

  13. The Model and Quadratic Stability Problem of Buck Converter in DCM

    Directory of Open Access Journals (Sweden)

    Li Xiaojing

    2016-01-01

    Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.

  14. A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming

    National Research Council Canada - National Science Library

    Ye, Y; Gueler, O; Tapia, Richard A; Zhang, Y

    1991-01-01

    ...)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap...

  15. The influence of anharmonic vibrations of the core to M2-transition between low-lying states in 115Sn

    International Nuclear Information System (INIS)

    Sy Savane, Y.

    1995-12-01

    The influence of the anharmonicity of the core vibration, on the magnetic transition 11/2 - 1 → 7/2 + 1 in 115 Sn have been investigated in the frame of the quasiparticle-phonon nuclear model. The model wave function includes a ''quasiparticle + two phonons'' component. The performed numerical calculations show that those effects cannot explain the strong reduction of the M2-transition observed in the experiment. A full agreement with the experimental value is obtained with g eff s = 0.42g free s . (author). 10 refs, 2 figs, 1 tab

  16. Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb2ZnCl4

    International Nuclear Information System (INIS)

    Li, Liang; Wölfel, Alexander; Schönleber, Andreas; Mondal, Swastik; Schreurs, Antoine M. M.; Kroon-Batenburg, Loes M. J.; Smaalen, Sander van

    2011-01-01

    The superspace maximum entropy method (MEM) density in combination with structure refinements has been used to uncover the modulation in incommensurate Rb 2 ZnCl 4 close to the lock-in transition. Modulated atomic displacement parameters (ADPs) and modulated anharmonic ADPs are found to form an intrinsic part of the modulation. Refined values for the displacement modulation function depend on the presence or absence of modulated ADPs in the model. A combination of structure refinements, analysis of the superspace MEM density and interpretation of difference-Fourier maps has been used to characterize the incommensurate modulation of rubidium tetrachlorozincate, Rb 2 ZnCl 4 , at a temperature of T = 196 K, close to the lock-in transition at T lock-in = 192 K. The modulation is found to consist of a combination of displacement modulation functions, modulated atomic displacement parameters (ADPs) and modulated third-order anharmonic ADPs. Up to fifth-order Fourier coefficients could be refined against diffraction data containing up to fifth-order satellite reflections. The center-of-charge of the atomic basins of the MEM density and the displacive modulation functions of the structure model provide equivalent descriptions of the displacive modulation. Modulations of the ADPs and anharmonic ADPs are visible in the MEM density, but extracting quantitative information about these modulations appears to be difficult. In the structure refinements the modulation parameters of the ADPs form a dependent set, and ad hoc restrictions had to be introduced in the refinements. It is suggested that modulated harmonic ADPs and modulated third-order anharmonic ADPs form an intrinsic part, however small, of incommensurately modulated structures in general. Refinements of alternate models with and without parameters for modulated ADPs lead to significant differences between the parameters of the displacement modulation in these two types of models, thus showing the modulation of ADPs to

  17. Carrier relaxation in (In,Ga)As quantum dots with magnetic field-induced anharmonic level structure

    Energy Technology Data Exchange (ETDEWEB)

    Kurtze, H.; Bayer, M. [Experimentelle Physik 2, TU Dortmund, D-44221 Dortmund (Germany)

    2016-07-04

    Sophisticated models have been worked out to explain the fast relaxation of carriers into quantum dot ground states after non-resonant excitation, overcoming the originally proposed phonon bottleneck. We apply a magnetic field along the quantum dot heterostructure growth direction to transform the confined level structure, which can be approximated by a Fock–Darwin spectrum, from a nearly equidistant level spacing at zero field to strong anharmonicity in finite fields. This changeover leaves the ground state carrier population rise time unchanged suggesting that fast relaxation is maintained upon considerable changes of the level spacing. This corroborates recent models explaining the relaxation by polaron formation in combination with quantum kinetic effects.

  18. Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

    International Nuclear Information System (INIS)

    Huveneers, François

    2013-01-01

    We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter ϵ > 0. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in ϵ as ϵ → 0. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz (2008 Phys. Rev. Lett. 100 134301), and to a classic spin chain recently investigated by Oganesyan, Pal and Huse (2009 Phys. Rev. B 80 115104). (paper)

  19. Dynamical instability, strong anharmonicity and electron-phonon coupling in KOs2O6: First-principles calculations

    Science.gov (United States)

    Wang, Wei; Sun, Jiafa; Li, Bin; He, Junqi

    2017-09-01

    First-principles pseudopotential calculations on phonon and electronic properties of β -pyrochlore superconductor KOs2O6 are performed. The imaginary soft-phonon modes with a special double-well potential for the lowest Eu(1) mode and the second lowest T1u(1) mode are reported, which indicates the dynamical instability in KOs2O6. However, the double wells are too small to induce a structural phase transformation in KOs2O6. The strong anharmonicity especially for K T2g(1) phonon mode is got, which is approved to be from the strong electron-phonon coupling that supports the superconductivity in KOs2O6.

  20. Cooper-pair formation by anharmonic rattling modes in the β-pyrochlore superconductor KOs2O6

    Science.gov (United States)

    Chang, Jun; Eremin, Ilya; Thalmeier, Peter

    2009-05-01

    We study the influence of anharmonic rattling phonons in the β-pyrochlore superconductor KOs2O6 using the strong-coupling Eliashberg approach. In particular, by analyzing the specific heat data, we find that the rattling phonon frequency changes discontinuously at the critical temperature of the first-order phase transition. Solving the strong-coupling Eliashberg equations with effective temperature-dependent α2F(ω), we investigate the consequence of this first-order phase transition for the anomalous temperature dependence of the superconducting gap. We discuss our results in the context of the recent experimental data.

  1. Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

    DEFF Research Database (Denmark)

    Sørensen, Dan Erik Krarup

    1996-01-01

    We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

  2. Diagonalizing quadratic bosonic operators by non-autonomous flow equations

    CERN Document Server

    Bach, Volker

    2016-01-01

    The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

  3. Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics

    Directory of Open Access Journals (Sweden)

    J. Petrzela

    2012-04-01

    Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided

  4. Absence of the Gribov ambiguity in a quadratic gauge

    International Nuclear Information System (INIS)

    Raval, Haresh

    2016-01-01

    The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S 3 , when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge. (orig.)

  5. Absence of the Gribov ambiguity in a quadratic gauge

    Energy Technology Data Exchange (ETDEWEB)

    Raval, Haresh [Indian Institute of Technology, Bombay, Department of Physics, Mumbai (India)

    2016-05-15

    The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S{sup 3}, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge. (orig.)

  6. Quadratic time dependent Hamiltonians and separation of variables

    Science.gov (United States)

    Anzaldo-Meneses, A.

    2017-06-01

    Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

  7. Trajectory generation for manipulators using linear quadratic optimal tracking

    Directory of Open Access Journals (Sweden)

    Olav Egeland

    1989-04-01

    Full Text Available The reference trajectory is normally known in advance in manipulator control which makes it possible to apply linear quadratic optimal tracking. This gives a control system which rounds corners and generates optimal feedforward. The method may be used for references consisting of straight-line segments as an alternative to the two-step method of using splines to smooth the reference and then applying feedforward. In addition, the method can be used for more complex trajectories. The actual dynamics of the manipulator are taken into account, and this results in smooth and accurate tracking. The method has been applied in combination with the computed torque technique and excellent performance was demonstrated in a simulation study. The method has also been applied experimentally to an industrial spray-painting robot where a saw-tooth reference was tracked. The corner was rounded extremely well, and the steady-state tracking error was eliminated by the optimal feedforward.

  8. Quadratic rational rotations of the torus and dual lattice maps

    CERN Document Server

    Kouptsov, K L; Vivaldi, F

    2002-01-01

    We develop a general formalism for computed-assisted proofs concerning the orbit structure of certain non ergodic piecewise affine maps of the torus, whose eigenvalues are roots of unity. For a specific class of maps, we prove that if the trace is a quadratic irrational (the simplest nontrivial case, comprising 8 maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of exceptional families. The proof is based on exact computations with algebraic numbers, where units play the role of scaling parameters. Exploiting a duality existing between these maps and lattice maps representing rounded-off planar rotations, we establish the global periodicity of the latter systems, for a set of orbits of full density.

  9. Low photon count based digital holography for quadratic phase cryptography.

    Science.gov (United States)

    Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

    2017-07-15

    Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

  10. Limits to compression with cascaded quadratic soliton compressors

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Krolikowski, Wieslaw

    2008-01-01

    We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong....... This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find......, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account....

  11. Wind turbine power tracking using an improved multimodel quadratic approach.

    Science.gov (United States)

    Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

    2010-07-01

    In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Neural network for solving convex quadratic bilevel programming problems.

    Science.gov (United States)

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

    2014-03-01

    In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

  13. Quadratic Finite Element Method for 1D Deterministic Transport

    International Nuclear Information System (INIS)

    Tolar, D R Jr.; Ferguson, J M

    2004-01-01

    In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms

  14. Schwarz and multilevel methods for quadratic spline collocation

    Energy Technology Data Exchange (ETDEWEB)

    Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)

    1994-12-31

    Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

  15. Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

    Science.gov (United States)

    Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan

    2018-03-01

    Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.

  16. Estimation of stature from sternum - Exploring the quadratic models.

    Science.gov (United States)

    Saraf, Ashish; Kanchan, Tanuj; Krishan, Kewal; Ateriya, Navneet; Setia, Puneet

    2018-04-14

    Identification of the dead is significant in examination of unknown, decomposed and mutilated human remains. Establishing the biological profile is the central issue in such a scenario, and stature estimation remains one of the important criteria in this regard. The present study was undertaken to estimate stature from different parts of the sternum. A sample of 100 sterna was obtained from individuals during the medicolegal autopsies. Length of the deceased and various measurements of the sternum were measured. Student's t-test was performed to find the sex differences in stature and sternal measurements included in the study. Correlation between stature and sternal measurements were analysed using Karl Pearson's correlation, and linear and quadratic regression models were derived. All the measurements were found to be significantly larger in males than females. Stature correlated best with the combined length of sternum, among males (R = 0.894), females (R = 0.859), and for the total sample (R = 0.891). The study showed that the models derived for stature estimation from combined length of sternum are likely to give the most accurate estimates of stature in forensic case work when compared to manubrium and mesosternum. Accuracy of stature estimation further increased with quadratic models derived for the mesosternum among males and combined length of sternum among males and females when compared to linear regression models. Future studies in different geographical locations and a larger sample size are proposed to confirm the study observations. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

  17. Effects of cosmic-string framework on the thermodynamical properties of anharmonic oscillator using the ordinary statistics and the q-deformed superstatistics approaches

    Energy Technology Data Exchange (ETDEWEB)

    Sobhani, Hadi; Hassanabadi, Hassan [Shahrood University of Technology, Faculty of Physics, Shahrood (Iran, Islamic Republic of); Chung, Won Sang [Gyeongsang National University, Department of Physics and Research Institute of Natural Science, College of Natural Science, Jinju (Korea, Republic of)

    2018-02-15

    In this article, we determine the thermodynamical properties of the anharmonic canonical ensemble within the cosmic-string framework. We use the ordinary statistics and the q-deformed superstatistics for this study. The q-deformed superstatistics is derived by modifying the probability density in the original superstatistics. The Schroedinger equation is rewritten in the cosmic-string framework. Next, the anharmonic oscillator is investigated in detail. The wave function and the energy spectrum of the considered system are derived using the bi-confluent Heun functions. In the next step, we first determine the thermodynamical properties for the canonical ensemble of the anharmonic oscillator in the cosmic-string framework using the ordinary statistics approach. Also, these quantities have been obtained in the q-deformed superstatistics. For vanishing deformation parameter, the ordinary results are obtained. (orig.)

  18. Impact of future price increase on ordering policies for deteriorating items under quadratic demand

    Directory of Open Access Journals (Sweden)

    Nita H. Shah

    2016-06-01

    Full Text Available When a supplier announces a price increase at a certain time in the future, for each retailer it is important to choose whether to purchase supplementary stock to take benefit of the current lower price or procure at a new price. This article focuses on the possible effects of price increase on a retailer’s replenishment strategy for constant deterioration of items. Here, quadratic demand is debated; which is appropriate for the products for which demand increases initially and subsequently it starts to decrease with the new version of the substitute. We discuss two scenarios in this study: (I when the special order time coincides with the retailer’s replenishment time and (II when the special order time falls during the retailer’s sales period. We determine an optimal ordering policy for each case by maximizing total cost savings between special and regular orders during the depletion time of the special order quantity. Scenarios are established and illustrated with numerical examples. Through, sensitivity analysis important inventory parameters are classified. Graphical results, in two and three dimensions, are exhibited with supervisory decision.

  19. Time-dependent tumour repopulation factors in linear-quadratic equations

    International Nuclear Information System (INIS)

    Dale, R.G.

    1989-01-01

    Tumour proliferation effects can be tentatively quantified in the linear-quadratic (LQ) method by the incorporation of a time-dependent factor, the magnitude of which is related both to the value of α in the tumour α/β ratio, and to the tumour doubling time. The method, the principle of which has been suggested by a numbre of other workers for use in fractionated therapy, is here applied to both fractionated and protracted radiotherapy treatments, and examples of its uses are given. By assuming that repopulation of late-responding tissues is significant during normal treatment strategies in terms of the behaviour of the Extrapolated Response Dose (ERD). Although the numerical credibility of the analysis used here depends on the reliability of the LQ model, and on the assumption that the rate of repopulation is constant throughout treatment, the predictions are consistent with other lines of reasoning which point to the advantages of accelerated hyperfractionation. In particular, it is demonstrated that accelerated fractionation represents a relatively 'foregiving' treatment which enables tumours of a variety of sensitivities and clonogenic growth rates to be treated moderately successfully, even though the critical cellular parameters may not be known in individual cases. The analysis also suggests that tumours which combine low intrinsic sensitivity with a very short doubling time might be bettter controlled by low dose-rate continuous therapy than by almost any form of accelerated hyperfractionation. (author). 24 refs.; 5 figs

  20. The influence of anharmonic core vibrations in the X-ray bond charge analysis of A/sup N/B/sup 8-N/ compounds

    International Nuclear Information System (INIS)

    Pietsch, U.

    1982-01-01

    X-ray structure amplitudes of elemental and A 3 B 5 semiconductors can be described by means of spherical atomic form factors and an additional scattered particle at the position of the centre of the covalent bond between next neighbours named bond charge. For this analysis anharmonic core vibrations were neglegted. In this note the influence is estimated of anharmonic core vibrations on the total structure amplitudes of some zinc-blende compounds (GaAs, ZnSe, CuBr, InSb, and CuCl)

  1. High-pressure phase diagram of hydrogen and deuterium sulfides from first principles: Structural and vibrational properties including quantum and anharmonic effects

    Science.gov (United States)

    Bianco, Raffaello; Errea, Ion; Calandra, Matteo; Mauri, Francesco

    2018-06-01

    We study the structural and vibrational properties of the high-temperature superconducting sulfur trihydride and trideuteride in the high-pressure I m 3 ¯m and R 3 m phases by first-principles density-functional-theory calculations. On lowering pressure, the rhombohedral transition I m 3 ¯m →R 3 m is expected, with hydrogen-bond desymmetrization and occurrence of trigonal lattice distortion. With both Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, in hydrostatic conditions we find that, contrary to what is suggested in some recent experiments, if the rhombohedral distortion exists it affects mainly the hydrogen bonds, whereas the resulting cell distortion is minimal. We estimate that the occurrence of a stress anisotropy of approximately 10 % could explain this discrepancy. Assuming hydrostatic conditions, we calculate the critical pressure at which the rhombohedral transition occurs. Quantum and anharmonic effects, which are relevant in this system, are included at nonperturbative level with the stochastic self-consistent harmonic approximation. Within this approach, we determine the transition pressure by calculating the free-energy Hessian, a method that allows to estimate the critical pressure with much higher precision (and much lower computational cost) compared with the free-energy "finite-difference" approach previously used. Using PBE and BLYP, we find that quantum anharmonic effects are responsible for a strong reduction of the critical pressure with respect to the one obtained with the classical harmonic approach. Interestingly, for the two functionals, even if the transition pressures at classical harmonic level differ by 83 GPa, the transition pressures including quantum anharmonic effects differ only by 23 GPa. Moreover, we observe a prominent isotope effect, as we estimate higher transition pressure for D3S than for H3S . Finally, within the stochastic self-consistent harmonic approximation, with PBE

  2. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    International Nuclear Information System (INIS)

    Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

    2014-01-01

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

  3. Elongational flow of polymer melts at constant strain rate, constant stress and constant force

    Science.gov (United States)

    Wagner, Manfred H.; Rolón-Garrido, Víctor H.

    2013-04-01

    Characterization of polymer melts in elongational flow is typically performed at constant elongational rate or rarely at constant tensile stress conditions. One of the disadvantages of these deformation modes is that they are hampered by the onset of "necking" instabilities according to the Considère criterion. Experiments at constant tensile force have been performed even more rarely, in spite of the fact that this deformation mode is free from necking instabilities and is of considerable industrial relevance as it is the correct analogue of steady fiber spinning. It is the objective of the present contribution to present for the first time a full experimental characterization of a long-chain branched polyethylene melt in elongational flow. Experiments were performed at constant elongation rate, constant tensile stress and constant tensile force by use of a Sentmanat Extensional Rheometer (SER) in combination with an Anton Paar MCR301 rotational rheometer. The accessible experimental window and experimental limitations are discussed. The experimental data are modelled by using the Wagner I model. Predictions of the steady-start elongational viscosity in constant strain rate and creep experiments are found to be identical, albeit only by extrapolation of the experimental data to Hencky strains of the order of 6. For constant stress experiments, a minimum in the strain rate and a corresponding maximum in the elongational viscosity is found at a Hencky strain of the order of 3, which, although larger than the steady-state value, follows roughly the general trend of the steady-state elongational viscosity. The constitutive analysis also reveals that constant tensile force experiments indicate a larger strain hardening potential than seen in constant elongation rate or constant tensile stress experiments. This may be indicative of the effect of necking under constant elongation rate or constant tensile stress conditions according to the Considère criterion.

  4. Unified dark energy and dust dark matter dual to quadratic purely kinetic K-essence

    International Nuclear Information System (INIS)

    Guendelman, Eduardo; Nissimov, Emil; Pacheva, Svetlana

    2016-01-01

    We consider a modified gravity plus single scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. As shown in a previous paper, the pertinent scalar-field dynamics provides an exact unified description of both dark energy via dynamical generation of a cosmological constant, and dark matter as a ''dust'' fluid with geodesic flow as a result of a hidden Noether symmetry. Here we extend the discussion by considering a non-trivial modification of the purely gravitational action in the form of f(R) = R -αR 2 generalized gravity. Upon deriving the corresponding ''Einstein-frame'' effective action of the latter modified gravity-scalar-field theory we find explicit duality (in the sense of weak versus strong coupling) between the original model of unified dynamical dark energy and dust fluid dark matter, on one hand, and a specific quadratic purely kinetic ''k-essence'' gravity-matter model with special dependence of its coupling constants on only two independent parameters, on the other hand. The canonical Hamiltonian treatment and Wheeler-DeWitt quantization of the dual purely kinetic ''k-essence'' gravity-matter model is also briefly discussed. (orig.)

  5. Quadratic curvature terms and deformed Schwarzschild–de Sitter black hole analogues in the laboratory

    Directory of Open Access Journals (Sweden)

    R. da Rocha

    2017-12-01

    Full Text Available Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschild–de Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes. Keywords: Black holes, Fluid branes, Fluid dynamics, Quadratic curvature gravity, de Laval nozzle

  6. Inelastic neutron scattering, Raman, vibrational analysis with anharmonic corrections, and scaled quantum mechanical force field for polycrystalline L-alanine

    Energy Technology Data Exchange (ETDEWEB)

    Williams, Robert W. [Department of Biomedical Informatics, Uniformed Services University, 4301 Jones Bridge Road, Bethesda, MD 20815 (United States)], E-mail: bob@bob.usuhs.mil; Schluecker, Sebastian [Institute of Physical Chemistry, University of Wuerzburg, Wuerzburg (Germany); Hudson, Bruce S. [Department of Chemistry, Syracuse University, Syracuse, NY (United States)

    2008-01-22

    A scaled quantum mechanical harmonic force field (SQMFF) corrected for anharmonicity is obtained for the 23 K L-alanine crystal structure using van der Waals corrected periodic boundary condition density functional theory (DFT) calculations with the PBE functional. Scale factors are obtained with comparisons to inelastic neutron scattering (INS), Raman, and FT-IR spectra of polycrystalline L-alanine at 15-23 K. Calculated frequencies for all 153 normal modes differ from observed frequencies with a standard deviation of 6 wavenumbers. Non-bonded external k = 0 lattice modes are included, but assignments to these modes are presently ambiguous. The extension of SQMFF methodology to lattice modes is new, as are the procedures used here for providing corrections for anharmonicity and van der Waals interactions in DFT calculations on crystals. First principles Born-Oppenheimer molecular dynamics (BOMD) calculations are performed on the L-alanine crystal structure at a series of classical temperatures ranging from 23 K to 600 K. Corrections for zero-point energy (ZPE) are estimated by finding the classical temperature that reproduces the mean square displacements (MSDs) measured from the diffraction data at 23 K. External k = 0 lattice motions are weakly coupled to bonded internal modes.

  7. Inelastic neutron scattering, Raman, vibrational analysis with anharmonic corrections, and scaled quantum mechanical force field for polycrystalline L-alanine

    International Nuclear Information System (INIS)

    Williams, Robert W.; Schluecker, Sebastian; Hudson, Bruce S.

    2008-01-01

    A scaled quantum mechanical harmonic force field (SQMFF) corrected for anharmonicity is obtained for the 23 K L-alanine crystal structure using van der Waals corrected periodic boundary condition density functional theory (DFT) calculations with the PBE functional. Scale factors are obtained with comparisons to inelastic neutron scattering (INS), Raman, and FT-IR spectra of polycrystalline L-alanine at 15-23 K. Calculated frequencies for all 153 normal modes differ from observed frequencies with a standard deviation of 6 wavenumbers. Non-bonded external k = 0 lattice modes are included, but assignments to these modes are presently ambiguous. The extension of SQMFF methodology to lattice modes is new, as are the procedures used here for providing corrections for anharmonicity and van der Waals interactions in DFT calculations on crystals. First principles Born-Oppenheimer molecular dynamics (BOMD) calculations are performed on the L-alanine crystal structure at a series of classical temperatures ranging from 23 K to 600 K. Corrections for zero-point energy (ZPE) are estimated by finding the classical temperature that reproduces the mean square displacements (MSDs) measured from the diffraction data at 23 K. External k = 0 lattice motions are weakly coupled to bonded internal modes

  8. Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

    Science.gov (United States)

    Kolmann, Stephen J.; Jordan, Meredith J. T.

    2010-02-01

    One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

  9. Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: application to SSSH.

    Science.gov (United States)

    Kolmann, Stephen J; Jordan, Meredith J T

    2010-02-07

    One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

  10. Systematic Studies on Anharmonicity of Rattling Phonons in Type I Clathrates by Low Temperature Heat Capacity Measurements

    Science.gov (United States)

    Tanigaki, Katsumi; Wu, Jiazhen; Tanabe, Yoichi; Heguri, Satoshi; Shiimotani, Hidekazu; Tohoku University Collaboration

    2014-03-01

    Clathrates are featured by cage-like polyhedral hosts mainly composed of the IVth group elements of Si, Ge, or Sn and alkali metal or alkaline-earth metal elements can be accommodated inside as a guest atom. One of the most intriguing issues in clathrates is their outstanding high thermoelectric performances thanks to the low thermal conductivity. Being irrespective of good electric conductivity σ, the guest atom motions provide a low-energy lying less-dispersive phonons and can greatly suppress thermal conductivity κ. This makes clathrates close to the concept of ``phonon glass electron crystal: PGEC'' and useful in thermoelectric materials from the viewpoint of the figure of merit. In the present study, we show that the local phonon anharmonicity indicated by the tunneling-term of the endohedral atoms (αT) and the itinerant-electron term (γeT), both of which show T-linear dependences in specific heat Cp, can successfully be separated by employing single crystals with various carrier concentrations in a wide range of temperture experimennts. The factors affecting on the phonon anharmonicity as well as the strength of electron-phonon interactions will be discussed based on our recent experiments. The research was financially supported by Ministry of Education, Science, Sports and Culture, Grant in Aid for Science, and Technology of Japan.

  11. Accurate energy levels for the anharmonic oscillator and a summable series for the double-well potential in perturbation theory

    International Nuclear Information System (INIS)

    Caswell, W.E.

    1979-01-01

    We introduce a generalization of Wick-ordering which maps the anharmonic oscillator (AO) Hamiltonian for mass m and coupling lambda exactly into a ''Wick-ordered'' Hamiltonian with an effective mass M which is a simple analytic function of lambda and m. The effective coupling Λ=lambda/M 3 is bounded. We transform the AO perturbation series in lambda into one in Λ. This series may then be summed using Borel summation methods. We also introduce a new summation method for the AO series (which is a practical necessity to obtain accurate energy levels of the excited states). We obtain a numerical accuracy for (E/sub P/T--E/sub e/xact)/ E/sub e/xact of at least 10 -7 (using 20 orders of perturbation theory) and 10 -3 (using only 2 orders of perturbation theory) for all couplings and all energy levels of the anharmonic oscillator. The methods are applicable also to the double-well potential (DWP, the AO with a negative mass-squared). The only change is that now the effective coupling is unbounded as lambda→0. The series in Λ is, however, still summable. The relative accuracy in the energy levels for 20 orders of perturbation theory varies from 10 -7 for large coupling to 1% at lambda=0.1 and to 10% at lambda=.05. We also present results for the sextic oscillator

  12. Spectrophotometric determination of association constant

    DEFF Research Database (Denmark)

    2016-01-01

    Least-squares 'Systematic Trial-and-Error Procedure' (STEP) for spectrophotometric evaluation of association constant (equilibrium constant) K and molar absorption coefficient E for a 1:1 molecular complex, A + B = C, with error analysis according to Conrow et al. (1964). An analysis of the Charge...

  13. Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

    NARCIS (Netherlands)

    de Klerk, E.; Sotirov, R.

    2007-01-01

    We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,

  14. Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities (vol 24, pg 2752, 2007)

    DEFF Research Database (Denmark)

    Bache, Morten; Moses, J.; Wise, F.W.

    2010-01-01

    Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)].......Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)]....

  15. An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints

    Directory of Open Access Journals (Sweden)

    Xuewen Mu

    2015-01-01

    quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.

  16. The regular indefinite linear-quadratic problem with linear endpoint constraints

    NARCIS (Netherlands)

    Soethoudt, J.M.; Trentelman, H.L.

    1989-01-01

    This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that

  17. A Novel Single Switch Transformerless Quadratic DC/DC Buck-Boost Converter

    DEFF Research Database (Denmark)

    Mostaan, Ali; A. Gorji, Saman; N. Soltani, Mohsen

    2017-01-01

    A novel quadratic buck-boost DC/DC converter is presented in this study. The proposed converter utilizes only one active switch and can step-up/down the input voltage, while the existing single switch quadratic buck/boost converters can only work in step-up or step-down mode. First, the proposed ...

  18. Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

    Science.gov (United States)

    Pathak, H. K.; Grewal, A. S.

    2002-01-01

    This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

  19. Estimating sample size for a small-quadrat method of botanical ...

    African Journals Online (AJOL)

    Reports the results of a study conducted to determine an appropriate sample size for a small-quadrat method of botanical survey for application in the Mixed Bushveld of South Africa. Species density and grass density were measured using a small-quadrat method in eight plant communities in the Nylsvley Nature Reserve.

  20. Generation and dynamics of quadratic birefringent spatial gap solitons

    International Nuclear Information System (INIS)

    Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.

    2011-01-01

    A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe 2 (LGT) crystals. Once irradiated by a cw laser beam of 10 μm wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.

  1. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

    Science.gov (United States)

    Orr, Jeb S.

    2012-01-01

    A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

  2. Quadratic stabilisability of multi-agent systems under switching topologies

    Science.gov (United States)

    Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long

    2014-12-01

    This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

  3. Asymptotic behavior for a quadratic nonlinear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Pavel I. Naumkin

    2008-02-01

    Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

  4. Quadratic electromechanical strain in silicon investigated by scanning probe microscopy

    Science.gov (United States)

    Yu, Junxi; Esfahani, Ehsan Nasr; Zhu, Qingfeng; Shan, Dongliang; Jia, Tingting; Xie, Shuhong; Li, Jiangyu

    2018-04-01

    Piezoresponse force microscopy (PFM) is a powerful tool widely used to characterize piezoelectricity and ferroelectricity at the nanoscale. However, it is necessary to distinguish microscopic mechanisms between piezoelectricity and non-piezoelectric contributions measured by PFM. In this work, we systematically investigate the first and second harmonic apparent piezoresponses of a silicon wafer in both vertical and lateral modes, and we show that it exhibits an apparent electromechanical response that is quadratic to the applied electric field, possibly arising from ionic electrochemical dipoles induced by the charged probe. As a result, the electromechanical response measured is dominated by the second harmonic response in the vertical mode, and its polarity can be switched by the DC voltage with the evolving coercive field and maximum amplitude, in sharp contrast to typical ferroelectric materials we used as control. The ionic activity in silicon is also confirmed by the scanning thermo-ionic microscopy measurement, and the work points toward a set of methods to distinguish true piezoelectricity from the apparent ones.

  5. Asymptotic performance of regularized quadratic discriminant analysis based classifiers

    KAUST Repository

    Elkhalil, Khalil

    2017-12-13

    This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.

  6. Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube

    International Nuclear Information System (INIS)

    Mittelmann, Hans; Peng Jiming; Wu Xiaolin

    2009-01-01

    In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs.Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n 3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.

  7. Separability of diagonal symmetric states: a quadratic conic optimization problem

    Directory of Open Access Journals (Sweden)

    Jordi Tura

    2018-01-01

    Full Text Available We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS states. First, we show that separability in the case of DS in $C^d\\otimes C^d$ (symmetric qudits can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT is sufficient and necessary for separability of DS states for $d \\leq 4$. Furthermore, for $d \\geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

  8. Linear versus quadratic portfolio optimization model with transaction cost

    Science.gov (United States)

    Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

    2014-06-01

    Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

  9. Evolution of universes in quadratic theories of gravity

    International Nuclear Information System (INIS)

    Barrow, John D.; Hervik, Sigbjoern

    2006-01-01

    We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Because of the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic Friedmann-Robertson-Walker (FRW) universe acting as a past attractor. This may indicate that there is an isotropization mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated center manifold structure, and show that there exists a set of nonzero measure which has the Kasner solutions as a past attractor. Regarding the late-time behavior, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behavior with phantomlike behavior. New types of anisotropic inflationary behavior are found which do not have counterparts in general relativity

  10. Methods of using the quadratic assignment problem solution

    Directory of Open Access Journals (Sweden)

    Izabela Kudelska

    2012-09-01

    Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.

  11. Noise-induced chaos in a quadratically nonlinear oscillator

    International Nuclear Information System (INIS)

    Gan Chunbiao

    2006-01-01

    The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

  12. Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

    Science.gov (United States)

    Momeni, F.; Naderi, M. H.

    2018-05-01

    In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

  13. Intrinsic anharmonic effects on the phonon frequencies and effective spin-spin interactions in a quantum simulator made from trapped ions in a linear Paul trap

    Science.gov (United States)

    McAneny, M.; Freericks, J. K.

    2014-11-01

    The Coulomb repulsion between ions in a linear Paul trap gives rise to anharmonic terms in the potential energy when expanded about the equilibrium positions. We examine the effect of these anharmonic terms on the accuracy of a quantum simulator made from trapped ions. To be concrete, we consider a linear chain of Yb171+ ions stabilized close to the zigzag transition. We find that for typical experimental temperatures, frequencies change by no more than a factor of 0.01 % due to the anharmonic couplings. Furthermore, shifts in the effective spin-spin interactions (driven by a spin-dependent optical dipole force) are also, in general, less than 0.01 % for detunings to the blue of the transverse center-of-mass frequency. However, detuning the spin interactions near other frequencies can lead to non-negligible anharmonic contributions to the effective spin-spin interactions. We also examine an odd behavior exhibited by the harmonic spin-spin interactions for a range of intermediate detunings, where nearest-neighbor spins with a larger spatial separation on the ion chain interact more strongly than nearest neighbors with a smaller spatial separation.

  14. Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles

    Science.gov (United States)

    Ribeiro, Guilherme A. S.; Paulatto, Lorenzo; Bianco, Raffaello; Errea, Ion; Mauri, Francesco; Calandra, Matteo

    2018-01-01

    At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient γ =2.3 ×10-5K-1 , finding it to be in good agreement with experimental value of γ =2.04 ×10-5K-1 . Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the Γ X direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the self-consistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the third- and fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric

  15. Varying Constants, Gravitation and Cosmology

    Directory of Open Access Journals (Sweden)

    Jean-Philippe Uzan

    2011-03-01

    Full Text Available Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

  16. A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

    Science.gov (United States)

    Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

    2015-11-01

    We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

  17. Stabilized power constant alimentation; Alimentation regulee a puissance constante

    Energy Technology Data Exchange (ETDEWEB)

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

    1968-06-01

    The study and realization of a stabilized power alimentation variable from 5 to 100 watts are described. In order to realize a constant power drift of Lithium compensated diodes, we have searched a 1 per cent precision of regulation and a response time minus than 1 sec. Recent components like Hall multiplicator and integrated amplifiers give this possibility and it is easy to use permutable circuits. (author) [French] On decrit l'etude et la realisation d'une alimentation a puissance constante reglable dans une gamme de 5 a 100 watts. Prevue pour le drift a puissance constante des diodes compensees au lithium, l'etude a ete menee en vue d'obtenir une precision de regulation de 1 pour cent et un temps de reponse inferieur a la seconde. Des systemes recents tels que multiplicateurs a effet Hall et circuits integres ont permis d'atteindre ce but tout en facilitant l'emploi de modules interchangeables. (auteur)

  18. From the Rydberg constant to the fundamental constants metrology

    International Nuclear Information System (INIS)

    Nez, F.

    2005-06-01

    This document reviews the theoretical and experimental achievements of the author since the beginning of his scientific career. This document is dedicated to the spectroscopy of hydrogen, deuterium and helium atoms. The first part is divided into 6 sub-sections: 1) the principles of hydrogen spectroscopy, 2) the measurement of the 2S-nS/nD transitions, 3) other optical frequency measurements, 4) our contribution to the determination of the Rydberg constant, 5) our current experiment on the 1S-3S transition, 6) the spectroscopy of the muonic hydrogen. Our experiments have improved the accuracy of the Rydberg Constant by a factor 25 in 15 years and we have achieved the first absolute optical frequency measurement of a transition in hydrogen. The second part is dedicated to the measurement of the fine structure constant and the last part deals with helium spectroscopy and the search for optical references in the near infrared range. (A.C.)

  19. Mismatch management for optical and matter-wave quadratic solitons

    International Nuclear Information System (INIS)

    Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A.

    2007-01-01

    We propose a way to control solitons in χ (2) (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM

  20. Quadratic adaptive algorithm for solving cardiac action potential models.

    Science.gov (United States)

    Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

    2016-10-01

    An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights