WorldWideScience

Sample records for harmonic oscillator representation

  1. Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

    Directory of Open Access Journals (Sweden)

    Sadolah Nasiri

    2008-02-01

    Full Text Available In a previous work the concept of quantum potential is generalized into extended phase space (EPS for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.

  2. The harmonic oscillator and nuclear physics

    Science.gov (United States)

    Rowe, D. J.

    1993-01-01

    The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

  3. Representation Discovery using Harmonic Analysis

    CERN Document Server

    Mahadevan, Sridhar

    2008-01-01

    Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu

  4. Renormalization for free harmonic oscillators

    OpenAIRE

    Sonoda, H.

    2013-01-01

    We introduce a model of free harmonic oscillators that requires renormalization. The model is similar to but simpler than the soluble Lee model. We introduce two concrete examples: the first, resembling the three dimensional $\\phi^4$ theory, needs only mass renormalization, and the second, resembling the four dimensional $\\phi^4$ theory and the Lee model, needs additional renormalization of a coupling and a wave function.

  5. Effective harmonic oscillator description of anharmonic molecular ...

    Indian Academy of Sciences (India)

    Administrator

    Abstract. The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic ...

  6. Making space for harmonic oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Michelotti, Leo; /Fermilab

    2004-11-01

    If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.

  7. Introduction to classical and quantum harmonic oscillators

    CERN Document Server

    Bloch, Sylvan C

    2013-01-01

    From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con

  8. Effective harmonic oscillator description of anharmonic molecular ...

    Indian Academy of Sciences (India)

    ... a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.

  9. Discretized representations of harmonic variables by bilateral Jacobi operators

    Directory of Open Access Journals (Sweden)

    Andreas Ruffing

    2000-01-01

    Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.

  10. Coherent states of general time-dependent harmonic oscillator

    Indian Academy of Sciences (India)

    The wave function can then be found easily, by making use of these ladder operators. Glauber proposed standard coherent states for a harmonic oscillator which is the prototype for most of the coherent states [3,4]. The coherent states form a very convenient representation for problems of quantum mechanics and can be ...

  11. Maximal Regularity of the Discrete Harmonic Oscillator Equation

    Directory of Open Access Journals (Sweden)

    Airton Castro

    2009-01-01

    Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.

  12. Harmonic Oscillator SUSY Partners and Evolution Loops

    Directory of Open Access Journals (Sweden)

    David J. Fernández

    2012-07-01

    Full Text Available Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.

  13. Harmonic Analysis and Group Representation

    CERN Document Server

    Figa-Talamanca, Alessandro

    2011-01-01

    This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.

  14. Information cloning of harmonic oscillator coherent states

    Indian Academy of Sciences (India)

    Abstract. We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state.

  15. Hyperchaotic circuit with damped harmonic oscillators

    DEFF Research Database (Denmark)

    Lindberg, Erik; Murali, K.; Tamasevicius, A.

    2001-01-01

    A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...

  16. Information cloning of harmonic oscillator coherent states

    Indian Academy of Sciences (India)

    We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use ...

  17. Sobolev spaces associated to the harmonic oscillator

    Indian Academy of Sciences (India)

    2Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de. Madrid, Spain. E-mail: bbongio@math.unl.edu.ar; joseluis.torrea@uam.es. MS received 27 September 2005. Abstract. We define the Hermite–Sobolev spaces naturally associated to the harmonic oscillator H = − + |x|2. Structural properties ...

  18. Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator

    Directory of Open Access Journals (Sweden)

    Kunle Adegoke

    2016-01-01

    Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.

  19. Unitary representations and harmonic analysis an introduction

    CERN Document Server

    Sugiura, M

    1990-01-01

    The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou''s theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

  20. Supersymmetry, quark confinement and the harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Bruce, S A; Minning, P C [Department of Physics, University of Concepcion, PO Box 160C, Concepcion (Chile)

    2007-12-07

    We study some quantum systems described by noncanonical commutation relations formally expressed as [q-hat,p-hat] = i h-bar(I-hat+{chi}-hatH-hat{sub HO}), where H-hat{sub HO} is the associated (harmonic-oscillator-like) Hamiltonian of the system and {chi}-hat is a Hermitian (constant) operator, i.e. [H-hat{sub HO},{chi}-hat]=O-hat. In passing, we also consider a simple ({chi}-hat=O-hat canonical) model, in the framework of a relativistic Klein-Gordon-like wave equation.

  1. Spectral inverse problem for q-deformed harmonic oscillator

    Indian Academy of Sciences (India)

    The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this ...

  2. Coherent states for the relativistic harmonic oscillator

    Science.gov (United States)

    Aldaya, Victor; Guerrero, J.

    1995-01-01

    Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

  3. First harmonic injection locking of 24-GHz-oscillators

    Directory of Open Access Journals (Sweden)

    M. R. Kühn

    2003-01-01

    Full Text Available An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.

  4. On quantum harmonic oscillator being subjected to absolute ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 1. On quantum ... In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. ... This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity.

  5. Generation of higher harmonic internal waves by oscillating spheroids

    Science.gov (United States)

    Shmakova, Natalia; Ermanyuk, Evgeny; Flór, Jan-Bert

    2017-11-01

    Oscillating bodies in stratified fluids may emit higher harmonics in addition to fundamental waves. In the present experimental study, we consider higher harmonics of an internal wave field generated by a horizontally oscillating spheroid in a linearly stratified fluid for moderate to high oscillation amplitudes, i.e., scaled oscillation amplitude A /a ≥0.5 , with a the minor radius of the spheroid. Three different spheroid shapes are tested. The results are discussed in the context of the different theories on the generation of higher harmonics. Higher harmonics are observed at the intersections of fundamental wave beams, and at the critical points of the topography where the topographic slope equals the wave slope. The velocity amplitudes of the fundamental, second, and third harmonic waves grow respectively linearly, quadratically, and with the third power of the scaled oscillation amplitude A /a . Though these amplitudes are generally higher when the object's slope is larger, the increase in amplitude above and below the axisymmetric oscillating objects is found to be due to the effect of focusing. In order to discern the relative importance of the harmonics to the fundamental wave, the horizontal structure of the wave amplitude is measured. The results suggest that the n th harmonic of the internal wave field is associated with a radiation diagram corresponding to a multipole of order 2n, with 2 n directions of propagation.

  6. Driven damped harmonic oscillator resonance with an Arduino

    Science.gov (United States)

    Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.

    2017-07-01

    In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.

  7. A harmonic oscillator having “volleyball damping”

    Science.gov (United States)

    Mickens, R. E.; Oyedeji, K.; Rucker, S. A.

    2006-05-01

    Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.

  8. The Study of Damped Harmonic Oscillations Using an Electronic Counter

    Science.gov (United States)

    Wadhwa, Ajay

    2009-01-01

    We study damped harmonic oscillations in mechanical systems like the loaded spring and simple pendulum with the help of an oscillation measuring electronic counter. The experimental data are used in a software program that solves the differential equation for damped vibrations of any system and determines its position, velocity and acceleration as…

  9. Fundamental and Harmonic Oscillations in Neighboring Coronal Loops

    Science.gov (United States)

    Li, Hongbo; Liu, Yu; Vai Tam, Kuan

    2017-06-01

    We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.

  10. L-functions and the oscillator representation

    CERN Document Server

    Rallis, Stephen

    1987-01-01

    These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N

  11. Harmonic oscillator in an elastic medium with a spiral dislocation

    Science.gov (United States)

    Maia, A. V. D. M.; Bakke, K.

    2018-02-01

    We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.

  12. Violation of smooth observable macroscopic realism in a harmonic oscillator.

    Science.gov (United States)

    Leshem, Amir; Gat, Omri

    2009-08-14

    We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.

  13. Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

    Science.gov (United States)

    Norbury, J. W.; Badavi, F. F.; Townsend, L. W.

    1986-01-01

    The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.

  14. Nonclassical phase-space trajectories for the damped harmonic quantum oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Pachon, L.A. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); CeiBA - Complejidad, Bogota D.C. (Colombia); Ingold, G.-L., E-mail: gert.ingold@physik.uni-augsburg.de [Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); Dittrich, T. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); CeiBA - Complejidad, Bogota D.C. (Colombia)

    2010-10-05

    Graphical abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation and the appearance of nonclassical trajectories is discussed. - Abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.

  15. Adomian Decomposition approach to solve the simple harmonic quantum oscillator

    Science.gov (United States)

    Jaradat, Adnan; Adnan Jardat Team; Maen Gharaibeh Team; Mohammad Qaseer Team; Abdalla Obeidat Team

    2015-04-01

    The simple harmonic quantum oscillator problem has been solved using two methods namely, the algebraic method where the raising and lower operators used and the Frobenius method. Here, we will adopt the Adomian decomposition method to solve this problem and derive the Hermite polynomials in much easier way than the above mentioned methods. This work is supported by Jordan University of Science and Technolgy.

  16. Spectral inverse problem for q-deformed harmonic oscillator

    Indian Academy of Sciences (India)

    only the knowledge of bound-state spectra of q-deformed harmonic oscillator. We have also studied the ... that these will be continued both at sophisticated and pedagogical levels [2]. In an interesting work, Engelke ... concepts, exact knowledge of the spectrum is not enough for the reconstruction of the potential. For a given ...

  17. Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps

    Science.gov (United States)

    Pendrill, Ann-Marie; Eager, David

    2015-01-01

    Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…

  18. Thermal state of the general time-dependent harmonic oscillator

    Indian Academy of Sciences (India)

    Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator ...

  19. The harmonic oscillator in a space with a screw dislocation

    Science.gov (United States)

    Amore, Paolo; Fernández, Francisco M.

    2018-01-01

    We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of values of the space-deformation parameter. The energies exhibit a rich structure of avoided crossings in terms of such model parameter.

  20. Phase-space treatment of the driven quantum harmonic oscillator

    Indian Academy of Sciences (India)

    2017-02-22

    Feb 22, 2017 ... Phase-space quantum mechanics; coherent states; harmonic oscillator; Husimi distribution; cross- ... is the Weyl operator assigned to the phase-space ...... formulae used in this work. The Hermite polynomials satisfy the following relations: 1. [19, Section 5.6.4],. Hη(y + σ) = η. ∑ k=0. ( η k. ) Hk(y)(2σ)η−k. = η.

  1. Quantum theory of damped harmonic oscillator | Antia | Global ...

    African Journals Online (AJOL)

    The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...

  2. Harmonic oscillator in Snyder space: The classical case and the ...

    Indian Academy of Sciences (India)

    This modified parameters give us a modified energy spectrum also. Keywords. Harmonic oscillator ... time where the non-commutativity of space operators is proportional to non-linear combinations of phase ... in §4. 2. The classical case. Classical n dimensional Snyder space is characterized by its non-linear commutation.

  3. Harmonic oscillator in Snyder space: The classical case and the ...

    Indian Academy of Sciences (India)

    The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...

  4. Phase-space treatment of the driven quantum harmonic oscillator

    Indian Academy of Sciences (India)

    A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...

  5. Brownian motion with adhesion: harmonic oscillator with fluctuating mass.

    Science.gov (United States)

    Gitterman, M; Klyatskin, V I

    2010-05-01

    In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.

  6. Nonlinear analysis of a cross-coupled quadrature harmonic oscillator

    DEFF Research Database (Denmark)

    Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens

    2005-01-01

    The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...... in the coupling transconductances, in conjunction with a finite amplitude relaxation time and de-tuning of the individual oscillators, cause close-to-carrier AM-to-PM noise conversion. A discussion is presented of how the theoretic results translate into design rules for quadrature oscillator ICs. SPECTRE RF...

  7. Geometric phase and nonadiabatic effects in an electronic harmonic oscillator.

    Science.gov (United States)

    Pechal, M; Berger, S; Abdumalikov, A A; Fink, J M; Mlynek, J A; Steffen, L; Wallraff, A; Filipp, S

    2012-04-27

    Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.

  8. The q-harmonic oscillators, q-coherent states and the q-symplecton

    Science.gov (United States)

    Biedenharn, L. C.; Lohe, M. A.; Nomura, Masao

    1993-01-01

    The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.

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

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, Augusto [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, Carolina [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)

    2007-11-19

    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.

  10. Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the classical harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)

    2011-09-19

    We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.

  11. Quantum harmonic oscillator: an elementary derivation of the energy spectrum

    Science.gov (United States)

    Borghi, Riccardo

    2017-03-01

    An elementary treatment of the quantum harmonic oscillator is proposed. No previous knowledge of linear differential equation theory or Fourier analysis are required, but rather only a few basics of elementary calculus. The pivotal role in our analysis is played by the sole particle localization constraint, which implies square integrability of stationary-state wavefunctions. The oscillator ground-state characterization is then achieved in a way that could be grasped, in principle, even by first-year undergraduates. A very elementary approach to build up and to characterize all higher-level energy eigenstates completes our analysis.

  12. Pisot q-coherent states quantization of the harmonic oscillator

    Science.gov (United States)

    Gazeau, J. P.; del Olmo, M. A.

    2013-03-01

    We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0states form an overcomplete set that resolves the unity with respect to an explicit measure. We restrict our study to the case in which q-1 is a quadratic unit Pisot number, since then the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.

  13. Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis.

    Science.gov (United States)

    Kienzler, D; Lo, H-Y; Negnevitsky, V; Flühmann, C; Marinelli, M; Home, J P

    2017-07-21

    We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the sqrt[n] scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n=6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.

  14. Pisot q-coherent states quantization of the harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)

    2013-03-15

    We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0oscillator.

  15. Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process

    Science.gov (United States)

    Ma, Shan; Woolley, Matthew J.; Petersen, Ian R.; Yamamoto, Naoki

    2017-03-01

    We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2\\aleph +1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2\\aleph +1) -mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. This parametrization allows us to determine the steady-state entanglement properties of such quantum harmonic oscillator chains.

  16. Detecting the harmonics of oscillations with time-variable frequencies

    Science.gov (United States)

    Sheppard, L. W.; Stefanovska, A.; McClintock, P. V. E.

    2011-01-01

    A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.

  17. Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator

    Science.gov (United States)

    Mouayn, Zouhaïr

    2017-12-01

    We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and ɛ >0 by replacing the coefficients zn/√{n!} of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit ɛ → 0+ and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed.

  18. The two capacitor problem revisited: simple harmonic oscillator model approach

    CERN Document Server

    Lee, Keeyung

    2012-01-01

    The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that \\emph {exactly half} the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be \\emph {exactly half} the supplied energy whether that is caused by the Joule heat or by the radiation. This paper which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem is suitable for all undergraduate...

  19. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    Science.gov (United States)

    Chou, Chia-Chun

    2016-10-01

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  20. Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

    Directory of Open Access Journals (Sweden)

    P. A. Deymier

    2016-12-01

    Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.

  1. The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications

    Science.gov (United States)

    Earl, Boyd L.

    2008-01-01

    A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

  2. Modeling stock return distributions with a quantum harmonic oscillator

    Science.gov (United States)

    Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

    2017-11-01

    We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

  3. Spectral theory of non-commutative harmonic oscillators an introduction

    CERN Document Server

    Parmeggiani, Alberto

    2010-01-01

    This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.

  4. Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Sandev, Trifce, E-mail: trifce.sandev@drs.gov.mk [Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Petreska, Irina, E-mail: irina.petreska@pmf.ukim.mk [Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss Cyril and Methodius University, P.O. Box 162, 1001 Skopje (Macedonia, The Former Yugoslav Republic of); Lenzi, Ervin K., E-mail: eklenzi@dfi.uem.br [Departamento de Fisica, Universidade Estadual de Maringá, Avenida Colombo 5790, Maringá, 87020-900, PR (Brazil)

    2014-01-10

    We present new results for time-independent solutions for a Schrödinger equation with noninteger dimension by considering different, harmonic and anharmonic, forms for the potential energy. The solutions obtained for these potentials are exact and expressed in terms of the special functions such as Laguerre and Gegenbauer polynomials, associated Legendre functions, and hypergeometric functions. Graphical comparison of the probability density function with the ones for two-dimensional and three-dimensional case is given. We derive the mean values r{sup β}sin{sup δ}θ{sup ¯} for the harmonic oscillator in noninteger dimensions, which may be of interest in the perturbation theory for calculation of energy corrections. We consider anharmonic Kratzer potential energy function and we obtain bound and scattering states. Exact results in case of different forms of θ-dependent potentials are presented. In addition, they can be connected to rich variety of situations which enable us to model anisotropic interactions in real space.

  5. The quantum harmonic oscillator on a circle and a deformed quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Rego-Monteiro, M.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: regomont@cbpf.br

    2001-05-01

    We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)

  6. West Coast Swing Dancing as a Driven Harmonic Oscillator Model

    Science.gov (United States)

    Ferrara, Davon; Holzer, Marie; Kyere, Shirley

    The study of physics in sports not only provides valuable insight for improved athletic performance and injury prevention, but offers undergraduate students an opportunity to engage in both short- and long-term research efforts. In this project, conducted by two non-physics majors, we hypothesized that a driven harmonic oscillator model can be used to better understand the interaction between two west coast swing dancers since the stiffness of the physical connection between dance partners is a known factor in the dynamics of the dance. The hypothesis was tested by video analysis of two dancers performing a west coast swing basic, the sugar push, while changing the stiffness of the physical connection. The difference in stiffness of the connection from the ideal was estimated by the leader; the position with time data from the video was used to measure changes in the amplitude and phase difference between the leader and follower. While several aspects of our results agree with the proposed model, some key characteristics do not, possibly due to the follower relying on visual leads. Corresponding author and principal investigator.

  7. Calorimetric measurement of work for a driven harmonic oscillator

    Science.gov (United States)

    Sampaio, Rui; Suomela, Samu; Ala-Nissila, Tapio

    2016-12-01

    A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of work in a driven quantum harmonic oscillator. We employ a scheme based on a two-level approximation that makes use of an experimentally accessible quantity and show how it relates to the work obtained through the standard two-measurement protocol. We find that the average work is well approximated in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.

  8. Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.

    Science.gov (United States)

    Viñales, A D; Wang, K G; Despósito, M A

    2009-07-01

    The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.

  9. Asymptotic representation of relaxation oscillations in lasers

    CERN Document Server

    Grigorieva, Elena V

    2017-01-01

    In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.

  10. Comment on ``Harmonic oscillator with time-dependent mass and frequency and a perturbative potential''

    Science.gov (United States)

    Maamache, M.; Bencheikh, K.; Hachemi, H.

    1999-04-01

    The correct wave function for the problem of a harmonic oscillator of time-dependent mass and frequency is obtained following the same approach used in the paper of Dantas et al. [Phys. Rev. A 45, 1320 (1992)].

  11. Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)

    2002-07-01

    It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)

  12. Coherent states and uncertainty relations for the damped harmonic oscillator with time-dependent frequency

    Science.gov (United States)

    Yeon, Kyu-Hwang; Um, Chung-In; George, Thomas F.; Pandey, Lakshmi N.

    1993-01-01

    Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have.

  13. Phase of the quantum harmonic oscillator with applications to optical polarization

    Science.gov (United States)

    Shepard, Scott R.

    1993-01-01

    The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.

  14. A system of Schrodinger equations and the oscillator representation

    Directory of Open Access Journals (Sweden)

    Markus Hunziker

    2015-10-01

    Full Text Available We construct a copy of the oscillator representation of the metaplectic group Mp(n in the space of solutions to a system of Schrodinger type equations on $\\mathbb{R}^{n}\\times\\hbox{Sym}(n,\\mathbb{R}$ that has very simple intertwining maps to the realizations given by Kashiwara and Vergne.

  15. Thermal state of the general time-dependent harmonic oscillator

    Indian Academy of Sciences (India)

    the thermal state. In Ü2, we investigate quantum mechanical solution of the general time-dependent har- monic oscillator. The thermal state of the system is discussed in Ü3 on the basis of. Liouville–von Neumann approach. InÜ4, we will apply our theory for a special case which is the forced Caldirola–Kanai oscillator.

  16. Design requirements and calculated performance of an XUV FEL oscillator operating on a higher harmonic

    Energy Technology Data Exchange (ETDEWEB)

    Goldstein, J.C.; Warren, R.W.; Newnam, B.E.

    1990-01-01

    We study, using numerical simulation methods, the design requirements for the electron beam, wiggler, and optical resonator of an extreme-ultraviolet (XUV, 100 nm {ge} {lambda} {ge} 10 nm) free-electron laser oscillator operating on a higher harmonic. Our previous theoretical studies of an XUV FEL oscillator have assumed operation at the fundamental wavelength. Higher harmonic operation is attractive because the energy of the electrons can be reduced, thus reducing the cost of the linac. A further reduction in beam energy is possible with the use of short-period wigglers: in the present work, we use the expected properties of pulsed-wire wigglers. Operation of an FEL oscillator on the third harmonic has been experimentally demonstrated at Stanford University and Los Alamos, and this mode of operation may also be both possible and desirable for an XUV device. 12 refs., 2 tabs.

  17. SYNCHRONIZATION IN NETWORKS OF COUPLED HARMONIC OSCILLATORS WITH STOCHASTIC PERTURBATION AND TIME DELAYS

    Directory of Open Access Journals (Sweden)

    Yilun Shang

    2012-07-01

    Full Text Available In this paper, we investigate the leader-follower synchronization ofcoupled second-order linear harmonic oscillators with the presence ofrandom noises and time delays. The interaction topology is modeledby a weighted directed graph and the weights are perturbed by whitenoise. On the basis of stability theory of stochastic differential delayequations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withrandom perturbation and time delays. Numerical examples are presentedto illustrate our theoretical results.

  18. Planck scale corrections to the harmonic oscillator, coherent, and squeezed states

    Science.gov (United States)

    Bosso, Pasquale; Das, Saurya; Mann, Robert B.

    2017-09-01

    The generalized uncertainty principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of quantum gravity. It consists of a modified commutator between the position and momentum. In this work, we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent, and squeezed states in quantum mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.

  19. Time dependent quantum harmonic oscillator subject to a sudden change of mass: continuous solution

    Energy Technology Data Exchange (ETDEWEB)

    Moya C, H. [INAOE, Coordinacion de Optica, AP 51 y 216, 72000 Puebla (Mexico); Fernandez G, M. [Depto. de Fisica, CBI, Universidad Autonoma Metropolitana - Iztapalapa, 09340, Mexico, D.F. AP 55-534 (Mexico)

    2007-07-01

    We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a sub period function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism requires an ad hoc transformation of the original differential equation and is also applicable for rapid, although not necessarily instantaneous, mass variations. (Author)

  20. Coupled harmonic oscillators for the measurement of a weak classical force at the standard quantum limit

    Science.gov (United States)

    Leaci, Paola; Ortolan, Antonello

    2007-12-01

    We discuss limitations in precision measurements of a weak classical force coupled to quantum mechanical systems, the so-called standard quantum limit (SQL). Among the several contexts exploiting the measurement of classical signals, gravitational wave (GW) detection is of paramount importance. In this framework, we analyze the quantum limited sensitivity of a free test mass, a quantum mechanical harmonic oscillator, two harmonic oscillators with equal masses and different resonance frequencies, and finally two mechanical oscillators with different masses and resonating at the same frequency. The sensitivity analysis of the latter two cases illustrates the potentialities of back-action reduction and classical impedance matching schemes, respectively. By examining coupled quantum oscillators as detectors of classical signals, we found a viable path to approach the SQL for planned or operating GW detectors, such as DUAL and AURIGA.

  1. Asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise

    Energy Technology Data Exchange (ETDEWEB)

    Sandev, Trifce [Radiation Safety Directorate, Blv. Partizanski Odredi 143, PO Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Tomovski, Zivorad, E-mail: trifce.sandev@avis.gov.m, E-mail: tomovski@iunona.pmf.ukim.edu.m [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)

    2010-12-15

    The asymptotic behavior of a harmonic oscillator driven by a generalized Mittag-Leffler noise was studied by analyzing the generalized Langevin equation. The mean square displacement (MSD) and the velocity autocorrelation function (VACF) of a diffusing particle were obtained by using the Laplace transform method and Tauberian theorem. It was found that the MSD and VACF for various values of the parameters show a power-law decay, i.e. an anomalous diffusive behavior of the oscillator.

  2. Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator

    DEFF Research Database (Denmark)

    Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens

    2004-01-01

    We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...... increases with the coupling strength. The results are compared with SPECTRE RF simulations....

  3. A new look at the quantum mechanics of the harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Kastrup, H.A.

    2006-12-15

    At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to

  4. Parity-doublet representation of Majorana fermions and neutron oscillation

    Science.gov (United States)

    Fujikawa, Kazuo; Tureanu, Anca

    2016-12-01

    We present a parity-doublet theorem for the representation of the intrinsic parity of Majorana fermions, which is expected to be useful also in condensed matter physics, and it is illustrated to provide a criterion of neutron-antineutron oscillation in a Bardeen-Cooper-Schrieffer type of effective theory with Δ B =2 baryon number-violating terms. The C P violation in the present effective theory causes no direct C P -violating effects in the oscillation itself, which is demonstrated by the exact solution, although it influences the neutron electric dipole moment in the leading order of small Δ B =2 parameters. An analog of Bogoliubov transformation, which preserves P and C P , is crucial in the analysis.

  5. On approximations of first integrals for a system of weakly nonlinear, coupled harmonic oscillators

    NARCIS (Netherlands)

    Waluya, S.B.; van Horssen, W.T.

    2001-01-01

    In this paper a system of weakly nonlinear, coupled harmonic oscillators will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate rst integrals and periodic solutions. To show how this perturbation method works the

  6. Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space

    CERN Document Server

    Das, Saurya; Walton, Mark A

    2016-01-01

    We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.

  7. Energy-dependent harmonic oscillator in noncommutative space: A path integral approach

    Science.gov (United States)

    Benchikha, A.; Merad, M.

    2017-11-01

    In the context of noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is solved via path integral approach. The propagator of the system is calculated using polar coordinates. The normalized wave functions and the energy eigenvalues are obtained in two different cases.

  8. Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

    DEFF Research Database (Denmark)

    Jensen, Arne; Yajima, Kenji

    2010-01-01

    We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...

  9. Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

    DEFF Research Database (Denmark)

    Jensen, Arne; Yajima, Kenji

    We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...

  10. Attainable conditions and exact invariant for the time-dependent harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)

    2006-09-22

    The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.

  11. Analytic energy-level densities of separable harmonic oscillators including approximate hindered rotor corrections

    Directory of Open Access Journals (Sweden)

    M. Döntgen

    2016-09-01

    Full Text Available Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.

  12. New trends in applied harmonic analysis sparse representations, compressed sensing, and multifractal analysis

    CERN Document Server

    Cabrelli, Carlos; Jaffard, Stephane; Molter, Ursula

    2016-01-01

    This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and covers both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

  13. Entropy evolution of a damped harmonic oscillator driven by quasimonochromatic noise and external periodic force

    Science.gov (United States)

    Qin, Jie; Ning, Lijuan

    2017-08-01

    This paper addresses the entropy evolution of a damped harmonic oscillator driven by quasimonochromatic noise (QMN). Due to QMN is distinct from white noise, so this paper studied the effect of QMN noise on the upper bound of time derivative of entropy for a damped harmonic oscillator. Through the comparison of probability density function (PDF) and the upper bound for the time derivative of entropy, we find that the entropy evolution is also a useful tool to describe the system dynamic behavior. Then we discuss the interplay of the parameters of QMN, damping constant, the frequency of oscillator and external periodic force and their effects on the upper bound for the rate of entropy change. Finally, some beneficial conclusions are obtained.

  14. Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation

    Directory of Open Access Journals (Sweden)

    Wayne Cheng-Wei Huang

    2013-01-01

    Full Text Available Stochastic electrodynamics (SED predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.

  15. Underdamped stochastic harmonic oscillator driven by Lévy noise

    Science.gov (United States)

    Dybiec, Bartłomiej; Gudowska-Nowak, Ewa; Sokolov, Igor M.

    2017-10-01

    We investigate the distribution of potential and kinetic energy in stationary states of the linearly damped stochastic oscillator driven by Lévy noises. In the long time limit distributions of kinetic and potential energies of the oscillator follow the power-law asymptotics and do not fulfill the equipartition theorem. The partition of the mechanical energy is controlled by the damping coefficient. In the limit of vanishing damping a stochastic analog of the equipartition theorem can be proposed, namely, the statistical properties of potential and kinetic energies attain distributions characterized by the same widths. For larger damping coefficient the larger fraction of energy is stored in its potential form. In the limit of very strong damping the contribution of kinetic energy becomes negligible. Finally, we demonstrate that the ratio of instantaneous kinetic and potential energies, which signifies departure from the mechanical energy equipartition, follows universal power-law asymptotics, regardless of the symmetric α -stable noise parameters. Altogether our investigations clearly indicate strongly nonequilibrium character of Lévy-stable fluctuations with the stability index α <2 .

  16. When Simple Harmonic Motion is not That Simple: Managing Epistemological Complexity by Using Computer-based Representations

    Science.gov (United States)

    Parnafes, Orit

    2010-12-01

    Many real-world phenomena, even "simple" physical phenomena such as natural harmonic motion, are complex in the sense that they require coordinating multiple subtle foci of attention to get the required information when experiencing them. Moreover, for students to develop sound understanding of a concept or a phenomenon, they need to learn to get the same type of information across different contexts and situations (diSessa and Sherin 1998; diSessa and Wagner 2005). Rather than simplifying complex situations, or creating a linear instructional sequence in which students move from one context to another, this paper demonstrates the use of computer-based representations to facilitate developing understanding of complex physical phenomena. The data is collected from 8 studies in which pairs of students are engaged in an exploratory activity, trying to understand the dynamic behavior of a simulation and, at the same time, to attribute meaning to it in terms of the physical phenomenon it represents. The analysis focuses on three episodes. The first two episodes demonstrate the epistemological complexity involved in attempting to make sense of natural harmonic oscillation. A third episode demonstrates the process by which students develop understanding in this complex perceptual and conceptual territory, through the mediation (Vygotsky 1978) of computer-based representations designed to facilitate understanding in this topic.

  17. Integral representations of equally positive integer-indexed harmonic sums at infinity

    OpenAIRE

    Jiu, Lin

    2016-01-01

    We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special cases coincide with zeta values at positive integer arguments.

  18. A classical limit-cycle system that mimics the quantum-mechanical harmonic oscillator

    Science.gov (United States)

    Zarmi, Yair

    2017-11-01

    Classical harmonic oscillators affected by appropriately chosen nonlinear dissipative perturbations can exhibit infinite sequences of limit cycles, which mimic quantized systems. For properly chosen perturbations, the large-amplitude limit cycles approach circles. The higher the amplitude of the limit cycle is, the smaller are the dissipative deviations from energy conservation. The weaker the perturbation is, the earlier on does the asymptotic behavior show up already in low-lying limit cycles. Simple modifications of the Rayleigh and van der Pol oscillators yield infinite sequences of limit cycles such that the energy spectrum of the higher-amplitude limit cycles tends to that of the quantum-mechanical particle in a box. For another judiciously chosen dissipative perturbation, the energy spectrum of the higher-amplitude limit cycles tends to that of the quantum-mechanical harmonic oscillator. In all cases, one first finds the limit-cycle solutions for dissipation strength, ε ≠ 0. The "energy of each limit cycle" then oscillates around an average value. In the limit ε → 0 these oscillations vanish, and the limit cycles in the infinite sequence attain constant values for their energies, a characteristic that is required for such classical systems to mimic Hamiltonian quantum-mechanical systems.

  19. Detection of the Second Harmonic of Decay-less Kink Oscillations in the Solar Corona

    Science.gov (United States)

    Duckenfield, T.; Anfinogentov, S. A.; Pascoe, D. J.; Nakariakov, V. M.

    2018-02-01

    EUV observations of a multi-thermal coronal loop, taken by the Atmospheric Imaging Assembly of the Solar Dynamics Observatory, which exhibits decay-less kink oscillations are presented. The data cube of the quiet-Sun coronal loop was passed through a motion magnification algorithm to accentuate transverse oscillations. Time–distance maps are made from multiple slits evenly spaced along the loop axis and oriented orthogonal to the loop axis. Displacements of the intensity peak are tracked to generate time series of the loop displacement. Fourier analysis on the time series shows the presence of two periods within the loop: {P}1={10.3}-1.7+1.5 minutes and {P}2={7.4}-1.3+1.1 minutes. The longer period component is greatest in amplitude at the apex and remains in phase throughout the loop length. The shorter period component is strongest further down from the apex on both legs and displays an anti-phase behavior between the two loop legs. We interpret these results as the coexistence of the fundamental and second harmonics of the standing kink mode within the loop in the decay-less oscillation regime. An illustration of seismological application using the ratio P 1/2P 2 ∼ 0.7 to estimate the density scale height is presented. The existence of multiple harmonics has implications for understanding the driving and damping mechanisms for decay-less oscillations and adds credence to their interpretation as standing kink mode oscillations.

  20. A Second Harmonic Self-Oscillating Mixer Incorporating Resonant Cell Structure

    Directory of Open Access Journals (Sweden)

    Leung Chiu

    2012-01-01

    Full Text Available A downconverting second harmonic self-oscillating mixer (SOM is developed for low-cost wireless communications applications. Incorporating resonant cell in the SOM, we can provide suitable oscillation for generating LO and terminations to all major unwanted mixing products, leading to high conversion gain design. The proposed SOM was measured with 8.5 dB downconversion gain at the RF frequency of 8.2 GHz RF, LO frequency of 4.0 GHz, and IF frequency of 0.2 GHz. The proposed design achieves higher conversion gain than that of the SOM without resonant cell.

  1. Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

    Directory of Open Access Journals (Sweden)

    A. M. El-Naggar

    2015-11-01

    Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.

  2. Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry

    CERN Document Server

    Buccella, F; Savoy, C A

    1972-01-01

    The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).

  3. Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator.

    Science.gov (United States)

    Horowitz, Jordan M

    2012-03-01

    I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.

  4. Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator

    OpenAIRE

    Horowitz, Jordan M.

    2011-01-01

    I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously-monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum t...

  5. A stochastic harmonic function representation for non-stationary stochastic processes

    Science.gov (United States)

    Chen, Jianbing; Kong, Fan; Peng, Yongbo

    2017-11-01

    The time-domain representation of non-stationary stochastic processes is of paramount importance, in particular for response analysis and reliability evaluation of nonlinear structures. In the present paper a stochastic harmonic function (SHF) representation originally developed for stationary processes is extended to evolutionary non-stationary processes. Utilizing the new scheme, the time-domain representation of non-stationary stochastic processes is expressed as the linear combination of a series of stochastic harmonic components. Different from the classical spectral representation (SR), not only the phase angles but also the frequencies and their associated amplitudes, are treated as random variables. The proposed method could also be regarded as an extension of the classical spectral representation method. However, it is rigorously proved that the new scheme well accommodates the target evolutionary power spectral density function. Compared to the classical spectral representation method, moreover, the new scheme needs much fewer terms to be retained. The first four moments and the distribution properties, e.g., the asymptotical Gaussianity, of the simulated stochastic process via SHF representation are studied. Numerical examples are addressed for illustrative purposes, showing the effectiveness of the proposed scheme.

  6. Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis. (I) the method

    Energy Technology Data Exchange (ETDEWEB)

    Dobaczewski, J.; Dudek, J. [Strasbourg-1 Univ., 67 (France). Centre de Recherches Nucleaires; Dobaczewski, J. [Warsaw Univ. (Poland)

    1996-12-31

    We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent fields is presented, and an implementation of the self-consistent symmetries is discussed. Formulas to calculate matrix elements in the Cartesian harmonic oscillator basis are derived for the nuclear and Coulomb interactions. (authors). 39 refs.

  7. Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)

    2008-09-22

    An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.

  8. Representation of Cognitive Reappraisal Goals in Frontal Gamma Oscillations

    Science.gov (United States)

    Kang, Jae-Hwan; Jeong, Ji Woon; Kim, Hyun Taek; Kim, Sang Hee; Kim, Sung-Phil

    2014-01-01

    Recently, numerous efforts have been made to understand the neural mechanisms underlying cognitive regulation of emotion, such as cognitive reappraisal. Many studies have reported that cognitive control of emotion induces increases in neural activity of the control system, including the prefrontal cortex and the dorsal anterior cingulate cortex, and increases or decreases (depending upon the regulation goal) in neural activity of the appraisal system, including the amygdala and the insula. It has been hypothesized that information about regulation goals needs to be processed through interactions between the control and appraisal systems in order to support cognitive reappraisal. However, how this information is represented in the dynamics of cortical activity remains largely unknown. To address this, we investigated temporal changes in gamma band activity (35–55 Hz) in human electroencephalograms during a cognitive reappraisal task that was comprised of three reappraisal goals: to decease, maintain, or increase emotional responses modulated by affect-laden pictures. We examined how the characteristics of gamma oscillations, such as spectral power and large-scale phase synchronization, represented cognitive reappraisal goals. We found that left frontal gamma power decreased, was sustained, or increased when the participants suppressed, maintained, or amplified their emotions, respectively. This change in left frontal gamma power appeared during an interval of 1926 to 2453 ms after stimulus onset. We also found that the number of phase-synchronized pairs of gamma oscillations over the entire brain increased when participants regulated their emotions compared to when they maintained their emotions. These results suggest that left frontal gamma power may reflect cortical representation of emotional states modulated by cognitive reappraisal goals and gamma phase synchronization across whole brain regions may reflect emotional regulatory efforts to achieve these goals

  9. Chord Label Personalization through Deep Learning of Integrated Harmonic Interval-based Representations

    Science.gov (United States)

    Koops, H. V.; de Haas, W. B.; Bransen, J.; Volk, A.

    2017-05-01

    The increasing accuracy of automatic chord estimation systems, the availability of vast amounts of heterogeneous reference annotations, and insights from annotator subjectivity research make chord label personalization increasingly important. Nevertheless, automatic chord estimation systems are historically exclusively trained and evaluated on a single reference annotation. We introduce a first approach to automatic chord label personalization by modeling subjectivity through deep learning of a harmonic interval-based chord label representation. After integrating these representations from multiple annotators, we can accurately personalize chord labels for individual annotators from a single model and the annotators' chord label vocabulary. Furthermore, we show that chord personalization using multiple reference annotations outperforms using a single reference annotation.

  10. The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

    Science.gov (United States)

    Verreault, René

    2017-08-01

    In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

  11. Neural Representation of Harmonic Complex Tones in Primary Auditory Cortex of the Awake Monkey

    Science.gov (United States)

    Micheyl, Christophe; Steinschneider, Mitchell

    2013-01-01

    Many natural sounds are periodic and consist of frequencies (harmonics) that are integer multiples of a common fundamental frequency (F0). Such harmonic complex tones (HCTs) evoke a pitch corresponding to their F0, which plays a key role in the perception of speech and music. “Pitch-selective” neurons have been identified in non-primary auditory cortex of marmoset monkeys. Noninvasive studies point to a putative “pitch center” located in a homologous cortical region in humans. It remains unclear whether there is sufficient spectral and temporal information available at the level of primary auditory cortex (A1) to enable reliable pitch extraction in non-primary auditory cortex. Here we evaluated multiunit responses to HCTs in A1 of awake macaques using a stimulus design employed in auditory nerve studies of pitch encoding. The F0 of the HCTs was varied in small increments, such that harmonics of the HCTs fell either on the peak or on the sides of the neuronal pure tone tuning functions. Resultant response-amplitude-versus-harmonic-number functions (“rate-place profiles”) displayed a periodic pattern reflecting the neuronal representation of individual HCT harmonics. Consistent with psychoacoustic findings in humans, lower harmonics were better resolved in rate-place profiles than higher harmonics. Lower F0s were also temporally represented by neuronal phase-locking to the periodic waveform of the HCTs. Findings indicate that population responses in A1 contain sufficient spectral and temporal information for extracting the pitch of HCTs by neurons in downstream cortical areas that receive their input from A1. PMID:23785145

  12. Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons

    Energy Technology Data Exchange (ETDEWEB)

    Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2014-09-02

    A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.

  13. Structure of the harmonic oscillator in the space of n-particle Glauber correlators

    Science.gov (United States)

    Zubizarreta Casalengua, E.; López Carreño, J. C.; del Valle, E.; Laussy, F. P.

    2017-06-01

    We map the Hilbert space of the quantum harmonic oscillator to the space of Glauber's nth-order intensity correlators, in effect showing "the correlations between the correlators" for a random sampling of the quantum states. In particular, we show how the popular g(2) function is correlated to the mean population and how a recurrent criterion to identify single-particle states or emitters, namely, g ( 2 ) physically more intuitive way that can be used to classify quantum sources by surveying which territory they can access.

  14. Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device.

    Science.gov (United States)

    Picone, Rico A R; Davis, Solomon; Devine, Cameron; Garbini, Joseph L; Sidles, John A

    2017-04-01

    We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.

  15. Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device

    Science.gov (United States)

    Picone, Rico A. R.; Davis, Solomon; Devine, Cameron; Garbini, Joseph L.; Sidles, John A.

    2017-04-01

    We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.

  16. A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)

    2009-05-01

    We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.

  17. Temperature effects on a network of dissipative quantum harmonic oscillators: collective damping and dispersion processes

    Science.gov (United States)

    de Ponte, M. A.; Mizrahi, S. S.; Moussa, M. H. Y.

    2009-09-01

    In this paper we extend the results presented in (de Ponte, Mizrahi and Moussa 2007 Phys. Rev. A 76 032101) to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whatever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. These solutions are shown to be significantly involved when temperature effects are considered, making difficult the analysis of collective decoherence and dispersion in dissipative bosonic networks. To circumvent these difficulties, we turn to the Wigner distribution function which enables us to present a technique to estimate the decoherence time of network states. Our technique proceeds by computing separately the effects of dispersion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the dispersion mechanism is also presented through the evolution of the Wigner function. The interesting collective dispersion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.

  18. Temperature effects on a network of dissipative quantum harmonic oscillators: collective damping and dispersion processes

    Energy Technology Data Exchange (ETDEWEB)

    De Ponte, M A; Mizrahi, S S [Departamento de Fisica, Universidade Federal de Sao Carlos, Caixa Postal 676, Sao Carlos, 13565-905, Sao Paulo (Brazil); Moussa, M H Y [Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Caixa Postal 369, 13560-590 Sao Carlos, SP (Brazil)

    2009-09-11

    In this paper we extend the results presented in (de Ponte, Mizrahi and Moussa 2007 Phys. Rev. A 76 032101) to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whatever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. These solutions are shown to be significantly involved when temperature effects are considered, making difficult the analysis of collective decoherence and dispersion in dissipative bosonic networks. To circumvent these difficulties, we turn to the Wigner distribution function which enables us to present a technique to estimate the decoherence time of network states. Our technique proceeds by computing separately the effects of dispersion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the dispersion mechanism is also presented through the evolution of the Wigner function. The interesting collective dispersion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.

  19. Use of quantum self-friction potentials and forces in standard convention for study of harmonic oscillator

    Science.gov (United States)

    Guseinov, I. I.; Mamedov, B. A.

    2017-04-01

    In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L^{{(pl^{ * } )}}-SF Laguerre polynomials (L^{{(pl^{ * } )}}-SFLPs) and L^{{(α^{*} )}}-modified SFLPs (L^{{(α^{*} )}}-MSFLPs) in standard convention, the V^{{(pl^{ * } )}}-SF potentials (V^{{(pl^{ * } )}}-SFPs), V^{{(α^{*} )}}-modified SFPs (V^{{(α^{*} )}}-MSFPs), F^{{(pl^{ * } )}}-SF forces (F^{{(pl^{ * } )}}-SFFs) and F^{{(α^{*} )}}-modified SFFs (F^{{(α^{*} )}}-MSFFs) are investigated, where pl^{ * } = 2l + 2 - α^{*} and α^{*} is the integer (α^{*} = α, - ∞ forces (F^{{(pl^{ * } )}}-SFFs and F^{{(α^{*} )}}-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V_{num}^{{(pl^{ * } )}} = V_{num}^{{(α^{*} )}} and F_{num}^{{(pl^{ * } )}} = F_{num}^{{(α^{*} )}}. The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.

  20. On the local virial theorems for linear and isotropic harmonic oscillator potentials in d dimensions

    Science.gov (United States)

    Bencheikh, K.; Nieto, L. M.

    2010-09-01

    For the system of noninteracting fermions in a one-body potential V(\\overrightarrow{\\vphantom{A}r}), the local virial theorems (LVT) are relations, at a given point \\overrightarrow{\\vphantom{A}r} in space, between this potential, kinetic energy and particle densities. It was recently shown (Brack et al 2010 J. Phys. A: Math. Theor. 43 255204) that for d-dimensional linear and also for isotropic harmonic oscillator potentials these LVTs are exactly satisfied. We present alternative and simple proofs of these theorems, by consideration of the canonical or Bloch density matrix and its relation to the kinetic energy density. The explicit analytical forms of the Bloch density matrix are used for the above-mentioned potentials to achieve the proofs. For the case of linear potential, we obtain a more general result for the so-called semilocal virial theorem, and for the harmonic oscillator potential case we derive a new relationship between the diagonal part of the canonical bloch density and the kinetic energy density.

  1. Solving a fuzzy initial value problem of a harmonic oscillator model

    Science.gov (United States)

    Karim, M. A.; Gunawan, A. Y.; Apri, M.; Sidarto, K. A.

    2017-03-01

    Modeling in systems biology is often faced with challenges in terms of measurement uncertainty. This is possibly either due to limitations of available data, environmental or demographic changes. One of typical behavior that commonly appears in the systems biology is a periodic behavior. Since uncertainties would get involved into the systems, the change of solution behavior of the periodic system should be taken into account. To get insight into this issue, in this work a simple mathematical model describing periodic behavior, i.e. a harmonic oscillator model, is considered by assuming its initial value has uncertainty in terms of fuzzy number. The system is known as Fuzzy Initial Value Problems. Some methods to determine the solutions are discussed. First, solutions are examined using two types of fuzzy differentials, namely Hukuhara Differential (HD) and Generalized Hukuhara Differential (GHD). Application of fuzzy arithmetic leads that each type of HD and GHD are formed into α-cut deterministic systems, and then are solved by the Runge-Kutta method. The HD type produces a solution with increasing uncertainty starting from the initial condition. While, GHD type produces an oscillatory solution but only until a certain time and above it the uncertainty becomes monotonic increasing. Solutions of both types certainly do not provide the accuracy for harmonic oscillator model during its evolution. Therefore, we propose the third method, so called Fuzzy Differential Inclusions (FDI), to attack the problem. Using this method, we obtain oscillatory solutions during its evolution.

  2. On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R

    OpenAIRE

    Álvarez Nodarse, Renato; Atakishiyeva Kyazim Zade, Messouma; Atakishiyev Mektiyev, Natig

    2005-01-01

    We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics, based on a q-extension of the classical Hermite polynomials Hn(x), recently introduced by us in [1] R. Alvarez-Nodarse, M. K. Atakishiyeva, and N. M. Atakishiyev.. On a q-extension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R. Boletín de la Sociedad Matemática Mexicana (3), 8, No.2, pp.127–139, 2002. The wave functions in this q-model of the quantum harmonic oscillator posses...

  3. On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ

    Science.gov (United States)

    Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.

    2005-11-01

    We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.

  4. Approaching Resonant Absorption of Environmental Xenobiotics Harmonic Oscillation by Linear Structures

    Directory of Open Access Journals (Sweden)

    Cornelia A. Bulucea

    2012-03-01

    Full Text Available Over the last several decades, it has become increasingly accepted that the term xenobiotic relates to environmental impact, since environmental xenobiotics are understood to be substances foreign to a biological system, which did not exist in nature before their synthesis by humans. In this context, xenobiotics are persistent pollutants such as dioxins and polychlorinated biphenyls, as well as plastics and pesticides. Dangerous and unstable situations can result from the presence of environmental xenobiotics since their harmful effects on humans and ecosystems are often unpredictable. For instance, the immune system is extremely vulnerable and sensitive to modulation by environmental xenobitics. Various experimental assays could be performed to ascertain the immunotoxic potential of environmental xenobiotics, taking into account genetic factors, the route of xenobiotic penetration, and the amount and duration of exposure, as well as the wave shape of the xenobiotic. In this paper, we propose an approach for the analysis of xenobiotic metabolism using mathematical models and corresponding methods. This study focuses on a pattern depicting mathematically modeled processes of resonant absorption of a xenobiotic harmonic oscillation by an organism modulated as an absorbing oscillator structure. We represent the xenobiotic concentration degree through a spatial concentration vector, and we model and simulate the oscillating regime of environmental xenobiotic absorption. It is anticipated that the results could be used to facilitate the assessment of the processes of environmental xenobiotic absorption, distribution, biotransformation and removal within the framework of compartmental analysis, by establishing appropriate mathematical models and simulations.

  5. Electron-bunch lengthening on higher-harmonic oscillations in storage-ring free-electron lasers.

    Science.gov (United States)

    Sei, Norihiro; Ogawa, Hiroshi; Okuda, Shuichi

    2017-09-01

    The influence of higher-harmonic free-electron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJI-IV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavity-length detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonator-type FELs by using higher harmonics in the extreme-ultraviolet and the X-ray regions.

  6. An alternative factorization of the quantum harmonic oscillator and two-parameter family of self-adjoint operators

    Energy Technology Data Exchange (ETDEWEB)

    Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)

    2012-10-01

    We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.

  7. Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)

    2009-02-16

    The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.

  8. Symmetries and Laplacians introduction to harmonic analysis, group representations and applications

    CERN Document Server

    Gurarie, D

    1992-01-01

    Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...

  9. Sea quark densities in the effective chiral quark model with generalized harmonic oscillator potential

    Energy Technology Data Exchange (ETDEWEB)

    Yazdanpannah, M.M.; Dehghanzadeh, M. [Shahid Bahonar University of Kerman, Faculty of Physics, Kerman (Iran, Islamic Republic of); Mirjalili, A. [Yazd University, Physics Department, P.O. Box 89195-741, Yazd (Iran, Islamic Republic of)

    2012-11-15

    The solution of the Dirac equation with a generalized harmonic oscillator potential is used to extract the constituent bare parton densities. The results are firstly in spatial space which are converted to momentum space, using the Fourier transformation. The final results are presented in terms of the Bjorken x-variable. Employing the effective chiral quark model and the related convolutions, the parton densities inside the proton are obtained. Choosing an appropriate radius of proton, they indicate reasonable behavior. Although the initial framework is completely theoretical, the results for the sea and valence quark densities and also the ratio of d to u valence quarks inside the proton are in good agreement with the available experimental data and some theoretical models. (orig.)

  10. Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System

    Directory of Open Access Journals (Sweden)

    Lock Yue Chew

    2014-04-01

    Full Text Available In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.

  11. The optimal performance of a quantum refrigeration cycle working with harmonic oscillators

    CERN Document Server

    Lin Bi Hong; Hua Ben

    2003-01-01

    The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...

  12. A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Borondo, F [Departamento de Quimica, and Instituto Mixto de Ciencias Matematicas CSIC-UAM-UC3M-UCM, Universidad Autonoma de Madrid, Cantoblanco-28049 Madrid (Spain); Luque, A; Villanueva, J [Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, 08028 Barcelona (Spain); Wisniacki, D A [Departamento de Fisica ' J. J. Giambiagi' , FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina)], E-mail: f.borondo@uam.es, E-mail: alejandro.luque@upc.edu, E-mail: jordi.villanueva@upc.edu, E-mail: wisniacki@df.uba.ar

    2009-12-11

    Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two-dimensional isotropic harmonic oscillator is presented as an illustration.

  13. Energy spectrum inverse problem of q-deformed harmonic oscillator and entanglement of composite bosons

    Science.gov (United States)

    Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

    2017-06-01

    Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.

  14. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations

    CERN Document Server

    Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R

    2016-01-01

    Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...

  15. Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator

    Science.gov (United States)

    Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan

    2018-01-01

    The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.

  16. The optimal performance of a quantum refrigeration cycle working with harmonic oscillators

    Science.gov (United States)

    Lin, Bihong; Chen, Jincan; Hua, Ben

    2003-02-01

    The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily.

  17. DYNAMICAL SIMULATION OF A QUANTUM HARMONIC-OSCILLATOR IN A NOBLE-GAS BATH BY DENSITY-MATRIX EVOLUTION

    NARCIS (Netherlands)

    MAVRI, J; BERENDSEN, HJC

    A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the

  18. An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)

    2009-08-03

    The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.

  19. The particle flow oscillations of rotating non-interacting gases in a two-dimensional harmonic trap

    Energy Technology Data Exchange (ETDEWEB)

    Li, Yushan [Department of Physics, University of Science and Technology Beijing, Beijing 100083 (China); Department of Physics, Heze University, Heze 274015 (China); Gu, Qiang, E-mail: qgu@ustb.edu.cn [Department of Physics, University of Science and Technology Beijing, Beijing 100083 (China)

    2016-01-28

    The spatial distribution of particle flow and atomic density of the two-dimensional, harmonically trapped, ideal atomic gases in synthetic magnetic field and rotating frame are systematically investigated in various regimes of temperature. The magnetization and particle flow of rotating fermions exhibit a de Haas–van Alphen-like oscillation at relatively low temperature. This phenomenon is analogous to the quantum oscillation of orbital magnetism and current in confined electron system. An elaborate comparison with Bose system is also proposed. - Highlights: • Oscillations of particle flow in rotating trapped gases are comprehensively studied. • Fermions exhibit de Haas–van Alphen-like oscillation at low temperature. • Rotating fermions can be easily used to illustrate magnetic properties of confined electrons. • Diamagnetism of bosons increases with increasing rotation frequency. • Characteristic dependency of magnetization on temperature is reflected in particle flow.

  20. Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: the oddness of its even-parity solutions

    Energy Technology Data Exchange (ETDEWEB)

    Viana-Gomes, J; Peres, N M R, E-mail: zgomes@fisica.uminho.pt [Physics Department, University of Minho, CFUM, P-4710-057 Braga (Portugal)

    2011-09-15

    We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem.

  1. Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.

    Science.gov (United States)

    Insinga, Andrea; Andresen, Bjarne; Salamon, Peter

    2016-07-01

    Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

  2. Shannon and Fisher entropy measures for a parity-restricted harmonic oscillator

    Science.gov (United States)

    Shi, Ye-Jiao; Sun, Guo-Hua; Jing, Jian; Dong, Shi-Hai

    2017-12-01

    We first present the analytical solutions to the Schrödinger equation with the parity-restricted harmonic oscillator V(x)=\\frac{1}{2}m{{ω }2}{{x}2} (x>0)~ and then calculate the Shannon information entropies Sxn and Spn both in position space and in momentum space. It is interesting to find that the variation of the Shannon information entropy Spn in momentum space is different from our previous studies, i.e. the Spn first increases with the quantum number n and then decreases with the number n. This is a new and abnormal phenomenon and may be explained by the parity-restricted system. The BBM inequality is verified to be saturated, but the sum of the entropies first increases with the number n and then decreases with it. The entropy densities ρ s (x) and ρ s (p) are also demonstrated. We find that the Fisher entropy is exactly given by {{I}F}=8n+6,n=0,1,2,\\ldots .

  3. Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards.

    Science.gov (United States)

    Chen, Y F; Tung, J C; Tuan, P H; Yu, Y T; Liang, H C; Huang, K F

    2017-01-01

    A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

  4. Solution of the Schroedinger equation for time-dependent 1D harmonic oscillators using the orthogonal functions invariant

    Energy Technology Data Exchange (ETDEWEB)

    Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)

    2003-02-28

    An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.

  5. Land-cover separability analysis of MODIS time-series data using a combined simple harmonic oscillator and a mean reverting stochastic process

    CSIR Research Space (South Africa)

    Grobler, TL

    2012-06-01

    Full Text Available It is proposed that the time series extracted from moderate resolution imaging spectroradiometer satellite data be modeled as a simple harmonic oscillator with additive colored noise. The colored noise ismodeled with an Ornstein–Uhlenbeck process...

  6. Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

    Science.gov (United States)

    Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

    1995-08-01

    The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

  7. Analysis of Intermolecular Coordinate Contributions to Third-order Ultrafast Spectroscopy of Liquids in the Harmonic Oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Thantu, Napoleon; McMorrow, D.; Melinger, J. S.; Kleiman, V.; Lotshaw, W. T.

    2001-07-01

    The apparently-multicomponent subpicosecond intermolecular dynamics of carbon disulfide liquid are addressed in a unified manner in terms of an inhomogeneously broadened quantum mechanical harmonic oscillator model for a single vibrational coordinate. For an inhomogeneously broadened (Gaussian) distribution of oscillators, the model predicts naturally the bimodal character of the subpicosecond intermolecular dynamics of carbon disulfide liquid, and also the spectral evolution effects (spectral narrowing and saturation) that are observed for solutions of carbon disulfide in weakly interacting alkane solvents. The unique dynamical signature of these low-frequency vibrational coordinates is determined largely by the physical constraints on the coordinates (near equality of oscillator frequency, dephasing frequency, and inhomogeneous bandwidth), such that constructive and destructive interference effects play a dominant role in shaping the experimental observable.

  8. Pattern formation in singly resonant second-harmonic generation with competing parametric oscillation

    DEFF Research Database (Denmark)

    Lodahl, P.; Saffman, M.

    1999-01-01

    fundamental field, and its coupling to a pair of nondegenerate parametric fields. The parametric fields are driven by the nonresonant second-harmonic field. Analysis indicates the existence of transverse instability of the pump field alone, as well as the possibility of simultaneous instability of the pump......We theoretically investigate the generation of spatial patterns in intracavity second-harmonic generation. We consider a cavity with planar mirrors that is resonant at the fundamental frequency, but not at the second-harmonic frequency. A mean-field model is derived that describes the resonant...

  9. Parametric resonance for solitons in the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez-Tenorio, C. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico) and Universidad Autonoma del Estado de Mexico (Mexico)]. E-mail: celso1@hotmail.com; Belyaeva, T.L. [Universidad Autonoma del Estado de Mexico (Mexico); Serkin, V.N. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico)

    2007-09-01

    The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered.

  10. Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics

    DEFF Research Database (Denmark)

    Nørrelykke, Simon F; Flyvbjerg, Henrik

    2011-01-01

    -lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems-e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system......The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... of finite sampling rate and sampling time for these models as well....

  11. Optimal Bounded Control for Stationary Response of Strongly Nonlinear Oscillators under Combined Harmonic and Wide-Band Noise Excitations

    Directory of Open Access Journals (Sweden)

    Yongjun Wu

    2011-01-01

    Full Text Available We study the stochastic optimal bounded control for minimizing the stationary response of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. The stochastic averaging method and the dynamical programming principle are combined to obtain the fully averaged Itô stochastic differential equations which describe the original controlled strongly nonlinear system approximately. The stationary joint probability density of the amplitude and phase difference of the optimally controlled systems is obtained from solving the corresponding reduced Fokker-Planck-Kolmogorov (FPK equation. An example is given to illustrate the proposed procedure, and the theoretical results are verified by Monte Carlo simulation.

  12. An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth

    Directory of Open Access Journals (Sweden)

    Marcin Salamaga

    2013-09-01

    Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.

  13. Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)

    2008-02-15

    A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.

  14. Interaction between the molecular coherent states for a discrete variable harmonic oscillator and the coherent radiation

    Energy Technology Data Exchange (ETDEWEB)

    Draganescu, Gheorghe Eugen [Department of Mechanics, Polytechnic University of Timisoara, Bd M Viteazu No1, Timisoara and Department of Physics, West University of Timisoara (Romania)

    2012-08-17

    We used the dicrete variable three-dimmensional Charlier oscillator. For a system of molecules interacting with the coherent radiation field the temporal variation of the refractive index has been established.

  15. Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators

    DEFF Research Database (Denmark)

    Momeni, M.; Jamshidi, j.; Barari, Amin

    2011-01-01

    In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....

  16. Neural Representation of Concurrent Harmonic Sounds in Monkey Primary Auditory Cortex: Implications for Models of Auditory Scene Analysis

    Science.gov (United States)

    Steinschneider, Mitchell; Micheyl, Christophe

    2014-01-01

    The ability to attend to a particular sound in a noisy environment is an essential aspect of hearing. To accomplish this feat, the auditory system must segregate sounds that overlap in frequency and time. Many natural sounds, such as human voices, consist of harmonics of a common fundamental frequency (F0). Such harmonic complex tones (HCTs) evoke a pitch corresponding to their F0. A difference in pitch between simultaneous HCTs provides a powerful cue for their segregation. The neural mechanisms underlying concurrent sound segregation based on pitch differences are poorly understood. Here, we examined neural responses in monkey primary auditory cortex (A1) to two concurrent HCTs that differed in F0 such that they are heard as two separate “auditory objects” with distinct pitches. We found that A1 can resolve, via a rate-place code, the lower harmonics of both HCTs, a prerequisite for deriving their pitches and for their perceptual segregation. Onset asynchrony between the HCTs enhanced the neural representation of their harmonics, paralleling their improved perceptual segregation in humans. Pitches of the concurrent HCTs could also be temporally represented by neuronal phase-locking at their respective F0s. Furthermore, a model of A1 responses using harmonic templates could qualitatively reproduce psychophysical data on concurrent sound segregation in humans. Finally, we identified a possible intracortical homolog of the “object-related negativity” recorded noninvasively in humans, which correlates with the perceptual segregation of concurrent sounds. Findings indicate that A1 contains sufficient spectral and temporal information for segregating concurrent sounds based on differences in pitch. PMID:25209282

  17. Mechanism of equivalent electric dipole oscillation for high-order harmonic generation from grating-structured solid-surface by femtosecond laser pulse

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn

    2017-07-12

    Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.

  18. The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation

    Directory of Open Access Journals (Sweden)

    Xi Fu

    2016-01-01

    Full Text Available Let B be the real unit ball in Rn and f∈CN(B. Given a multi-index m=(m1,…,mn of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r,x≠y(1-|x|2α(1-|y|2β|∂mf(x-∂mf(y|/|x-y|γ[x,y]1-γ,  x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.

  19. ELM-free and inter-ELM divertor heat flux broadening induced by edge harmonics oscillation in NSTX

    Science.gov (United States)

    Gan, K. F.; Ahn, J.-W.; Gray, T. K.; Zweben, S. J.; Fredrickson, E. D.; Scotti, F.; Maingi, R.; Park, J.-K.; Canal, G. P.; Soukhanovskii, V. A.; Mclean, A. G.; Wirth, B. D.

    2017-12-01

    A new n  =  1 dominated edge harmonic oscillation (EHO) has been found in NSTX. The new EHO, rotating toroidally in the counter-current direction and the opposite direction of the neutral beam, was observed during certain inter-ELM and ELM-free periods of H-mode operation. This EHO is associated with a significant broadening of the integral heat flux width ({λ\\operatorname{int}} ) by up to 150%, and a decrease in the divertor peak heat flux by  >60%. An EHO induced filament was also observed by the gas puff imaging diagnostic. The toroidal rotating filaments could change the edge magnetic topology resulting in toroidal rotating strike point splitting and heat flux broadening. Experimental result of the counter current rotation of strike points splitting is consistent with the counter-current EHO.

  20. Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis. (II) the program HFODD

    Energy Technology Data Exchange (ETDEWEB)

    Dobaczewski, J.; Dudek, J. [Strasbourg-1 Univ., 67 (France). Centre de Recherches Nucleaires; Dobaczewski, J. [Warsaw Univ. (Poland)

    1996-12-31

    We describe the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the deformed Cartesian harmonic oscillator basis. The user has a possibility of choosing among various symmetries of the nuclear HF problem for rotating or non-rotating nuclei; they vary from the non-axial parity-invariant nuclear shapes, through those also breaking the intrinsic parity, towards the least-restrictive case corresponding to only one symmetry plane. The code provides a solution for a complete superdeformed rotational band in an A{approx}150 nucleus within one CPU hour of the CRAY C-90 supercomputer or within two-three CPU hours of a fast workstation. (authors). 22 refs.

  1. Benchmark Calculation of Radial Expectation Value \\varvec{< r^{-2} \\rangle } for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators

    Science.gov (United States)

    Yu, Rong Mei; Zan, Li Rong; Jiao, Li Guang; Ho, Yew Kam

    2017-09-01

    Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies.

  2. AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator

    DEFF Research Database (Denmark)

    Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens

    2006-01-01

    We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...... with the coupling strength. A simple linear time-domain model is employed to illustrate the results...

  3. Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation

    Science.gov (United States)

    Boujo, E.; Noiray, N.

    2017-04-01

    We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.

  4. Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

    Directory of Open Access Journals (Sweden)

    M. K. Bahar

    2013-01-01

    Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

  5. The quantum 2D-harmonic oscillator in 1:1 resonance with time-dependent perturbation : averaging applied to slowly varying quantum systems

    NARCIS (Netherlands)

    Huveneers, R.

    1994-01-01

    In this paper we will study the 2D-harmonic oscillator in 1:1 resonance. We add a general third- and fourth order perturbation which is slowly time-dependent, and are interested in the resulting interaction between the unperturbed orbits (states). By treating this system quantummechanically we get a

  6. A simple strobe to study high-order harmonics and multifrequency oscillations in mechanical resonators

    Science.gov (United States)

    Castellanos-Gomez, A.

    2013-01-01

    A simple strobe setup with the potential to study higher-order eigenmodes and multifrequency oscillations in micromechanical resonators is described. It requires standard equipment, commonly found in many laboratories, and it can thus be employed for public demonstrations of mechanical resonances. Moreover, the work presented here can be used by undergraduate students and/or teachers to prepare practical work in laboratory courses at physics or engineering universities. The dynamics of a micromachined cantilever is analysed as an example. In fact, using our stroboscopic setup, the first and second flexural eigenmodes, as well as a multifrequency oscillation composed by a superposition of both modes, have been successfully filmed with a conventional optical microscope equipped with a digital camera.

  7. A three-body force model for the harmonic and anharmonic oscillator

    Directory of Open Access Journals (Sweden)

    A. A. Rajabi

    2005-06-01

    Full Text Available   We present a mathematical method to describe motion of a system based on 3 identical body forces. The 3-body forces are more easily introduced and treated within the hyperspherical harmonics. We have obtained an exact solution of the radial Schrödinger equation for a 3- body system in three dimensions. The interact potential  V  is assumed to depend on the hyperradius X only where X is a function of the Jacobi relative coordinates ρ and λ which are functions of the three identical particles, relative positions r12 , r23 and r31 . This method has been extensively used in nuclear and molecular physics. This work is interesting to those who are studying hadronic and bosonics physics and problems consisting three - body systems.

  8. LBO optical parametric oscillator pumped by second harmonic of a Nd:YAG laser

    Science.gov (United States)

    Dabu, Razvan V.; Fenic, Constantin G.; Stratan, Aurel; Luculescu, C.; Muscalu, G. L.

    1998-07-01

    We describe a pulsed doubly resonant LiB3O5 (LBO) optical parametric oscillator (OPO) pumped with a frequency doubled Q- switched Nd:YAG laser amplifier. The threshold power density near degeneracy was found to be 29 MW/cm2. The OPO was continuously tuned from 970 nm to 1175 nm by rotation of the LBO crystal. The linewidth of the signal radiation at 998 nm, and idler radiation at 1136 nm wavelength, were found to be 10 nm, and 13 nm respectively. The OPO output pulse energy of signal and idler near degeneracy was 1.51 mJ for 18 mJ pump energy.

  9. SevenOperators, a Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions

    Science.gov (United States)

    Haxton, Wick; Lunardini, Cecilia

    2008-09-01

    Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

  10. Relevance of Damped Harmonic Oscillation for Modeling the Training Effects on Daily Physical Performance Capacity in Team Sport.

    Science.gov (United States)

    Morin, Stéphane; Ahmaïdi, Saïd; Leprêtre, Pierre-Marie

    2016-10-01

    Positive and negative effects of training induce apparent oscillations of performance, suggesting that the delayed cumulative effects of training on daily performance capacity (DPC) are best fitted by sine waves damped over time. To compare the criterion validity of the impulse-response (IR) model of Banister et al and the damped harmonic oscillation (DHO) model for quantifying the training load (TL)-DPC relationship. Six female professional volleyball players (20.8 ± 2.4 y) were monitored using the session rating of perceived exertion (sRPE) for 9 mo to quantify TL. Countermovement-jump (CMJ) and 4-step-approach-CMJ (4sCMJ) performances were recorded once a month. Parameters of models were determined by minimizing residual-sum squares between predicted and real performances with a nonlinear regression. DPC was best fitted by the DHO model rather than the IR model (CMJ, R(2) = .80 ±.08 and.69 ±.20, respectively; 4sCMJ, R(2) = .86 ± .09 and .67 ± .29, respectively). The damping parameter θ and the period T were positively correlated with age (ρ = 0.81, P training and recovery days. DPC could be considered the expression of the individual process of accumulation and dissipation of fatigue induced by training. DHO-model parameters were correlated with age, which prompts one to postulate that expertise has a major influence on DPC. The DHO model will help coaches develop a greater understanding of training effects and make monitoring of the training process more effective.

  11. Intermodulation and harmonic distortion in slow light Microwave Photonic phase shifters based on Coherent Population Oscillations in SOAs.

    Science.gov (United States)

    Gasulla, Ivana; Sancho, Juan; Capmany, José; Lloret, Juan; Sales, Salvador

    2010-12-06

    We theoretically and experimentally evaluate the propagation, generation and amplification of signal, harmonic and intermodulation distortion terms inside a Semiconductor Optical Amplifier (SOA) under Coherent Population Oscillation (CPO) regime. For that purpose, we present a general optical field model, valid for any arbitrarily-spaced radiofrequency tones, which is necessary to correctly describe the operation of CPO based slow light Microwave Photonic phase shifters which comprise an electrooptic modulator and a SOA followed by an optical filter and supplements another recently published for true time delay operation based on the propagation of optical intensities. The phase shifter performance has been evaluated in terms of the nonlinear distortion up to 3rd order, for a modulating signal constituted of two tones, in function of the electrooptic modulator input RF power and the SOA input optical power, obtaining a very good agreement between theoretical and experimental results. A complete theoretical spectral analysis is also presented which shows that under small signal operation conditions, the 3rd order intermodulation products at 2Ω1 + Ω2 and 2Ω2 + Ω1 experience a power dip/phase transition characteristic of the fundamental tones phase shifting operation.

  12. On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

    Energy Technology Data Exchange (ETDEWEB)

    Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr [Departamento de Matemática, Universidad de Costa Rica. S.O (Costa Rica); Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu [Department of Mathematical Sciences, University of Puerto Rico, Mayagüez, Puerto Rico 00681-5000 (United States)

    2015-07-15

    In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.

  13. Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

    Science.gov (United States)

    Chae, Jongchul; Litvinenko, Yuri E.

    2017-08-01

    The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D2 and Hα lines.

  14. Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

    Energy Technology Data Exchange (ETDEWEB)

    Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)

    2017-08-01

    The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.

  15. Density Profiles, Energy, and Oscillation Strength of a Quantum Dot in Two Dimensions with a Harmonic Oscillator External Potential using an Orbital-free Energy Functional Based on Thomas–Fermi Theory

    Directory of Open Access Journals (Sweden)

    Suhufa Alfarisa

    2016-03-01

    Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free density functional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.

  16. Harmonic oscillators: the quantization of simple systems in the old quantum theory and their functional roles in biology.

    Science.gov (United States)

    Steele, Richard H

    2008-03-01

    This article introduces quantum physics into biology in an intuitive and non-intimidating manner. It extends the quantum aspects of harmonic oscillators, and electromagnetic fields, to their functional roles in biology. Central to this process are the De Broglie wave-particle duality equation, and the adiabatic invariant parameters, magnetic moment, angular momentum and magnetic flux, determined by Ehrenfest as imposing quantum constraints on the dynamics of charges in motion. In mechanisms designed to explain the generation of low-level light emissions in biology we have adopted a biological analog of the electrical circuitry modeled on the parallel plated capacitor, traversed by helical protein structures, capable of generating electromagnetic radiation in the optical spectral region. The charge carrier required for the emissions is an accelerating electron driven, in a cyclotron-type mechanism, by ATP-induced reverse electron transfer with the radial, emission, components, mediated by coulombic forces within the helical configurations. Adenine, an essential nucleotide constituent of DNA, was examined with its long wavelength absorption maximum determining the energetic parameters for the calculations. The calculations were made for a virtual 5-turn helix where each turn of the helix emits a different frequency, generating a biological quantum series. The components of six adiabatic invariant equations were found to be embedded in Planck's constant rendering them discrete, finite, non-random, non-statistical-Planck's constant precludes probability. A mechanism for drug-induced hallucination is described that might provide insights as to the possible role of electromagnetic fields in consciousness. Sodium acceleration through a proposed nerve membrane helical channel generated electromagnetic emissions in the microwave region in confirmation of reported microwave emission for active nerves and may explain saltatory nerve conduction. Theoretical calculations for a

  17. Representation of the Antarctic Oscillation and related precipitation in the MPI Earth System Model

    Science.gov (United States)

    Babian, Stella; Rust, Henning W.; Grieger, Jens; Cubasch, Ulrich

    2015-04-01

    The Antarctic Oscillation (AAO) is the dominant mode of atmospheric variability on the southern hemisphere. It is obtained via a principal component analysis (PCA) for geopotential height anomalies. In this study the 700hPa geopotential field are used to comply with the NOAAs definition of the AAO. Being the southern hemisphere's dominant mode, an adequate representation in earth system models is desirable. This study evaluates to what extend the AAO and related precipitation is represented in the Max Planck Institute's earth system model (MPI-ESM). To this end the AAO spatial patterns (Empirical Orthogonal Functions, EOFs), spectral properties of the associated principal components (PCs) and AAO-related precipitation of MPI-ESM are compared to three reanalyses: the ECMWF's ERA-40 and ERA-Interim, and the NCEP/NCAR 40-year reanalysis project. Differences between MPI-ESM and ERA-Interim leading EOFs reveal that the three typical centres of action are less pronounced and slightly shifted in the model. Spectral density estimates of the associated PCs show reduced variability in the MPI-ESM for periods between 4 to 5 months. The relation between AAO and southern hemispheric precipitation is assessed via composites and correlation analysis. In both, model and reanalyses, a negative AAO index leads to a general increase of precipitation between 30°S and 50°S and a decrease south of 50°S. Differences between correlation maps are most prominent near Indonesia and Antarctica. In summary, the MPI-ESM underestimates the relation of AAO and southern hemispheric precipitation but gives the correct sign and spatial distribution of correlation values.

  18. Representation of the Antarctic Oscillation and related precipitation patterns in the MPI Earth System Model

    Directory of Open Access Journals (Sweden)

    Stella Babian

    2016-12-01

    Full Text Available The Antarctic Oscillation (AAO is the dominant mode of atmospheric variability in the southern hemisphere. It is obtained via a principal component analysis (PCA for geopotential height anomalies. Being the southern hemisphere's dominant mode, an adequate representation in earth system models is desirable. This paper evaluates to what extent the AAO and related precipitation is represented in the Max Planck Institute's Earth System Model (MPI-ESM. To this end we compare AAO spatial patterns (empirical orthogonal functions, EOFs, spectral properties of the associated principal components (PCs and AAO-related precipitation patterns of MPI-ESM to three reanalyses: the ECMWF's ERA-40 and ERA-Interim, and the NCEP/NCAR 40-year reanalysis project. Differences between MPI-ESM and ERA-Interim leading EOFs reveal that the three typical centres of action are less pronounced and slightly shifted in the model. Spectral density estimates of the associated PCs show reduced variability in the MPI-ESM for periods between 4 to 5 months. The relation between AAO and southern hemispheric precipitation is assessed via composites and correlation analysis. In both, model and reanalyses, a negative AAO index leads to a general increase of precipitation between 30° S and 50° S and a decrease south of 50° S. Differences between maps of correlation for AAO and precipitation are most prominent near Indonesia and Antarctica probably due to a lack of pressure around Antarctica in the model. Altogether the MPI-ESM underestimates the relation of AAO and southern hemispheric precipitation but gives the correct sign and spatial distribution of correlation values.

  19. Considerations on 'Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring'

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)

    2009-11-09

    In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.

  20. Wigner’s Space-Time Symmetries Based on the Two-by-Two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere

    Directory of Open Access Journals (Sweden)

    Sibel Başkal

    2014-06-01

    Full Text Available The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2. It is shown that this oscillator system contains the essential features of Wigner’s little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the Sp(2 symmetry to that of SL(2, c corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincaré sphere contains the SL(2, c symmetry. In addition, it has a non-Lorentzian parameter allowing us to reduce the mass continuously to zero. It is thus possible to construct the little group for massless particles from that of the massive particle by reducing its mass to zero. Spin-1/2 particles and spin-1 particles are discussed in detail.

  1. Evaluated Excited-State Time-Independent Correlation Function and Eigenfunction of the Harmonics Oscillator Cosine Asymmetric Potential via Numerical Shooting Method

    Directory of Open Access Journals (Sweden)

    Artit Hutem

    2015-01-01

    Full Text Available We aimed to evaluate the ground-state and excite-state energy eigenvalue (En, wave function, and the time-independent correlation function of the atomic density fluctuation of a particle under the harmonics oscillator Cosine asymmetric potential (Saad et al. 2013. Instead of using the 6-point kernel of 4 Green’s function (Cherroret and Skipetrov, 2008, averaged over disorder, we use the numerical shooting method (NSM to solve the Schrödinger equation of quantum mechanics system with Cosine asymmetric potential. Since our approach does not use complicated formulas, it requires much less computational effort when compared to the Green functions techniques (Cherroret and Skipetrov, 2008. We show that the idea of the program of evaluating time-independent correlation function of atomic density is underdamped motion for the Cosine asymmetric potential from the numerical shooting method of this problem. Comparison of the time-independent correlation function obtained from numerical shooting method by Boonchui and Hutem (2012 and correlation function experiment by Kasprzak et al. (2008. We show the intensity of atomic density fluctuation (δn(x=n~(x-m~(x in harmonics oscillator Cosine asymmetric potential by numerical shooting method.

  2. Harmonic engine

    Science.gov (United States)

    Bennett, Charles L.; Sewall, Noel; Boroa, Carl

    2014-08-19

    An engine based on a reciprocating piston engine that extracts work from pressurized working fluid. The engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into of the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. Upon releasing the inlet valve the inlet valve head undergoes a single oscillation past the equilibrium positio to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. Protrusions carried either by the inlet valve head or piston head are used to bump open the inlet valve from the closed position and initiate the single oscillation of the inlet valve head, and protrusions carried either by the outlet valve head or piston head are used to close the outlet valve ahead of the bump opening of the inlet valve.

  3. Harmonic engine

    Science.gov (United States)

    Bennett, Charles L [Livermore, CA

    2009-10-20

    A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.

  4. UF-CHERS Measurements of Ion Temperature and Toroidal Rotation Fluctuations Associated with the Edge Harmonic Oscillation in Quiescent H-mode Plasmas

    Science.gov (United States)

    Truong, D. D.; Fonck, R. J.; McKee, G. R.; Yan, Z.; Grierson, B. A.

    2016-10-01

    The UF-CHERS (Ultra Fast CHarge Exchange Recombination Spectroscopy) diagnostic at DIII-D measures local, long-wavelength ion temperature and toroidal velocity fluctuations at turbulence-relevant spatiotemporal scales from emission of the CVI n=8 ->7 transition. During Quiescent H-mode (QH-mode) plasmas, which offer ELM-free improved confinement, UF-CHERS measurements observed coherent, low frequency (fo 10kHz) pedestal oscillations in Ti and vtor at the Edge Harmonic Oscillation (EHO) frequency while several modes between 35-75 kHz are suppressed when the EHO appears. Although broadband ion temperature and density fluctuations were reduced by the EHO, the toroidal rotation showed increased fluctuation amplitude. Investigating ion temperature and toroidal fluctuations associated with the EHO may provide insights into the saturated instability driving the EHO. Supported by DOE Grants DE-FG02-08ER54999, DE-FC02-04ER54698, and NSF GRFP Grant DGE-1256259.

  5. An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth

    OpenAIRE

    Marcin Salamaga

    2013-01-01

    Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981). In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory...

  6. Discussion on climate oscillations: CMIP5 general circulation models versus a semi empirical harmonic model based on astronomical cycles

    CERN Document Server

    Scafetta, Nicola

    2013-01-01

    Power spectra of global surface temperature (GST) records reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC (2013), are analyzed and found not able to reconstruct this variability. From 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 K/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. The climate sensitivity to CO2 doubling should be reduced by half, e.g. from the IPCC-2007 2.0-4.5 K range to 1.0-2.3 K with 1.5 C median. Also modern paleoclimatic temperature reconstructions yield the same conclusion. The observed natural oscillations could be driven by astronomical forcings. Herein I propose a semi empirical climate model made of six specific astronomical oscillations as constructors of the natural climate variability spanning ...

  7. Representation of monsoon intraseasonal oscillations in regional climate model: sensitivity to convective physics

    KAUST Repository

    Umakanth, U.

    2015-11-07

    The aim of the study is to evaluate the performance of regional climate model (RegCM) version 4.4 over south Asian CORDEX domain to simulate seasonal mean and monsoon intraseasonal oscillations (MISOs) during Indian summer monsoon. Three combinations of Grell (G) and Emanuel (E) cumulus schemes namely, RegCM-EG, RegCM-EE and RegCM-GE have been used. The model is initialized at 1st January, 2000 for a 13-year continuous simulation at a spatial resolution of 50 km. The models reasonably simulate the seasonal mean low level wind pattern though they differ in simulating mean precipitation pattern. All models produce dry bias in precipitation over Indian land region except in RegCM-EG where relatively low value of dry bias is observed. On seasonal scale, the performance of RegCM-EG is more close to observation though it fails at intraseasonal time scales. In wave number-frequency spectrum, the observed peak in zonal wind (850 hPa) at 40–50 day scale is captured by all models with a slight change in amplitude, however, the 40–50 day peak in precipitation is completely absent in RegCM-EG. The space–time characteristics of MISOs are well captured by RegCM-EE over RegCM-GE, however it fails to show the eastward propagation of the convection across the Maritime Continent. Except RegCM-EE all other models completely underestimates the moisture advection from Equatorial Indian Ocean onto Indian land region during life-cycle of MISOs. The characteristics of MISOs are studied for strong (SM) and weak (WM) monsoon years and the differences in model performances are analyzed. The wavelet spectrum of rainfall over central India denotes that, the SM years are dominated by high frequency oscillations (period <20 days) whereas little higher periods (>30 days) along with dominated low periods (<20 days) observed during WM years. During SM, RegCM-EE is dominated with high frequency oscillations (period <20 days) whereas in WM, RegCM-EE is dominated with periods >20

  8. Harmonic uniflow engine

    Science.gov (United States)

    Bennett, Charles L.

    2016-03-22

    A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. When released, the inlet valve head undergoes a single oscillation past the equilibrium position to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.

  9. Representations of the Schroedinger group and matrix orthogonal polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Vinet, Luc [Centre de recherches mathematiques, Universite de Montreal, CP 6128, succ. Centre-ville, Montreal, QC H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)

    2011-09-02

    The representations of the Schroedinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural formulas (recurrence relations, difference equations, Rodrigues' formula, etc) that these matrix orthogonal polynomials satisfy. (paper)

  10. Human brain networks function in connectome-specific harmonic waves.

    Science.gov (United States)

    Atasoy, Selen; Donnelly, Isaac; Pearson, Joel

    2016-01-21

    A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.

  11. Propagator for a spin-Bose system with the Bose field coupled to a reservoir of harmonic oscillators

    CERN Document Server

    Banerjee, S

    2003-01-01

    We consider the general problem of a single two-level atom interacting with a multimode radiation field (without the rotating-wave approximation), and additionally take the field to be coupled to a thermal reservoir. Using the method of bosonization of the spin operators in the Hamiltonian, and working in the Bargmann representation for all the boson operators, we obtain the propagator for the composite system using the techniques of functional integration, under a reasonable approximation scheme. The propagator is explicitly evaluated for a simplified version of the system with one spin and a dynamically coupled single-mode field. The results are also checked on the known problem of quantum Brownian motion.

  12. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

    Energy Technology Data Exchange (ETDEWEB)

    Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

    2015-11-15

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

  13. Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

    Energy Technology Data Exchange (ETDEWEB)

    Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)

    2016-05-15

    The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.

  14. Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

    Science.gov (United States)

    Montoya-Castillo, Andrés; Reichman, David R

    2017-01-14

    We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

  15. Considerations for an appropriate representation of non attenuated oscillations in electrical systems; Consideraciones para una adequada representacion de oscilaciones no amortiguadas en sistemas electricos

    Energy Technology Data Exchange (ETDEWEB)

    Sarasua, Antonio E. [Universidad Nacional de San Juan (Argentina). Inst. de Energia Electrica]. E-mail: sarasua@iee.unsj.edu.ar; Handschin, Edmund [Dortmund Univesitaet (Germany); Mercado, Pedro E. [Consejo Nacional de Investigaciones Cientficas y Tecnicas (CONICET), Buenos Aires (Argentina)]|[Universidad Nacional de San Juan (Argentina). Inst. de Energia Electrica; Rehtanz, Christian [ABB (Switzerland)

    2001-07-01

    This article analyses and proposes the most important considerations to be taken into account regarding the models development which suitably represent not amortized oscillations observed in electric power transmission systems, which are not susceptible of being detected by the current calculation tools. Among others considerations, it has been discussed the technique applications of non-lineal analysis, such as the Bifurcation theory, and it is proposed necessary calculation tools in relation to their representation.

  16. Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic oscillations

    Science.gov (United States)

    Chen, Xi; Burrell, K. H.; Osborne, T. H.; Barada, K.; Ferraro, N. M.; Garofalo, A. M.; Groebner, R. J.; McKee, G. R.; Petty, C. C.; Porkolab, M.; Rhodes, T. L.; Rost, J. C.; Snyder, P. B.; Solomon, W. M.; Yan, Z.; The DIII-D Team

    2017-08-01

    New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E  ×  B shear required for the EHO decreases linearly with pedestal collisionality ν \\text{e}\\ast , which is favorable for operating QH-mode in machines with low collisionality and low rotation such as ITER. In addition, the QH-mode regime in DIII-D has recently been found to bifurcate into a new ‘wide-pedestal’ state at low torque in double-null shaped plasmas, characterized by increased pedestal height, width and thermal energy confinement (Burrell 2016 Phys. Plasmas 23 056103, Chen 2017 Nucl. Fusion 57 022007). This potentially provides an alternate path for achieving high performance ELM-stable operation at low torque, in addition to the low-torque QH-mode sustained with applied 3D fields. Multi-branch low-k and intermediate-k turbulences are observed in the ‘wide-pedestal’. New experiments support the hypothesis that the decreased edge E  ×  B shear enables destabilization of broadband turbulence, which relaxes edge pressure gradients, improves peeling-ballooning stability and allows a wider and thus higher pedestal. The ability to accurately predict the critical E  ×  B shear for EHO and maintain high performance QH-mode at low torque is an essential requirement for projecting QH-mode operation to ITER and future machines.

  17. Plasma harmonics

    CERN Document Server

    Ganeev, Rashid A

    2014-01-01

    Preface; Why plasma harmonics? A very brief introduction Early stage of plasma harmonic studies - hopes and frustrations New developments in plasma harmonics studies: first successes Improvements of plasma harmonics; Theoretical basics of plasma harmonics; Basics of HHG Harmonic generation in fullerenes using few-cycle pulsesVarious approaches for description of observed peculiarities of resonant enhancement of a single harmonic in laser plasmaTwo-colour pump resonance-induced enhancement of odd and even harmonics from a tin plasmaCalculations of single harmonic generation from Mn plasma;Low-o

  18. Four-dimensional quantum oscillator and magnetic monopole with U(1) dynamical group

    Science.gov (United States)

    Bakhshi, Z.; Panahi, H.; Golchehre, S. G.

    2017-09-01

    By using an appropriate transformation, it was shown that the quantum system of four-dimensional (4D) simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the Dirac magnetic monopole has the hidden algebra of U(1) symmetry and by reducing the dimensions of space, the U(1) × U(1) dynamical group for 4D harmonic oscillator quantum system was obtained. Using the group representation and based on explicit solution of the obtained differential equation, the spectrum of system was calculated.

  19. Classical oscillator driven by an oscillating chirped force

    NARCIS (Netherlands)

    Khachatryan, A.G.; van Goor, F.A.; Boller, Klaus J.

    2006-01-01

    The motion of a classical (harmonic) oscillator is studied in the case where the oscillator is driven by a pulsed oscillating force with a frequency varying in time (frequency chirp). The amplitude and phase of the oscillations left after the pulsed force in dependence on the profile and strength of

  20. Solution of the Skyrme Hartree Fock Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

    Science.gov (United States)

    Dobaczewski, J.; Olbratowski, P.

    2005-05-01

    We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program SummaryTitle of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format:tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero

  1. New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization

    Energy Technology Data Exchange (ETDEWEB)

    Bagchi, Bijan, E-mail: bbagchi123@gmail.com [Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia)

    2015-08-14

    We derive a one-step extension of the well known Swanson oscillator that describes a specific type of pseudo-Hermitian quadratic Hamiltonian connected to an extended harmonic oscillator model. Our analysis is based on the use of the techniques of supersymmetric quantum mechanics and addresses various representations of the ladder operators starting from a seed solution of the harmonic oscillator expressed in terms of a pseudo-Hermite polynomial. The role of the resulting chain of Hamiltonians related to similarity transformation is then exploited. In the second part we write down a two dimensional generalization of the Swanson Hamiltonian and establish superintegrability of such a system. - Highlights: • We show that the Swanson system admits a 1-step rational extension. • We provide a flow-chart linking the Swanson model to its generalized counterpart. • We examine superintegrability of the Hermitian equivalence of the Swanson oscillator.

  2. Quantum harmonically kicked environments

    Science.gov (United States)

    Custódio, M. S.; Strunz, W. T.; Beims, M. W.

    2017-11-01

    In this work we derive a generalized map which describes the time evolution of a quantum system coupled to a quantum environment composed by a finite number of free particles kicked harmonically at periodic times. Dissipation is introduced via the interaction between system and environment, which is switched on and off simultaneously at regular time intervals. The dynamics of the environmental particles occurs along rotated ellipsis in phase space and can be described by unrotated harmonic oscillators with a new frequency which depends on the kicking time. With the definition of a thermal bath we show that our quantum kicked environment induces an unusual fluctuation-dissipation relation.

  3. Representations of Lie algebras and partial differential equations

    CERN Document Server

    Xu, Xiaoping

    2017-01-01

    This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students.  Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certai...

  4. Golden quantum oscillator and Binet-Fibonacci calculus

    Energy Technology Data Exchange (ETDEWEB)

    Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)

    2012-01-13

    The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

  5. Three-dimensional simulations of harmonic radiation and harmonic lasing

    Energy Technology Data Exchange (ETDEWEB)

    Schmitt, M.J.; McVey, B.D.

    1990-01-01

    Characteristics of the harmonic emission from free-electron lasers (FELs) are examined in the spontaneous, coherent-spontaneous and stimulated emission regimes. The radiation at both odd and even harmonic frequencies is treated for electron beams with finite emittance and energy spread. In the spontaneous emission regime, the transverse radiation patterns including the transverse frequency dependences, are given. How this expression is modified to include energy spread and emittance is described. In the coherent-spontaneous emission and stimulated emission regimes, the interaction of the radiation fields with the electrons must be treated self-consistently. Here, a single-frequency distributed transverse source function for each electron is used in the harmonic version of the 3-D code FELEX to model the harmonic radiation. The code has recently been modified to simultaneously model the fundamental and harmonic interactions for multiple-pass oscillator simulations. These modifications facilitate the examination of FELs under various operating conditions. When the FEL is lasing at the fundamental, the evolution of the harmonic fields can be examined. This evolution is unique in the sense that the electron beam radiates at the harmonic frequencies in the presence of the harmonic radiation circulating in the cavity. As a result, enhancements of the harmonic emission can be observed. Finally, harmonic lasing can occur in cases where there is sufficient gain to overcome cavity losses and lasing at the fundamental can be suppressed. The characteristics and efficiency of these interactions are explored. 11 refs., 9 figs.

  6. Harmonic generation in the generalized Sagdeev pseudopotential

    Science.gov (United States)

    Akbari-Moghanjoughi, M.

    2017-09-01

    In this paper, we study the nonlinear harmonic generation effect in different oscillator models. For weakly nonlinear systems, we use the generalized forced Korteweg de Vries Burgers (KdVB) and modified KdVB (mKdVB) models in order to classify three fundamentally different harmonic structures in a nonlinear dynamical system. The first is called the internal harmonic structure which exists due to the self oscillation of the system in the absence of dissipation effect and is shown to follow either relations of nf or (2n - 1)f depending on the symmetry of oscillator potential in which n is an integer number and f is the fundamental frequency which is exactly obtained for the Helmholtz oscillator. The second structure is the resonant harmonics which appears in the presence of damping and follows the harmonic structure nf0 in which f0 is the linear resonance frequency. Finally, the last harmonic structure appears in the presence of dissipation and external periodic forcing effects which we call the external harmonic pattern. It is shown that the external harmonic pattern, in which f1 is the driving frequency, always follows the nf1 rule regardless of the potential symmetry. We then extend our analysis to study the harmonic generation in the fully nonlinear generalized Sagdeev potential for real plasmas with isothermal and adiabatic ion fluids and investigate the effects of different plasma parameters such as the fractional ion temperature and normalized ion acoustic speed on all three kinds of harmonic generation.

  7. Probabilistic Harmonic Modeling of Wind Power Plants

    DEFF Research Database (Denmark)

    Guest, Emerson; Jensen, Kim H.; Rasmussen, Tonny Wederberg

    2017-01-01

    A probabilistic sequence domain (SD) harmonic model of a grid-connected voltage-source converter is used to estimate harmonic emissions in a wind power plant (WPP) comprised of Type-IV wind turbines. The SD representation naturally partitioned converter generated voltage harmonics into those...... with deterministic phase and those with probabilistic phase. A case study performed on a string of ten 3MW, Type-IV wind turbines implemented in PSCAD was used to verify the probabilistic SD harmonic model. The probabilistic SD harmonic model can be employed in the planning phase of WPP projects to assess harmonic...

  8. Conductivity oscillations in 2D superlattice with non-harmonical dispersion law under non-quantizing electric and magnetic fields (in Russian)

    OpenAIRE

    Shmelev, Gennady

    2012-01-01

    We calculate the current density in a semiconductor superlattice with parabolic miniband under crossed non-quantizing electric and magnetic fields. The Corbino disk geometry is considered. The current-voltage curve contains oscillations with period proportional to the magnetic field. The possibility is shown of the negative absolute conductivity. The Ampere-Gauss characteristics also contain overshoots under high enough electric fields. In all cases, the peaks smear with temperature rising.

  9. Harmonic statistics

    Energy Technology Data Exchange (ETDEWEB)

    Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

    2017-05-15

    The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

  10. Transient state work fluctuation theorem for a classical harmonic ...

    Indian Academy of Sciences (India)

    theorem for a classical harmonic oscillator coupled linearly to a harmonic bath. Because of the coupling to the bath, the system becomes dissipative. We start from a Hamiltonian description for the system plus the harmonic heat bath and then the system is driven by an external agent for a time period of τ for a series. 666.

  11. Solution of the Skyrme-Hartree-Fock-Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) HFODD (v2.73y): A new version of the program

    Science.gov (United States)

    Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.

    2017-07-01

    We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code HFBTHO, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.

  12. Sums of Generalized Harmonic Series

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 9. Sums of Generalized Harmonic Series: For Kids from Five to Fifteen. Zurab Silagadze. General Article Volume 20 Issue 9 September 2015 pp 822-843 ... Keywords. Riemann zeta function; integral representation; Basel problem.

  13. Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics

    Science.gov (United States)

    Voros, A.

    1989-01-01

    It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

  14. Harmonic Analysis

    Indian Academy of Sciences (India)

    Harish-Chandra, Gelfand and several other mathematicians and physicists, group-theoretic harmonic analysis is a flourishing industry today paving the way to new developments in the con- text of noncompact Lie groups as well as quantum groups. Since B(n, z) = zn the expansion (3) suggests a link between Fourier series.

  15. Harmonic Analysis

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 10. Harmonic Analysis Fourier Series and Beyond. K R Parthasarathy. Book Review Volume 1 Issue 10 October 1996 pp 87-91. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/10/0087-0091 ...

  16. Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators

    Science.gov (United States)

    Munoz, R.; Gonzalez-Garcia, G.; Izquierdo-De La Cruz, E.; Fernandez-Anaya, G.

    2011-01-01

    A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present…

  17. Experimental observation of a theoretically predicted nonlinear sleep spindle harmonic in human EEG.

    Science.gov (United States)

    Abeysuriya, R G; Rennie, C J; Robinson, P A; Kim, J W

    2014-10-01

    To investigate the properties of a sleep spindle harmonic oscillation previously predicted by a theoretical neural field model of the brain. Spindle oscillations were extracted from EEG data from nine subjects using an automated algorithm. The power and frequency of the spindle oscillation and the harmonic oscillation were compared across subjects. The bicoherence of the EEG was calculated to identify nonlinear coupling. All subjects displayed a spindle harmonic at almost exactly twice the frequency of the spindle. The power of the harmonic scaled nonlinearly with that of the spindle peak, consistent with model predictions. Bicoherence was observed at the spindle frequency, confirming the nonlinear origin of the harmonic oscillation. The properties of the sleep spindle harmonic were consistent with the theoretical modeling of the sleep spindle harmonic as a nonlinear phenomenon. Most models of sleep spindle generation are unable to produce a spindle harmonic oscillation, so the observation and theoretical explanation of the harmonic is a significant step in understanding the mechanisms of sleep spindle generation. Unlike seizures, sleep spindles produce nonlinear effects that can be observed in healthy controls, and unlike the alpha oscillation, there is no linearly generated harmonic that can obscure nonlinear effects. This makes the spindle harmonic a good candidate for future investigation of nonlinearity in the brain. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

  18. Perturbative Semiclassical Trace Formulae for Harmonic Oscillators

    DEFF Research Database (Denmark)

    Møller-Andersen, Jakob; Ögren, Magnus

    2015-01-01

    U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...... the conclusion that the gross structure of the quantum spectrum is determined from only classical circular and diameter orbits for this class of systems....

  19. Sobolev spaces associated to the harmonic oscillator

    Indian Academy of Sciences (India)

    Author Affiliations. B Bongioanni1 J L Torrea2. Departamento de Matemática, Facultad de Ingeniería Qímica, Universidad Nacional del Litoral, and Instituto de Matemática Aplicada del Litoral, Santa Fe (3000), Argentina; Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de Madrid, Spain ...

  20. Third Harmonic Mechanism in Complex Plasmonic Fano Structures.

    Science.gov (United States)

    Metzger, Bernd; Schumacher, Thorsten; Hentschel, Mario; Lippitz, Markus; Giessen, Harald

    2014-06-18

    We perform third harmonic spectroscopy of dolmen-type nanostructures, which exhibit plasmonic Fano resonances in the near-infrared. Strong third harmonic emission is predominantly radiated close to the low energy peak of the Fano resonance. Furthermore, we find that the third harmonic polarization of the subradiant mode interferes destructively and diminishes the nonlinear signal in the far-field. By comparing the experimental third harmonic spectra with finite element simulations and an anharmonic oscillator model, we find strong indications that the source of the third harmonic is the optical nonlinearity of the bare gold enhanced by the resonant plasmonic polarization.

  1. Harmonic analysis

    CERN Document Server

    Helson, Henry

    2010-01-01

    This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.

  2. Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

    Science.gov (United States)

    Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

    2017-11-01

    We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton

  3. Brownian parametric oscillators

    Science.gov (United States)

    Zerbe, Christine; Jung, Peter; Hänggi, Peter

    1994-05-01

    We discuss the stochastic dynamics of dissipative, white-noise-driven Floquet oscillators, characterized by a time-periodic stiffness. Thus far, little attention has been paid to these exactly solvable nonstationary systems, although they carry a rich potential for several experimental applications. Here, we calculate and discuss the mean values and variances, as well as the correlation functions and the Floquet spectrum. As one main result, we find for certain parameter values that the fluctuations of the position coordinate are suppressed as compared to the equilibrium value of a harmonic oscillator (parametric squeezing).

  4. Phononic High Harmonic Generation

    OpenAIRE

    Ganesan, Adarsh; Do, Cuong; Seshia, Ashwin A.

    2016-01-01

    This paper reports the first experimental evidence for phononic low-order to high-order harmonic conversion leading to high harmonic generation. Similar to parametric resonance, phononic high harmonic generation is also mediated by a threshold dependent instability of a driven phonon mode. Once the threshold for instability is met, a cascade of harmonic generation processes is triggered. Firstly, the up-conversion of first harmonic phonons into second harmonic phonons is established. Subseque...

  5. Transient state work fluctuation theorem for a classical harmonic ...

    Indian Academy of Sciences (India)

    Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...

  6. Second and third harmonic waves excited by focused Gaussian beams.

    Science.gov (United States)

    Levy, Uri; Silberberg, Yaron

    2015-10-19

    Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1).

  7. Tomography on f-oscillators

    Science.gov (United States)

    Dudinets, I. V.; Man’ko, V. I.; Marmo, G.; Zaccaria, F.

    2017-11-01

    Symplectic tomographies of classical and quantum states are shortly reviewed. The concept of nonlinear f-oscillators and their properties are recalled. The tomographic probability representations of oscillator coherent states and the problem of entanglement are then discussed. The entanglement of even and odd f-coherent states is evaluated by the linear entropy.

  8. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

    Science.gov (United States)

    Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

    2012-01-01

    We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution

  9. HARMONIC DRIVE SELECTION

    Directory of Open Access Journals (Sweden)

    Piotr FOLĘGA

    2014-03-01

    Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.

  10. Mathematical simulation of a gas flow in the vicinity of the open end of a tube for harmonic oscillations of a piston at the resonance frequency at the other end of the tube

    Science.gov (United States)

    Bulovich, S. V.

    2017-11-01

    The structure of the gas flow in the vicinity of the open end of a tube for the oscillating gas flow caused by piston oscillations at the first resonance frequency at the other end of the tube has been determined by numerical integration of the Navier-Stokes equations using the ANSYS FLUENT program package. For the variant of the tube with an infinitely long flange and a sharp edge, the influence of the piston displacement amplitude on the gas flow rate in the tube is investigated, and the phases of gas inflow and outflow during the period of oscillation have been determined.

  11. Resonant second harmonic generation of a Gaussian electromagnetic beam in a collisional magnetoplasma

    Science.gov (United States)

    Kaur, Sukhdeep; Sharma, A. K.; Salih, Hyder A.

    2009-04-01

    Second harmonic generation of a right circularly polarized Gaussian electromagnetic beam in a magnetized plasma is investigated. The beam causes Ohmic heating of electrons and subsequent redistribution of the plasma, leading to self-defocusing. The radial density gradient, in conjunction with the oscillatory electron velocity, produces density oscillation at the wave frequency. The density oscillation beats with the oscillatory velocity to produce second harmonic current density, giving rise to resonant second harmonic radiation when the wave frequency is one-third of electron cyclotron frequency. The second harmonic field has azimuthal dependence as exp(iθ). The self-defocusing causes a reduction in the efficiency of harmonic generation.

  12. Harmonic factors in the perception of tonal melodies

    NARCIS (Netherlands)

    Povel, D.J.L.; Jansen, E.L.

    2002-01-01

    By common assumption, the first step in processing a tonal melody consists in setting up the appropriate metrical and harmonic frames required for the mental representation of the sequence of tones. Focusing on the generation of a harmonic frame, this study aims (a) to discover the factors that

  13. Small Oscillations via Conservation of Energy

    Science.gov (United States)

    Troy, Tia; Reiner, Megan; Haugen, Andrew J.; Moore, Nathan T.

    2017-01-01

    The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small…

  14. Harmonic polynomials, hyperspherical harmonics, and atomic spectra

    Science.gov (United States)

    Avery, John Scales

    2010-01-01

    The properties of monomials, homogeneous polynomials and harmonic polynomials in d-dimensional spaces are discussed. The properties are shown to lead to formulas for the canonical decomposition of homogeneous polynomials and formulas for harmonic projection. Many important properties of spherical harmonics, Gegenbauer polynomials and hyperspherical harmonics follow from these formulas. Harmonic projection also provides alternative ways of treating angular momentum and generalised angular momentum. Several powerful theorems for angular integration and hyperangular integration can be derived in this way. These purely mathematical considerations have important physical applications because hyperspherical harmonics are related to Coulomb Sturmians through the Fock projection, and because both Sturmians and generalised Sturmians have shown themselves to be extremely useful in the quantum theory of atoms and molecules.

  15. Thirring model partition functions and harmonic differentials

    Science.gov (United States)

    Freedman, D. Z.; Pilch, K.

    1988-10-01

    The partition function of the Thirring model on a Riemann surface is calculated using the representation of the model as a fermion interacting with an auxiliary vector potential. The Hodge decomposition of the potential is used and the integral over the harmonic forms is shown to reproduce exactly the soliton sum in the bosonic version of the theory.

  16. Entanglement between Collective Operators in a Linear Harmonic Chain

    OpenAIRE

    Kofler, Johannes; Vedral, Vlatko; Kim, Myungshik S.; Brukner, Caslav

    2005-01-01

    We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not e...

  17. Small oscillations via conservation of energy

    Science.gov (United States)

    Troy, Tia; Reiner, Megan; Haugen, Andrew J.; Moore, Nathan T.

    2017-11-01

    The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small oscillations about the static equilibrium state. The problem was developed and implemented in a standard University Physics course at Winona State University.

  18. Quantum dissipative effect of one dimension coupled anharmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Sulaiman, A. [Badan Pengkajian dan Penerapan Teknologi, BPPT Bld. II (19thfloor), Jl. M.H. Thamrin 8, Jakarta 10340 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10, Bandung 40132 (Indonesia); Zen, Freddy P. [Theoretical Physics Laboratory (THEPI), Department of Physics, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Jl. Ganesha 10, Bandung 40132 (Indonesia)

    2015-04-16

    Quantum dissipative effect of one dimension coupled anharmonic oscillator is investigated. The systems are two coupled harmonic oscillator with the different masses. The dissipative effect is studied based on the quantum state diffusion formalism. The result show that the anharmonic effect increase the amplitude but the lifetime of the oscillation depend on the damping coefficient and do not depend on the temperature.

  19. Harmonics of circadian gene transcription in mammals.

    Directory of Open Access Journals (Sweden)

    Michael E Hughes

    2009-04-01

    Full Text Available The circadian clock is a molecular and cellular oscillator found in most mammalian tissues that regulates rhythmic physiology and behavior. Numerous investigations have addressed the contribution of circadian rhythmicity to cellular, organ, and organismal physiology. We recently developed a method to look at transcriptional oscillations with unprecedented precision and accuracy using high-density time sampling. Here, we report a comparison of oscillating transcription from mouse liver, NIH3T3, and U2OS cells. Several surprising observations resulted from this study, including a 100-fold difference in the number of cycling transcripts in autonomous cellular models of the oscillator versus tissues harvested from intact mice. Strikingly, we found two clusters of genes that cycle at the second and third harmonic of circadian rhythmicity in liver, but not cultured cells. Validation experiments show that 12-hour oscillatory transcripts occur in several other peripheral tissues as well including heart, kidney, and lungs. These harmonics are lost ex vivo, as well as under restricted feeding conditions. Taken in sum, these studies illustrate the importance of time sampling with respect to multiple testing, suggest caution in use of autonomous cellular models to study clock output, and demonstrate the existence of harmonics of circadian gene expression in the mouse.

  20. Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions

    OpenAIRE

    Mustafa, M. T.

    2012-01-01

    For Riemannian manifolds $M$ and $N$ , admitting a submersion $\\varphi $ with compact fibres, we introduce the projection of a function via its decomposition intohorizontal and vertical components. By comparing the Laplacians on $M$ and $N$ , we determine conditions under which a harmonic function on $U={\\varphi }^{-1}(V)\\subset M$ projects down, via its horizontal component, to a harmonic function on $V\\subset N$ .

  1. Modelling of UWB Antenna Perturbed by Human Phantom in Spherical Harmonics Space

    DEFF Research Database (Denmark)

    Mhedhbi, Meriem; Avrillon, Stephane; Pedersen, Troels

    2014-01-01

    In this paper we study how the antenna radiation pattern is perturbed in the presence of a human phantom in terms of changes in the coefficients of the spherical harmonic antenna representation. The spherical harmonic basis allows for a compact representation of the antenna pattern which is attra......In this paper we study how the antenna radiation pattern is perturbed in the presence of a human phantom in terms of changes in the coefficients of the spherical harmonic antenna representation. The spherical harmonic basis allows for a compact representation of the antenna pattern which...... is attractive for simulation purposes. We propose a simple model for the spherical harmonics coefficients allowing to predict the antenna behavior perturbed by a human phantom. The model is based on knowledge of the spherical harmonic coefficients of antenna in free space and the antenna-phantom distance....

  2. Harmonic sums and polylogarithms generated by cyclotomic polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2011-05-15

    The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincare-iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of N is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument x=1, resp., for the cyclotomic harmonic sums at N{yields}{infinity}, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight w=1,2 sums up to cyclotomy l=20. (orig.)

  3. Adaptive harmonic analysis

    NARCIS (Netherlands)

    Heemink, Arnold; de Jong, B.; Prins, Harrie

    1991-01-01

    In this paper we describe a new approach to the harmonic analysis of the tide. For a number of reasons the harmonic constants are not really constant but vary slowly in time. Therefore, we introduce a narrow-band noise process to model the time-varying behaviour of these harmonic parameters.

  4. Primer on coupling collective electronic oscillations to nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Solem, J.C.; Biedenharn, L.C. Jr.

    1987-07-01

    On the basis of simple heuristic models, we show that atomic electrons can amplify fields observed at the nucleus, generate harmonics, and drive higher multipolarities. Considered is a model with the nucleus at the focus of a uniformly charged ellipsoid. It amplifies an oscillating external electric field and produces an oscillating electric-field gradient but no higher derivatives. The electric field has only odd harmonics and the electric-field gradient has only even harmonics. There is an optimum intensity for driving each harmonic. Commented on is the relevance of these results to the U/sup 235/ experiment and to the gamma-ray laser.

  5. Harmonic function theory

    CERN Document Server

    Axler, Sheldon; Ramey, Wade

    2013-01-01

    This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.

  6. Calculation and manipulation of the chirp rates of high-order harmonics

    OpenAIRE

    Murakami, M.; Mauritsson, Johan; L'Huillier, Anne; Schafer, KJ; Gaarde, Mette

    2005-01-01

    We calculate the linear chirp rates of high-order harmonics in argon, generated by intense, 810 nm laser pulses, and explore the dependence of the chirp rate on harmonic order, driving laser intensity, and pulse duration. By using a time-frequency representation of the harmonic fields we can identify several different linear chirp contributions. to the plateau harmonics. Our results, which are based on numerical integration of the time-dependent Schrodinger equation, are in good agreement wit...

  7. High harmonic phase in molecular nitrogen

    Energy Technology Data Exchange (ETDEWEB)

    McFarland, Brian K.

    2009-10-17

    Electronic structure in atoms and molecules modulates the amplitude and phase of high harmonic generation (HHG). We report measurements of the high harmonic spectral amplitude and phase in N{sub 2}. The phase is measured interferometrically by beating the N{sub 2} harmonics with those of an Ar reference oscillator in a gas mixture. A rapid phase shift of 0.2{pi} is observed in the vicinity of the HHG spectral minimum, where a shift of {pi} had been presumed [J. Itatani et al., Nature 432, 867 (2004)]. We compare the phase measurements to a simulation of the HHG recombination step in N{sub 2} that is based on a simple interference model. The results of the simulation suggest that modifications beyond the simple interference model are needed to explain HHG spectra in molecules.

  8. 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.

  9. A Passive Harmonic Tag for Humidity Sensing

    OpenAIRE

    Antonio Lazaro; Ramon Villarino; David Girbau

    2014-01-01

    This paper describes a passive harmonic tag for radio frequency identification (RFID) and wireless sensor applications. The tag uses a dual polarized UHF patch antenna as an input antenna. One of the outputs is connected to a frequency doubler, which consists of a Schottky diode with its output connected to a patch tuned at twice the input frequency. The other output of the input antenna feeds a DC power harvested converter that drives an oscillator which modulates its output signal by contro...

  10. Decay of oscillating universes

    Science.gov (United States)

    Mithani, Audrey Todhunter

    2016-08-01

    It has been suggested by Ellis et al that the universe could be eternal in the past, without beginning. In their model, the "emergent universe'' exists forever in the past, in an "eternal'' phase before inflation begins. We will show that in general, such an "eternal'' phase is not possible, because of an instability due to quantum tunneling. One candidate model, the "simple harmonic universe'' has been shown by Graham et al to be perturbatively stable; we find that it is unstable with respect to quantum tunneling. We also investigate the stability of a distinct oscillating model in loop quantum cosmology with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to collapse by quantum tunneling to zero size. In addition, we investigate the effect of vacuum corrections, due to the trace anomaly and the Casimir effect, on the stability of an oscillating universe with respect to decay by tunneling to the singularity. We find that these corrections do not generally stabilize an oscillating universe. Finally, we determine the decay rate of the oscillating universe. Although the wave function of the universe lacks explicit time dependence in canonical quantum cosmology, time evolution may be present implicitly through the semiclassical superspace variables, which themselves depend on time in classical dynamics. Here, we apply this approach to the simple harmonic universe, by extending the model to include a massless, minimally coupled scalar field φ which has little effect on the dynamics but can play the role of a "clock''.

  11. Scleronomic holonomic constraints and conservative nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Munoz, R; Gonzalez-Garcia, G; Izquierdo-De La Cruz, E Izquierdo-De La [Universidad Autonoma de la Ciudad de Mexico, Centro Historico, Fray Servando Teresa de Mier 92, Col Centro, Del Cuauhtemoc, Mexico DF, CP 06080 (Mexico); Fernandez-Anaya, G, E-mail: rodrigo.munoz@uacm.edu.mx, E-mail: gggharper@gmail.com, E-mail: erickidc@gmail.com, E-mail: guillermo.fernandez@uia.mx [Universidad Iberoamericana, Departamento de Fisica y Matematicas, Prolongacon Paseo de de la Reforma 880, Col Lomas de Santa Fe, Del Alvaro Obregn, Mexico DF, CP 01219 (Mexico)

    2011-05-15

    A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present cases in which the effective potential acting on the bead is not analytical around a minimum. The small oscillation approximation cannot be applied to such pathological cases. Nonetheless, these latter instances are studied with other standard techniques.

  12. Ladder operators for isospectral oscillators

    Science.gov (United States)

    Seshadri, S.; Balakrishnan, V.; Lakshmibala, S.

    1998-02-01

    We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed "distorted" Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the nonlocal operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.

  13. Coherent harmonic production using a two-section undulator FEL

    Energy Technology Data Exchange (ETDEWEB)

    Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others

    1995-12-31

    We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.

  14. Periodic motions and resonances of impact oscillators

    Science.gov (United States)

    Dyskin, Arcady V.; Pasternak, Elena; Pelinovsky, Efim

    2012-06-01

    Bilinear oscillators - the oscillators whose springs have different stiffnesses in compression and tension - model a wide range of phenomena. A limiting case of bilinear oscillator with infinite stiffness in compression - the impact oscillator - is studied here. We investigate a special set of impact times - the eigenset, which corresponds to the solution of the homogeneous equation, i.e. the oscillator without the driving force. We found that this set and its subsets are stable with respect to variation of initial conditions. Furthermore, amongst all periodic sets of impact times with the period commensurate with the period of driving force, the eigenset is the only one which can support resonances, in particular the multi-'harmonic' resonances. Other resonances should produce non-periodic sets of impact times. This funding indicates that the usual simplifying assumption [e.g., S.W. Shaw, P.J. Holmes, A periodically forced piecewise linear oscillator, Journal of Sound and Vibration 90 (1983) 129-155] that the times between impacts are commensurate with the period of the driving force does not always hold. We showed that for the first sub-'harmonic resonance' - the resonance achieved on a half frequency of the main resonance - the set of impact times is asymptotically close to the eigenset. The envelope of the oscillations in this resonance increases as a square root of time, opposite to the linear increase characteristic of multi-'harmonic' resonances.

  15. Neurodynamic oscillators

    Science.gov (United States)

    Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz

    1995-01-01

    Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.

  16. Hidden symmetries of deformed oscillators

    Directory of Open Access Journals (Sweden)

    Sergey Krivonos

    2017-11-01

    Full Text Available We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schrödinger algebra, these equations reduce to a system of ordinary harmonic oscillators. We provide two clarifying examples of such deformed oscillators: one system invariant under SO(2,3 transformations, and another system featuring G2(2 symmetry. The construction of invariant actions requires adding semi-dynamical degrees of freedom; we illustrate the algorithm with the two examples mentioned.

  17. The non-local oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Maccari, A. [Istituto Tecnico `G. Cardano`, Monterotondo, Rome (Italy)

    1996-08-01

    The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kitta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.

  18. Soft-x-ray harmonic comb from relativistic electron spikes.

    Science.gov (United States)

    Pirozhkov, A S; Kando, M; Esirkepov, T Zh; Gallegos, P; Ahmed, H; Ragozin, E N; Faenov, A Ya; Pikuz, T A; Kawachi, T; Sagisaka, A; Koga, J K; Coury, M; Green, J; Foster, P; Brenner, C; Dromey, B; Symes, D R; Mori, M; Kawase, K; Kameshima, T; Fukuda, Y; Chen, L; Daito, I; Ogura, K; Hayashi, Y; Kotaki, H; Kiriyama, H; Okada, H; Nishimori, N; Imazono, T; Kondo, K; Kimura, T; Tajima, T; Daido, H; Rajeev, P; McKenna, P; Borghesi, M; Neely, D; Kato, Y; Bulanov, S V

    2012-03-30

    We demonstrate a new high-order harmonic generation mechanism reaching the "water window" spectral region in experiments with multiterawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving μJ/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.

  19. The electronic system for mechanical oscillation parameters registration

    Directory of Open Access Journals (Sweden)

    Bulavin L. A.

    2008-08-01

    Full Text Available On the basis of the 8-bit microcontroller Microchip PIC16F630 the digital electronic device for harmonic oscillation parameters registration was developed. The device features are simple electric circuit and high operating speed (response time is less than 10 microseconds. The relevant software for the computer-controlled recording of harmonic oscillation parameters was designed. The device can be used as a part of the experimental setup for consistent fluids rheological parameters measurements.

  20. Harmonic and applied analysis from groups to signals

    CERN Document Server

    Mari, Filippo; Grohs, Philipp; Labate, Demetrio

    2015-01-01

    This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction ...

  1. Oscillations of a polarizable vacuum

    Directory of Open Access Journals (Sweden)

    James G. Gilson

    1991-01-01

    Full Text Available A classical basis for one-dimensional Schrödinger quantum theory is constructed from simple vacuum polarization harmonic oscillators within standard stochastic theory. The model is constructed on a two-dimensional phase configuration surface with phase velocity vectors that have a speed of light zitterbewegung behaviour character. The system supplies a natural Hermitian scalar product describing probability density which is derived from angular momentum considerations. The generality of the model which is extensive is discussed.

  2. Quantum Oscillators

    CERN Document Server

    Blaise, Paul

    2011-01-01

    An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other p

  3. Chemical Oscillations

    Indian Academy of Sciences (India)

    processes at the cellular level like the glycolytic pathway, peroxi- dase-catalysed reaction or the biosynthesis of certain proteins. A systematic study of oscillating chemical reactions is of consider- able interest, since these oscillating reactions can be used as prototype examples of the behaviours possible in reactions gov-.

  4. Erratum to “Ultra-Broadband Photonic Harmonic Mixer Based on Optical Comb Generation”

    DEFF Research Database (Denmark)

    Zhao, Ying; Pang, Xiaodan; Deng, Lei

    2012-01-01

    We propose a novel photonic harmonic mixer operating at frequencies up to the millimeter-wave (MMW) band. By combining a broadband fiber-wireless signal with highorder harmonics of a fundamental local oscillator in an optical frequency comb generator, frequency down-conversion can be implemented ...

  5. A Spectrum Sensing Technique for Cognitive Radios in the Presence of Harmonic Images

    NARCIS (Netherlands)

    Moseley, N.A.; Klumperink, Eric A.M.; Nauta, Bram

    2008-01-01

    Abstract—Harmonic downmixing is an important effect that must be taken into account when performing sensitive spectrum sensing using direct-conversion receivers. When the local oscillator waveform contains harmonics of the fundamental frequency, the quadrature mixer in the receiver will downconvert

  6. Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

    OpenAIRE

    Kfir Kuchuk; Uri Sivan

    2015-01-01

    Summary The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic...

  7. Geometric phases, evolution loops and generalized oscillator potentials

    Science.gov (United States)

    Fernandez, David J.

    1995-01-01

    The geometric phases for dynamical processes where the evolution operator becomes the identity (evolution loops) are studied. The case of time-independent Hamiltonians with equally spaced energy levels is considered; special emphasis is made on the potentials having the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and their recently found coherent states.

  8. Dynamics of 'quantumness' measures in the decohering harmonic ...

    Indian Academy of Sciences (India)

    2016-07-26

    Jul 26, 2016 ... Abstract. We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given ...

  9. Exact complex integrals in two dimensions for shifted harmonic ...

    Indian Academy of Sciences (India)

    We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.

  10. Manipulating single enzymes by an external harmonic force

    DEFF Research Database (Denmark)

    Lomholt, Michael A; Urbakh, Michael; Metzler, Ralf

    2007-01-01

    We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzym...

  11. Harmonizing Tort Law

    NARCIS (Netherlands)

    W.H. van Boom (Willem)

    2009-01-01

    textabstractThis paper presents a review of the literature on comparative tort law and economics. It pays special attention to the economics arguments against and in favour of harmonization of tort law in Europe.

  12. Harmonic vibro-acoustography.

    Science.gov (United States)

    Chen, Shigao; Kinnick, Randall R; Greenleaf, James F; Fatemi, Mostafa

    2007-07-01

    Vibro-acoustography is an imaging method that uses the radiation force of two interfering ultrasound beams of slightly different frequency to probe an object. An image is made using the acoustic emission resulted from the object vibration at the difference frequency. In this paper, the feasibility of imaging objects at twice the difference frequency (harmonic acoustic emission) is studied. Several possible origins of harmonic acoustic emission are explored. As an example, it is shown that microbubbles close to resonance can produce significant harmonic acoustic emission due to its high nonlinearity. Experiments demonstrate that, compared to the fundamental acoustic emission, harmonic acoustic emission greatly improves the contrast between microbubbles and other objects in vibro-acoustography (an improvement of 17-23 dB in these experiments). Applications of this technique include imaging the nonlinearity of the object and selective detection of microbubbles for perfusion imaging. The impact of microbubble destruction during the imaging process also is discussed.

  13. Fibonacci oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Arik, M. (Istanbul Technical Univ. (Turkey). Dept. of Mathematics Bogazici Univ., Istanbul (Turkey). Dept. of Physics); Demircan, E.; Turgut, T. (Texas Univ., Austin, TX (United States). Dept. of Physics); Ekinci, L.; Mungan, M. (Bogazici Univ., Istanbul (Turkey). Dept. of Physics)

    1992-07-01

    We discuss the properties of oscillators whose spectrum is given by a generalized Fibonacci sequence. The properties include: Invariance under the unitary quantum group, generalized angular momentum, coherent states and difference calculus, relativistic interpretation. (orig.).

  14. 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.

  15. Entanglement of higher-derivative oscillators in holographic systems

    Energy Technology Data Exchange (ETDEWEB)

    Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)

    2017-05-15

    We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.

  16. Harmonic Brain Modes: A Unifying Framework for Linking Space and Time in Brain Dynamics.

    Science.gov (United States)

    Atasoy, Selen; Deco, Gustavo; Kringelbach, Morten L; Pearson, Joel

    2017-09-01

    A fundamental characteristic of spontaneous brain activity is coherent oscillations covering a wide range of frequencies. Interestingly, these temporal oscillations are highly correlated among spatially distributed cortical areas forming structured correlation patterns known as the resting state networks, although the brain is never truly at "rest." Here, we introduce the concept of harmonic brain modes-fundamental building blocks of complex spatiotemporal patterns of neural activity. We define these elementary harmonic brain modes as harmonic modes of structural connectivity; that is, connectome harmonics, yielding fully synchronous neural activity patterns with different frequency oscillations emerging on and constrained by the particular structure of the brain. Hence, this particular definition implicitly links the hitherto poorly understood dimensions of space and time in brain dynamics and its underlying anatomy. Further we show how harmonic brain modes can explain the relationship between neurophysiological, temporal, and network-level changes in the brain across different mental states ( wakefulness, sleep, anesthesia, psychedelic). Notably, when decoded as activation of connectome harmonics, spatial and temporal characteristics of neural activity naturally emerge from the interplay between excitation and inhibition and this critical relation fits the spatial, temporal, and neurophysiological changes associated with different mental states. Thus, the introduced framework of harmonic brain modes not only establishes a relation between the spatial structure of correlation patterns and temporal oscillations (linking space and time in brain dynamics), but also enables a new dimension of tools for understanding fundamental principles underlying brain dynamics in different states of consciousness.

  17. Coupled Person Orientation Estimation and Appearance Modeling using Spherical Harmonics

    NARCIS (Netherlands)

    Liem, M.C.; Gavrila, D.M.

    2014-01-01

    We present a novel approach for the estimation of a person's overall body orientation, 3D shape and texture, from overlapping cameras. A distinguishing aspect of our approach is the use of spherical harmonics for 3D shape- and texture-representation; it offers a compact, low-dimensional

  18. Quality of potential harmonics expansion method for dilute Bose ...

    Indian Academy of Sciences (India)

    Abstract. We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correla- tions for dilute Bose–Einstein condensates. .... in coupled angular momentum representation. Now Y[K](Ω) must be totally sym- metric under any pair ...

  19. Prominence Oscillations

    Directory of Open Access Journals (Sweden)

    Iñigo Arregui

    2012-04-01

    Full Text Available Prominences are intriguing, but poorly understood, magnetic structures of the solar corona. The dynamics of solar prominences has been the subject of a large number of studies, and of particular interest is the study of prominence oscillations. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences that are difficult to measure by direct means. Here, we review the observational information gathered about prominence oscillations as well as the theoretical models developed to interpret small amplitude oscillations and their temporal and spatial attenuation. Finally, several prominence seismology applications are presented.

  20. Fast Harmonic Chirp Summation

    DEFF Research Database (Denmark)

    Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm; Jensen, Jesper Rindom

    2017-01-01

    The harmonic chirp signal model has only very recently been in- troduced for modelling approximately periodic signals with a time- varying fundamental frequency. A number of estimators for the pa- rameters of this model have already been proposed, but they are ei- ther inaccurate, non-robust to n......The harmonic chirp signal model has only very recently been in- troduced for modelling approximately periodic signals with a time- varying fundamental frequency. A number of estimators for the pa- rameters of this model have already been proposed, but they are ei- ther inaccurate, non......-robust to noise, or very computationally inten- sive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the liter- ature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also...

  1. Second harmonic generation imaging

    CERN Document Server

    2013-01-01

    Second-harmonic generation (SHG) microscopy has shown great promise for imaging live cells and tissues, with applications in basic science, medical research, and tissue engineering. Second Harmonic Generation Imaging offers a complete guide to this optical modality, from basic principles, instrumentation, methods, and image analysis to biomedical applications. The book features contributions by experts in second-harmonic imaging, including many pioneering researchers in the field. Written for researchers at all levels, it takes an in-depth look at the current state of the art and possibilities of SHG microscopy. Organized into three sections, the book: Provides an introduction to the physics of the process, step-by-step instructions on how to build an SHG microscope, and comparisons with related imaging techniques Gives an overview of the capabilities of SHG microscopy for imaging tissues and cells—including cell membranes, muscle, collagen in tissues, and microtubules in live cells—by summarizing experi...

  2. Poetic representation

    DEFF Research Database (Denmark)

    Wulf-Andersen, Trine Østergaard

    2012-01-01

    be written up and disseminated. The article takes a methodological focus, considering general aims and methods of the research project, before turning to the elaboration on how poetic representations have been constructed and employed as a vehicle for certain kinds of participation, representation......, and dialogue, of situated participants. The article includes a lengthy example of a poetic representation of one participant’s story, and the author comments on the potentials of ‘doing’ poetic representations as an example of writing in ways that challenges what sometimes goes unasked in participative social...

  3. General Criterion for Harmonicity

    Science.gov (United States)

    Proesmans, Karel; Vandebroek, Hans; Van den Broeck, Christian

    2017-10-01

    Inspired by Kubo-Anderson Markov processes, we introduce a new class of transfer matrices whose largest eigenvalue is determined by a simple explicit algebraic equation. Applications include the free energy calculation for various equilibrium systems and a general criterion for perfect harmonicity, i.e., a free energy that is exactly quadratic in the external field. As an illustration, we construct a "perfect spring," namely, a polymer with non-Gaussian, exponentially distributed subunits which, nevertheless, remains harmonic until it is fully stretched. This surprising discovery is confirmed by Monte Carlo and Langevin simulations.

  4. Harmonic arbitrary waveform generator

    Energy Technology Data Exchange (ETDEWEB)

    Roberts, Brock Franklin

    2017-11-28

    High frequency arbitrary waveforms have applications in radar, communications, medical imaging, therapy, electronic warfare, and charged particle acceleration and control. State of the art arbitrary waveform generators are limited in the frequency they can operate by the speed of the Digital to Analog converters that directly create their arbitrary waveforms. The architecture of the Harmonic Arbitrary Waveform Generator allows the phase and amplitude of the high frequency content of waveforms to be controlled without taxing the Digital to Analog converters that control them. The Harmonic Arbitrary Waveform Generator converts a high frequency input, into a precision, adjustable, high frequency arbitrary waveform.

  5. Booster Double Harmonic Setup Notes

    Energy Technology Data Exchange (ETDEWEB)

    Gardner, C. J. [Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.

    2015-02-17

    The motivation behind implementing a booster double harmonic include the reduced transverse space charge force from a reduced peak beam current and reduced momentum spread of the beam, both of which can be achieved from flattening the RF bucket. RF capture and acceleration of polarized protons (PP) is first set up in the single harmonic mode with RF harmonic h=1. Once capture and acceleration have been set up in the single harmonic mode, the second harmonic system is brought on and programmed to operate in concert with the single harmonic system.

  6. Symmetric functions and B sub N -invariant spherical harmonics

    CERN Document Server

    Dunkl, C F

    2002-01-01

    The wavefunctions of a quantum isotropic harmonic oscillator modified by reflecting barriers at the coordinate planes in N-dimensional space can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type weight function on the sphere. Their analysis is carried out by means of differential-difference operators. The symmetries of this system involve the Weyl group of type B, generated by permutations and changes of sign of the coordinates. A new basis for symmetric functions as well as an explicit transition matrix to the monomial basis is constructed. This basis leads to a basis for invariant spherical harmonics. The determinant of the Gram matrix for the basis in the natural inner product over the sphere is evaluated. When the underlying parameter is specialized to zero, the basis consists of ordinary spherical harmonics with cube group symmetry, as used for wavefunctions of electrons in crystals. The harmonic oscillator can also be considered as a degenerate in...

  7. Chromosperic oscillations

    NARCIS (Netherlands)

    Rutten, R.J.

    1999-01-01

    This review concentrates on the quiet-Sun chromosphere. Its internetwork areas are dynamically dominated by the so-called chromospheric three-minute oscillation. They are interpretationally dominated by the so-called Ca II K 2V and H 2V grains. The main points of this review are that the one

  8. Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

    Directory of Open Access Journals (Sweden)

    Kfir Kuchuk

    2015-01-01

    Full Text Available The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range.

  9. Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM.

    Science.gov (United States)

    Kuchuk, Kfir; Sivan, Uri

    2015-01-01

    The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range.

  10. Application of the mixed time-averaging semiclassical initial value representation method to complex molecular spectra

    Science.gov (United States)

    Buchholz, Max; Grossmann, Frank; Ceotto, Michele

    2017-10-01

    The recently introduced mixed time-averaging semiclassical initial value representation of the molecular dynamics method for spectroscopic calculations [M. Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 144, 094102 (2016)] is applied to systems with up to 61 dimensions, ruled by a condensed phase Caldeira-Leggett model potential. By calculating the ground state as well as the first few excited states of the system Morse oscillator, changes of both the harmonic frequency and the anharmonicity are determined. The method faithfully reproduces blueshift and redshift effects and the importance of the counter term, as previously suggested by other methods. Different from previous methods, the present semiclassical method does not take advantage of the specific form of the potential and it can represent a practical tool that opens the route to direct ab initio semiclassical simulation of condensed phase systems.

  11. Harmonic Intravascular Ultrasound

    NARCIS (Netherlands)

    M.E. Frijlink (Martijn)

    2006-01-01

    textabstractMedical ultrasound is a popular imaging modality in cardiology. Harmonic Imaging is a technique that has been shown to increase the image quality of diagnostic ultrasound at frequencies below 10 MHz. However, Intravascular Ultrasound, which is a technique to acoustically investigate

  12. Behavioral oscillation in priming: competing perceptual predictions conveyed in alternating theta-band rhythms.

    Science.gov (United States)

    Huang, Yan; Chen, Lin; Luo, Huan

    2015-02-11

    The brain constantly creates perceptual predictions about forthcoming stimuli to guide perception efficiently. Abundant studies have demonstrated that perceptual predictions modulate sensory activities depending on whether the actual inputs are consistent with one particular prediction. In real-life contexts, however, multiple and even conflicting predictions might concurrently exist to be tested, requiring a multiprediction coordination process. It remains largely unknown how multiple hypotheses are conveyed and harmonized to guide moment-by-moment perception. Based on recent findings revealing that multiple locations are sampled alternatively in various phase of attentional rhythms, we hypothesize that this oscillation-based temporal organization mechanism may also underlie the multiprediction coordination process. To address the issue, we used well established priming paradigms in combination with a time-resolved behavioral approach to investigate the fine temporal dynamics of the multiprediction harmonization course in human subjects. We first replicate classical priming effects in slowly developing trends of priming time courses. Second, after removing the typical priming patterns, we reveal a new theta-band (∼4 Hz) oscillatory component in the priming behavioral data regardless of whether the prime was masked. Third, we show that these theta-band priming oscillations triggered by congruent and incongruent primes are in an out-of-phase relationship. These findings suggest that perceptual predictions return to low-sensory areas not continuously but recurrently in a theta-band rhythm (every 200-300 ms) and that multiple predictions are dynamically coordinated in time by being conveyed in different phases of the theta-band oscillations to achieve dissociated but temporally organized neural representations. Copyright © 2015 the authors 0270-6474/15/352830-08$15.00/0.

  13. A Passive Harmonic Tag for Humidity Sensing

    Directory of Open Access Journals (Sweden)

    Antonio Lazaro

    2014-01-01

    Full Text Available This paper describes a passive harmonic tag for radio frequency identification (RFID and wireless sensor applications. The tag uses a dual polarized UHF patch antenna as an input antenna. One of the outputs is connected to a frequency doubler, which consists of a Schottky diode with its output connected to a patch tuned at twice the input frequency. The other output of the input antenna feeds a DC power harvested converter that drives an oscillator which modulates its output signal by controlling the bias point of the Schottky diode. The antenna’s output is also used as a humidity sensor. To achieve this, the antenna is loaded with an interdigital capacitor with humidity-dependent capacitance. The antenna is consequently detuned when humidity varies, and therefore the second harmonic power is received. The tag is manufactured using standard fiberglass substrate. The basic theory of harmonic tag operation is described and compared with the standard backscattering approach. Experimental results with a proof of concept using commercial components are presented.

  14. Young children's harmonic perception.

    Science.gov (United States)

    Costa-Giomi, Eugenia

    2003-11-01

    Harmony and tonality are two of the most difficult elements for young children to perceive and manipulate and are seldom taught in the schools until the end of early childhood. Children's gradual harmonic and tonal development has been attributed to their cumulative exposure to Western tonal music and their increasing experiential knowledge of its rules and principles. Two questions that are relevant to this problem are: (1) Can focused and systematic teaching accelerate the learning of the harmonic/tonal principles that seem to occur in an implicit way throughout childhood? (2) Are there cognitive constraints that make it difficult for young children to perceive and/or manipulate certain harmonic and tonal principles? A series of studies specifically addressed the first question and suggested some possible answers to the second one. Results showed that harmonic instruction has limited effects on children's perception of harmony and indicated that the drastic improvement in the perception of implied harmony noted approximately at age 9 is due to development rather than instruction. I propose that young children's difficulty in perceiving implied harmony stems from their attention behaviors. Older children have less memory constraints and more strategies to direct their attention to the relevant cues of the stimulus. Younger children focus their attention on the melody, if present in the stimulus, and specifically on its concrete elements such as rhythm, pitch, and contour rather than its abstract elements such as harmony and key. The inference of the abstract harmonic organization of a melody required in the perception of implied harmony is thus an elusive task for the young child.

  15. Mutual phase-locking of planar nano-oscillators

    Directory of Open Access Journals (Sweden)

    K. Y. Xu

    2014-06-01

    Full Text Available Characteristics of phase-locking between Gunn effect-based planar nano-oscillators are studied using an ensemble Monte Carlo (EMC method. Directly connecting two oscillators in close proximity, e.g. with a channel distance of 200 nm, only results in incoherent oscillations. In order to achieve in-phase oscillations, additional considerations must be taken into account. Two coupling paths are shown to exist between oscillators. One coupling path results in synchronization and the other results in anti-phase locking. The coupling strength through these two paths can be adjusted by changing the connections between oscillators. When two identical oscillators are in the anti-phase locking regime, fundamental components of oscillations are cancelled. The resulting output consists of purely second harmonic oscillations with a frequency of about 0.66 THz. This type of second harmonic generation is desired for higher frequency applications since no additional filter system is required. This transient phase-locking process is further analyzed using Adler's theory. The locking range is extracted, and a criterion for the channel length difference required for realizing phased arrays is obtained. This work should aid in designing nano-oscillator arrays for high power applications and developing directional transmitters for wireless communications.

  16. Harmonic Patterns in Forex Trading

    OpenAIRE

    Nemček, Sebastian

    2013-01-01

    This diploma thesis is committed to examination of validity of Harmonic Patterns in Forex trading. Scott Carney described existing and introduced new Harmonic Patterns in 1999 in his book Harmonic Trader. These patterns use the Fibonacci principle to analyze price action and to provide both bullish and bearish trading signals. The goal of this thesis is to find out whether harmonic trading strategy on selected pairs is profitable in FX market, which patterns are the most profitable and what i...

  17. FEL Oscillators

    Energy Technology Data Exchange (ETDEWEB)

    George Neil

    2003-05-12

    FEL Oscillators have been around since 1977 providing not only a test bed for the physics of Free Electron Lasers and electron/photon interactions but as a workhorse of scientific research. More than 30 FEL oscillators are presently operating around the world spanning a wavelength range from the mm region to the ultraviolet using DC and rf linear accelerators and storage rings as electron sources. The characteristics that have driven the development of these sources are the desire for high peak and average power, high micropulse energies, wavelength tunability, timing flexibility, and wavelengths that are unavailable from more conventional laser sources. Substantial user programs have been performed using such sources encompassing medicine, biology, solid state research, atomic and molecular physics, effects of non-linear fields, surface science, polymer science, pulsed laser vapor deposition, to name just a few.

  18. Euler Sums and Contour Integral Representations

    OpenAIRE

    Flajolet, Philippe; Salvy, Bruno

    1996-01-01

    This paper develops an approach to the evaluation of Euler sums involving harmonic numbers either linearly or nonlinearly. We give explicit formul{æ} for certain classes of Euler sums in terms of values of the Riemann zeta function at positive integers. The approach is based on simple contour integral representations and residue computations.

  19. Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. I. Gaussian-white case

    NARCIS (Netherlands)

    Steffen, T; Tanimura, Y

    The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by

  20. Recursive Harmonic Numbers and Binomial Coefficients

    OpenAIRE

    Maw, Aung Phone; Kyaw, Aung

    2017-01-01

    We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula for recursive harmonic numbers containing binomial coefficients is also presented.

  1. Dynamical evolution of quantum oscillators toward equilibrium.

    Science.gov (United States)

    Usha Devi, A R; Rajagopal, A K

    2009-07-01

    A pure quantum state of large number N of oscillators, interacting via harmonic coupling, evolves such that any small subsystem noscillator is found to relax in a mixed density matrix of the Boltzmann canonical form. In two oscillator stationary subsystems, intraentanglement within the "system" oscillators is found to exist when the magnitude of the squeezing parameter of the bath is comparable in magnitude with that of the coupling strength.

  2. Symmetries and conservation laws of the damped harmonic oscillator

    Indian Academy of Sciences (India)

    We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...

  3. Spatial analysis of harmonic oscillation of gypsy moth outbreak intensity

    Science.gov (United States)

    Kyle J. Haynes; Andrew M. Liebhold; Derek M. Johnson

    2009-01-01

    Outbreaks of many forest-defoliating insects are synchronous over broad geographic areas and occur with a period of approximately 10 years. Within the range of the gypsy moth in North America, however, there is considerable geographic heterogeneity in strength of periodicity and the frequency of outbreaks. Furthermore, gypsy moth outbreaks exhibit two significant...

  4. On quantum harmonic oscillator being subjected to absolute ...

    Indian Academy of Sciences (India)

    2016-12-03

    . Differentiating the relation A = πxP with respect to time, we have .... paper, is strongly supported by a recent research con- ducted by the physicists of Large Hadron Collider. (LHC). The LHC physicists anticipate the existence.

  5. Energy bounds for the spinless Salpeter equation: harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Hall, Richard L. [Department of Mathematics and Statistics, Concordia University, Montreal, PQ (Canada)]. E-mail: rhall@mathstat.concordia.ca; Lucha, Wolfgang [Institut fuer Hochenergiephysik, Oesterreichische Akademie der Wissenschaften, Vienna (Austria)]. E-mail: wolfgang.lucha@oeaw.ac.at; Schoeberl, Franz F. [Institut fuer Theoretische Physik, Universitaet Wien, Vienna (Austria)]. E-mail: franz.schoeberl@univie.ac.at

    2001-06-22

    We study the eigenvalues E{sub nl} of the Salpeter Hamiltonian H={beta}(m{sup 2}+p{sup 2}){sup 1/2}+vr{sup 2}, v>0, {beta}>0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semiclassical formula E{sub nl}{approx}min{sub r>0}{l_brace}v(P{sub nl}/r){sup 2}+{beta}(m{sup 2}+r{sup 2}){sup 1/2}{r_brace} provides both upper and lower energy bounds for all the eigenvalues of the problem. (author)

  6. Chemical potential of one-dimensional simple harmonic oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Mungan, Carl E [Physics Department, US Naval Academy, Annapolis, MD 21402-5002 (United States)], E-mail: mungan@usna.edu

    2009-09-15

    Expressions for the chemical potential of an Einstein solid, and of ideal Fermi and Bose gases in an external one-dimensional oscillatory trap, are calculated by two different methods and are all found to share the same functional form. These derivations are easier than traditional textbook calculations for an ideal gas in an infinite three-dimensional square well. Furthermore, the results indicate some important features of chemical potential that could promote student learning in an introductory course in statistical mechanics at the undergraduate level.

  7. Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath

    Science.gov (United States)

    Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M.

    2017-06-01

    Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an additional damping channel to mechanical motion while keeping its thermal noise at the same level, and, as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red-detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

  8. Symmetries and conservation laws of the damped harmonic oscillator

    Indian Academy of Sciences (India)

    Abstract. We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have ...

  9. Diatomic Molecules Effective Potential for an Harmonic Oscillator ...

    African Journals Online (AJOL)

    Journal of the Nigerian Association of Mathematical Physics. Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives · Journal Home > Vol 30 (2015) >. Log in or Register to get access to full text downloads.

  10. Principles of harmonic analysis

    CERN Document Server

    Deitmar, Anton

    2014-01-01

    This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

  11. Rotating ideal Fermi gases under a harmonic potential

    Science.gov (United States)

    Li, Yushan

    2016-01-01

    We present a numerical analysis on thermodynamics of a harmonically trapped ideal Fermi gases subjected to either rotating frame or synthetic magnetic field. We discuss the rotation frequency dependency of chemical potential, specific heat, magnetization, particle flow and density profile. Our results demonstrate that the magnetization displays three characteristic regions: mesoscopic fluctuation, de Haas-van Alphen oscillation and Landau diamagnetism. The center and amplitude of oscillation peaks in particle flow in rotating frame exhibit much stronger dependence on rotation frequency than those in synthetic magnetic field.

  12. Rotating ideal Fermi gases under a harmonic potential

    Energy Technology Data Exchange (ETDEWEB)

    Li, Yushan, E-mail: lysh507@163.com [Department of Physics, University of Science and Technology Beijing, Beijing 100083 (China); Department of Physics, Heze University, Heze 274015 (China)

    2016-01-15

    We present a numerical analysis on thermodynamics of a harmonically trapped ideal Fermi gases subjected to either rotating frame or synthetic magnetic field. We discuss the rotation frequency dependency of chemical potential, specific heat, magnetization, particle flow and density profile. Our results demonstrate that the magnetization displays three characteristic regions: mesoscopic fluctuation, de Haas–van Alphen oscillation and Landau diamagnetism. The center and amplitude of oscillation peaks in particle flow in rotating frame exhibit much stronger dependence on rotation frequency than those in synthetic magnetic field.

  13. Harmonics in transmission power systems

    DEFF Research Database (Denmark)

    Wiechowski, Wojciech Tomasz

    Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need...... to perform more detailed harmonic studies emerged. Since the transmission network has a complex structure and its impedance varies with frequency in a nonlinear fashion, such harmonic study would require a detailed computer model of the network. Consequently, a PhD project proposal titled "Harmonics......, provided that background harmonic distortion, and the network configuration, are not changing during the measurement. It is shown that switching of a shunt linear power system component can result in variation of the harmonic levels that can be measured and used to verify the harmonic model of the network...

  14. Harmonic and geometric analysis

    CERN Document Server

    Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao

    2015-01-01

    This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights.  The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...

  15. Fractal Scaling Models of Natural Oscillations in Chain Systems and the Mass Distribution of Particles

    Directory of Open Access Journals (Sweden)

    Müller H.

    2010-04-01

    Full Text Available The paper presents a fractal scaling model of a chain system of quantum harmonic oscillators, that reproduces some systematic features in the mass distribution of hadrons, leptons and gauge bosons.

  16. Bose Einstein condensation of gases in a harmonic potential trap

    Directory of Open Access Journals (Sweden)

    M. E. Zomorrodian

    2005-03-01

    Full Text Available One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature  below  which  all bosons condensate into  the ground state. This phenomenon is called Bose – Einstein Condensation (BEC. In  this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical  temperature . Possible explanation for all these features will be explained in this paper.

  17. Oscillators and Eigenvalues

    DEFF Research Database (Denmark)

    Lindberg, Erik

    1997-01-01

    In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos.......In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear...

  18. Harmonic Instability Source Identification in Large Wind Farms

    DEFF Research Database (Denmark)

    Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei

    2017-01-01

    A large-scale power electronics based power system like a wind farm introduces the passive and active impedances. The interactions between the active and passive impedances can lead to harmonic-frequency oscillations above the fundamental frequency, which can be called harmonic instability....... This paper presents an approach to identify which wind turbine and which bus has more contribution to the harmonic instability problems. In the approach, a wind farm is modeled as a Multi-Input Multi-Output (MIMO) dynamic system. The poles of the MIMO transfer matrix are used to predict the system...... instability and the eigenvalues sensitivity analysis in respect to the elements of the MIMO matrix locates the most influencing buses of the wind farm. Time-domain simulations in PSCAD software environment for a 400-MW wind farm validate that the presented approach is an effective tool to determine the main...

  19. Oscillator circuits

    CERN Document Server

    Graf, Rudolf F

    1996-01-01

    This series of circuits provides designers with a quick source for oscillator circuits. Why waste time paging through huge encyclopedias when you can choose the topic you need and select any of the specialized circuits sorted by application?This book in the series has 250-300 practical, ready-to-use circuit designs, with schematics and brief explanations of circuit operation. The original source for each circuit is listed in an appendix, making it easy to obtain additional information.Ready-to-use circuits.Grouped by application for easy look-up.Circuit source listing

  20. Power oscillation damping controller

    DEFF Research Database (Denmark)

    2012-01-01

    A power oscillation damping controller is provided for a power generation device such as a wind turbine device. The power oscillation damping controller receives an oscillation indicating signal indicative of a power oscillation in an electricity network and provides an oscillation damping control...... signal in response to the oscillation indicating signal, by processing the oscillation damping control signal in a signal processing chain. The signal processing chain includes a filter configured for passing only signals within a predetermined frequency range....

  1. A Comparative Study on q-Deformed Fermion Oscillators

    Science.gov (United States)

    Algin, Abdullah

    2011-05-01

    In this paper, the algebras, representations, and thermostatistics of four types of fermionic q-oscillator models, called fermionic Newton (FN), Chaichian-Kulish-Ng (CKN), Parthasarathy-Viswanathan-Chaichian (PVC), Viswanathan-Parthasarathy-Jagannathan-Chaichian (VPJC), are discussed. Similarities and differences among the properties of these models are revealed. Particular emphasis is given to the VPJC-oscillators model so that its Fock space representation is analyzed in detail. Possible physical applications of these models are concisely pointed out.

  2. Minimal Surfaces for Hitchin Representations

    DEFF Research Database (Denmark)

    Li, Qiongling; Dai, Song

    2018-01-01

    . In this paper, we investigate the properties of immersed minimal surfaces inside symmetric space associated to a subloci of Hitchin component: $q_n$ and $q_{n-1}$ case. First, we show that the pullback metric of the minimal surface dominates a constant multiple of the hyperbolic metric in the same conformal...... class and has a strong rigidity property. Secondly, we show that the immersed minimal surface is never tangential to any flat inside the symmetric space. As a direct corollary, the pullback metric of the minimal surface is always strictly negatively curved. In the end, we find a fully decoupled system......Given a reductive representation $\\rho: \\pi_1(S)\\rightarrow G$, there exists a $\\rho$-equivariant harmonic map $f$ from the universal cover of a fixed Riemann surface $\\Sigma$ to the symmetric space $G/K$ associated to $G$. If the Hopf differential of $f$ vanishes, the harmonic map is then minimal...

  3. Value Representations

    DEFF Research Database (Denmark)

    Rasmussen, Majken Kirkegaard; Petersen, Marianne Graves

    2011-01-01

    Stereotypic presumptions about gender affect the design process, both in relation to how users are understood and how products are designed. As a way to decrease the influence of stereotypic presumptions in design process, we propose not to disregard the aspect of gender in the design process......, as the perspective brings valuable insights on different approaches to technology, but instead to view gender through a value lens. Contributing to this perspective, we have developed Value Representations as a design-oriented instrument for staging a reflective dialogue with users. Value Representations...

  4. Why plasma harmonics?

    Energy Technology Data Exchange (ETDEWEB)

    Ganeev, R A [Ophthalmology and Advanced Laser Medical Center, Saitama Medical University, Saitama 350-0495 (Japan)

    2015-09-30

    We discuss the emergence of interest in the high-order harmonic generation (HHG) of ultrashort pulses propagated through laser-produced plasmas. It is shown that, during the last few years, substantial amendments of plasma HHG allowed in some cases the characteristics of gas HHG to be surpassed. The attractiveness of a new approach in coherent extreme ultraviolet radiation generation is demonstrated, which can also be used as a tool for laser-ablation-induced HHG spectroscopy of a giant class of solids. We present general ideas and prospects for this relatively new field of nonlinear optics. (review)

  5. Harmonic analysis and applications

    CERN Document Server

    Heil, Christopher

    2007-01-01

    This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto's achievements and expresses an appreciation for the mathematical and personal inspiration he has given to

  6. Josephson flux-flow oscillators in nonuniform microwave fields

    DEFF Research Database (Denmark)

    Salerno, Mario; Samuelsen, Mogens Rugholm

    2000-01-01

    We present a simple theory for Josephson flux-flow oscillators in the presence of nonuniform microwave fields. In particular we derive an analytical expression for the I-V characteristic of the oscillator from which we show that satellite steps are spaced around the main flux-flow resonance by on...... even harmonics of the rf frequency. This result is found to be in good agreement with our numerical results and with experiments....

  7. Representational Machines

    DEFF Research Database (Denmark)

    Petersson, Dag; Dahlgren, Anna; Vestberg, Nina Lager

    to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...

  8. Harmonic states for the free particle

    Energy Technology Data Exchange (ETDEWEB)

    Guerrero, J [Departamento de Matematica Aplicada, Universidad de Murcia, Campus de Espinardo, 30100 Murcia (Spain); Lopez-Ruiz, F F; Aldaya, V; Cossio, F, E-mail: juguerre@um.es, E-mail: flopez@iaa.es, E-mail: valdaya@iaa.es, E-mail: focossiop@gmail.com [Instituto de Astrofisica de Andalucia, CSIC, Apartado Postal 3004, 18080 Granada (Spain)

    2011-11-04

    Different families of states, which are solutions of the time-dependent free Schroedinger equation, are imported from the harmonic oscillator using the quantum Arnold transformation introduced in Aldaya et al (2011 J. Phys. A: Math. Theor.44 065302). Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined. (paper)

  9. Harmonic Stability Assessment for Multi-Paralleled, Grid-Connected Inverters

    DEFF Research Database (Denmark)

    Yoon, Changwoo; Bai, Haofeng; Beres, Remus Narcis

    2016-01-01

    This paper investigates the harmonic interactions of current controllers in multi-paralleled grid-connected inverters. Potential harmonic instability phenomenon, which features oscillations above the fundamental frequency are evaluated by the impedance-based stability criterion. The possible...... to load changes or by the new connections of other grid-connected inverters. Time domain simulations in the PSCAD/EMTDC environment and experimental results shows the corresponding harmonic interaction problems may exist in nowadays power system and the impedance-based stability analysis can...

  10. A psicologia do mercado acionário: representações sociais de investidores da BOVESPA sobre as oscilações dos preços The stock market psychology: social representations of BOVESPA investors about oscillation of prices

    Directory of Open Access Journals (Sweden)

    Tatiana Renaux Tomaselli

    2007-12-01

    Full Text Available Diferentes formas de entender o ser humano levam a psicologia e a economia a diferentes concepções do mercado acionário. Este artigo utiliza-se da teoria das representações sociais para entender esta prática social a partir dos próprios investidores. Partindo da teoria das representações sociais e contribuições de alguns estudos cognitivos aplicados ao campo da tomada de decisão, pudemos compreender a visão do grupo estudado. Foram analisados 94 fóruns de discussão, onde foram identificados 317 investidores. Nossas conclusões mostram que para o grupo investigado o mercado é formado por pessoas em relação, e a oscilação dos preços é atribuída à disputa entre grandes e pequenos investidores.Different ways to understand the human being have taken economy and psychology to different conceptions of stock market. This article has used the social representation theory to understand this social practice applied by the investors themselves. Starting from the social representations theory and some cognitive studies about decision making, we achieved the group's point of view. We analyzed 94 discussion forums in which 317 investors have been identified. Our conclusion shows that for the examined group the market is formed by people in interaction and prices' oscillation is attributed to the competition among big and small investors.

  11. Harmonic Quantum Coherence of Multiple Excitons in PbS/CdS Core-Shell Nanocrystals

    Science.gov (United States)

    Tahara, Hirokazu; Sakamoto, Masanori; Teranishi, Toshiharu; Kanemitsu, Yoshihiko

    2017-12-01

    The generation and recombination dynamics of multiple excitons in nanocrystals (NCs) have attracted much attention from the viewpoints of fundamental physics and device applications. However, the quantum coherence of multiple exciton states in NCs still remains unclear due to a lack of experimental support. Here, we report the first observation of harmonic dipole oscillations in PbS/CdS core-shell NCs using a phase-locked interference detection method for transient absorption. From the ultrafast coherent dynamics and excitation-photon-fluence dependence of the oscillations, we found that multiple excitons cause the harmonic dipole oscillations with ω , 2 ω , and 3 ω oscillations, even though the excitation pulse energy is set to the exciton resonance frequency, ω . This observation is closely related to the quantum coherence of multiple exciton states in NCs, providing important insights into multiple exciton generation mechanisms.

  12. Time-Dependent Simulation of Free-Electron Laser Amplifiers and Oscillators

    CERN Document Server

    Freund, H

    2005-01-01

    Time-dependent FEL simulations use a variety of techniques. Most simulations use a slowly varying envelope approximation (SVEA). One such technique assumes that the envelope varies only in z combined with a field representation as an ensemble of discrete harmonics, which is equivalent to a time-dependent simulation [1] but is computationally prohibitive. A second technique uses an SVEA in both in z and t [2]. The particles and fields are advanced in z using the same process as in steady-state simulations and then the time derivative describing slippage is applied. This is used in wiggler-averaged codes such as GINGER [3] and GENESIS [4]. We describe the inclusion of this technique in the non-wiggler-averaged code MEDUSA [5], which is applied to amplifiers and oscillators. MEDUSA differs from GINGER and GENESIS also in the way the field is treated. GINGER and GENESIS use a field solver and must explicitly propagate the field outside the wiggler oscillators. This is computationally intensive. MEDUSA uses a Gaus...

  13. Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators

    CERN Document Server

    Arroyo, Sebastián I

    2014-01-01

    We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, disclose new effects of nonlinearities on oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in particular, micromechanical oscillators- provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency whe...

  14. Harmonic Series Meets Fibonacci Sequence

    Science.gov (United States)

    Chen, Hongwei; Kennedy, Chris

    2012-01-01

    The terms of a conditionally convergent series may be rearranged to converge to any prescribed real value. What if the harmonic series is grouped into Fibonacci length blocks? Or the harmonic series is arranged in alternating Fibonacci length blocks? Or rearranged and alternated into separate blocks of even and odd terms of Fibonacci length?

  15. Oscillations of a Meterstick on Two Rotating Shafts

    Science.gov (United States)

    Balta, Nuri

    2016-01-01

    Most students find real-world examples of harmonic oscillations interesting. Besides, normal and friction forces are the types of concepts in physics that are readily applicable to their everyday life. For instance, we depend on these forces to write, to drive cars, to pick up objects, and even to walk! And yet introductory physics students have…

  16. Location identification of closed crack based on Duffing oscillator transient transition

    Science.gov (United States)

    Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Deng, Mingxi; Hu, Ning

    2018-02-01

    The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.

  17. Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits

    KAUST Repository

    Ge, Xiaoqing

    2010-12-01

    Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.

  18. Investigating student understanding of simple harmonic motion

    Science.gov (United States)

    Somroob, S.; Wattanakasiwich, P.

    2017-09-01

    This study aimed to investigate students’ understanding and develop instructional material on a topic of simple harmonic motion. Participants were 60 students taking a course on vibrations and wave and 46 students taking a course on Physics 2 and 28 students taking a course on Fundamental Physics 2 on the 2nd semester of an academic year 2016. A 16-question conceptual test and tutorial activities had been developed from previous research findings and evaluated by three physics experts in teaching mechanics before using in a real classroom. Data collection included both qualitative and quantitative methods. Item analysis and whole-test analysis were determined from student responses in the conceptual test. As results, most students had misconceptions about restoring force and they had problems connecting mathematical solutions to real motions, especially phase angle. Moreover, they had problems with interpreting mechanical energy from graphs and diagrams of the motion. These results were used to develop effective instructional materials to enhance student abilities in understanding simple harmonic motion in term of multiple representations.

  19. OTRA based second and third order sinusoidal oscillators and their phase noise performance

    Science.gov (United States)

    Komanapalli, Gurumurthy; Pandey, Neeta; Pandey, Rajeshwari

    2017-07-01

    In this paper operational transresistance amplifier (OTRA) based second and third order sinusoidal oscillators are proposed. The proposed second order oscillator is designed using single OTRA based Sallen Key low pass filter structure and third order oscillator is obtained by cascading three low pass filters and placing in a loop. The non-ideality and phase noise analyses of the circuits are also presented with necessary mathematical formulations. Workability of the proposed oscillators are verified through PSPICE simulations using 0.18µm AGILENT CMOS process parameters. The total harmonic distortion (THD) for proposed second order and third order oscillators are found as 3.27% and 0.631% respectively.

  20. The Morse oscillator in position space, momentum space, and phase space

    DEFF Research Database (Denmark)

    Dahl, Jens Peder; Springborg, Michael

    1988-01-01

    We present a unified description of the position-space wave functions, the momentum-space wave functions, and the phase-space Wigner functions for the bound states of a Morse oscillator. By comparing with the functions for the harmonic oscillator the effects of anharmonicity are visualized. Analy...... for the Morse oscillator. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....

  1. Two port network analysis for three impedance based oscillators

    KAUST Repository

    Said, Lobna A.

    2011-12-01

    Two-port network representations are applied to analyze complex networks which can be dissolved into sub-networks connected in series, parallel or cascade. In this paper, the concept of two-port network has been studied for oscillators. Three impedance oscillator based on two port concept has been analyzed using different impedance structures. The effect of each structure on the oscillation condition and the frequency of oscillation have been introduced. Two different implementations using MOS and BJT have been introduced. © 2011 IEEE.

  2. Power quality issues current harmonics

    CERN Document Server

    Mikkili, Suresh

    2015-01-01

    Power Quality Issues: Current Harmonics provides solutions for the mitigation of power quality problems related to harmonics. Focusing on active power filters (APFs) due to their excellent harmonic and reactive power compensation in two-wire (single phase), three-wire (three-phase without neutral), and four-wire (three-phase with neutral) AC power networks with nonlinear loads, the text:Introduces the APF technology, describing various APF configurations and offering guidelines for the selection of APFs for specific application considerationsCompares shunt active filter (SHAF) control strategi

  3. A Simple Harmonic Universe

    Energy Technology Data Exchange (ETDEWEB)

    Graham, Peter W.; /Stanford U., ITP; Horn, Bart; Kachru, Shamit; /Stanford U., ITP /SLAC; Rajendran, Surjeet; /Johns Hopkins U. /Stanford U., ITP; Torroba, Gonzalo; /Stanford U., ITP /SLAC

    2011-12-14

    We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k = +1, and are supported by a negative cosmological term and matter with -1 < w < -1 = 3. In the case of moderate bounces (where the ratio of the maximal scale factor a{sub +} to the minimal scale factor a{sub -} is {Omicron}(1)), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a{sub +} = a{sub -}, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.

  4. Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation

    Energy Technology Data Exchange (ETDEWEB)

    Burghardt, Irene [Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt (Germany); Martinazzo, Rocco [Dipartimento di Chimica, Universita degli Studi di Milano, v. Golgi 19, 20133 Milano (Italy); Hughes, Keith H. [School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW (United Kingdom)

    2012-10-14

    A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.

  5. Three-halves harmonic emission from a laser filament in a plasma channel

    Energy Technology Data Exchange (ETDEWEB)

    Mishra, G.; Talukdar, I.; Tripathi, V.; Tripathi, V.K. (Indian Inst. of Tech., New Delhi (India). Dept. of Physics)

    1989-12-01

    A self-trapped laser filament is susceptible to decay-producing radially localized Langmuir waves. A nonlinear interaction of the pump wave with the density oscillation at the Langmuir frequency gives rise to three-halves harmonic emissions. Using a basis-function expansion technique, the emitted power in the backward direction is obtained. It decreases with the increasing size of the filament.

  6. Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

    DEFF Research Database (Denmark)

    V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.

    2014-01-01

    We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin...

  7. Study of 2ω and 3/2ω harmonics in ultrashort high-intensity laser ...

    Indian Academy of Sciences (India)

    is produced by electron plasma wave coupling at the critical density surface of the plasma. The other mechanism of generation of 2ω is when the intense laser field drives a relativistic oscillation of plasma surface, which causes a periodic phase modulation of the reflected light and, hence, the emission of harmonics of the ...

  8. X-ray FEL based on harmonics generation and electron beam outcoupling

    Energy Technology Data Exchange (ETDEWEB)

    Litvinenko, V.N.; Burnham, B. [Duke Univ., Durham, NC (United States)

    1995-12-31

    Electron beam outcoupling was suggested by N. A. Vinokurov as a method of optics independent outcoupling for high power FELs. The bunching of the electron beam is provided in a master oscillator. The prebunched electron beam then radiates coherently into an additional wiggler called the radiator. The electron beam is turned by an achromatic bend into this wiggler and its radiation propagates with a small angle with respect to the OK-4 optical axis. Thus, the radiation will pass around the mirror of the master oscillator optical cavity and can then be utilized. This scheme is perfectly suited for harmonic generation if the radiator wiggler is tuned on one of the master oscillator wavelength harmonics. This system is reminiscent of a klystron operating on a harmonic of the reference frequency. In this paper we present the theory of this device, its spectral and spatial characteristics of radiation, the optimization of the master oscillator, the achromatic bend and bunching for harmonic generation, and influence of beam parameters (energy spread, emittance, etc.) on generated power. Examples of possible storage ring and linac driven systems are discussed.

  9. Observation of self-pulsing in singly resonant optical second-harmonic generation with competing nonlinearities

    DEFF Research Database (Denmark)

    Bache, Morten; Lodahl, Peter; Mamaev, Alexander V.

    2002-01-01

    We predict and experimentally observe temporal self-pulsing in singly resonant intracavity second-harmonic generation under conditions of simultaneous parametric oscillation. The threshold for self-pulsing as a function of cavity tuning and phase mismatch are found from analysis of a three-compon...

  10. The Influence of Spring Length on the Physical Parameters of Simple Harmonic Motion

    Science.gov (United States)

    Triana, C. A.; Fajardo, F.

    2012-01-01

    The aim of this work is to analyse the influence of spring length on the simple harmonic motion of a spring-mass system. In particular, we study the effect of changing the spring length on the elastic constant "[kappa]", the angular frequency "[omega]" and the damping factor "[gamma]" of the oscillations. To characterize the behaviour of these…

  11. Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics

    Science.gov (United States)

    Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei

    2013-01-01

    At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

  12. Introduction to abstract harmonic analysis

    CERN Document Server

    Loomis, Lynn H

    2011-01-01

    Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.

  13. Tissue Harmonic Synthetic Aperture Imaging

    DEFF Research Database (Denmark)

    Rasmussen, Joachim

    The main purpose of this PhD project is to develop an ultrasonic method for tissue harmonic synthetic aperture imaging. The motivation is to advance the field of synthetic aperture imaging in ultrasound, which has shown great potentials in the clinic. Suggestions for synthetic aperture tissue...... system complexity compared to conventional synthetic aperture techniques. In this project, SASB is sought combined with a pulse inversion technique for 2nd harmonic tissue harmonic imaging. The advantages in tissue harmonic imaging (THI) are expected to further improve the image quality of SASB....... The first part of the scientific contribution investigates an implementation of pulse inversion for THI on the experimental ultrasound system SARUS. The technique is initially implemented for linear array transducers and then expanded for convex array transducers. The technique is evaluated based on spatial...

  14. Efficient forward second-harmonic generation from planar archimedean nanospirals

    Directory of Open Access Journals (Sweden)

    Davidson II Roderick B.

    2015-05-01

    Full Text Available The enhanced electric field at plasmonic resonances in nanoscale antennas can lead to efficient harmonic generation, especially when the plasmonic geometry is asymmetric on either inter-particle or intra-particle levels. The planar Archimedean nanospiral offers a unique geometrical asymmetry for second-harmonic generation (SHG because the SHG results neither from arranging centrosymmetric nanoparticles in asymmetric groupings, nor from non-centrosymmetric nanoparticles that retain a local axis of symmetry. Here, we report forward SHG from planar arrays of Archimedean nanospirals using 15 fs pulses from a Ti:sapphire oscillator tuned to 800 nm wavelength. The measured harmonic-generation efficiencies are 2.6·10−9, 8·10−9 and 1.3·10−8 for left-handed circular, linear, and right-handed circular polarizations, respectively. The uncoated nanospirals are stable under average power loading of as much as 300 μWper nanoparticle. The nanospirals also exhibit selective conversion between polarization states. These experiments show that the intrinsic asymmetry of the nanospirals results in a highly efficient, two-dimensional harmonic generator that can be incorporated into metasurface optics.

  15. Harmonic structures and intrinsic torsion

    DEFF Research Database (Denmark)

    Conti, Diego; Madsen, Thomas Bruun

    We discuss the construction of 8-manifolds with harmonic Sp(2)Sp(1)-structures. In particular, we find 10 new examples of nilmanifolds that admit a closed 4-form Omega whose stabiliser is Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough inv...... investigation of the intrinsic torsion of such structures; in addition to the construction of harmonic structures, this analysis leads to explicit Lie group examples with invariant intrinsic torsion....

  16. Oscillations in atmospheric water above Switzerland

    Science.gov (United States)

    Hocke, Klemens; Navas-Guzmán, Francisco; Moreira, Lorena; Bernet, Leonie; Mätzler, Christian

    2017-10-01

    Cloud fraction (CF), integrated liquid water (ILW) and integrated water vapour (IWV) were continuously measured from 2004 to 2016 by the TROpospheric WAter RAdiometer (TROWARA) in Bern, Switzerland. There are indications for interannual variations of CF and ILW. A spectral analysis shows that IWV is dominated by an annual oscillation, leading to an IWV maximum of 24 kg m-2 in July to August and a minimum of 8 kg m-2 in February. The seasonal behaviour of CF and ILW is composed by both the annual and the semiannual oscillation. However, the annual oscillation of CF has a maximum in December while the annual oscillation of ILW has a maximum in July. The semiannual oscillations of CF and ILW are strong from 2010 to 2014. The normalized power spectra of ILW and CF show statistically significant spectral components with periods of 76, 85, 97 and 150 days. We find a similarity between the power spectra of ILW and CF with those of zonal wind at 830 hPa (1.5 km) above Bern. Particularly, the occurrence of higher harmonics in the CF and ILW spectra is possibly forced by the behaviour of the lower-tropospheric wind. The mean amplitude spectra of CF, ILW and IWV show increased short-term variability on timescales less than 40 days from spring to fall. We find a weekly cycle of CF and ILW from June to September with increased values on Saturday, Sunday and Monday.

  17. Representational Thickness

    DEFF Research Database (Denmark)

    Mullins, Michael

    to improve design conditions for architects, thereby increasing the “thickness of representation”. The study commences from a broader theoretical enquiry, a review of previous research and examples of relevant context in which virtual reality has been used in practice. It develops from this discussion three......Contemporary communicational and informational processes contribute to the shaping of our physical environment by having a powerful influence on the process of design. Applications of virtual reality (VR) are transforming the way architecture is conceived and produced by introducing dynamic...... elements into the process of design. Through its immersive properties, virtual reality allows access to a spatial experience of a computer model very different to both screen based simulations as well as traditional forms of architectural representation. The dissertation focuses on processes of the current...

  18. Modeling and Identification of Harmonic Instability Problems In Wind Farms

    DEFF Research Database (Denmark)

    Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei

    2016-01-01

    to identify harmonic instability problems in wind farms, where many wind turbines, cables, transformers, capacitor banks, shunt reactors, etc, typically are located. This methodology introduces the wind farm as a Multi-Input Multi-Outpur (MIMO) control system, where the linearized models of fast inner control...... loops of the grid-side converters are considered. Therefore, instability problems of the whole wind farm are predicted based on the poles of the introduced MIMO system. In order to confirm the effectiveness of the proposed analytical approach, time-domain simulations are performed in the PSCAD......In power electronics based power systems like wind farms, the interactions between the inner control systems of the power converters and the passive components may lead to high frequency oscillations, which can be called harmonic instability. In this paper, a simple methodology is presented...

  19. Electron motion enhanced high harmonic generation in xenon clusters

    CERN Document Server

    Li, Na; Bai, Ya; Peng, Peng; Li, Ruxin; Xu, Zhizhan

    2016-01-01

    Atomic clusters presents an isolated system that models the bulk materials whose mechanism of HHG remains uncertain, and a promising medium to produce HHG beyond the limited conversion efficiency for gaseous atoms. Here we reveal that the oscillation of collective electron motion within clusters develops after the interaction of intense laser fields, and it significantly enhances the harmonic dipole and increases the quantum phase of the harmonics. Experimentally, the phase matching conditions of HHG from nanometer xenon clusters and atoms are distinguished, which confirms the enhanced internal field that was proposed theoretically a decade ago. The separation of HHG from atoms and clusters allows the determination of the amplitude of the HHG for clusters to be 5 orders higher, corresponding to 4 times higher conversion efficiency for atomic response. The finding provides an insight on the HHG mechanism of bulk materials and a means by which an efficient coherent X-ray source can be developed.

  20. A coupled-oscillator model of olfactory bulb gamma oscillations.

    Directory of Open Access Journals (Sweden)

    Guoshi Li

    2017-11-01

    Full Text Available The olfactory bulb transforms not only the information content of the primary sensory representation, but also its underlying coding metric. High-variance, slow-timescale primary odor representations are transformed by bulbar circuitry into secondary representations based on principal neuron spike patterns that are tightly regulated in time. This emergent fast timescale for signaling is reflected in gamma-band local field potentials, presumably serving to efficiently integrate olfactory sensory information into the temporally regulated information networks of the central nervous system. To understand this transformation and its integration with interareal coordination mechanisms requires that we understand its fundamental dynamical principles. Using a biophysically explicit, multiscale model of olfactory bulb circuitry, we here demonstrate that an inhibition-coupled intrinsic oscillator framework, pyramidal resonance interneuron network gamma (PRING, best captures the diversity of physiological properties exhibited by the olfactory bulb. Most importantly, these properties include global zero-phase synchronization in the gamma band, the phase-restriction of informative spikes in principal neurons with respect to this common clock, and the robustness of this synchronous oscillatory regime to multiple challenging conditions observed in the biological system. These conditions include substantial heterogeneities in afferent activation levels and excitatory synaptic weights, high levels of uncorrelated background activity among principal neurons, and spike frequencies in both principal neurons and interneurons that are irregular in time and much lower than the gamma frequency. This coupled cellular oscillator architecture permits stable and replicable ensemble responses to diverse sensory stimuli under various external conditions as well as to changes in network parameters arising from learning-dependent synaptic plasticity.

  1. General Lp-harmonic Blaschke bodies

    Indian Academy of Sciences (India)

    Lutwak introduced the harmonic Blaschke combination and the harmonic Blaschke body of a star body. Further, Feng and Wang introduced the concept of the -harmonic Blaschke body of a star body. In this paper, we define the notion of general -harmonic Blaschke bodies and establish some of its properties.

  2. General Lp-harmonic Blaschke bodies

    Indian Academy of Sciences (India)

    Abstract. Lutwak introduced the harmonic Blaschke combination and the harmonic. Blaschke body of a star body. Further, Feng and Wang introduced the concept of the L p- harmonic Blaschke body of a star body. In this paper, we define the notion of general. L p-harmonic Blaschke bodies and establish some of its ...

  3. Platonic polyhedra tune the three-sphere: II. Harmonic analysis on cubic spherical three-manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Kramer, Peter [Institut fuer Theoretische Physik, University Tuebingen (Germany)], E-mail: peter.kramer@uni-tuebingen.de

    2009-08-15

    From the homotopy groups of two distinct cubic spherical three-manifolds, we construct the isomorphic groups of deck transformations acting on the three-sphere. These groups become the cyclic group of order eight and the quaternion group, respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmonic analysis on the three-manifolds, which have applications to cosmic topology.

  4. Prony Analysis for Power System Transient Harmonics

    Directory of Open Access Journals (Sweden)

    David Cartes

    2007-01-01

    Full Text Available Proliferation of nonlinear loads in power systems has increased harmonic pollution and deteriorated power quality. Not required to have prior knowledge of existing harmonics, Prony analysis detects frequencies, magnitudes, phases, and especially damping factors of exponential decaying or growing transient harmonics. In this paper, Prony analysis is implemented to supervise power system transient harmonics, or time-varying harmonics. Further, to improve power quality when transient harmonics appear, the dominant harmonics identified from Prony analysis are used as the harmonic reference for harmonic selective active filters. Simulation results of two test systems during transformer energizing and induction motor starting confirm the effectiveness of the Prony analysis in supervising and canceling power system transient harmonics.

  5. Validation of phantom-based harmonization for patient harmonization.

    Science.gov (United States)

    Panetta, Joseph V; Daube-Witherspoon, Margaret E; Karp, Joel S

    2017-07-01

    To improve the precision of multicenter clinical trials, several efforts are underway to determine scanner-specific parameters for harmonization using standardized phantom measurements. The goal of this study was to test the correspondence between quantification in phantom and patient images and validate the use of phantoms for harmonization of patient images. The National Electrical Manufacturers' Association image quality phantom with hot spheres was scanned on two time-of-flight PET scanners. Whole-body [18 F]-fluorodeoxyglucose (FDG)-PET scans were acquired of subjects on the same systems. List-mode events from spheres (diam.: 10-28 mm) measured in air on each scanner were embedded into the phantom and subject list-mode data from each scanner to create lesions with known uptake with respect to the local background in the phantom and each subject's liver and lung regions, as a proxy to characterize true lesion quantification. Images were analyzed using the contrast recovery coefficient (CRC) typically used in phantom studies and serving as a surrogate for the standardized uptake value used clinically. Postreconstruction filtering (resolution recovery and Gaussian smoothing) was applied to determine if the effect on the phantom images translates equivalently to subject images. Three postfiltering strategies were selected to harmonize the CRCmean or CRCmax values between the two scanners based on the phantom measurements and then applied to the subject images. Both the average CRCmean and CRCmax values for lesions embedded in the lung and liver in four subjects (BMI range 25-38) agreed to within 5% with the CRC values for lesions embedded in the phantom for all lesion sizes. In addition, the relative changes in CRCmean and CRCmax resulting from the application of the postfilters on the subject and phantom images were consistent within measurement uncertainty. Further, the root mean squared percent difference (RMSpd ) between CRC values on the two scanners

  6. Design of 12-phase, 2-stage Harmonic Rejection Mixer for TV Tuners

    Directory of Open Access Journals (Sweden)

    D. Lee

    2016-06-01

    Full Text Available A two-stage 12-phase harmonic rejection mixer (HRM for TV tuners is proposed in order to reject the local oscillator (LO harmonics up to the ninth order. The proposed weighing scheme for 12-phase, 2-stage harmonic mixing can reduce the harmonic rejection (HR sensitivity to the amplitude error caused by irrational numbers such as . To verify this HR, the 2-stage HR circuit is designed with baseband gm weighting in order to save power and improve the HR ratios without calibration. The proposed HRM achieves the third to ninth worst HR ratios, more than 55 dB, according to Monte Carlo simulations. It consumes 6.5 mA under a 2.5 V supply voltage.

  7. Collapse of simple harmonic universe

    Energy Technology Data Exchange (ETDEWEB)

    Mithani, Audrey T.; Vilenkin, Alexander, E-mail: audrey.todhunter@tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

    2012-01-01

    In a recent paper Graham et al constructed oscillating and static universe models which are stable with respect to all classical perturbations. Here we show that such universes are quantum-mechanically unstable and can collapse by quantum tunneling to zero radius. We also present instantons describing nucleation of oscillating and static universes from nothing.

  8. Microelectronic oscillator, 2

    Science.gov (United States)

    Kleinberg, L. L.

    1969-01-01

    Microelectronic oscillator uses a bipolar transistor to circumvent the problem of developing suitable inductors for lower frequencies. The oscillator is fabricated by hybrid thin film techniques or by monolithic construction. Discrete microminiature components may also be employed.

  9. Oscillating heat pipes

    CERN Document Server

    Ma, Hongbin

    2015-01-01

    This book presents the fundamental fluid flow and heat transfer principles occurring in oscillating heat pipes and also provides updated developments and recent innovations in research and applications of heat pipes. Starting with fundamental presentation of heat pipes, the focus is on oscillating motions and its heat transfer enhancement in a two-phase heat transfer system. The book covers thermodynamic analysis, interfacial phenomenon, thin film evaporation,  theoretical models of oscillating motion and heat transfer of single phase and two-phase flows, primary  factors affecting oscillating motions and heat transfer,  neutron imaging study of oscillating motions in an oscillating heat pipes, and nanofluid’s effect on the heat transfer performance in oscillating heat pipes.  The importance of thermally-excited oscillating motion combined with phase change heat transfer to a wide variety of applications is emphasized. This book is an essential resource and learning tool for senior undergraduate, gradua...

  10. Phenomenology of neutrino oscillations

    Indian Academy of Sciences (India)

    Abstract. The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.

  11. Thermal transport in out-of-equilibrium quantum harmonic chains.

    Science.gov (United States)

    Nicacio, F; Ferraro, A; Imparato, A; Paternostro, M; Semião, F L

    2015-04-01

    We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyze carefully. In particular, we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.

  12. Thermal transport in out-of-equilibrium quantum harmonic chains

    Science.gov (United States)

    Nicacio, F.; Ferraro, A.; Imparato, A.; Paternostro, M.; Semião, F. L.

    2015-04-01

    We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyze carefully. In particular, we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.

  13. The colpitts oscillator family

    DEFF Research Database (Denmark)

    Lindberg, Erik; Murali, K.; Tamasevicius, A.

    A tutorial study of the Colpitts oscillator family defined as all oscillators based on a nonlinear amplifier and a three- terminal linear resonance circuit with one coil and two capacitors. The original patents are investigated. The eigenvalues of the linearized Jacobian for oscillators based...

  14. TAX HARMONIZATION VERSUS FISCAL COMPETITION

    Directory of Open Access Journals (Sweden)

    Florin Alexandru MACSIM

    2016-12-01

    Full Text Available Recent years have brought into discussion once again subjects like tax harmonization and fiscal competition. Every time the European Union tends to take a step forward critics enter the scene and give contrary arguments to European integration. Through this article we have offered our readers a compelling view over the “battle” between tax harmonization and fiscal competition. While tax harmonization has key advantages as less costs regarding public revenues, leads to higher degree of integration and allows the usage of fiscal transfers between regions, fiscal competition is no less and presents key advantages as high reductions in tax rates and opens a large path for new investments, especially FDI. Choosing tax harmonization or fiscal competition depends on a multitude of variables, of circumstances, the decision of choosing one path or the other being ultimately influenced by the view of central and local authorities. Our analysis indicates that if we refer to a group of countries that are a part of a monetary union or that form a federation, tax harmonization seems to be the best path to choose. Moving the analysis to a group of regions that aren’t taking any kind of correlated actions or that have not signed any major treaties regarding monetary or fiscal policies, the optimal solution is fiscal competition.

  15. Harmonic Issues Assessment on PWM VSC-Based Controlled Microgrids using Newton Methods

    DEFF Research Database (Denmark)

    Agundis-Tinajero, Gibran; Segundo-Ramirez, Juan; Peña-Gallardo, Rafael

    2017-01-01

    This paper presents the application of Newton-based methods in the time-domain for the computation of the periodic steady state solutions of microgrids with multiple distributed generation units, harmonic stability and power quality analysis. Explicit representation of the commutation process...

  16. Modeling of VSC-Based Power Systems in The Extended Harmonic Domain

    DEFF Research Database (Denmark)

    Esparza, Miguel; Segundo-Ramirez, Juan; Kwon, Jun Bum

    2017-01-01

    Averaged modeling is a commonly used approach used to obtain mathematical representations of VSC-based systems. However, essential characteristics mainly related to the modulation process and the harmonic distortion of the signals are not able to be accurately captured and analyzed. The extended ...

  17. Singular Isotonic Oscillator, Supersymmetry and Superintegrability

    Directory of Open Access Journals (Sweden)

    Ian Marquette

    2012-09-01

    Full Text Available In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner H_a, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where are located the singularities on the real axis and recover isospectrality. This method was applied to superpartners of the harmonic oscillator with one singularity. In this paper, we apply this method to the singular isotonic oscillator with two singularities on the real axis. We also applied these results to four 2D superintegrable systems with second and third-order integrals of motion obtained by Gravel for which polynomial algebras approach does not allow to obtain the energy spectrum of square integrable wavefunctions. We obtain solutions involving parabolic cylinder functions.

  18. Optimal Wavelets for Speech Signal Representations

    Directory of Open Access Journals (Sweden)

    Shonda L. Walker

    2003-08-01

    Full Text Available It is well known that in many speech processing applications, speech signals are characterized by their voiced and unvoiced components. Voiced speech components contain dense frequency spectrum with many harmonics. The periodic or semi-periodic nature of voiced signals lends itself to Fourier Processing. Unvoiced speech contains many high frequency components and thus resembles random noise. Several methods for voiced and unvoiced speech representations that utilize wavelet processing have been developed. These methods seek to improve the accuracy of wavelet-based speech signal representations using adaptive wavelet techniques, superwavelets, which uses a linear combination of adaptive wavelets, gaussian methods and a multi-resolution sinusoidal transform approach to mention a few. This paper addresses the relative performance of these wavelet methods and evaluates the usefulness of wavelet processing in speech signal representations. In addition, this paper will also address some of the hardware considerations for the wavelet methods presented.

  19. HARMONIZED EUROPE OR EUROPEAN HARMONY?

    Directory of Open Access Journals (Sweden)

    Cosmin Marinescu

    2007-07-01

    Full Text Available Recent evolutions in Europe raise questions on the viability of the present economic and social model that defines the European construction project. In this paper, the author will try to explain the viability of institutional European model that sticks between free market mechanisms and protectionism. The main challenge for the EU is about the possibility to bring together the institutional convergence and the welfare for all Europeans. This is the result of the view, still dominant, of European politics elite, according to which institutional harmonization is the solution of a more dynamic and prosper Europe. But, economic realities convince us that, more and more, a harmonized, standardized Europe is not necessarily identical with a Europe of harmony and social cooperation. If „development through integration” seems to be harmonization through „institutional transplant”, how could then be the European model one sufficiently wide open to market, which creates the prosperity so long waited for by new member countries?

  20. Elements of abstract harmonic analysis

    CERN Document Server

    Bachman, George

    2013-01-01

    Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give

  1. Harmonic functions with varying coefficients

    Directory of Open Access Journals (Sweden)

    Jacek Dziok

    2016-05-01

    Full Text Available Abstract Complex-valued harmonic functions that are univalent and sense preserving in the open unit disk can be written in the form f = h + g ‾ $f=h+\\overline{g}$ , where h and g are analytic. In this paper we investigate some classes of univalent harmonic functions with varying coefficients related to Janowski functions. By using the extreme points theory we obtain necessary and sufficient convolution conditions, coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. The radii of starlikeness and convexity for these classes are also determined.

  2. Nature's Autonomous Oscillators

    Science.gov (United States)

    Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.

    2012-01-01

    Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.

  3. Controlled excitation of resonance self-oscillations in one-dimensional distributed systems

    Science.gov (United States)

    Izrailovich, M. Ya.

    2004-03-01

    On the basis of the method of equivalent linearization combined with the method of moments, laws of self-oscillation excitation are obtained that provide the modes with maximum intensity of resonance (or quasi-resonance) oscillations in one-dimensional systems with distributed parameters. A restriction of a general type is imposed on the law of excitation. In the particular case of an integral quadratic restriction, the law of excitation leads to the generation of purely harmonic self-oscillations. The use of an extended (multiplicatively stabilizing) control provides the uniqueness and stability of the quasi-optimal mode of self-oscillation.

  4. Optimal Selective Harmonic Control for Power Harmonics Mitigation

    DEFF Research Database (Denmark)

    Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede

    2015-01-01

    of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...

  5. Energetics of oscillating lifting surfaces using integral conservation laws

    Science.gov (United States)

    Ahmadi, Ali R.; Widnall, Sheila E.

    1987-01-01

    The energetics of oscillating flexible lifting surfaces in two and three dimensions is calculated by the use of integral conservation laws in inviscid incompressible flow for general and harmonic transverse oscillations. Total thrust is calculated from the momentum theorem and energy loss rate due to vortex shedding in the wake from the principle of conservation of mechanical energy. Total power required to maintain the oscillations and hydrodynamic efficiency are also determined. In two dimensions, the results are obtained in closed form. In three dimensions, the distribution of vorticity on the lifting surface is also required as input to the calculations. Thus, unsteady lifting-surface theory must be used as well. The analysis is applicable to oscillating lifting surfaces of arbitrary planform, aspect ratio, and reduced frequency and does not require calculation of the leading-edge thrust.

  6. Solution Hamilton-Jacobi equation for oscillator Caldirola-Kanai

    Directory of Open Access Journals (Sweden)

    LEONARDO PASTRANA ARTEAGA

    2016-12-01

    Full Text Available The method allows Hamilton-Jacobi explicitly determine the generating function from which is possible to derive a transformation that makes soluble Hamilton's equations. Using the separation of variables the partial differential equation of the first order called Hamilton-Jacobi equation is solved; as a particular case consider the oscillator Caldirola-Kanai (CK, which is characterized in that the mass presents a temporal evolution exponentially  . We demonstrate that the oscillator CK position presents an exponential decay in time similar to that obtained in the damped sub-critical oscillator, which reflects the dissipation of total mechanical energy. We found that in the limit that the damping factor  is small, the behavior is the same as an oscillator with simple harmonic motion, where the effects of energy dissipation is negligible.

  7. Structural relations of harmonic sums and Mellin transforms up to weight w=5

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes

    2009-01-15

    We derive the structural relations between the Mellin transforms of weighted Nielsen integrals emerging in the calculation of massless or massive single-scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients, and other hard scattering cross sections depending on a single scale. The set of all multiple harmonic sums up to weight five cover the sums needed in the calculation of the 3-loop anomalous dimensions. The relations extend the set resulting from the quasi-shuffle product between harmonic sums studied earlier. Unlike the shuffle relations, they depend on the value of the quantities considered. Up to weight w=5, 242 nested harmonic sums contribute. In the present physical applications it is sufficient to consider the sub-set of harmonic sums not containing an index i=-1, which consists out of 69 sums. The algebraic relations reduce this set to 30 sums. Due to the structural relations a final reduction of the number of harmonic sums to 15 basic functions is obtained. These functions can be represented in terms of factorial series, supplemented by harmonic sums which are algebraically reducible. Complete analytic representations are given for these 15 meromorphic functions in the complex plane deriving their asymptotic- and recursion relations. A general outline is presented on the way nested harmonic sums and multiple zeta values emerge in higher order calculations of zero- and single scale quantities. (orig.)

  8. Harmonic Stability Assessment for Multi-Paralleled, Grid-Connected Inverters

    DEFF Research Database (Denmark)

    Yoon, Changwoo; Wang, Xiongfei; Silva, Filipe Miguel Faria da

    2014-01-01

    This paper investigates the dynamic interactions of current controllers for multi-paralleled, grid-connected inverters. The consequent harmonics instability phenomena, which features with oscillations above the fundamental frequency, are evaluated by the impedance-based stability criterion....... The frequency range of effective impedance-based stability analysis is first identified. The effect of each inverter on the system harmonic instability is then identified by case studies on different groups of inverters. Lastly, the PSCAD/EMTDC simulations on a system with five passivelydamped, LCL...

  9. Chemical potential for the Bose gases in a one-dimensional harmonic trap

    Energy Technology Data Exchange (ETDEWEB)

    Liu, T G; Niu, M Y [Key Laboratory for Micro-Nano Optoelectronic Devices of Ministry of Education and State Key Laboratory for Chemo/Biosensing and Chemometrics, Hunan University, Changsha, 410082 (China); Liu, Q H, E-mail: quanhuiliu@gmail.co [School for Theoretical Physics and Department of Applied Physics, Hunan University, Changsha, 410082 (China)

    2010-05-15

    A closed expression for the chemical potential of Bose gases in an external one-dimensional harmonic trap, reported recently in this journal (Mungan 2009 Chemical potential of one-dimensional simple harmonic oscillators Eur. J. Phys. 30 1131-6), is approximate and not applicable for temperatures lower than a characteristic value below which the ground state becomes occupied by a macroscopic number of particles. In this letter, the correct behaviour of the chemical potential at low temperature is addressed. (letters and comments)

  10. Ultra-broadband Photonic Harmonic Mixer Based on Optical Comb Generation

    DEFF Research Database (Denmark)

    Zhao, Ying; Pang, Xiaodan; Deng, Lei

    2012-01-01

    We propose a novel photonic harmonic mixer operating at frequencies up to the millimeter-wave (MMW) band. By combining a broadband fiber-wireless signal with highorder harmonics of a fundamental local oscillator in an optical frequency comb generator, frequency down-conversion can be implemented...... without using costly ultra-broadband photodiode. It is theoretically shown that the down-conversion efficiency and the bandwidth of the mixer is highly dependent on the optical modulation indices and the fundamental frequency of comb lines. Down-conversion of a W-band (75-110GHz) fiberwireless signal...

  11. A memristor-based third-order oscillator: beyond oscillation

    Science.gov (United States)

    Talukdar, A.; Radwan, A. G.; Salama, K. N.

    2011-09-01

    This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.

  12. A memristor-based third-order oscillator: beyond oscillation

    KAUST Repository

    Talukdar, Abdul Hafiz Ibne

    2012-10-06

    This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.

  13. Discrete oscillator design linear, nonlinear, transient, and noise domains

    CERN Document Server

    Rhea, Randall W

    2014-01-01

    Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and today's engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of os

  14. Tides and tidal harmonics at Umbharat, Gujarat

    Digital Repository Service at National Institute of Oceanography (India)

    Suryanarayana, A.; Swamy, G.N.

    A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...

  15. Angularly resolved RABBITT using a second harmonic pulse

    Science.gov (United States)

    Loriot, Vincent; Marciniak, Alexandre; Karras, Gabriel; Schindler, Baptiste; Renois-Predelus, Gina; Compagnon, Isabelle; Concina, Bruno; Brédy, Richard; Celep, Gulabi; Bordas, Christian; Constant, Eric; Lépine, Franck

    2017-11-01

    Processes in atoms or molecules on the attosecond timescale have been measured using XUV attosecond and IR femtosecond pulses overlapping in time and controlled with attosecond accuracy. Within this general framework, many strategies have been developed using the harmonics of the fundamental pulse. In this paper, we focus on a specific configuration where the attosecond pulse train is composed by odd harmonics and is dressed by the second harmonic of the fundamental light. Measuring the angularly resolved photoelectron spectrum as a function of the delay between the pulses, a clear oscillation of the anisotropy parameters appears revealing attosecond controlled interferences. This process, is assigned to interferences between two quantum paths involving one XUV photon, on one path, and a XUV+UV photons on the other path. The XUV-UV delay dependent up–down asymmetry can be interpreted following the usual RABBITT formalism, where the dressing photon energy corresponds to the energy separation between the XUV photons of the attosecond pulse train. This approach allows an intuitive analysis of the interference and provides a well suited method for the study of complex valence band systems thanks to the limited congestion of the resulting spectrum.

  16. Efficient Forward Second-Harmonic Generation from Planar Archimedean Nanospirals

    CERN Document Server

    Davidson, Roderick B; Vargas, Guillermo; Avanesyan, Sergey M; Haglund, Richard F

    2015-01-01

    The enhanced electric field at plasmonic resonances in nanoscale antennas can lead to efficient harmonic generation, especially when the plasmonic geometry is asymmetric on either inter-particle or intra-particle levels. The planar Archimedean nanospiral offers a unique geometrical asymmetry for second-harmonic generation (SHG) because the SHG results neither from arranging centrosymmetric nanoparticles in asymmetric groupings, nor from non-centrosymmetric nanoparticles that retain a local axis of symmetry. Here we report forward SHG from planar arrays of Archimedean nanospirals using 15 fs pulse from a Ti:sapphire oscillator tuned to 800 nm wavelength. The measured harmonic-generation efficiencies are 2.6*10-9, 8*10-9 and 1.3*10-8 for left-handed circular, linear, and right-handed circular polarizations, respectively. The uncoated nanospirals are stable under average power loading of as much as 300 uW per nanoparticle. The nanospirals also exhibit a selective conversion between polarization states. These exp...

  17. High harmonic generation from impulsively aligned SO2

    Science.gov (United States)

    Devin, Julien; Wang, Song; Kaldun, Andreas; Bucksbaum, Phil

    2016-05-01

    Previous work in high harmonics generation (HHG) in aligned molecular gases has mainly focused on rotational dynamics in order to determine the contributions of different orbitals to the ionization step. In our experiment, we focus on the shorter timescale of vibrational dynamics. We generate high harmonics from impulsively aligned SO2 molecules in a gas jet and record the emitted attosecond pulse trains in a home-built high resolution vacuum ultra violet (VUV) spectrometer. Using the high temporal resolution of our setup, we are able to map out the effects of vibrational wavepackets with a sub-femtosecond resolution. The target molecule, SO2 gas, is impulsively aligned by a near-infrared laser pulse and has accessible vibrations on the timescale of the short laser pulse used. We present first experimental results for the response to this excitation in high-harmonics. We observe both fast oscillations in the time domain as well as shifts of the VUV photon energy outside of the pulse overlaps. Research supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), Chemical Sciences, Geosciences, and Biosciences Division and by the National Science Foundation Graduate Research Fellowship.

  18. Damped driven coupled oscillators: entanglement, decoherence and the classical limit

    Energy Technology Data Exchange (ETDEWEB)

    Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co

    2009-03-13

    We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.

  19. Detection of Harmonic Occurring using Kalman Filtering

    DEFF Research Database (Denmark)

    Hussain, Dil Muhammad Akbar; Shoro, Ghulam Mustafa; Imran, Raja Muhammed

    2014-01-01

    As long as the load to a power system is linear which has been the case before 80's, typically no harmonics are produced. However, the modern power electronic equipment for controlled power consumption produces harmonic disturbances, these devices/equipment possess nonlinear voltage/current chara...... using Kalman filter. This may be very useful for example to quickly switching on certain filters based on the harmonic present. We are using a unique technique to detect the occurrence of harmonics....

  20. Equatorial oscillations maintained by gravity waves as described with the Doppler Spread Parameterization: II. Heuristic analysis

    Science.gov (United States)

    Mayr, H. G.; Hartle, R. E.; Chan, K. L.

    1998-01-01

    The Doppler Spread Parameterization (DSP) for gravity waves (GW) developed by Hines is applied to the zonal momentum budget at the equator. For sufficiently large oscillation amplitudes in the background zonal winds, comparable to the GW induced wind variability, the momentum source is intermittent and as such it represents a nonlinearity of third or generally odd order. This kind of nonlinearity generates, besides higher harmonics, the fundamental harmonic itself which is retained in a simplified analytical solution that can describe self-sustained oscillations without invoking external, time dependent forcing. The formulation is discussed to provide some understanding of the numerical results presented in the companion paper.

  1. Oscillations of disks

    CERN Document Server

    Kato, Shoji

    2016-01-01

    This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...

  2. Third Harmonic Imaging using a Pulse Inversion

    DEFF Research Database (Denmark)

    Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt

    2011-01-01

    The pulse inversion (PI) technique can be utilized to separate and enhance harmonic components of a waveform for tissue harmonic imaging. While most ultrasound systems can perform pulse inversion, only few image the 3rd harmonic component. PI pulse subtraction can isolate and enhance the 3rd...

  3. Harmonic Detection at Initialization With Kalman Filter

    DEFF Research Database (Denmark)

    Hussain, Dil Muhammad Akbar; Imran, Raja Muhammad; Shoro, Ghulam Mustafa

    2014-01-01

    the affect of harmonics on the supply. For the detection of these harmonics various techniques are available and one of that technique is the Kalman filter. In this paper we investigate that what are the consequences when harmonic detection system based on Kalman Filtering is initialized...

  4. Oscillation of a rigid rod in the special relativity

    CERN Document Server

    Paiva, F M

    2012-01-01

    In the special relativity, a rigid rod slides upon itself, with one extremity oscillating harmonically. We discovered restrictions in the amplitude of the motion and in the length of the rod, essential to eliminate unphysical solutions. ------- Cxe la speciala relativeco, rigida stango movigxas sur si mem, kun unu fino oscilante harmonie. Ni malkovris limigajn kondicxojn pri la amplitudo de movado kaj pri la longo de stango, necesegaj por elimini ne-fizikajn solvojn.

  5. The radio-frequency fluctuation effect on the floating harmonic method

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jaewon; Kim, Kyung-Hyun [Department of Electrical Engineering, Hanyang University, Wangsimni-ro 222, Seongdong-gu, Seoul 04763 (Korea, Republic of); Kim, Dong-Hwan [Department of Nanoscale Semiconductor Engineering, Hanyang University, Wangsimni-ro 222, Seongdong-gu, Seoul 04763 (Korea, Republic of); Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr [Department of Electrical Engineering, Hanyang University, Wangsimni-ro 222, Seongdong-gu, Seoul 04763 (Korea, Republic of); Department of Nanoscale Semiconductor Engineering, Hanyang University, Wangsimni-ro 222, Seongdong-gu, Seoul 04763 (Korea, Republic of)

    2016-08-15

    The radio-frequency (RF) plasma diagnostics with an electrical probe facing a challenge, because the RF fluctuation oscillates the plasma potential and distorts the current-voltage (I-V) curve. As Langmuir probe is widely used in plasma diagnostics, many researchers have been studying the effect of RF fluctuation on probe and compensation methods. On the other hand, there have not been enough studies on the fluctuation effect on the floating harmonic method. Therefore, we investigated the impact of RF fluctuation on the floating harmonic method theoretically and experimentally. When the electrons are in ideal Maxwellian distribution, the floating potential is negatively shifted by the RF fluctuation, but the fluctuation does not distort I-V curve around the floating potential. However, in practical plasmas, the I-V curve and their harmonic components are distorted. This RF fluctuation effect becomes more significant in a low density plasma with a high impedance sheath. The second harmonic current decreases with the RF fluctuation while the first harmonic current is merely affected. Therefore, the electron temperatures measured with the floating harmonic method under low density plasma with uncompensated probe are overestimated than the results obtained with the compensated probe.

  6. Analytical representation of time correlation functions and application to relaxation problems; Representation analytique des fonctions de correlation temporelle et application a des problemes de relaxation

    Energy Technology Data Exchange (ETDEWEB)

    Dupuis, M. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires, departement de physico-chimie, services des isotopes stables

    1971-07-01

    Two analytical representations of the Laplace transform of the time autocorrelation of a dynamical variable, namely the moment expansion and Mori's continued fraction expansion, are investigated from the point of view of structure and convergence properties, and the relation between them is established. The general theory is applied first to a dynamical model exactly solvable, the isotopic impurity in a linear chain of coupled harmonic oscillators, and then to two stochastic models recently introduced by Gordon for the rotational diffusion of molecules. In the latter case, the continued fraction expansion yields simple analytical expressions for the infrared absorption band shapes, showing that these models contain all the features of observed shapes in compressed gases, liquids and solutions. (author) [French] Deux representations analytiques de la transformee de Laplace de la fonction d'autocorrelation temporelle d'une variable dynamique, le developpement en moments et le developpement en fraction continue recemment introduit par Mori, sont etudiees du point de vue de leurs proprietes de structure et de convergence, en meme temps que la relation qui existe entre elles est etablie. La theorie generale est appliquee, d'une part, a un modele dynamique exactement soluble, celui d'une particule isotopique dans une chaine lineaire d'oscillateurs harmoniques couples, et, d'autre part, a deux modeles stochastiques recemment proposes par Gordon pour la diffusion rotationnelle des molecules. Dans ce dernier cas, la voie de la fraction continue fournit des expressions analytiques simples pour les formes de bande d'absorption infrarouge, montrant que ces modeles possedent les caracteristiques des formes observees dans les gaz comprimes, les liquides ou les solutions. (auteur)

  7. Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

    Science.gov (United States)

    Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

    2017-08-01

    Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

  8. Harmonically resonant cavity as a bunch-length monitor

    Directory of Open Access Journals (Sweden)

    B. Roberts

    2016-05-01

    Full Text Available A compact, harmonically resonant cavity with fundamental resonant frequency 1497 MHz was used to evaluate the temporal characteristics of electron bunches produced by a 130 kV dc high voltage spin-polarized photoelectron source at the Continuous Electron Beam Accelerator Facility (CEBAF photoinjector, delivered at 249.5 and 499 MHz repetition rates and ranging in width from 45 to 150 picoseconds (FWHM. A cavity antenna attached directly to a sampling oscilloscope detected the electron bunches as they passed through the cavity bore with a sensitivity of ∼1  mV/μA. The oscilloscope waveforms are a superposition of the harmonic modes excited by the beam, with each cavity mode representing a term of the Fourier series of the electron bunch train. Relatively straightforward post-processing of the waveforms provided a near-real time representation of the electron bunches revealing bunch-length and the relative phasing of interleaved beams. The noninvasive measurements from the harmonically resonant cavity were compared to measurements obtained using an invasive RF-deflector-cavity technique and to predictions from particle tracking simulations.

  9. Entropic Fluctuations in Thermally Driven Harmonic Networks

    Science.gov (United States)

    Jakšić, V.; Pillet, C.-A.; Shirikyan, A.

    2017-02-01

    We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence and uniqueness of the steady state of the resulting process, we construct a canonical entropy production functional S^t which satisfies the Gallavotti-Cohen fluctuation theorem. More precisely, we prove that there exists κ _c>1/2 such that the cumulant generating function of S^t has a large-time limit e(α ) which is finite on a closed interval [1/2-κ _c,1/2+κ _c], infinite on its complement and satisfies the Gallavotti-Cohen symmetry e(1-α )=e(α ) for all α in R. Moreover, we show that e(α ) is essentially smooth, i.e., that e'(α )→ ∓ ∞ as α → 1/2 ∓ κ _c. It follows from the Gärtner-Ellis theorem that S^t satisfies a global large deviation principle with a rate function I( s) obeying the Gallavotti-Cohen fluctuation relation I(-s)-I(s)=s for all sin R. We also consider perturbations of S^t by quadratic boundary terms and prove that they satisfy extended fluctuation relations, i.e., a global large deviation principle with a rate function that typically differs from I( s) outside a finite interval. This applies to various physically relevant functionals and, in particular, to the heat dissipation rate of the network. Our approach relies on the properties of the maximal solution of a one-parameter family of algebraic matrix Riccati equations. It turns out that the limiting cumulant generating functions of S^t and its perturbations can be computed in terms of spectral data of a Hamiltonian matrix depending on the harmonic potential of the network and the parameters of the Langevin reservoirs. This approach is well adapted to both analytical and numerical investigations.

  10. Data harmonization and model performance

    Science.gov (United States)

    The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.

  11. The Oscillator Principle of Nature

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2012-01-01

    Oscillators are found on all levels in Nature. The general oscillator concept is defined and investigated. Oscillators may synchronize into fractal patterns. Apparently oscillators are the basic principle in Nature. The concepts of zero and infinite are discussed. Electronic manmade oscillators...

  12. The Spectrum of Particles with Short-Ranged Interactions in a Harmonic Trap

    Directory of Open Access Journals (Sweden)

    Metsch B. Ch.

    2010-04-01

    Full Text Available The possibility to control short-ranged interactions of cold gases in optical traps by Feshbachresonances makes these systems ideal candidates to study universal scaling properties and Efimov physics. The spectrum of particles in a trap, idealised by a harmonic oscillator potential, in the zero range limit with 2- and 3-particle contact interactions is studied numerically. The Hamiltonian is regularised by restricting the oscillator basis and the coupling constants are tuned such that the ground state energies of the 2- and 3-particle sector are reproduced [1],[2]. Results for 2-, 3-, and 4 particle systems are presented and compared to exact results [3],[4].

  13. Oscillations in atmospheric water above Switzerland

    Directory of Open Access Journals (Sweden)

    K. Hocke

    2017-10-01

    Full Text Available Cloud fraction (CF, integrated liquid water (ILW and integrated water vapour (IWV were continuously measured from 2004 to 2016 by the TROpospheric WAter RAdiometer (TROWARA in Bern, Switzerland. There are indications for interannual variations of CF and ILW. A spectral analysis shows that IWV is dominated by an annual oscillation, leading to an IWV maximum of 24 kg m−2 in July to August and a minimum of 8 kg m−2 in February. The seasonal behaviour of CF and ILW is composed by both the annual and the semiannual oscillation. However, the annual oscillation of CF has a maximum in December while the annual oscillation of ILW has a maximum in July. The semiannual oscillations of CF and ILW are strong from 2010 to 2014. The normalized power spectra of ILW and CF show statistically significant spectral components with periods of 76, 85, 97 and 150 days. We find a similarity between the power spectra of ILW and CF with those of zonal wind at 830 hPa (1.5 km above Bern. Particularly, the occurrence of higher harmonics in the CF and ILW spectra is possibly forced by the behaviour of the lower-tropospheric wind. The mean amplitude spectra of CF, ILW and IWV show increased short-term variability on timescales less than 40 days from spring to fall. We find a weekly cycle of CF and ILW from June to September with increased values on Saturday, Sunday and Monday.

  14. Harmonic vibrations of multispan beams

    DEFF Research Database (Denmark)

    Dyrbye, Claes

    1996-01-01

    Free and forced harmonic vibrations of multispan beams are determined by a method which implies 1 equation regardless of the configuration. The necessary formulas are given in the paper. For beams with simple supports and the same length of all (n) spans, there is a rather big difference between...... the n´th and the (n+1)´th eigenfrequency. The reason for this phenomenon is explained.Keywords: Vibrations, Eigenfrequencies, Beams....

  15. Harmonic ratcheting for fast acceleration

    Directory of Open Access Journals (Sweden)

    N. Cook

    2014-04-01

    Full Text Available A major challenge in the design of rf cavities for the acceleration of medium-energy charged ions is the need to rapidly sweep the radio frequency over a large range. From low-power medical synchrotrons to high-power accelerator driven subcritical reactor systems, and from fixed focus alternating gradient accelerators to rapid cycling synchrotrons, there is a strong need for more efficient, and faster, acceleration of protons and light ions in the semirelativistic range of hundreds of MeV/u. A conventional way to achieve a large, rapid frequency sweep (perhaps over a range of a factor of 6 is to use custom-designed ferrite-loaded cavities. Ferrite rings enable the precise tuning of the resonant frequency of a cavity, through the control of the incremental permeability that is possible by introducing a pseudoconstant azimuthal magnetic field. However, rapid changes over large permeability ranges incur anomalous behavior such as the “Q-loss” and “f-dot” loss phenomena that limit performance while requiring high bias currents. Notwithstanding the incomplete understanding of these phenomena, they can be ameliorated by introducing a “harmonic ratcheting” acceleration scheme in which two or more rf cavities take turns accelerating the beam—one turns on when the other turns off, at different harmonics—so that the radio frequency can be constrained to remain in a smaller range. Harmonic ratcheting also has straightforward performance advantages, depending on the particular parameter set at hand. In some typical cases it is possible to halve the length of the cavities, or to double the effective gap voltage, or to double the repetition rate. This paper discusses and quantifies the advantages of harmonic ratcheting in general. Simulation results for the particular case of a rapid cycling medical synchrotron ratcheting from harmonic number 9 to 2 show that stability and performance criteria are met even when realistic engineering details

  16. Design of High Power FELS and the Effects of Diffraction on Detuning in an FEL Oscillator

    Science.gov (United States)

    2015-12-01

    a 2D representation of the optical wavefront at the left and right mirrors with the peak value indicated in the top right. 18 *** FEL OSCILLATOR 4D...NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DESIGN OF HIGH POWER FELS AND THE EFFECTS OF DIFFRACTION ON DETUNING IN AN FEL OSCILLATOR by...to 12-18-2015 4. TITLE AND SUBTITLE DESIGN OF HIGH POWER FELS AND THE EFFECTS OF DIFFRACTION ON DE- TUNING IN AN FEL OSCILLATOR 5. FUNDING NUMBERS 6

  17. Rank-Size Distribution of Notes in Harmonic Music: Hierarchic Shuffling of Distributions

    Science.gov (United States)

    Del Río, Manuel Beltrán; Cocho, Germinal

    We trace the rank size distribution of notes in harmonic music, which on previous works we suggested was much better represented by the Two-parameter, first class Beta distribution than the customary power law, to the ranked mixing of distributions dictated by the harmonic and instrumental nature of the piece. The same representation is shown to arise in other fields by the same type of ranked shuffling of distributions. We include the codon content of intergenic DNA sequences and the ranked distribution of sizes of trees in a determined area as examples. We show that the fittings proposed increase their accuracy with the number of distributions that are mixed and ranked.

  18. Numerical investigation of airfoil dynamic stall in simultaneous harmonic oscillatory and translatory motion

    DEFF Research Database (Denmark)

    Ekaterinaris, J.A.; Sørensen, Niels N.; Rasmussen, F.

    1998-01-01

    Wind turbine blades are subject to complex flow conditions. For operation in yaw and turbulent inflow the blade sections appear to execute a motion more complex than a harmonic blade oscillation which causes dynamic stall. Predictions of dynamic stall caused by simple harmonic oscillation...... are crucial to efforts in understanding and improving wind turbine performance. investigation of dynamic stall development caused by a combined oscillatory and translatory motion contributes to better understand blade loading under complex flow conditions. In this paper, numerical predictions of light...... and deep stall caused by simple oscillatory motion are obtained first. The ability of the numerical solution to predict dynamic stall lends caused by a combined motion is further investigated The numerical solution is obtained with a factorized, upwind-biased numerical scheme. The turbulent flow region...

  19. Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink

    Science.gov (United States)

    Zang, Jian; Chen, Li-Qun

    2017-08-01

    Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass, a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra, and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed. The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.

  20. Resonance-modulated wavelength scaling of high-order-harmonic generation from H2+

    Science.gov (United States)

    Wang, Baoning; He, Lixin; Wang, Feng; Yuan, Hua; Zhu, Xiaosong; Lan, Pengfei; Lu, Peixiang

    2018-01-01

    Wavelength scaling of high-order harmonic generation (HHG) in a non-Born-Oppenheimer treatment of H2+ is investigated by numerical simulations of the time-dependent Schrödinger equation. The results show that the decrease in the wavelength-dependent HHG yield is reduced compared to that in the fixed-nucleus approximation. This slower wavelength scaling is related to the charge-resonance-enhanced ionization effect, which considerably increases the ionization rate at longer driving laser wavelengths due to the relatively larger nuclear separation. In addition, we find an oscillation structure in the wavelength scaling of HHG from H2+. Upon decreasing the laser intensity or increasing the nuclear mass, the oscillation structure will shift towards a longer wavelength of the laser pulse. These results permit the generation of an efficient harmonic spectrum in the midinfrared regime by manipulating the nuclear dynamics of molecules.

  1. A Conspiracy of Oscillators

    DEFF Research Database (Denmark)

    Hjorth, Poul G.

    2008-01-01

    We discuss nonlinear mechanical systems containing several oscillators whose frequecies are all much higher than frequencies associated with the remaining degrees of freedom. In this situation a near constant of the motion, an adiabatic invariant, exists which is the sum of all the oscillator...

  2. Hyperchaotic Oscillator with Gyrators

    DEFF Research Database (Denmark)

    Tamasevicius, A; Cenys, A; Mykolaitis, G.

    1997-01-01

    A fourth-order hyperchaotic oscillator is described. It contains a negative impedance converter, two gyratots, two capacitors and a diode. The dynamics of the oscillator is shown to be characterised by two positive Lyapunov exponents. The performance of the circuit is investigated by means...

  3. Grazing Impact Oscillations

    NARCIS (Netherlands)

    Weger, J.G.; Water, van de W.; Molenaar, J.

    2000-01-01

    An impact oscillator is a periodically driven system that hits a wall when its amplitude exceeds a critical value. We study impact oscillations where collisions with the wall are with near-zero velocity (grazing impacts). A characteristic feature of grazing impact dynamics is a geometrically

  4. Synchronization of hyperchaotic oscillators

    DEFF Research Database (Denmark)

    Tamasevicius, A.; Cenys, A.; Mykolaitis, G.

    1997-01-01

    Synchronization of chaotic oscillators is believed to have promising applications in secure communications. Hyperchaotic systems with multiple positive Lyapunov exponents (LEs) have an advantage over common chaotic systems with only one positive LE. Three different types of hyperchaotic electronic...... oscillators are investigated demonstrating synchronization by means of only one properly selected variable....

  5. Prediction of resonant oscillation

    DEFF Research Database (Denmark)

    2010-01-01

    oscillations and compare the measured oscillations using FFT analysis of signal correlations, variance analysis of signals and other comparisons. As an example, the presence of a growing peak around a frequency that doubles the roll natural frequency indicates the possibility that parametric roll is going...

  6. Representation as the representation of experience

    NARCIS (Netherlands)

    Ankersmit, FR

    This essay deals, mainly, with the notion of representation. Representation is associated with texts and, as such, is contrasted to the true singular statement. It is argued that the relationship between the text and what the text represents can never be modeled on the relationship between the true

  7. Magnetostatic wave oscillator frequencies

    Science.gov (United States)

    Sethares, J. C.; Stiglitz, M. R.; Weinberg, I. J.

    1981-03-01

    The frequencies of magnetostatic wave (MSW) oscillators employing three principal modes of propagation, surface (MSSW), forward (MSFVW), and backward (MSBVW) volume waves, have been investigated. Previous (MSW) oscillator papers dealt with MSSW. Oscillators were fabricated using LPE-YIG MSW delay lines in a feedback loop of a 2-4 GHz amplifier. Wide and narrow band transducers were employed. Oscillator frequency as a function of biasing field is in agreement with a theoretical analysis. The analysis predicts frequency in terms of material parameters, biasing field, and transducer geometry. With wide band transducers a comb of frequencies is generated. Narrow band transducers for MSSW and MSFVW select a single mode; and MSBVW selects two modes. Spurious modes, attributed to instrumentation, are more than 20 dB below the main response, and bandwidths are less than 0.005 percent. No other spurious modes are observed. MSW oscillators produce clean electronically tunable signals and appear attractive in frequency agile systems.

  8. Second Harmonic Detection of Spin-Dependent Transport in Magnetic Nanostructures

    Science.gov (United States)

    Yu, Hai-Ming; Granville, S.; Yu, Da-Peng; J-ph., Ansermet

    2010-02-01

    Detection of the second harmonic response of magnetic nanostructures to an ac current is shown to be a very sensitive probe of the magnetization reversal process. A temperature oscillation is obtained by Joule heating instead of using a laser as the heat source, as in thermo-galvanic voltage measurements (TGV). Joule heating is used to produce a large local temperature gradient in asymmetric Co/Cu/Co spin valves. Evidence is found for an effect of a heat current on magnetization.

  9. Anomalous diffusion: exact solution of the generalized Langevin equation for harmonically bounded particle.

    Science.gov (United States)

    Viñales, A D; Despósito, M A

    2006-01-01

    We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.

  10. Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

    Science.gov (United States)

    Gurgiolo, Chris; Vinas, Adolfo F.

    2009-01-01

    This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

  11. Highlighting the harmonic regime generated by electric locomotives equipped with DC motors

    Science.gov (United States)

    Baciu, I.; Cunţan, C. D.

    2018-01-01

    The paper presents the results of measurements made using the C.A. 8334 power quality analyzer on an electric locomotive equipped with DC motors. We carried out determinations of the current-voltage regime using a locomotive motor. The harmonic regime of the other motors being identical to the analysed one, we could easily deduce the effects caused by the entire locomotive. The data measured with the analyzer were firstly transferred into a computer system using the Qualistar software, followed by data processing in Excel, enabling therefore a graphical representation of the characteristic parameters of power quality. Based on the acquired data, we determined the power factor, as well as the active, reactive and apparent power. The measurements revealed high values of the current harmonics, fact that required some measures to be taken for reducing the values of these harmonics. For this, we ran a simulation using the PSCAD/EMTDC software, by introducing LC filters in tune with the harmonic frequencies. The result was a significant reduction in the harmonic regime, either in the harmonics values or the power factor and reactive power.

  12. Input Harmonic Analysis on the Slim DC-Link Drive Using Harmonic State Space Model

    DEFF Research Database (Denmark)

    Yang, Feng; Kwon, Jun Bum; Wang, Xiongfei

    2017-01-01

    variation according to the switching instant, the harmonics at the steady-state condition, as well as the coupling between the multiple harmonic impedances. By using this model, the impaction on the harmonics performance by the film capacitor and the grid inductance is derived. Simulation and experimental......The harmonic performance of the slim dc-link adjustable speed drives has shown good performance in some studies but poor in some others. The contradiction indicates that a feasible theoretical analysis is still lacking to characterize the harmonic distortion for the slim dc-link drive. Considering...... the shortcomings of the present harmonic analysis methods, such as the time-domain simulation, or the Fourier analysis, this paper proposes a Harmonic State Space model to study the harmonics performance for this type of drive. In this study, this model is utilized to describe the behavior of the harmonic...

  13. Cellular harmonic information transfer through a tissue tensegrity-matrix system.

    Science.gov (United States)

    Pienta, K J; Coffey, D S

    1991-01-01

    Cells and intracellular elements are capable of vibrating in a dynamic manner with complex harmonics, the frequency of which can now be measured and analyzed in a quantitative manner by Fourier analysis. Cellular events such as changes in shape, membrane ruffling, motility, and signal transduction occur within spatial and temporal harmonics that have potential regulatory importance. These vibrations can be altered by growth factors and the process of carcinogenesis. It is important to understand the mechanism by which this vibrational information is transferred directly throughout the cell. From these observations we propose that vibrational information is transferred through a tissue tensegrity-matrix which acts as a coupled harmonic oscillator operating as a signal transucing system from the cell periphery to the nucleus and ultimately to the DNA. The vibrational interactions occur through a tissue matrix system consisting of the nuclear matrix, the cytoskeleton, and the extracellular matrix that is poised to couple the biologic oscillations of the cell from the peripheral membrane to the DNA through a tensegrity-matrix structure. Tensegrity has been defined as a structural system composed of discontinuous compression elements connected by continuous tension cables, which interact in a dynamic fashion. A tensegrity tissue matrix system allows for specific transfer of information through the cell by direct transmission of vibrational chemomechanical energy through harmonic wave motion.

  14. Light-Matter Interactions: A Coupled Oscillator Description

    CERN Document Server

    Frimmer, Martin

    2016-01-01

    The semiclassical theory of light-matter interactions describes the interaction between a classical electromagnetic field with a quantum mechanical two-level system.We show that the quantum mechanical two-level system can be modeled by a system of two coupled classical harmonic oscillators whose eigenstates are split in frequency according to the coupling strength and play the roles of the two levels of the quantum mechanical two-level system. The effect of the light field on the mechanical system is modeled as a modulation of the spring constants of the individual oscillators. Using this fully classical model, we derive the Bloch equations for a two-level system and discuss the mechanical analogues of Rabi oscillations and coherent control experiments

  15. Emergence of a negative resistance in noisy coupled linear oscillators

    Science.gov (United States)

    Quiroz-Juárez, M. A.; Aragón, J. L.; León-Montiel, R. de J.; Vázquez-Medina, R.; Domínguez-Juárez, J. L.; Quintero-Torres, R.

    2016-12-01

    We report on the experimental observation of an emerging negative resistance in a system of coupled linear electronic RLC harmonic oscillators under the influence of multiplicative noise with long correlation time. When two oscillators are coupled by a noisy inductor, an analysis in the Fourier space of the electrical variables unveils the presence of an effective negative resistance, which acts as an energy transport facilitator. This might constitute a simple explanation of the now fashionable problem of energy transport assisted by noise in classical systems. The experimental setup is based on the working principle of an analog computer and by itself constitutes a versatile platform for studying energy transport in noisy systems by means of coupled electrical oscillator systems.

  16. Measurements of High-Degree Solar Oscillation Parameters

    Science.gov (United States)

    Bachmann, K. T.; Duvall, T. L., Jr.; Harvey, J. W.; Hill, F.

    1994-12-01

    We present results obtained from full-disk, 1000times 1024 pixel, Ca II intensity images of the Sun collected with the High-L Helioseismometer (HLH). Our measurement of p- and f-mode oscillation frequencies over the frequency range 1.8<=nu <=5.0 mHz and the spherical harmonic degree range 100<=l<=1200 from 22-25 June 1993 data represents an improvement over previous measurements. We are able to differentiate among the predictions of several solar models, thus constraining physical models of the solar convection zone. We also include recent splitting and frequency results from data collected during the entire month of June 1994. The purpose of the HLH research program is to measure high-degree solar oscillation parameters for the remainder of this decade in support of the Solar Oscillations Investigation - Michelson Doppler Imager collaboration, which is part of the Solar and Heliospheric Observatory, a joint ESA-NASA satellite mission.

  17. Neutrino Oscillation Physics

    CERN Document Server

    Kayser, Boris

    2014-04-10

    To complement the neutrino-physics lectures given at the 2011 International School on Astro Particle Physics devoted to Neutrino Physics and Astrophysics (ISAPP 2011; Varenna, Italy), at the 2011 European School of High Energy Physics (ESHEP 2011; Cheila Gradistei, Romania), and, in modified form, at other summer schools, we present here a written description of the physics of neutrino oscillation. This description is centered on a new way of deriving the oscillation probability. We also provide a brief guide to references relevant to topics other than neutrino oscillation that were covered in the lectures.

  18. The Harmonics of Kansei Images

    DEFF Research Database (Denmark)

    Su, Jianning; Restrepo-Giraldo, John Dairo

    2008-01-01

    Delivering the right product experience, which is a user’s reflection of a combination of functionality, usage, cost and appearance, is a key factor for product acquisition and commercial success. Establishing and representing the relation between a product’s shape and the perceived aesthetic...... sensibility it elicits on a person (kansei), is a key factor in the design of tools to support designers in delivering the right product’s appearance. This paper presents an approach to mathematically represent a product’s kansei based on the frequency signature (harmonics) of a shape. This mathematical...

  19. Harmonic focus in thyroidectomy for substernal goiter

    DEFF Research Database (Denmark)

    Hahn, Christoffer Holst; Trolle, Waldemar; Sørensen, Christian Hjort

    2015-01-01

    OBJECTIVES: No previous prospective study has evaluated harmonic scalpel in thyroidectomy for substernal goiter. The objective of this study was to evaluate the use of harmonic scalpel (FOCUS shear, Ethicon Endo-Surgery) in thyroidectomy for substernal goiter for blood loss, operative time...... and 121 patients had harmonic scalpel thyroidectomy. RESULTS: The use of harmonic scalpel was associated with significant reduction in intraoperative blood loss (50 vs. 100mL, p=0.001), postoperative haemorrhage (4% vs. 12%, p=0.03) and length of hospital stay (2 vs. 3 days, p=0.001). The mean operative...... time was significantly longer in the harmonic group. CONCLUSION: Harmonic scalpel is a safe tool for thyroidectomy for substernal goiter. Its utilisation is associated with reduced blood loss, lower incidence of postoperative haemorrhage and shorter hospital stay....

  20. The Projective Andoyer transformation and the connection between the 4-D isotropic oscillator and Kepler systems

    OpenAIRE

    Ferrer, Sebastián

    2010-01-01

    Extending to 4 degrees of freedom a symplectomorphism used in attitude dynamics it is shown in a direct way the connection between the 4-D isotropic harmonic oscillator and the 3-D Kepler systems. This approach made transparent that only when we refer to rectilinear solutions, the {\\sl bilinear relation} defining the KS transformation is needed.

  1. Experimental bifurcation analysis of an impact oscillator - Tuning a non-invasive control scheme

    DEFF Research Database (Denmark)

    Bureau, Emil; Schilder, Frank; Santos, Ilmar

    2013-01-01

    We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromag...

  2. A 60 GHz Frequency Generator Based on a 20 GHz Oscillator and an Implicit Multiplier

    NARCIS (Netherlands)

    Zong, Z.; Babaie, M.; Staszewski, R.B.

    2016-01-01

    This paper proposes a mm-wave frequency generation technique that improves its phase noise (PN) performance and power efficiency. The main idea is that a fundamental 20 GHz signal and its sufficiently strong third harmonic at 60 GHz are generated simultaneously in a single oscillator. The desired 60

  3. Quantum trajectory in a time-dependent potential : oscillator in a monochromatic field

    OpenAIRE

    Nishiyama, Yoshio

    2002-01-01

    The 'quantum trajectory' obeying the Schrodinger equation with a time dependent potential is theoretically determined. As an illustration of the theory the trajectory of a charged harmonic oscillator in an electromagnetic field obeying the wave equation is shown along with the orbital motion of the corresponding classical particle.

  4. Non-radial oscillations of the rapidly rotating Be star HD 163868

    NARCIS (Netherlands)

    Savonije, G.J.

    2007-01-01

    Context: Oscillations in rotating stars with frequency barsigma of the same order or smaller than the rotation rate Omega cannot be described by a single spherical harmonic due to the effect of the Coriolis force. This is a serious complication which is usually treated by writing the eigenfunctions

  5. Representations of Circular Words

    Directory of Open Access Journals (Sweden)

    László Hegedüs

    2014-05-01

    Full Text Available In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The latter form can also be used as a graphical representation of periodic properties of finite (in some cases, infinite words. We also define iterative representations which can be seen as an encoding utilizing the flexible properties of circular words. Every word over the two letter alphabet can be constructed starting from ab by applying the fractional power and the cyclic shift operators one after the other, iteratively.

  6. Efficient third harmonic generation in photonic nanowires

    OpenAIRE

    Broderick, N.G.R.; Lohe, M. A.; Lee, T; Shaaram, Afshar V.; Monro, T.M.

    2013-01-01

    In a photonic nanowire the strong optical confinement allows for the phase matching of nonlinear interactions that would not normally be phase matched, while the large longitudinal component of the electric field serves to further enhance the effective nonlinearity. Thus such waveguides are good choices for studying nonlinear effects such as third harmonic generation. In this paper we analyse third harmonic generation analytically and present the criteria for optimal harmonic generation. In a...

  7. Harmonics Monitoring Survey on LED Lamps

    OpenAIRE

    Abdelrahman Ahmed Akila; Kamelia Youssef; Ibrahim Yassin

    2017-01-01

    Light Emitting Diode (LED) lamps are being increasingly used in many applications. These LED lamps operate using a driver, which is a switching device. Hence, LED lamps will be a source of harmonics in the power system. These harmonics if not well treated, may cause severe performance and operational problems. In this paper, harmonics (amplitude and phase angles) generated by both LED lamps and conventional fluorescent lamps will be studied practically. Then they will be analyzed and evaluate...

  8. High frequency nanotube oscillator

    Science.gov (United States)

    Peng, Haibing [Houston, TX; Zettl, Alexander K [Kensington, TX

    2012-02-21

    A tunable nanostructure such as a nanotube is used to make an electromechanical oscillator. The mechanically oscillating nanotube can be provided with inertial clamps in the form of metal beads. The metal beads serve to clamp the nanotube so that the fundamental resonance frequency is in the microwave range, i.e., greater than at least 1 GHz, and up to 4 GHz and beyond. An electric current can be run through the nanotube to cause the metal beads to move along the nanotube and changing the length of the intervening nanotube segments. The oscillator can operate at ambient temperature and in air without significant loss of resonance quality. The nanotube is can be fabricated in a semiconductor style process and the device can be provided with source, drain, and gate electrodes, which may be connected to appropriate circuitry for driving and measuring the oscillation. Novel driving and measuring circuits are also disclosed.

  9. Neutrino anomalies without oscillations

    Indian Academy of Sciences (India)

    conventional' neutrino oscillations induced by mass-mixing. Several of these require non-zero neutrino masses as well. Author Affiliations. Sandip Pakvasa1. Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA ...

  10. Neural Oscillators Programming Simplified

    Directory of Open Access Journals (Sweden)

    Patrick McDowell

    2012-01-01

    Full Text Available The neurological mechanism used for generating rhythmic patterns for functions such as swallowing, walking, and chewing has been modeled computationally by the neural oscillator. It has been widely studied by biologists to model various aspects of organisms and by computer scientists and robotics engineers as a method for controlling and coordinating the gaits of walking robots. Although there has been significant study in this area, it is difficult to find basic guidelines for programming neural oscillators. In this paper, the authors approach neural oscillators from a programmer’s point of view, providing background and examples for developing neural oscillators to generate rhythmic patterns that can be used in biological modeling and robotics applications.

  11. Effects of harmonic roving on pitch discrimination

    DEFF Research Database (Denmark)

    Santurette, Sébastien; de Kérangal, Mathilde le Gal; Joshi, Suyash Narendra

    2015-01-01

    to impair pitch discrimination performance. Fundamental-frequency difference limens (F0DLs) were obtained in normal-hearing listeners with and without musical training for complex tones filtered between 1.5 and 3.5 kHz with F0s of 300 Hz (resolved harmonics) and 75 Hz (unresolved harmonics). The harmonicity...... of the tone complexes was varied by systematically roving the frequency of individual harmonics, which was taken from a Gaussian distribution centered on the nominal frequency in every stimulus presentation. The amount of roving was determined by the standard deviation of this distribution, which varied...

  12. solar neutrino oscillation phenomenology

    Indian Academy of Sciences (India)

    The sMA region and a large part of the vacuum oscillation region are seen to have been washed away with the inclusion of the sK spectrum data. In the left panel of figure 4 we show the dependence of the probabilities on energy. In the sMA and the VO oscillation regions the probability has a non- monotonic dependence ...

  13. Effect of undulator harmonics field on free-electron laser harmonic generation

    Directory of Open Access Journals (Sweden)

    Qika Jia

    2011-06-01

    Full Text Available The harmonics field effect of a planar undulator on free-electron laser (FEL harmonic generation has been analyzed. For both the linear case and the nonlinear case, the harmonic fraction of the radiation can be characterized by the coupling coefficients. The modification of the coupling coefficients is given when the third harmonics magnetic field component exists, thus the enhancement of the harmonic radiation can be predicted. The numerical results show that with the third harmonics magnetic field component that has the opposite sign to the fundamental, the intensity of third-harmonic radiation can be increased distinctly for both the small signal gain and the nonlinear harmonic generation. The increase is larger for the smaller undulator deflecting parameter.

  14. Modified Legendre Wavelets Technique for Fractional Oscillation Equations

    Directory of Open Access Journals (Sweden)

    Syed Tauseef Mohyud-Din

    2015-10-01

    Full Text Available Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.

  15. Self-oscillation

    CERN Document Server

    Jenkins, Alejandro

    2011-01-01

    Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain linear systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy from the environment into the vibration: no external rate needs to be tuned to the resonant frequency. A paper from 1830 by G. B. Airy gives us the opening to introduce self-oscillation as a sort of "perpetual motion" responsible for the human voice. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the more recent swaying of the London Millenium Footbridge. Clocks are self-oscillators, as are bowed and wind musical instruments, and the heartbeat. We review the criterion that determines whether an arbitrary line...

  16. Pitch representations in the auditory nerve: two concurrent complex tones.

    Science.gov (United States)

    Larsen, Erik; Cedolin, Leonardo; Delgutte, Bertrand

    2008-09-01

    Pitch differences between concurrent sounds are important cues used in auditory scene analysis and also play a major role in music perception. To investigate the neural codes underlying these perceptual abilities, we recorded from single fibers in the cat auditory nerve in response to two concurrent harmonic complex tones with missing fundamentals and equal-amplitude harmonics. We investigated the efficacy of rate-place and interspike-interval codes to represent both pitches of the two tones, which had fundamental frequency (F0) ratios of 15/14 or 11/9. We relied on the principle of scaling invariance in cochlear mechanics to infer the spatiotemporal response patterns to a given stimulus from a series of measurements made in a single fiber as a function of F0. Templates created by a peripheral auditory model were used to estimate the F0s of double complex tones from the inferred distribution of firing rate along the tonotopic axis. This rate-place representation was accurate for F0s greater, similar900 Hz. Surprisingly, rate-based F0 estimates were accurate even when the two-tone mixture contained no resolved harmonics, so long as some harmonics were resolved prior to mixing. We also extended methods used previously for single complex tones to estimate the F0s of concurrent complex tones from interspike-interval distributions pooled over the tonotopic axis. The interval-based representation was accurate for F0s less, similar900 Hz, where the two-tone mixture contained no resolved harmonics. Together, the rate-place and interval-based representations allow accurate pitch perception for concurrent sounds over the entire range of human voice and cat vocalizations.

  17. Propagation properties and radiation forces of the Airy Gaussian vortex beams in a harmonic potential.

    Science.gov (United States)

    Pang, Zihao; Deng, Dongmei

    2017-06-12

    We investigate the propagation properties and the radiation forces of Airy Gaussian vortex (AiGV) beams in a harmonic potential analytically and numerically in this paper. Obtaining the propagation expression of AiGV beams by solving the dimensionless linear (2+1) D Schrödinger equation in a harmonic potential, we perform the track, the intensity and phase distributions, the propagation shapes, the energy flow and the angular momentum of AiGV beams in a harmonic potential with the method of numerical simulations. The trajectory acting like a cosine curve is shown. Periodic inversion and phase oscillation are demonstrated during propagation. The influence of the distribution factor and the vortex factor on the propagation of AiGV beams in a harmonic potential are discussed. Likewise, the motion of the Poynting vector and the angular momentum is elucidated respectively. As for the radiation forces, we explore the gradient and scattering forces on Rayleigh dielectric particles induced by AiGV beams. In particular, it's found that the value of the scattering force is approximately seven orders of magnitude larger than that of the gradient force during the propagation in a harmonic potential.

  18. Effect of Sawtooth Oscillations on Energetic Ions

    Energy Technology Data Exchange (ETDEWEB)

    R.B. White; V.V. Lutsenko; Ya. I. Kolesnichenko; Yu. V. Yakovenko

    1999-12-10

    The work summarizes results of the authors' studies on the energetic ion transport induced by sawtooth oscillations in tokamaks. The main attention is paid to description of physical mechanisms responsible for the transport. In addition to overview, the work contains new material. The new results concern the resonant interaction of the particles and the electromagnetic field of the sawtooth crash. In particular, it is discovered that the dominant harmonic of the crash (m = n = 1) can lead to stochastic motion of particles having large orbit width (potatoes). Regular motion of potatoes and quasi-stagnation particles in the presence of an n = 1 mode is studied, and their characteristic displacements associated with quick switching on/off the mode are found.

  19. Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths

    OpenAIRE

    Lecouvey, Cédric; Lesigne, Emmanuel; Peigné, Marc

    2014-01-01

    27 pages, minor corrections and a simpler definition of the Pitman inverse.; We introduce and characterize central probability distributions on Littelmann paths. Next we establish a law of large numbers and a central limit theorem for the generalized Pitmann transform. We then study harmonic functions on multiplicative graphs defined from the tensor powers of finite-dimensional Lie algebras representations. Finally, we show there exists an inverse of the generalized Pitman transform defined a...

  20. An extension of spherical harmonics to region-based rotationally invariant descriptors for molecular shape description and comparison.

    Science.gov (United States)

    Mak, Lora; Grandison, Scott; Morris, Richard J

    2008-04-01

    The use of spherical harmonics in the molecular sciences is widespread. They have been employed with success in, for instance, the crystallographic fast rotation function, small-angle scattering particle reconstruction, molecular surface visualisation, protein-protein docking, active site analysis and protein function prediction. An extension of the spherical harmonic expansion method is presented here that enables regions (bodies) rather than contours (surfaces) to be described and which lends itself favourably to the construction of rotationally invariant shape descriptors. This method introduces a radial term that extends the spherical harmonics to 3D polynomials. These polynomials maintain the advantages of the spherical harmonics (orthonormality, completeness, uniqueness and fast computation) but correct the drawbacks (contour based shape description and star-shape objects) and give rise to powerful invariant descriptors. We provide proof-of-principle examples illustrating the potential of this method for accurate object representation, an analysis of the descriptor classification power, and comparisons to other methods.

  1. Introduction of a co-resonant detection concept for mechanical oscillation-based sensors.

    Science.gov (United States)

    Reiche, Christopher F; Körner, Julia; Büchner, Bernd; Mühl, Thomas

    2015-08-21

    Micro- and nanoelectromechanical oscillators driven at or close to their resonance frequency are used as sensors in many fields of science and technology. A decrease in the oscillator's effective spring constant and/or mass holds great potential for an increase in the sensor's sensitivity. This is usually accompanied by a reduction in spatial dimensions, which in most cases requires more complex detection methods. By analyzing the complex behavior of a simple asymmetric coupled harmonic oscillator model we propose a novel sensor concept which combines the advantages of bigger and smaller oscillators, i.e. ease of detection and high sensitivity. The concept is based on matching the resonance frequencies of two otherwise very different oscillators. To support our theoretical considerations, we present an experimental implementation of such a sensor and respective experimental data, verifying a substantial signal enhancement by several orders of magnitude.

  2. Phase-conjugated mirror-induced oscillations outside the rotating-wave approximation

    Energy Technology Data Exchange (ETDEWEB)

    Hassan, S S [Ain Shams University, Faculty of Science, Mathematics Department, Cairo (Egypt); Frege, O [Ain Shams University, Faculty of Education, Mathematics Department, Cairo (Egypt)

    2002-06-01

    Dynamical behaviour of a single harmonic oscillator (HO) and of a single and two cooperative atoms in front of a phase-conjugated mirror is investigated without using the rotating-wave approximation. The mean photon number of the HO shows transient oscillation of frequency (2{omega}{sub 0}) and O({gamma}/{omega}{sub 0}), the ratio of the free-space decay rate to the oscillation frequency, and the fluorescent spectrum becomes asymmetric due to additional resonant and non-resonant dispersive terms. In the single-two-level-atom case, the mean atomic inversion and the fluorescent intensity show steady oscillation O({gamma}{sub 0}/{omega}{sub 0}), the ratio of the A-coefficient to the atomic transition frequency. The amplitude of this steady oscillation at frequency (2{omega}{sub 0}) is larger in the case of two cooperative atoms.

  3. The Harmonic Organization of Auditory Cortex

    Directory of Open Access Journals (Sweden)

    Xiaoqin eWang

    2013-12-01

    Full Text Available A fundamental structure of sounds encountered in the natural environment is the harmonicity. Harmonicity is an essential component of music found in all cultures. It is also a unique feature of vocal communication sounds such as human speech and animal vocalizations. Harmonics in sounds are produced by a variety of acoustic generators and reflectors in the natural environment, including vocal apparatuses of humans and animal species as well as music instruments of many types. We live in an acoustic world full of harmonicity. Given the widespread existence of the harmonicity in many aspects of the hearing environment, it is natural to expect that it be reflected in the evolution and development of the auditory systems of both humans and animals, in particular the auditory cortex. Recent neuroimaging and neurophysiology experiments have identified regions of non-primary auditory cortex in humans and non-human primates that have selective responses to harmonic pitches. Accumulating evidence has also shown that neurons in many regions of the auditory cortex exhibit characteristic responses to harmonically related frequencies beyond the range of pitch. Together, these findings suggest that a fundamental organizational principle of auditory cortex is based on the harmonicity. Such an organization likely plays an important role in music processing by the brain. It may also form the basis of the preference for particular classes of music and voice sounds.

  4. Practical Tools to Foster Harmonic Understanding

    Science.gov (United States)

    Johnson, Erik

    2013-01-01

    Among the elements required to develop a comprehensive understanding of music is students' ability to perceive, recognize, and label the harmonies they hear. Harmonic dictation is among the strategies that teachers have traditionally chosen to help students develop harmonic awareness. However, the highly idiosyncratic ways that students approach…

  5. Harmonic manifolds with minimal horospheres are flat

    Indian Academy of Sciences (India)

    MS received 28 May 2013; revised 12 November 2013 ... The known examples of harmonic manifolds include flat ... periodic functions. Finally, using the characteristic property of an almost periodic function we prove that M is Ricci flat. In view of this, it is natural to ask: Can one affirm that harmonic manifolds with mini-.

  6. Harmonic dynamical behaviour of thallous halides

    Indian Academy of Sciences (India)

    Harmonic dynamical behaviour of thallous halides (TlCl and TlBr) have been studied using the ... that the incorporation of van der Waals interactions is essential for the complete harmonic dynamical behaviour of .... long-range coupling coefficients to the long-wavelength limit q → 0, the expression for zone centre optical ...

  7. Sunspots and Their Simple Harmonic Motion

    Science.gov (United States)

    Ribeiro, C. I.

    2013-01-01

    In this paper an example of a simple harmonic motion, the apparent motion of sunspots due to the Sun's rotation, is described, which can be used to teach this subject to high-school students. Using real images of the Sun, students can calculate the star's rotation period with the simple harmonic motion mathematical expression.

  8. determination of determination of total harmonic distortion

    African Journals Online (AJOL)

    eobe

    Harmonic Distortion (THD) of the Distribution lines in the 33kV distri. Harmonic Distortion (THD) of the Distribution lines in the 33kV distribution network of Island Business District, bution network of Island Business District,. Eko Electricity Distribution Plc, taken. Eko Electricity Distribution Plc, taken as a case study using a set ...

  9. Achieving sustainable development through tax harmonization ...

    African Journals Online (AJOL)

    Using Nigeria as a case study, this article examines the efficacy of tax harmonization as an option for the achievement of two objectives: the integration of a developing country with other economies, and its sustainable development. It highlights the nexus between tax harmonization – a tax policy option – and sustainable ...

  10. Harmonic Phase Response of Nonlinear Radar Targets

    Science.gov (United States)

    2015-10-01

    ARL-TR-7513 ● OCT 2015 US Army Research Laboratory Harmonic Phase Response of Nonlinear Radar Targets by Sean F McGowan, Dr...Laboratory Harmonic Phase Response of Nonlinear Radar Targets by Sean F McGowan and Kelly D Sherbondy Sensors and Electron Devices Directorate...

  11. The harmonic organization of auditory cortex

    Science.gov (United States)

    Wang, Xiaoqin

    2013-01-01

    A fundamental structure of sounds encountered in the natural environment is the harmonicity. Harmonicity is an essential component of music found in all cultures. It is also a unique feature of vocal communication sounds such as human speech and animal vocalizations. Harmonics in sounds are produced by a variety of acoustic generators and reflectors in the natural environment, including vocal apparatuses of humans and animal species as well as music instruments of many types. We live in an acoustic world full of harmonicity. Given the widespread existence of the harmonicity in many aspects of the hearing environment, it is natural to expect that it be reflected in the evolution and development of the auditory systems of both humans and animals, in particular the auditory cortex. Recent neuroimaging and neurophysiology experiments have identified regions of non-primary auditory cortex in humans and non-human primates that have selective responses to harmonic pitches. Accumulating evidence has also shown that neurons in many regions of the auditory cortex exhibit characteristic responses to harmonically related frequencies beyond the range of pitch. Together, these findings suggest that a fundamental organizational principle of auditory cortex is based on the harmonicity. Such an organization likely plays an important role in music processing by the brain. It may also form the basis of the preference for particular classes of music and voice sounds. PMID:24381544

  12. Uniformly locally univalent harmonic map- pings

    Indian Academy of Sciences (India)

    63

    Uniformly locally univalent harmonic map- pings. Saminathan Ponnusamy, Jinjing Qiao. ∗ and Xiantao Wang. Abstract. The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter fam-.

  13. Hyperspherical Harmonics and Their Physical Applications

    DEFF Research Database (Denmark)

    Avery, James Emil; Avery, John Scales

    Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered...

  14. Pairwise harmonics for shape analysis

    KAUST Repository

    Zheng, Youyi

    2013-07-01

    This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of shape descriptors that are more global, discriminative, and can effectively capture the variations in the underlying geometry. Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more efficient algorithms than the state-of-the-art methods for three applications: intrinsic reflectional symmetry axis computation, matching shape extremities, and simultaneous surface segmentation and skeletonization. © 2012 IEEE.

  15. Harmonic Interaction Analysis in Grid Connected Converter using Harmonic State Space (HSS) Modeling

    DEFF Research Database (Denmark)

    Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

    2015-01-01

    An increasing number of power electronics based Distributed Generation (DG) systems and loads generate coupled harmonic as well as non-characteristic harmonic with each other. Several methods like impedance based analysis, which is derived from conventional small signal- and average...... during the modeling process. This paper investigates grid connected converter by means of Harmonic State Space (HSS) small signal model, which is modeled from Linear Time varying Periodically (LTP) system. Further, a grid connected converter harmonic matrix is investigated to analyze the harmonic...

  16. Harmonics Monitoring Survey on LED Lamps

    Directory of Open Access Journals (Sweden)

    Abdelrahman Ahmed Akila

    2017-03-01

    Full Text Available Light Emitting Diode (LED lamps are being increasingly used in many applications. These LED lamps operate using a driver, which is a switching device. Hence, LED lamps will be a source of harmonics in the power system. These harmonics if not well treated, may cause severe performance and operational problems. In this paper, harmonics (amplitude and phase angles generated by both LED lamps and conventional fluorescent lamps will be studied practically. Then they will be analyzed and evaluated. Compared to each other harmonics generated by both LED and conventional florescent lamps, self mitigation may occur based on the phase angle of these harmonics. All data will be measured using power analyzer and will be done on a sample of actual lamps.

  17. High orbital angular momentum harmonic generation

    CERN Document Server

    Vieira, J; Alves, E P; Fonseca, R A; Mendonça, J T; Bingham, R; Norreys, P; Silva, L O

    2016-01-01

    We identify and explore a high orbital angular momentum (OAM) harmonics generation and amplification mechanism that manipulates the OAM independently of any other laser property, by preserving the initial laser wavelength, through stimulated Raman backscattering in a plasma. The high OAM harmonics spectra can extend at least up to the limiting value imposed by the paraxial approximation. We show with theory and particle-in-cell simulations that the orders of the OAM harmonics can be tuned according to a selection rule that depends on the initial OAM of the interacting waves. We illustrate the high OAM harmonics generation in a plasma using several examples including the generation of prime OAM harmonics. The process can also be realised in any nonlinear optical Kerr media supporting three-wave interactions.

  18. Harmonic Generation by Microwave-frequency Microplasma

    Science.gov (United States)

    Parsons, Stephen; Hoskinson, Alan; Hopwood, Jeffrey

    2013-09-01

    A microplasma may operate as a nonlinear circuit element and generate power at the harmonics of the drive frequency. As an example, microplasma is sustained using 1 W of power at 1.3 GHz in a small discharge gap formed in a split-ring resonator. A probe extends into the microplasma and extracts the 3rd harmonic power through a tuned resonator at 3.9 GHz. The experimental data show that this non-optimized system produces a +38 dB increase in 3rd harmonic power in the presence of a microplasma. Two origins of nonlinearity are described: the harmonic conduction current due to electron collection by microelectrodes, and the harmonic displacement current due to the voltage-dependent sheath capacitance. PIC-MC simulations suggest that the microplasma nonlinearity may also be exploited at frequencies of 100 GHz. Support was provided by the DARPA Microscale Plasma Devices program under award FA9550-12-1-0006.

  19. Social representations of women

    Directory of Open Access Journals (Sweden)

    Álvaro Estramiana, José Luis

    2006-05-01

    Full Text Available Social Representations is one of the most important theories in contemporary social psychology. Since the social psychologist Serge Moscovici developed his theory of social representations to explain how a scientific theory such as the psychoanalysis turns into a common sense knowledge many studies have been done by different social psychologists. The analysis of the social representations of women as represented in myths and popular beliefs is an excellent opportunity to study how this theory can be applied to this representational field. At the same time it makes possible to understand the formation of attitudes towards women

  20. Strong Enhancement of Second Harmonic Emission by Plasmonic Resonances at the Second Harmonic Wavelength.

    Science.gov (United States)

    Metzger, Bernd; Gui, Lili; Fuchs, Jaco; Floess, Dominik; Hentschel, Mario; Giessen, Harald

    2015-06-10

    We perform second harmonic spectroscopy of aluminum nanoantenna arrays that exhibit plasmonic resonances at the second harmonic wavelength between 450 and 570 nm by focusing sub-30 fs laser pulses tunable from 900 to 1140 nm onto the nanoantenna arrays. We find that a plasmonic resonance at the second harmonic wavelength boosts the overall nonlinear process by more than an order of magnitude. In particular, in the measurement the resonant second harmonic polarization component is a factor of about 70 stronger when compared to the perpendicular off-resonant second harmonic polarization. Furthermore, the maximum of the second harmonic conversion efficiency is found to be slightly blue-shifted with respect to the peak of the linear optical far-field spectrum. This fact can be understood from a simple model that accounts for the almost off-resonant absorption at the fundamental wavelength and the resonant emission process at the second harmonic.

  1. High order harmonic generation in rare gases

    Energy Technology Data Exchange (ETDEWEB)

    Budil, Kimberly Susan [Univ. of California, Davis, CA (United States)

    1994-05-01

    The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~1013-1014 W/cm2) is focused into a dense (~1017 particles/cm3) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as well as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.

  2. Quantitative analysis of harmonic convergence in mosquito auditory interactions

    Science.gov (United States)

    Aldersley, Andrew; Champneys, Alan; Robert, Daniel

    2016-01-01

    This article analyses the hearing and behaviour of mosquitoes in the context of inter-individual acoustic interactions. The acoustic interactions of tethered live pairs of Aedes aegypti mosquitoes, from same and opposite sex mosquitoes of the species, are recorded on independent and unique audio channels, together with the response of tethered individual mosquitoes to playbacks of pre-recorded flight tones of lone or paired individuals. A time-dependent representation of each mosquito's non-stationary wing beat frequency signature is constructed, based on Hilbert spectral analysis. A range of algorithmic tools is developed to automatically analyse these data, and used to perform a robust quantitative identification of the ‘harmonic convergence’ phenomenon. The results suggest that harmonic convergence is an active phenomenon, which does not occur by chance. It occurs for live pairs, as well as for lone individuals responding to playback recordings, whether from the same or opposite sex. Male–female behaviour is dominated by frequency convergence at a wider range of harmonic combinations than previously reported, and requires participation from both partners in the duet. New evidence is found to show that male–male interactions are more varied than strict frequency avoidance. Rather, they can be divided into two groups: convergent pairs, typified by tightly bound wing beat frequencies, and divergent pairs, that remain widely spaced in the frequency domain. Overall, the results reveal that mosquito acoustic interaction is a delicate and intricate time-dependent active process that involves both individuals, takes place at many different frequencies, and which merits further enquiry. PMID:27053654

  3. Representation of voice pitch in discharge patterns of auditory-nerve fibers.

    Science.gov (United States)

    Miller, M I; Sachs, M B

    1984-06-01

    Responses of populations of auditory-nerve fibers were measured for synthesized consonant-vowel stimuli. This paper explores the encoding of fundamental frequency (pitch) in these responses. Post-stimulus time (PST) histograms were computed from 25 ms segments of the spike trains. Discrete Fourier transforms with a 40 Hz resolution were computed from the histograms. Two representations of pitch are considered. The first representation is based on the pitch-related temporal properties of the speech signal. Histograms for individual units can show envelope modulations directly related to the pitch period. These modulations reflect the responses of these fibers to a number of stimulus harmonics near fiber CF. Responses of fibers near formant frequencies are dominated by a single large harmonic component, and thus show small or no pitch-related enveloped modulations. Envelope modulations are reduced in the presence of background noise. The second representation uses both temporal properties of auditory-nerve responses and cochlear place to encode the pitch-related harmonic structure of speech. As a measure of the response of the population of fibers to each harmonic of 40 Hz the magnitude of the component of the Fourier transform at that frequency was averaged across all fibers whose characteristic frequencies were within one-fourth octave of that harmonic. We call this measure the average localized synchronized rate (ALSR). The ALSR provides a good representation of stimulus spectrum, even in the presence of background noise. From the harmonic structure of the ALSR, we are able to extract the stimulus pitch frequency. The relationship of these two representations to pitch perception in both acoustic and electrical stimulation (via cochlear implants) is discussed.

  4. Estimation of the sinusoidal oscillation parameters in the adaptive optics system based on the example of the photovoltaic system

    Science.gov (United States)

    Kania, Dariusz

    2015-05-01

    In adaptive optics systems, there is a problem of a sinusoidal oscillations rejection. This paper presents the estimation method that can be used to reject these oscillations on the example of the photovoltaic system. In such a system, photovoltaic panels generate the DC signal converted by the inverter to the AC signal with specified parameters. This paper focuses on the fast and accurate estimation of these parameters taking into account the presence of harmonics in the sinusoidal signal. The estimation method is based on using maximum decay sidelobes windows and the Fast Fourier Transform procedure. In reality, the AC signal is not a pure sinusoid and it is often distorted in a deterministic manner by harmonics, and in a random manner by white, "colored" or quantization noise. The estimation error depends on the systematic error, i.e. the error caused by the quantization noise and the error caused by harmonic components. Several parameters determine which error component is dominant in the estimation results. The value of the error caused by harmonic components depends mainly on the distance between the harmonic component and the fundamental component in a frequency domain and the THD (Total Harmonic Distortion) ratio of the signal. The level of this maximum relative error is approximately 10-3 for the tested signal with THD=50%. It is important to use a filter that reduces unwanted harmonics before the data processing. The information provided in this paper can be used to determine the approximate level of estimation error before starting the estimation process.

  5. Oscillations in neutron stars

    Energy Technology Data Exchange (ETDEWEB)

    Hoeye, Gudrun Kristine

    1999-07-01

    We have studied radial and nonradial oscillations in neutron stars, both in a general relativistic and non-relativistic frame, for several different equilibrium models. Different equations of state were combined, and our results show that it is possible to distinguish between the models based on their oscillation periods. We have particularly focused on the p-, f-, and g-modes. We find oscillation periods of II approx. 0.1 ms for the p-modes, II approx. 0.1 - 0.8 ms for the f-modes and II approx. 10 - 400 ms for the g-modes. For high-order (l (>{sub )} 4) f-modes we were also able to derive a formula that determines II{sub l+1} from II{sub l} and II{sub l-1} to an accuracy of 0.1%. Further, for the radial f-mode we find that the oscillation period goes to infinity as the maximum mass of the star is approached. Both p-, f-, and g-modes are sensitive to changes in the central baryon number density n{sub c}, while the g-modes are also sensitive to variations in the surface temperature. The g-modes are concentrated in the surface layer, while p- and f-modes can be found in all parts of the star. The effects of general relativity were studied, and we find that these are important at high central baryon number densities, especially for the p- and f-modes. General relativistic effects can therefore not be neglected when studying oscillations in neutron stars. We have further developed an improved Cowling approximation in the non-relativistic frame, which eliminates about half of the gap in the oscillation periods that results from use of the ordinary Cowling approximation. We suggest to develop an improved Cowling approximation also in the general relativistic frame. (Author)

  6. Non-linear oscillations

    CERN Document Server

    Hagedorn, Peter

    1982-01-01

    Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.

  7. Friedel oscillations in graphene

    DEFF Research Database (Denmark)

    Lawlor, J. A.; Power, S. R.; Ferreira, M.S.

    2013-01-01

    Symmetry breaking perturbations in an electronically conducting medium are known to produce Friedel oscillations in various physical quantities of an otherwise pristine material. Here we show in a mathematically transparent fashion that Friedel oscillations in graphene have a strong sublattice...... asymmetry. As a result, the presence of impurities and/or defects may impact the distinct graphene sublattices very differently. Furthermore, such an asymmetry can be used to explain the recent observations that nitrogen atoms and dimers are not randomly distributed in graphene but prefer to occupy one...

  8. Comparison of Virtual Oscillator and Droop Control

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Rodriguez, Miguel [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Sinha, Mohit [University of Minnesota; Dhople, Sairaj [University of Minnesota

    2017-08-21

    Virtual oscillator control (VOC) and droop control are distinct methods to ensure synchronization and power sharing of parallel inverters in islanded systems. VOC is a control strategy where the dynamics of a nonlinear oscillator are used to derive control states to modulate the switch terminals of an inverter. Since VOC is a time-domain controller that reacts to instantaneous measurements with no additional filters or computations, it provides a rapid response during transients and stabilizes volatile dynamics. In contrast, droop control regulates the inverter voltage in response to the measured average real and reactive power output. Given that real and reactive power are phasor quantities that are not well-defined in real time, droop controllers typically use multiplicative operations in conjunction with low-pass filters on the current and voltage measurements to calculate such quantities. Since these filters must suppress low frequency ac harmonics, they typically have low cutoff frequencies that ultimately impede droop controller bandwidth. Although VOC and droop control can be engineered to produce similar steady-state characteristics, their dynamic performance can differ markedly. This paper presents an analytical framework to characterize and compare the dynamic response of VOC and droop control. The analysis is experimentally validated with three 120 V inverters rated at 1kW, demonstrating that for the same design specifications VOC is roughly 8 times faster and presents almost no overshoot after a transient.

  9. Semi-classical theory of magnetic quantum oscillations in a two-dimensional multiband canonical Fermi liquid

    OpenAIRE

    Alexandrov, A. S.; Bratkovsky, A. M.

    2000-01-01

    The semi-classical Lifshitz-Kosevich (LK) description of quantum oscillations is extended to a multiband two-dimensional Fermi liquid with a constant number of electrons. The amplitudes of novel oscillations with combination frequencies, recently predicted and observed experimentally, are analytically derived and compared with the single-band amplitudes. The combination amplitudes decay with temperature exponentially faster than the standard harmonics, and this provides a valuable tool for th...

  10. Representation and Reference

    NARCIS (Netherlands)

    Ankersmit, F.R.

    2010-01-01

    This essay focuses on the historical text as a whole. It does so by conceiving of the historical text as representation - in the way the we may say of a photo or a painting that it represents the person depicted on it. It is argued that representation cannot be properly understood by modelling it on

  11. Wigner's Symmetry Representation Theorem

    Indian Academy of Sciences (India)

    IAS Admin

    This article elucidates the important role the no- tion of symmetry has played in physics. It dis- cusses the proof of one of the important theorems of quantum mechanics, viz., Wigner's Symmetry. Representation Theorem. It also shows how the representations of various continuous and dis- crete symmetries follow from the ...

  12. MORPHOLOGICAL REPRESENTATION AND SEMANTIC ...

    African Journals Online (AJOL)

    MORPHOLOGICAL REPRESENTATION AND SEMANTIC INTERPRETATION. Rudolf P. Botha. Introduction ... The morphological representation assigned to a complex word must provide the formal structure required ..... It has been argued in the literature that "markedness" claims such as. (16)(a) and (b) are unacceptable ...

  13. Harness processes and harmonic crystals

    OpenAIRE

    Ferrari, Pablo A.; Niederhauser, Beat M.

    2003-01-01

    In the Hammersley harness processes the real-valued height at each site i in Z^d is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in Z^d. With this representation we compute covariances and show L^2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at ...

  14. Tailored semiconductors for high-harmonic optoelectronics.

    Science.gov (United States)

    Sivis, Murat; Taucer, Marco; Vampa, Giulio; Johnston, Kyle; Staudte, André; Naumov, Andrei Yu; Villeneuve, D M; Ropers, Claus; Corkum, P B

    2017-07-21

    The advent of high-harmonic generation in gases 30 years ago set the foundation for attosecond science and facilitated ultrafast spectroscopy in atoms, molecules, and solids. We explore high-harmonic generation in the solid state by means of nanostructured and ion-implanted semiconductors. We use wavelength-selective microscopic imaging to map enhanced harmonic emission and show that the generation medium and the driving field can be locally tailored in solids by modifying the chemical composition and morphology. This enables the control of high-harmonic technology within precisely engineered solid targets. We demonstrate customized high-harmonic wave fields with wavelengths down to 225 nanometers (ninth-harmonic order of 2-micrometer laser pulses) and present an integrated Fresnel zone plate target in silicon, which leads to diffraction-limited self-focusing of the generated harmonics down to 1-micrometer spot sizes. Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

  15. High-harmonic generation in amorphous solids.

    Science.gov (United States)

    You, Yong Sing; Yin, Yanchun; Wu, Yi; Chew, Andrew; Ren, Xiaoming; Zhuang, Fengjiang; Gholam-Mirzaei, Shima; Chini, Michael; Chang, Zenghu; Ghimire, Shambhu

    2017-09-28

    High-harmonic generation in isolated atoms and molecules has been widely utilized in extreme ultraviolet photonics and attosecond pulse metrology. Recently, high-harmonic generation has been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruct electronic band structures, as well as compact extreme ultraviolet light sources. So far these studies are confined to crystalline solids; therefore, decoupling the respective roles of long-range periodicity and high density has been challenging. Here we report the observation of high-harmonic generation from amorphous fused silica. We decouple the role of long-range periodicity by comparing harmonics generated from fused silica and crystalline quartz, which contain the same atomic constituents but differ in long-range periodicity. Our results advance current understanding of the strong-field processes leading to high-harmonic generation in solids with implications for the development of robust and compact extreme ultraviolet light sources.Although higher harmonic generation from solids has become of interest in many fields, its observation is typically limited to crystalline solids. Here, the authors demonstrate that higher harmonics can be generated from amorphous solids.

  16. Embedded data representations

    DEFF Research Database (Denmark)

    Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre

    2017-01-01

    We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...... are making it increasingly easier to display data in-context. While researchers and artists have already begun to create embedded data representations, the benefits, trade-offs, and even the language necessary to describe and compare these approaches remain unexplored. In this paper, we formalize the notion...... of physical data referents – the real-world entities and spaces to which data corresponds – and examine the relationship between referents and the visual and physical representations of their data. We differentiate situated representations, which display data in proximity to data referents, and embedded...

  17. Group and representation theory

    CERN Document Server

    Vergados, J D

    2017-01-01

    This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...

  18. Dynamic analysis of a tunable viscoelastic dielectric elastomer oscillator under external excitation

    Science.gov (United States)

    Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.

    2016-02-01

    As a category of soft electroactive materials, dielectric elastomers (DEs) show great potential for the development of tunable oscillators and resonators for actuating and sensing purposes. However, the dynamic performance of these DE-based vibration devices could be very susceptible to external environment (external loads and excitations) and material viscoelasticity of the DEs. Based on the finite-deformation viscoelasticity theory, this work first investigates the frequency tuning process of a viscoelastic DE membrane oscillator. A comparison of the frequency tuning process and the tunable frequency range between a viscoelastic and a purely elastic DE oscillator is presented. Moreover, particular considerations have been given to the nonlinear response of the oscillator to external harmonic excitation. It is found that the displacement transmissibility of the oscillator can also be actively tuned by changing the static voltage applied to the DE membrane. Under harmonic excitation, various vibration patterns of the oscillator could be actively achieved with the application of both static and alternating electric voltage. Simulation results in this work demonstrate that the material viscoelasticity has a significant effect on the electromechanical coupling and the dynamic performance of the DE-based vibration devices.

  19. A simple violin oscillator

    Science.gov (United States)

    Jones, R. T.

    1976-01-01

    For acoustic tests the violin is driven laterally at the bridge by a small speaker of the type commonly found in pocket transistor radios. An audio oscillator excites the tone which is picked up by a sound level meter. Gross patterns of vibration modes are obtained by the Chladni method.

  20. Oscillators and operational amplifiers

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2005-01-01

    A generalized approach to the design of oscillators using operational amplifiers as active elements is presented. A piecewise-linear model of the amplifier is used so that it make sense to investigate the eigenvalues of the Jacobian of the differential equations. The characteristic equation...